In my PChem class the instructor made the error of saying he didn't care what energy units we used on a test. He really meant it didn't matter to him whether we used joules or calories, but I took him at his word and turned in my test with all the energies expressed in liter-atmospheres.
@@v01dv01d yeah I thought that too, but the content what worth the watch. 3:30 is what got me turning my volume down and using CC for a better viewing experience. I like how expressive the piano is but not the volume of it in contrast with information is hard to understand already and listening closely is harder when volume isn’t balanced properly.
In middle school I wondered why rain was measured in mm instead of something logical like litres/m^2 until it clicked and I realized they are the basically the same unit.
daaaaaayummm it also boggled me why rain is measured in mm or inches. It makes sense now that volume/area is just a unit of length. Weird. Thanks for this info that I may never have to use. haha
they arent unrelated its an estimate assuming the hubble constant remains the same of when all galaxies were in the same place (the big bang) it just so happens the hubble constant hasnt always been consistant and the speed of the universe expanding has increased
I disagree. There is a reason background music is bland and boring, because it should not be the focus. Chromatic improvisation on a piano is the opposite, as the dissonance is unexpected, thus extremely distracting. This is the jazz nerd equivalent of doing a science video with Wake Me Up Inside blaring in the background. The fact that many are fine with it, either are deaf, or are not actually paying attention, which is a shame because the topic is super interesting. tl;dr: this video would've done better without any music EDIT: ah damn, the newer video doubled down with this musical nonsense.
I would like to listen to your note, but I suspect that it would be multiple instances of the universe I would have to suffer through in order to assemble enough peaks and valleys in order to reach an assemblance of hearing it.
I once had a physics problem recommend writing the charge of an electron as "1 electronvolt per volt" in order to help the units cancel nicely. I'll never forget staring at that problem and just thinking, "Huh, well I guess that's technically true"... Now that I'm an astronomy grad student, I see shit like "solar masses per year" and "joules per square centimeter per second per Hz" and it doesn't even seem out of place.
Gotta convert to something relatable, like the universal news units of school busses( large mass), football fields (intermediate lengths), and aircraft carriers ( real big mass).
Interestingly enough, when we get to proper spaceflight, it would make for more sense to use light speed measurements in general, like 2.2 Light Seconds, especially if we use laser weaponry. You A) get the measurement of a distance. B) you get the delay for how long ago the measurement was made. So in the example of 2.2 Light Seconds, you know they are 2.2 Light Seconds away, you also know that the delay of the measurement is at minimum 2.2s old. If you use laser weaponry, you will also intuitively know that you have to compensate by about 4.4 seconds, as the information is 2.2 seconds old, and if you need to hit it, you need to take into account that you also take around 2.2 seconds to hit. Especially useful for military applications.
As a fellow European myself (and to explain the reasoning behind that unit for non-EU people): If you have a lightbulb that will be on for quite a long time (1000h isn't hard to achieve in a year or so if you keep it on for maybe 3h/night) and thus I care about its energy efficiency, but guess what units are on my energy bill... That's right, kWh, so since 1000h is a minimum reasonable lifespan of a bulb, it isn't as dumb as you might think. Of course, we also have W (and at least on this side of Europe where I am from I've mostly seen them advertised as W), but oh well
i mean this is basically the frequency in which the universe expands, similar to how an APR interest rate would work, since %growth is unitless so it’s just 1/time as well
I just assumed that it was the "red shift" offset. Like, the Hubble constant is how much (on average) redder the light from other objects in the universe are compared to their true color.
Earth revolves 360° around its axis in 24 hours. 360° is 21,600 arc-minutes. 24 hours is 1,440 time-minutes. Your 15:1 arc over time is itself a fine "cursed unit."
@@robertarvanitis8852 First one about the bird poop is malformed. Does not take into the account size of poop and I could lay in my backyard and get pooped on or go to middle of the arctic sea and never get pooped on. I see bird poop on my car almost every day. And I see many cards in my hood with bird poop. So clearly we are not waiting 195 years per poop. You're taking the average of "never" and frequent and providing a useless and meaningless number.
The craziest unit I’ve ever worked with is an Erlang, which is equal to 60 minutes per hour. You read that right. It’s used by telecommunications engineers to describe the capacity of trunk phone lines (i.e. between exchanges) to carry multiple voice calls simultaneously. If you group 10 regular phone cables together, it will have a capacity of 10 Erlangs. Long live engineering.
You could call that a dimensionless number (ratio of spoken time to real time, or (usually average) number of calls at once) if you wanted to. I think there are a lot of numbers like this you could rewrite with "cursed" units for clarity if you wanted to.
I've seen in the notes of a friend of mine attending a urbanism class the unit "people/dumpster", which was used to measure how many people would be served by a single dumpster in a particular area. The first time I saw it I found it very funny, I read 500 people/dumpster as 500 people crammed into a single dumpster
@@Gabsboy123Considering how many US cities suffer from trash overflow, I would assume that this measurement does _not_ take people who create more trash into account.
@@Gabsboy123It sounds like an average. For every random person with a dropshipping business putting tons into the trash, there's a vegan committed to making no trash. They balance out eventually, especially if we're talking about a group of 500 people.
Person per toilet is even more complicated. There's a whole equation needed, it's also split per gender with up to 2/3 of male toilets being converted to urinals which makes it even more annoying
My favorite is s^-1 / s^-1, where the units don't actually cancel. (One is a frequency, the other is an _angular_ frequency, and so is off by a factor of 2pi.) In general, anything involving radians is 'fun', because people declare it to be unitless and then omit the unit, and then get really confused.
This always annoyed me, because degrees and radians are definitely units, and by declaring their unitlessness, it's easy to get confused when reading about models in papers where you're not familiar with the field's standards as to whether they're talking about radians or degrees. This issue comes up a lot in crystallography modelling, where the angle standard in physics is radians, but in measured X-ray diffraction data, it's degrees, and models either choose one or the other.
The same happened here with the gravitational constant at 9:30. Google covered it wrong. It went from 1/s to Hertz and multiple the unitless constant "revolution" without stating it. So, converting back to 1/s would introduce the 2pi or 360° factor incorrectly.
The most cursed unit I came across in my physics degree was for the frequency spindown rate of a pulsar, measured in seconds per second (or, every second, how many seconds longer each rotation of the pulsar increases by)
If the spindown rate of the pulsar was accelerating, you could measure that in seconds per second per second. How many seconds per second slower the pulsar is spinning every second.
Back when I was an astronomy grad student (c1990) one of my professors told us "a barn megaparsec is a teaspoon". I quickly responded "That can't be right - maybe 0.6 teaspoons?" The reasoning being: I knew a parsec was 3 x 10^something meters, a teaspoon was 5 ml = 5 x 10^something m^3, and a barn was 10^something m^2. So taking on trust that the powers of 10 cancelled as he claimed, there was still a factor of 3/5 left over. A bit later, I showed him on my shiny new HP48SX calculator, which could attach units to quantities and do conversions, that multiplying a megaparsec by a barn and converting the result into teaspoons indeed gave a result of about 0.6. That HP48SX's units functionality was absolutely wonderful for an astronomy grad student.
@@HobbitJack1 Back in the day, I wrote a program to turn the top five rows into a giant CST menu. It was very handy for keeping all the odd units and constants astronomers use close at hand.
There's an XKCD comic with a cursed measurement resulting from unit conversion. The unit is meters and Randall Munroe called it the "Oily House Index (OHI)". He noticed that real estate prices are stated in dollars per area while oil prices are dollars per volume. By cancelling these two units against each other, you get the OHI measured in meters. He then graphed it over time and some economical events even showed up (housing crisis, oil crisis, etc). The "intuitive" representation of the OHI would be: if I sold a piece of real estate and bought crude oil from that exact amount of money, how high could I fill the property with the oil I bought? Its absolutely lovely and the corresponding comic is one of my absolute favorites.
A long time ago I used to translate documents from English to Spanish. More often than not, they were of a technical nature. And often I had to review and fix someone else's work. One day I had to review someone else's translation of some very specialized industrial paint. The work also involved converting from customary units to SI. The original instructions indicated the lowest and highest temperatures at which the paint could be applied. And these had been properly converted from Fahrenheit to Celsius. But there was another important parameter provided by the instructions. For the first 24 hours after applying the paint, the ambient temperature should not fluctuate by more than 20F°. This had been duly converted to -6.7C°. So "for the first 24 hours the temperature should not fluctuate by more than -6.7C°". Whoever did this did not have a technical mind and did not understand that the 20F° referred to a relative change and not an absolute temperature. The correct value was about 11C°. The temperature should not fluctuate by more than 11C° over the first 24 hour period.
This reminds me of the basic issue of people having trouble with things like 30 or 0 degrees F being cold, so what is twice as cold??? But really we compare those to the reference 'room temp' where we are comfortable, not the numerical 0 (and I suspect the relationship is rather nonlinear to boot). So in your problem, they needed to know the difference in temperature from 0-20 degrees F, which meant calculating both and subtracting, or if they understand that this is a scaled difference, all they actually had to do is multiply by 5/9 since C and F differ by a constant ratio, plus an offset.
The most cursed units I've seen are "Hertz per dioptre". The dioptre comes from optics, measuring the optical power of a lens, and it's equal to an inverse meter. So, Hertz per dioptre is (s^-1) / (m^-1), which is speed if you flip the fraction to eliminate the negative exponents.
The speed of what is frequency per optical power measuring? I could conceivably see this unit in a graph that tracks the optical strength of a lens depending on light frequency in Hertz. Diopter is the inverse of the lens’ focal length, so it's focal lengths (of a lens with a certain optical power) per period (of light with a certain frequency) in this context.
@@adiaphoros6842 Brace yourself, because this answer might shock you. This is a unit for the speed of ANYTHING with a velocity. (s^-1)/(m^-1) = m/s. "Inverse seconds per inverse meter" equals "meters per second", which is a pretty common general unit of speed in physics.
@@emmeeemm It can’t just be anything, since the context of the units needs to be considered. In this case, the context is optics because “(light) frequency” and “optical power” are commonly used units. So, in that context, the speed of what is being measured?
5:40 Oh yes! I have taught physical chemistry at the university for quite a while, and dimensional analysis got very important pretty often. Students would divide quantities instead of multiplying, getting completely nonsensical results; but just evaluating the units of everything can reveal the error. I am glad my physics teacher back in high school drummed this into us relentlessly.
It's a great sanity check on any sort of ad hoc calculation from physical measures in daily life. For example, my wife and I live off grid, and we're going to be upgrading our domestic propane system end to end in the coming year. We will have to rethink the consumption rate of our appliances and determine the capacity of lines to supply them. Even before we get to drawing up a consumption budget, it's very helpful to think about the units of measure. Appliances here may be rated in either peak BTU/hour or equivalent Litres/hour, or more rarely kJ/h or Watts, as well as thermal efficiency. Line capacity will be a function of cross section and pressure, also possibly taking length into account. Tankage is rated by either weight or volume. So already there's a comfortable sense that peak L/h can be the common currency in drafting the budget and sizing the lines and regulators and tanks. We haven't cited a single number, and yet we have a good preliminary grasp of what we'll be talking about when we get together with the gas fitter. No doubt there will be some regulatory constraints, the need to work within standard pipe sizes and whatnot, but we have an easy conceptual framework to make sense of all that. It may also be that the trades have a preference for converting directly between particular units. That can seem cryptic at first encounter, but already having a dimensional analysis makes it much easier to follow. In short, it's an extremely valuable form of literacy.
This is what I keep telling the second semesters I'm supervising for 2.5 ECTs: Solving this homework is simple: Step 1: Google every formula that might be relevant and note it down Step 2: Figure out how to get from what units you start with to where you want to end up Step 3: Calculate the unit to make sure you don't end up with a hamster whose mass is measured in km²/C Step 4: Calculate the order of magnitude and ask yourself "Does it make sense for this hamster to have a mass of a few 10^36kg?" Step 5 (optional): calculate the numeric value
It's amazing how many chemistry and physics problems can be reduced to just "dimensional analysis" and I used to try to impress that on the students in my chemistry recitation sections. What does the problem give you? Mass. What does it want you to find out? Volume. What do you know that relates mass to volume? Density. Boom, problem solved, the rest is just arithmetic.
By far my favorite cursed unit in electronics is Ohms per Square. It's used to measure resistance of flat copper planes (such as in a printed circuit board). It turns out the length and width of the square cancel out, so the square is unitless. Any square you draw on a copper plane will have the same constant resistance regardless of size.
@@MrNicoJac Pretty much, yeah! If you have a long thin trace it'll have higher resistance because you have to draw a bunch of tiny squares in series to cover it. A thicker trace means each square covers more of the distance since both the length and width can expand to fill the wider trace, and thus the overall resistance is lower for the same length of trace.
Yesss ! Just today I had to redo some of my older experiments for a paper involving a four probe sheet resistance and I was just thinking about what an actual bullshit 'Ω/sq' is, and then this video pops up on my way back ! 😂😂😂
The music adds a lot of value to the presentation here. It's cool that the topic is interesting enough, but having an inherently emotional component validate the audience's interest in a topic, in particular by matching a reasonable emotional understanding, kept me hooked in. Sort of like helping you suspend your disbelief, but without the disbelief because the thing in itself is science.
Dimensional analysis kind of saved my butt in high school physics and even some college physics. When you understand unit multiplication, I find it WAY easier to remember equations. Sometimes you can derive unit breakdowns in the exam and get a eureka moment which makes you remember the equation from your studying.
I did this in high school physics too. I was in AP calc at the time, so rather than spend time studying, I used calculus on the tests to re-derive the equations from dimensional analysis, because that way I basically only had to remember calculus which I needed to do for my other class anyway.
Dimensional analysis turns out to be a nontrivial part of our understanding of *quantum field theory*, so this feeling never goes away even at the highest levels of physics :p.
In a dynamics test I had forgotten the formula for final velocity given distance and acceleration so I used dimensional analysis to recreate it on the spot. I did however forget the 2.
My father used to say: "always check the units". It helped me being a bit above average in my physics courses at university. Keeping the units in every step helped me not to be too lost in my own calculations. Your examples are fantastic, thx !
One of my best teacher got mad when he realized we weren't taught to think in units when solving equations "It makes it so easy!" he yelled. I've been checking my units all the time since then but gotta admit that getting in the game late can be veeeery confusing like when juggling with angular speed in rad/s... o.O and finding out that basically radians aren't real... or having to prove to myself in a middle of an exam that a Joule is a W/s so a Watt is a kg.m^2/s... Not the most efficient way to solve something I should have prepared instead of playing skyrim
Yep, retain units throughout and always write conversion factors out as longhand fractions like in Randall's example at the beginning. Can't go wrong then. I mean you can, you can always go wrong, but at least it won't be because you didn't write down units.
Conversion factors come in clutch, I write them out always, otherwise I make some dumb mistake like saying 1 day is 3600 seconds and the entire calculation from then on is wrong
I once saw (in an old technical report from Oak Ridge National Lab) thermal conductivity written in units of BTU/hr/ft/°R, and I still haven’t recovered.
It's actually crazier than that. Thermal conductivity is usually expressed in BTU*in/(hr*ft^2*°F). That is, the number of BTUs that will conduct through a material that is 1 inch thick, 1 foot square, and has a 1°F difference in temperature between the hot and cold side in 1 hour.
Actually, both °R and °F are a very colloquial way to write that part of the unit. Technically correct would be R (without the ° symbol), i.e. just Rankine, as that signifies a temperature difference on the Fahrenheit scale (the same way a temperature difference on the Celsius scale would be K, Kelvin, without the ° symbol). °R (with the degree symbol) would be an absolute temperature with its zero point at "absolute zero", the lowest temperature possible. It's the same with the Celsius scale, where °K would be an absolute temperature with its zero point at the lowest temperature possible. And both °F and °C never go without the degree symbol, as they're both absolute temperatures, never temperature differences. (However, with a zero point at a physically silly - but useful in practice and more tangible for human consumption - temperature.)
As an astronomer I am delighted to see the cursed units of the Hubble constant featured. Also, the 2 AU distance between measurements in January and July is resolved by taking half of the angle between those two measurements. The January and July measurements make an isosceles triangle that you then slice in half to make right triangles. This phenomenon of apparent position change is called parallax!
Since you like cursed units, here is a cursed unit of volume: (Hubble Length*Acre/(Barn ^ 1/2) *(1 gallon)^(1/6)* (1 rod)^(1/2)/(1024)^16) ~ 2 cu in. And you can raise it to the 1/6th and divide by Milliparsecs squared, and pass an Earth Day as a duration to get a different, very fast growing Earth Days per square root ~1.1 in. per Milliparsec squared. A cursed unit you could use for... cooking checking... using solar panels and a goofy hourglass setup. Yeah, units get really cursed if you want them to.
Do we account for the fact that we're in an elliptical orbit around the sun? Theoretically, the January/July measurement would be a little different from say a March/September measure.
@@joshuaychung Well, I would assume they only take measurements in the months where the earth is 1 AU from the sun. Makes you wonder why AU is a unit when the earth’s distance from the sun is not always the same depending on where it is. The ellipse is probably not that big of a difference.
I can't remember any cursed units, but I gotta comment on how excellent the piano accompaniment was. The discordant sounds when you mention something confusing, the dramatic build-up as you build up to a conclusion, the sudden stop when you drop a surprising fact! Top-notch.
Don't forget the step up and step down when talking about the chance of the diffraction changing and the piano music being a musical random walk when talking about random walks!
@@mguddeti Except Torque isn't a form of work? Is It? It can't be... "Work" is Energy, It's the result of the action of a force inducing deplacement. The units are the same but the thing they measure isn't. For Work we consider the distance travelled by the object because of the force applied to it, If the object doesn't move It didn't recieve Energy. (unless it deforms or warms up or emit light or wathever ^^') But for Torque, we consider the distance from the force application point to the center of rotation of the object. Torque exists without displacement. you can apply a Torque without spending energy if nothing happens to the object. And this "rotational Inertia" equation is kinda misnamed because it's simply newton's second law F=ma applied to rotation it doesn't measure rotational energy. "Rotational kinetic Energy" does E = 1/2 * I * w^2 but Yes, this again has the same unit, Joules xD @ReySilverskin you truly are evil hahaha I'll keep using N.m for torque
Here’s a proof for those wondering: Torque => F * d => ((kg * m) / s^2) * m => (kg * m^2) / s^2 = Joules. Here’s the proof using the rotational inertia equation: Torque => Ia => (kg * m^2) (rad / s^2) => radians are unit-less so => (kg * m^2) / s^2 = Joules However, even though it’s possible to measure torque in joules, it doesn’t have the same intuition as energy, as torque is just the rotational version of force, which just by chance has the same units as energy, but it shouldn’t be thought of as that.
@@mguddeti Rotation energy is another form of energy, as with kinetic or potential energy etc… For extra fun, rotate or move fast enough that you need the lorenz transforms…
I mean most of those implication arrows (=>) should just be equal signs. "Implies" or "=>" is used when you have two statements, such as x = y => x+1 = y+1 rather something like 1 => 2-1
in chemistry, pH is the negative logarithm of the concentration of protons in a solution, and concentration is basically the number of particles in a volume. most equations using pH aren't that cursed, but i was never really able to figure out an intuitive way to understand the dimensional analysis of the henderson-hasselbalch equation
It comes from the fact that strictly speaking, generally the concentrations of protons in a solution is in fact quite low, so of course you're dealing with negative powers of 10 Hence, to make pH a sensible unit, and to reduce the scale in such a way as to be interpretable, you first take the logarithm, but that's a negative number, and you can't HAVE negative scalar units, so you then negate it. If there's enough protons in solution to suggest that there is indeed somehow one mole of loose protons per liter of solution, AKA 1 M, or pH = 0, or there are somehow so few protons per liter of solution that there's one mole of hydroxide ions instead, then the solution is likely so caustic as to be nigh-on uncontrollable without highly specialized and study equipment, thus handily explaining why pH is generally not measured once you go below 1 or go above 14.
Ultimately, it only really works because 'concentration' can be a dimensionless constant - Number of Protons per Number of Total Particles (mol/mol). The issue is that we measure concentration as mol/L. The only way to make that dimensionless so that the logaritm can log it without issue is to have an implied scaling constant of 1 L/mol on that concentration (instead of pH = -log(a), you have pH = -log(ka), where k = 1 L/mol). If we were to rescale this so that we were measuring concentration as mol/mol (dimensionless), we introduce a new scaling constant is the volume per mole of the solution (pH = -log(kma), where a is now our dimensionless concentration, and b is the mol/L of the solution, while k = 1 L/mol), and so varies based on the solution. Since most acid/base work is done in liquid water, 1 mole of water is 18 grams, which is 18 mL liquid water, so b = 1 mol/0.018L = 55.6 mol/L or so. Rewriting so as to only have one scaling constant, we have pH = -log(na), where a = concentration in moles per mole, and n ~= 55.6 dimensionless, for no real reason except to keep the final answer (also a dimensionless value) consistent with the existing pH scale. In theory, you could redefine pH to not need that constant - the constant factor only serves to shift the final number by about 1.74ish. A 7 pH would end up being a 'pH' (normalized to mol/mol) of 8.74 or so, which is less pretty, I guess. Which variation is 'more right' comes down to which option makes it easier to compare activity in different kinds of solutions (not just water). In this case, mol/L sort of makes sense as a 'how much activity by volume of liquid', but on the other hand, chemistry is done stoichiometrically, so you're more likely to want to know how much 'activity by mole of solution' you have, I would think. On the other other hand, 'activity by volume' is probably more readily accessible to a non-chemist, so is more comprehensible to the layman. So I don't really know.
the explanation I received is that there is an implicit "unitary concentration 1 mol/litre" inside of the logarithm or something like that. This is to cancel out all units, since logarithms (and trig functions) cant have units in their arguments. Specifically in logarithms and exponentials, it's always a ratio of something against something
In university, I had some work that was calculated in minutes per hour. We were doing a group project on how many toilets a building needed, estimating the time of a trip to the toilet, estimating the nukber of people in the building and estimating the number of toilet trips per day to try and estimate the amount of minutes of toilet usage per hour. One model had 2650minutes/8hours which became 331.25minutes/hour and then further simplified to 5.5208minutes/minutes.
@@chemtrailsmoker9852 I guess that's one way to interpret it. Although we mostly wamted to work with it to model theideal number of toilets for the building. I think it was something like 1 toilet per 20 people, plus an accessible toilet on every floor.
Urologist here, when I calculate the risk for prostate cancer on a patient, I measure the density of PSA. That number is obtained by dividing the PSA (ng/ml) and the prostate volume (cc or grams). The unit therefore can be expressed is in the unit ng/(ml · g) and that can be simplified into ml^-1 or ng/(ml · cc) which is ng/ml^2 or ng/cm^6
I just love how, when you were talking about random walks, you were also playing a hexatonic random walk on the piano! Great soundtrack, clear explanations, 10/10!
Can we appreciate the music in this video? Like, I've genuinely never seen someone have reactive, living music that plays with and compliments the video, rather than a few standard, unchanging backing tracks. It's so creative, I love it!
I remember the first time I thought about how strange unit cancellation is was when I learned that you can measure rainfall as either liters/meter², which is basically (0.1 meter)³/meter² or 1/1000ths of a meter, or 1 millimeter. So if you're expecting five millimeters of rain, that's just five liters per square meter of ground it's falling onto. Super obvious in retrospect, but it confused the heck out of me as a kid.
which incidentally is how you can "easily" measure rainfall: put out a 1m^2 pan outside, and measure how high the water is in the pan at the end of rain. in your example, it would be 5 milimeters. in fact, because of unit cancellation, you can see that any pan would have 5 mm of water on average.
So thats what that means, i thought they left some sort of rain catcher out and measured how much it filled, which always confused me as to how small of a number it was
@@Queue3612 That's exactly what you do, but you do not measure how much it fills but how *high*. That way you do not have to specify how big the container is.
@@Themoonisachees damn. I went and wrote a comment saying that measuring height is container agnostic, only to read the last line when I was done >_> On the other hand, if you don't have a ruler but you have a scale the size of the container matters
I stand by this statement with 100% confidence, this is the best video on RUclips. I can watch it so many times and it never gets old. This needs to be a series…
The bit about fuel consumption has an interesting update with the transition to electric cars: The specific energy consumption of an electric car can be given in kWh/km, which translates to 3600 kJ/km = 3600 J/m = 3600 Newtons. And it has a neat interpretation: It's the average force (air resistance, friction etc.) holding your car back over the distance of the trip (some overhead for onboard electronics notwithstanding).
Год назад+22
This explanation feels wrongs. The energy efficiency of a car does not only depend on external losses like air resistance. In fact, air resistiance and frictions can be considered constant, depending on the actual car design and implementation details.
@ but these resistances change with different driving conditions (speed, headwind, ...). I would also expect electrical and mechanical efficiency to change with variables such as temperature.
@ That's why it is not an explanation but rather an interpretation: Assuming that all losses were created by air resistance then it would have the exact force of your energy consumption.
@@MrHankeyYT I think it's a valid explanation too. Those newtons are the total forces the engine needs to overcome, including air resistance, wheel friction, and also internal resistance of the engine itself.
My AP physics teacher once told us a story about how one student would always write his test answers with ridiculous units just to make our teacher check the conversions to make sure he got it right. After beginning E&M and encountering the unit of "Ohm" for the first time, and him telling us "1/Ohm" was allowed to be written as "Mho", I got inspired to do something stupid just for fun. Long story short, after consulting the year's worth of notes to find the right connections, I found that all units can be written in terms of "Mho", with my favorite example being meters. c^2s/KgMhom=m, or Coulumbs squared seconds per Kilogram Mho Meter is equal to meters. The part about this both my friends and teacher thought was the most cursed, was the fact that meters appears its own definition of itself, which is just plain stupid.
Let's be completely honest. Meter IS derivative of itself, which was tied to physical world occurrences to have ability of consistently reproducing value within laws of our universe. Any measurement value is such, because it relied on people defining it in the first place and there were no good ways to create absolute measurements back then. And, as meter is one of the key values, as everything can be tied to meter, it is reasonable to assume you can actually derive meter or second from combinations of basically any existing metric values as well.
Unlike SI, CGS does not have a separate unit for charge. Instead it has the statcoulomb, a derived unit equal to 1 sqrt(g cm^3)/s. To add to the cursedness, it's not dimensionally consistent with the coulomb. The conversion factor depends on the context of the quantity it's measuring.
Better than having to use vacuum permittivity and permeability constants. Makes dimensional analysis a whole lot easier. Hardly any reason to ever convert charge itself, anyway, and CGS is consistent with SI on stuff like Energy.
I remember too many problems where cgs helped cut through the tangle and clarify the problem to think it’s completely useless. That said, the statcoulomb is pretty cursed.
In materials science, fracture toughness is measured in MPa/sqrt(m). If you account for the fact that Pa are N/m^2, you can end up with the unit N/m^3/2, which I’ve always found to be super cursed.
Finally, an outlet for the weirdest unit I came across in college. Sheet resistance, the measurement of electrical resistance of thin films of uniform thickness, uses a unit that is so cursed it has stuck with me for nearly a decade at this point, that being "ohms per square". This unit is referred to as such because, while bulk resistivity is measured in ohm*meters, which is actually stated as ohm*m^2/m (ohm*area/length), you then ALSO divide it by its sheet thickness, giving you straight ohms again. However, to designate the maddening process you've been through, it is designated as "ohms per square". Link here for more reading: en.wikipedia.org/wiki/Sheet_resistance
Electrical/electronic engineers are masters of using cursed units to designate stuff, at this point I've abandoned any hopes of ever doing a proper dimensional analysis and just look at the formula long enough until I'm convinced the units _probably_ line up lmao
After our physics teacher taught us about dimensional analysis in school, I never had to remember all these many complicated formulas again. It felt like enlightenment! I only remembered some basic formulas (F=m*a etc.) and in every test I simply derived the more complicated formulas again. It made everything so much easier!
This is what I teach to my students! Stop memorizing and just practice dimensional analysis until you're confident with it. It'll help you actually understand the relationships between the values.
My friend in college forgot ohms law during an electronics test. He used a few of our phisics 2 formulas to derive it. I still don't know if he was right or just got lucky, the prof wrote a bunch of question marks then circled ohms law on the formula sheet. (Yes he was being completely dumb)
Permability coefficient Pm which is: 10^-13(cm^3*STP)(cm)/(cm^2*s*Pa). Ohh and STP is 101,3kPa. The unit is from material science, seen in the book Callister
A rule of thumb in surveying is that the elevation of a horizontal line of sight changes by 8 inches per mile-squared. This turns out to be the reciprocal of the diameter of Earth.
The elevation drop is pretty much "the same number" in SI, for once(!), namely ≈ 8 cm/km². That's because, in the spirit of this video, (1 mi² × cm)/(1 km² × inch) = 1.02 ≈ 1, dimensionless.
In my nuclear education (I promise this isnt that boring) we had to do a lot of unit conversion, and to teach us how to do them well we had a sheet of obscure units broken down into their metric derivatives. Basically on that sheet was the "Miner's inch" and it became a meme between the boys because, y'know, yeah... If you were curious, its a measurement of volume/time.
We use miles per gallon in the UK but due to the unique way the Imperial system works, it’s not the same gallon as the Americans use. This means there are roughly 1.2 gallons per gallon.
For my cursed unit I'm gonna go with a plain old meter... USED FOR TENSILE STRENGTH OF A MATERIAL. I don't remember the exact equation, but basically it answears the question of "how many meters of a wire made form a specific material would it take to deform plastically under it's own weight". It's quite nice for aerospace science and other science branches where weight is important, because it combines strength properties with density of a material.
"Volts per square root hertz" often pops up in audio amplifier specs. My understanding is that this is fairly common when dealing with power distributions. Same thing for shock and vibe testing where power spectral densities are specified in units of G^2/Hz as a function of Hz.
That unit is often used to work with thermal noise, so what I get from it is that sqrt(unit) is expected to show up whenever dealing with probabilities (such as noise or random walk in the video)
You beat me to it. Another cursed unit in the audio world is decibel. I mean think about it, it is a ratio so no unit isn't actually needed and we always use it in its deci(1/10th) form no matter the context; it is even common to see mdB used which is like saying microcentimeter. To make things worse, it is also common to reference off standards that are just assumed and not always agreed on. So in an audio system, you might have amp gain measured in db(log scaled input voltage/output voltage) feeding into a speaker which produces db/V(but in this case, db is the log scaled ratio of volume vs a standard sound[20 micropascals]) as well as a signal-to-nose-ratio(SNR) which is also measured in dB(log scaled signal/noise). It wouldn't be so cursed if people didn't insist on using dB as both a method of comparison(what it mathematically is) and a unit(by comparing against unofficial standards).
My parents had to ask what comedy show I was watching when I kept laughing and wheezing at this video. The silence pause after you introduce each cursed unit is phenomenal, it's like you have to stop for a few seconds to massage your temples and be like 'ugh this again' before continuing. Instantly liked and subbed, I need more of this.
Unfortunately, too many people mistake this video for a serious science video. I'm giving him the benefit of the doubt in assuming he meant it to be humorous, because it is certainly not serious science.
This video has been on my youtube suggested list for some time and finally I decided to watch it today... YT algorithm was right! Not only I really enjoyed the video but also I realized that I had the same questions and reactions myself about these cursed units. Good work.
megaJansky per Steradian (10^-26W/m^2/Hz/sr) is a particularly cursed one I found while working on a power radiometer for radio astronomy. A jansky corresponds to the power per telescope dish area per hertz (flux density) and steradians the observed circular arc of the sky (rads^2)
So many little problems in life can be solved with a dimensional analysis exercise in like 10seconds. But when you do that people think you’re a god damn wizard or something
The best use of dimensional analysis imo is to find out that you modeling the whole thing wrong, especially when working with imperial vs SI distances raised to powers, etc.
My highschool physics and chem teachers 100% drilled dimensional analysis into our heads. I'm pretty sure they colluded on that fact. Also, for AP chem, the teacher would randomly ask students question about ions if he saw you in the hall and tally the total right/wrong answers to buff or nerf his curve for the final exam 🤣. People took it very seriously as his class was super hard.
props to the music in this video!!!! It very well ties together the background ambience with the words being spoken. I particularly love the example of the random walk in the section on PMD
the most cursed units for me are inverse centimeters, which are used for a sort of frequency because they're the inverse of the wavelength, but they're called wavenumbers and have a factor of 2pi thrown in, and they're also used for energy because you can convert a wavenumber of light to an energy in joules or eV pretty easily, and then physical chemists get excited and start just doing literally every single unit in inverse centimeters
Spectroscopists are a plague. I had to recall that RT thermal energy was roughly 200 cm-1 and that it corresponded to the much nicer 25 meV to remember the "conversion"
I wholeheartedly agree. Inverse centimeters are absolutely terrible. Luckily for me, nm is the standard for the near-IR so we get to work with beauties
The way you use music in this video (and I presume, in your other videos too) is perfect. Music is often used and made with a sort of standalone role, as if the whole purpose of it is to just listen to it. Sure, in movies, games, theatres and a lot of other form of art it plays a role of enchancing the emotion, but so rarely it is used in learning processes for that purpose. Using it like you did here is precisely what we often overlook in how we learn things. And it is crucial that you didn't just use some off the shelf piece but actually made it like a soundtrack for this particular video. This is just great and I appreciate it very much.
I personally found it extremely distracting and pretty annoying. It's cool and all, but imo this is the kind of content I want to be focusing on the presenting material , and the music is consistently pulling me away from that (as I'm a musician so I'm subconsciously analysing it as it goes along, and each time it changes (which happens when the info is changing in this vid especially), my mind goes to that for a couple seconds; I have to either fight that impulse or rewind the video a lot as a result...).
@@99jdave99 to each their own, I guess. As you are a professional musician and automatically focus on music more then the main content of the video I'd say it's more of a compulsion than a normal way to perceive such stuff. Some people of different professions can't de-focus from their field when they find it's footprints in other types of content, or when someone talks about something completely different. Don't take offense, I truly mean nothing bad, but there are a certain type of scientists, that can't help but tell you why and how some piece of science fiction is not realistic, and how they should've made it differently, as if they cannot enjoy sci-fi without constantly thinking about their work. It either means you are extremely passionate about your stuff, which is good and you'd most likely be able to give it more of your time than others, or there is a problem in how you view your profession. I don't know if it is a term in English, but in Russian we say it's a "professional deformation". And to be professionally deformed is to carry over some traits and particular views on things that are useful and ubiquitous in your field into other spheres of your life, where those traits are usually problematic to you or your surroundings.
In my photovoltaics lecture I really hated kWh/a (Kilowatt hours per year). The justification, which kinda makes sense, is, that you can see from the unit, that the value you are looking at signifies energy generated (or consumed) averaged over a whole year (with its different seasons etc.). Still, it seems stupid to me to have a time unit divided by a time unit.
@@suomeaboo well the unit makes sense culturally, we get our electricity bill yearly ( more or less you pay some estimate per quarter but it is always corrected at the end so doesnt matter), now on that bill it states you used e.g. 2500 kWh, therefore for a solar panel it makes sense to know how many kWh it generates per year to quickly figure out how much money you would save per year and if it is worth it. (of course for solar panels there are other factors and costs like batteries and stuff since you probably arent using all the energy during the day and so on)
The EU energy efficiency labels (for some products, like displays) are even weirder: the average consumption is stated as xyz kWh per 1000h. Weird way to write it consumes xyz watts...
The reason for kWh at all is because it makes accounting easier. Take the wattage in KW, multiply by the price of electricity, you have your hourly cost.
I just finished my first year in a university Particle Physics degree and I have a great addition: magnitude - a measure of brightness . This comment will only discuss apparent magnitude (so distance between observer and body can vary), absolute magnitude (M) is a measure of apparent magnitude when the body is at exactly 10pc away. The Greeks originally classed stars in 6 magnitudes, the brightest were m=1 and the dimmest were m=6. They aimed for each grade in magnitude to be merely twice as bright as the previous grade. Nowadays we've quantified magnitude into the formula: m = -2.5 log(F) + c. F is the flux (W m^-2) at the star's surface and c is complicated... The result of this modern equation is that if star A has magnitude 7 and star B has magnitude 6, that means star A is 2.5 times dimmer than star B. However, since we have more advanced apparatus for observing the sky, more stars have been discovered which are brighter or dimmer than the original 6 grade system (m = 1 to 6). This leads to very bright stars having a magnitude of 0 or even negative numbers! Alternatively we can have very dim bodies with magnitudes near 20. To make all of this worse, you need to consider that to observe something, you are detecting wavelengths of light that body is emitting. With this knowledge, let's discuss what c is in the magnitude equation. Consider some bands of light: U, B, V, R, and I. Ultraviolet, blue, visible, red, infrared. Different bodies may be brighter in some bands than others e.g. a star may emit more infrared light and thus have a smaller magnitude in the I band than the V band. The variable 'c' in the magnitude equation must be chosen such that it is m=0 across all bands. For most of my exam papers, the star chosen was Vega. Once you have chosen a reference magnitude/body, all subsequent calculations must use the same c if you want to compare any of them to each other. The result is an incredibly cursed, negative, non-linear, dimensionless system of measuring brightness. Could we not just have used the candela or something?
The funniest part of this whole story is that this convoluted system was made exclusively to be convertible to a brightness ranking from antiquity, which is so far removed from us that modern astronomers probably don't even know it other than as some thing that used to exist. (Disclaimer, I don't have a particle physics degree or much knowledge of luminosity related stuff lol) If we wanted to make a measure related to how much light you would detect at some distance maybe we could use photons per square meter at 10 parsecs or whatever distance of the star. After looking up how many photons hit one square meter of the Earth's surface which is apparently 3.8*(10^21) photons, I divided by 4.25 trillion (10 parsecs' worth of AU squared) to get 900 million of the Sun's photons inciting on a square meter sheet at a 10 parsec distance from the Sun in any given second, or an absolute magnitude for the sun of log 8.95 photons/m^2, and in my hypotherical scale stars would range from around magnitude log 6 (1000 times dimmer than sun, lowest bolometric luminosity I found for red dwarfs) to mag log 15,5 photons/m^2. (~5 million times brighter). Fairly complicated explanation but the photon is an absolute unit, so at least that much isn't arbitrary. Edit: After looking it up, it appears that the original figure of 3.85×10²¹ photons I encountered comes from people calculating how many photons of green light (which is what light the sun emits the most) would equal the 1400 joules of energy per second that a square meter of ground receives in the Earth, so my scale is in relation to 500/550 nanometer wavelength photons in specific, which keeps in a good deal of cursed-ness is kept in the details of my hypothetical brightness scale as that would mean my scale which is supposed to be for absolute and relative magnitude apparently has a bolometric correction effect built into it because it's measured in terms of Sun-like green photons.
@@frogflint4371 that one is hilarious. it does kind of illustrate the dishonesty of these tricks though. a joule of thermal energy per square meter of pizza per second is coherent. converting a joule of thermal energy to a kg of... something times a square meter of something else per square second is dodgy as hell, and canceling a square meter of undefined something-else with a square meter of pizza is just outright fraud.
I had a similar experience when we tried out ChatGPT 4 and asked it to calculate something for us. It kept referring to pressure as "meters", but the answer it got was correct. When we asked it why it uses meters are pressure, it said that it uses "meters of water" as a pressure unit...
If I remember right, you have a U shaped tube that's closed on one end, and open on the other, and you apply the pressure to the open end, and the pressure you measure is how far the water level on the closed end moves. We used inH2O as units in one of my labs
But that unit in that context would be incomplete. It would need to be water colum in meters under earth gravity. Because water pressure dpening on depth is connected to the gravity of the object it´s on, or in short, the weight of it.
That is absolutely a unit! I work with a lot of natural gas generators for my job, and frequently take pressure readings. Natural gas runs in most houses ~ 1/4 of a PSI, or .0172 bar. To be more precise, we use the unit “inches of water column” It’s amazing you can get enough power to run 20 houses at once with less pressure than is at the bottom of a glass of water
The unit barn (b) which is 10^-28m^2, which is still used as a unit for a cross sectional area of a target, usually used in the creation of new elements where barn came from the phrase "couldn't hit the broad side of a barn"
there's also a BarnMegaparsec which is a unit of volume. its the volume of a prism with base area of one barn and height of one megaparsec, used to measure the volume of space that a particle of cosmic radiation traverses in its long travels.
I used to despise the entire field of Fracture Mechanics because of MPa m^0.5… Until I had to start playing with T m^0.5 (Tesla root metres) in my Honours thesis…
One cursed unit I hated at uni was the barrer, often used in membrane engineering. As defined, 1 barrer = 10^-10 * [( cm_STP^3 * cm ) / ( cm^2 * s * cmHg )]. When the units are so awful, we have to invent new ones to try and handle it!
Similar to permeability (of rock samples, for instance) which is measured in m^2 when expressed in SI units. Since the values in m^2 are usually unwieldingly small, the Darcy or even millidarcy is more often used, one Darcy being about equal to 10^12 m2
@@klaasbil8459 and even smaller than the Darcy is the Barn, clocking in at about 100 square femtometers. It’s used in nuclear chemistry to measure the cross section of individual nuclei. And it’s not even a physical cross section, it’s a probability measurement!
Ever since I heard about about kWh for the first time i was obsessed with it since I found it to be so dumb. I didn't find anyone else getting annoyed by it until now. Thank you for finally discussing how absurd it is
Consider also the "kWh/a" (a=annum=year) that others have mentioned or "TWh per annum" that I described in my comment. It's a total farce, and harmful.
Thank God I have a friend in a random internet stranger. I always said that it is stupid to first you divide by time only to multiply with time later. Did we not learn to shorten down fractions? How can a math / phys teacher ever accept an answer given in kWh?!
From an engineering perspective, a power plant is more concerned about average power consumption over time. If a factory needs to run 8 hours a day and consumes 1600 kWh, then it will consume an average of 200KW of a plant's bandwidth. These conversions are of course doable in Joules, but it's a lot cleaner and easier to reason with if you just stick to kWh rather than converting to and from Joules all the time. It's also why lightyears/light-seconds is a thing: (300e8 m/s) * years is the same as 9,46e15 m, but in astronomy it's convenient to have a measure based on relativistic speed since it's a commonly desired conversion. tl; dr it's a convention borne from conversion convenience
I have a Masters degree in physics and absolutely detest that unit. I also teach high-school physics and it is quite difficult to help students understand it, which I honestly cannot fault them for.
Really if you think about it, there's a very simple reason why things have ended up this way. It's the one variable that doesn't comply with the SI prefixes in the whole thing: time. That's it. 1 Watt for 1 second is exactly 1 Joule. 1000 Watts for 1000 seconds is exactly 1 MJ. But the issue is that 1000 seconds is a completely arbitrary 16 minutes and 40 seconds. Instead we use 1 hour, which is 3,600 seconds, which is why we end up with the 3.6 factor from kWh to MJ. It's all because we never got around to metrifying time. Which tbh is understandable because our circadian rhythm and the sun doesn't give a shit if 86.4 ks is an awkward amount of time. Moral of the story: mixing metric units with non-metric units is cursed.
I remember in my engineering class we had an answer to a problem measured in "dozens of slugs per day", slug being the SAE unit of mass. That was an interesting result
The old school hackers will be familiar with the "jargon file" (you can still look it up on the internet). It refers to, amongst others, deliberately arcane units like nanoparsec per milliforthnight, roughly an inch per second.
I used to work installing optical fiber and not only do the cables have impurities, they also end up being installed in all kinds of crazy ways with a lot of bends which also scatters light. Fiber being as fast and consistent as it is even with all those things working against it is really cool.
8:30 the 2 is because 1 au is the distance from the earth to the sun (radius of orbit), but the second reference point isn’t the sun, it’s twice as far away - specifically, on the other side of the sun, or twice as far away (the diameter)
my math teacher once said: "science is just guessing, just really really smart guessing". and its the most funny, yet accurate thing ive ever heard from any teacher
@@bipl8989 Half right (so maybe we are down to quarter right now?) Yes smart^2 Guessing is the hypothesis, Science is proving it wrong, and Confidence in the hypothesis increases the more times competent people fail to prove it wrong. Only in mathematics can we prove the hypothesis (aka assertion/conjecture) is correct.
@user-xh9pt8zu2l No, the original commenter is correct. You see nothing can really be proved regarding the really world since there is always some uncertainty in the accuracy of our observations. Therefore science isn't about proving things exactly, just finding patterns that match reality very well. You can see this in how new developments in science often overwrite previous theories, such as newtonian mechanics vs gr
Not the most cursed unit I've encountered, but strain is worth mentioning. Put simply, if you put a material under tension (or compression) it will expand (or contract). For the tension case, the ratio of the material's new length to its old length will usually be some number very close to, but slightly larger than 1. If we subtract 1 from this number, we have a measure that starts at 0 when you apply no force and increases linearly for a little while (for "normal" materials). This measure is strain. If you consider the units, you have length/length, which is unitless, so subtracting 1 from it isn't nearly as insane as it might look. But then you find that it's not uncommon to report strain in units of mm/mm or inch/inch. I'm reminded of radians, which are technically unitless, but in practice are written as "rad", because it makes the bookkeeping easier.
i thought radians were also technically distance/distance, since its defenition is the length of a part of the circumference of a circle devided by the radius of the circle. i know you would never write an angle like m/m or smth, but i thought it was funny that both of your mentioned units could be defined by this m/m
the torque distribution unit is pretty cursed as well: Nm/m this type of stuff i usually just dont mind understanding because its just a matter of keeping things tight lol
The most cursed unit I've ever had to work with is Rankine, where some very old documentation on refrigeration used Rankine for all of it's temperature references. Rankine is the Kelvin of the Fahrenheit scale. R°=F°+459 and some change.
Hi, 3rd year engineer (i am very stoopid tho im a civil) For the Hubble constant, wouldn't've it be 2 Au because 1 au is the distance from the earth to the sun and they measured from. . . both sides of the sun? Like, the june and july "points" and the distant object "point" make an isosceles triangle. They convert it into 2 right triangles by splitting it down the middle, and in the process dividing the "base" of the triangle by 2. This new "base" is an averaged distance between the earth and the sun (the earth is closer to the sun in the winter or summer i forgor which tho) and this difference gets accounted for with the average (the average (i would assume) is why they waited 6 months to go 180 deg around rather than 3 months and only go 90 deg around). Aaaanyways, following the process backwards now, we have 3 points to start with. 1) the distant object 2) the telescope, and 3) the sun. We know the average distance between the earth and the sun (base), we know the angle (measured angle divided by two (isosceles triangle to right triangles)). NOW we can figure out wtf the distance from us to the body is . Hope this helps and sorry if anythings wrong, i study frames and dirt not space, but this jus feels like a big trig problem.
For the first question. It is measured as 1 au but the only suitable way of measuring it is by using 2 au. Kind of like how speed is measured in km/h but during short distances and short time, we can measure it using m/s and then convert.
There are a few papers on the fractal nature of some day-to-day objects, like paper balls. We use this experiment for our undergrad students to learn log-log linearization. What is interesting is that you find the mass is proportional to the diameter^n, where n is a real number between 2 and 3 for paper balls (usually around 2.3). Then, since M = k*D^2.3, the unit for k is kg/m^2.3, which is some sort of "fractal density".
@@Xnoob545 not quite. If you find that MODELLING them as a fractal gives you some insight, of course you can do it, but the fractal dimension for a "crumpled" 2D object (theoretical sheet of paper) will be greater than 2 but less than 3. (It approaches 3 as the paper ball approaches being a solid ball.) We can also see that if you have a line that is a fractal. Lines are 1-dimensional but once you make a fractal line it kind of starts to fill up area. The furrier and crazier it gets, the more area it fills up, and we say its dimension is increasing. A maximally furry fractal line would approach being a solid sheet of something, so approaches being 2D.
@@seesaw41 A tensile stress unit. Usually it is MPa for stress, and GPa for Young's modulus, since that's the order of magnitude we generally expect for these concepts.
I did my master´s in theoretical physics, so for the last few years I mostly used natural units, to the degree where you tend to forget that there even are units involved. But if you think about it, a unit system where hbar = c = 1 is incredibly cursed if you try to convert back to SI (but nobody ever does that).
Even though I understand why people would want to use natural units (or other units which simplify their customary work) I find dimensional analysis so useful for ensuring you get the right answer that a system where you tend to forget the units seems like it would make certain types of mistakes way easier to make. Some engineers I've worked with tend to do similar things where they routinely normalize their equations to make things unitless or they just ignore units while calculating and attach them at the end. It also feels similarly error prone.
I had a crazy teacher who wore dark glasses (tim buc 3) luckily I was still able to finish my doctorate in rocket science, meaning jet engine internals: thermodynamics and fluid dynamics.
I remember a funny answer on physics stack exchange about the conversion back to SI units which described how god might convey to Noah how much wood to buy for his ark but I can't find the link unfortunately.
@@doctorbobstone Yes, you want units to help you verify your algebra, even when you don't actually have units in this formal system; e.g. radians. In one of the Lockdown courses (I don't recall if it was Brian Green or Sean Carroll) he get to Natural Units, and then keeps going to Planck Units. Just like Time is equal to Space (length) once you eliminate the conversion factor of c, you can remove units entirely, as everything is either equivalent to Energy or inverse Energy.
And it doesn't get better if you use an electrical engine, because then you have something like joule per cubic meter, which has the dimension of kg m^-1 s^-2, which is Pascal :P
Jan Misali made a video where he derived a new set of standard units that were pretty cursed. Like instead of distance and time he used units of velocity and frequency with the speed of light c and middle C (256ish Hertz). But all the math works out.
You can to a lot of convoluted bullshit with math. In part that is also where math becomes pretty fun, because it can feel like magic to take some seemingly random stuff and pull something that you wouldn´t think by guessing could be calculated out of it. Makes you feel a bit like a wizard.
I like slugs, "A slug is defined as a mass that is accelerated by 1 ft/s2 when a net force of one pound (lbf) is exerted on it." I just remember opening up an old textbook and it talked about how the some 60's jet weighed about 900 slugs and being a little sleep deprived I just burst out laughing on the quietest floor of the library.
No. A slug is the imperial unit of mass. It is "equivalent" to a kg since they are both units of mass in their respective systems. The pound is technically a unit of force but it's also used as a unit of mass (lbf vs. lbm) since people who work in imperial units tend not to be quite so pedantic. But then again metric people tend to use kg as a unit of force as well as a unit of mass. After all, when is the last time you heard someone give their weight in Newtons? A mass of 1 slug weighs g pounds (32.2 pounds) just like a mass of 1 kg weighs g Newtons (9.81 Newtons) on Earth at sea level.
@@pjl22222 People don't measure their weight in Newtons because it changes constantly depending on your velocity and frame of reference. They just say weight when they mean mass. But in certain situations where the distinction matters (eg, climbing) people really do measure their actual moment to moment weight in a system in N and kN.
@@Barnaclebeard Unless you're leaving the surface of the Earth your weight isn't changing more than a miniscule amount that is probably less than the precision of the scale being used to measure it.
If you want complicated SI unit, most of the unit in electronics are absolutely horrible, like the Farad (for capacity of condensator) : F = 1 m−2. kg−1. s4. A2
@@markmarketing7365 Noise units are definitely cursed. All consequences of defining noise as the “power” in a 1 hertz bandwidth. The worst is it’s not a real power, but the power spectral density of the noise signal, so it’s V^2 / Hertz. Oh you want a unit that lets you compare amplifiers? Ok plot V/sqrt(Hz), divide it by the gain A(f), integrate over all frequency, and then turn it into the RMS voltage of a fictitious input voltage. 🎉
This is absolutely fantastic. I love the dynamic music. It reminds me of the excellent video essay on the music of Wii tanks (I know it sounds silly but trust me, this is a massive compliment). The music was certainly custom made for the video, and it's great. Subscriber well earned!
A cursed unit that immediately came to my mind is the reactivity from nuclear reactor physics because it is (somewhat commonly) measured in 1$ or 100ct. If you wonder why: A nuclear reactor can be in different states. These basically describe if the amount of nuclear fissions happening at a time is stable increasing or decreasing. For example a reactor being critical means the the amount of reactions stays the same over time (good). Then there is the supercritical state, which means the amount is increasing (not always good but necessary to power it up). The supercritical state corresponds to a reactivity of more than 1. However: There are two kinds of supercriticality, one which is easy to control (nice) and one which is impossible to control (bad things happen). Both have a reactivity larger than one but for the nice supercritical state it is maller than another variable (often called beta). Since beta is not constant it's good practice to divide the reactivity by it and define a new reactivity. With this new reactivity the "Nono-zone" corresponds to a value larger than one (very easy to remember). But now the problem arises that these values are both without any unit at all and bad things may happen if ever some reactor operator doesn't know if his colleague was talking about one reactivity or the other. So the one which should never go beyond a value of 1 was simply assigned the unit of 1 Dollar (1$) because Dollar is not otherwise used in physics as a unit.
Units of currency are cursed to begin with, just due to grammar. The dollar sign is supposed to go before the numeral, as in $1, but if you're using cents the cent sign goes after the numeral, as in 100¢
The smoot is a unit of length originally defined as the height of Oliver Smoot, a student at MIT. In 1958, the length of the Harvard Bridge in Boston was measured using Smoot as a unit, with the bridge being declared to be 364.4 smoots plus one ear.
log functions are all identical save for a constant scaling factor, so a log base of pi would probably be a *more* useful interpretation than a natural log combined with a scaling factor involving both e and pi
XKCD has got you: "If you ever find yourself raising log(anything)^e or taking the pi-th root of anything, set down the marker and back away from the whiteboard; something has gone horribly wrong."
The 2 factors in quite simply. Basically, as the base of the triangle doubles, the vertex angle doubles as well. So a parsec is equivalent to the height of a triangle with a base of 2 au and a vertex angle of 2 arcseconds.
Especially as you can convert any unit to eV and eV to any unit. That was proven in the 00s. The immediate result was half the science and engineering students started converting everything to furlongs per fortnight.
@@ExodiumTM any unit of measurement. grams, metres, kelvin, seconds, metres per second, any others I can't remember just now, and any unit that can be converted into these.
@@ExodiumTM Search results can be pretty bad these days, especially for uncommon knowledge which sounds like commonly known things, if that makes sense. I'm not sure what tips to give. I can't find anything myself today, but I'm too tired to look properly.
As a meteorologist, units of reflectance are a little funny, mm^6/m^3. It takes on a log relation whenever people use it so it comes out as dbZ, where db is decibels and Z is the reflectivity factor.
For weird dimensions, look at fractals, there is a snowflake with a dimension of 1.2619. For weird units, look at Planck units, where you set G=kb=h/2π=c=1, and then derive how to write down length in terms of these units. Momentum has sqrt(hbar c^3/G).
My favourite single SI unit is the becquerel, which is defined the same as the Hertz (1 becquerel = once a second), but for things that aren't cyclic. 1 Hz is once per second on the regular; 1 Bq is randomly, but once a second on average. (It's used to measure radioactive decay rates, which are random.) No, in civil engineering for flood resistance, you plan for a variety of potential floods, such as a once-in-40-years flood. Since floods are not clockwork, this means something like "the typical/average worst flood you'd expect to see in 40 years". So the figure "once-in-40-years" converts to 0.8 nano-becquerels. It gets worse. Consider the units hertz-second and bequerel-second. Multiply 1 Hz (once per second) by 1 second, and you get 1 per. Per what? It's not specified. Similarly 1 becquerel-second is "1 on average, at random". Now let's say my street is 2 kilometers long and has about a thousand potholes in it. That makes a pothole rate (not frequency as they're not evenly spaced!) of 0.5 pothole-bequerel-seconds per meter.
Instances of an event measured in hertz-seconds. Estimated instances of an event measured in becquerel-seconds. It's supposed to make sense but it just hurts to look at
That was SUCH a well-put-together presentation in all ways! My favorite cursed unit is Specific impulse, Isp. Essentially a whole bunch of units get cancelled out until the final dimension is 'seconds'. That's it 'seconds'. Super unintuitive. Sometimes its better to NOT cancel everything out...
"I personally find square roots cursed" ~Pythagorean Cultist, most likely
So cursed, apparently, that it even weeded out the comments, along with the other roots.
In my PChem class the instructor made the error of saying he didn't care what energy units we used on a test. He really meant it didn't matter to him whether we used joules or calories, but I took him at his word and turned in my test with all the energies expressed in liter-atmospheres.
Do you do good on the test?
@@the-pink-hacker Yes, he was a man of his word. He did privately express regret to me for phrasing it that way.
@@ptorqThat man took one look at your tests and instantly regretted everything
OMFG liter-atmospheres has me dying😂😂
Should've gone all out and done it in tablespoon-torre
I love how it feels like the background music is equally upset about all of this as the narrator
I believe it to be specially arranged but the musician likes just as much to talk as the vocal host :D
+
"Background music was me improvising on a piano." The man's a savant and narrates the video with his voice and his fingers
Also as loud. Which is annoying. I can't focus of what is said during the video :(
@@v01dv01d yeah I thought that too, but the content what worth the watch. 3:30 is what got me turning my volume down and using CC for a better viewing experience. I like how expressive the piano is but not the volume of it in contrast with information is hard to understand already and listening closely is harder when volume isn’t balanced properly.
In middle school I wondered why rain was measured in mm instead of something logical like litres/m^2 until it clicked and I realized they are the basically the same unit.
took me 34 years to figure that out :D
Damn, you just made me realize that..
daaaaaayummm it also boggled me why rain is measured in mm or inches. It makes sense now that volume/area is just a unit of length. Weird. Thanks for this info that I may never have to use. haha
@@cinchez007ohhh is this how it worked ? I didn’t realise that. Liter by itself didn’t seem like m^2
I thought they kept some kind of measuring jar and measured the height of the water collected in that jar
The hubble constant being simplified to Hertz and then it's inverse ending up as an approximation of the age of the universe absolutely blew my mind.
I was so disappointed to learn that the numbers being close to each other is pure coincidence.
@@jeroenritmeester73 I'm not so sure it is. The basic reasoning is sound even though it assumes a linear expansion which is a big simplification.
they arent unrelated its an estimate assuming the hubble constant remains the same of when all galaxies were in the same place (the big bang) it just so happens the hubble constant hasnt always been consistant and the speed of the universe expanding has increased
It blew my mind so hard that at very that moment I liked, shared and subscribed to this channel
I was alone in my apartment
I screamed "holy f***"
This was phenomenal
The little detail of the piano seemingly following a random walk on a whole tone scale while random walks are being discussed is amazing
Schoenberg would be proud
I disagree. There is a reason background music is bland and boring, because it should not be the focus. Chromatic improvisation on a piano is the opposite, as the dissonance is unexpected, thus extremely distracting. This is the jazz nerd equivalent of doing a science video with Wake Me Up Inside blaring in the background.
The fact that many are fine with it, either are deaf, or are not actually paying attention, which is a shame because the topic is super interesting.
tl;dr: this video would've done better without any music
EDIT: ah damn, the newer video doubled down with this musical nonsense.
@@sbef lol u could have said you found it distracting without calling everybody who doesn't mind deaf
Also going up at “increasing” and down at “decreasing” (15:50)
Edit after starting the second part: To be clear, I also love those details 😅
@@sbef "There is a reason background music is bland and boring, because I am bland and boring" fixed that for you.
Calculating the Hubble constant as a music note (all notes are just frequencies) gets us an E 67 octaves below middle C.
Reminds me of the video "a joke about measurement" by Jan Misali, some really cursed units there
we are just harmonics, maaan
@@cheeseplated I forgot about that video, I need to watch it again
I would like to listen to your note, but I suspect that it would be multiple instances of the universe I would have to suffer through in order to assemble enough peaks and valleys in order to reach an assemblance of hearing it.
I need to make this an art installation.
I once had a physics problem recommend writing the charge of an electron as "1 electronvolt per volt" in order to help the units cancel nicely. I'll never forget staring at that problem and just thinking, "Huh, well I guess that's technically true"...
Now that I'm an astronomy grad student, I see shit like "solar masses per year" and "joules per square centimeter per second per Hz" and it doesn't even seem out of place.
As someone with no degree and only an interest in astronomy, solar masses per year doesn't even sound remotely cursed. Am I missing something?
@@A-likprobably not. It’s just “solar masses” isn’t a unit we use every day 😂
Gotta convert to something relatable, like the universal news units of school busses( large mass), football fields (intermediate lengths), and aircraft carriers ( real big mass).
@@CatFish107Well, those sound less "relatable" and more "american"...
@@MrShadow1617Americans will use anything but the metric system
3:33 "using kWh is like using km.h^-1.min" that's basically what we do by measuring distance using light years
and in such scale,it do make sense sometime,like when you are calculating electricity bill of a factory,just like measuring distance between stars...
Interestingly enough, when we get to proper spaceflight, it would make for more sense to use light speed measurements in general, like 2.2 Light Seconds, especially if we use laser weaponry.
You A) get the measurement of a distance. B) you get the delay for how long ago the measurement was made.
So in the example of 2.2 Light Seconds, you know they are 2.2 Light Seconds away, you also know that the delay of the measurement is at minimum 2.2s old. If you use laser weaponry, you will also intuitively know that you have to compensate by about 4.4 seconds, as the information is 2.2 seconds old, and if you need to hit it, you need to take into account that you also take around 2.2 seconds to hit.
Especially useful for military applications.
@@SioxerNikita Inevitable transition from metric to planck units incoming in the next millennia?
@@sankang9425 Definitely not XD
@@SioxerNikita yeah then we would have like 9.43 * 10^32 units or something like that
Another great unit for power can be found on energy efficiency labels for light bulbs here in the EU. It's specified in kWh/1000h :D
wow by writing it like kWh/kh we can literally reduce it to W
@@rlachiecycethat's probably why they chose that exact one, while also making it obvious for the people used to kWh
As a fellow European myself (and to explain the reasoning behind that unit for non-EU people):
If you have a lightbulb that will be on for quite a long time (1000h isn't hard to achieve in a year or so if you keep it on for maybe 3h/night) and thus I care about its energy efficiency, but guess what units are on my energy bill... That's right, kWh, so since 1000h is a minimum reasonable lifespan of a bulb, it isn't as dumb as you might think.
Of course, we also have W (and at least on this side of Europe where I am from I've mostly seen them advertised as W), but oh well
@@stefanalecu9532 1 kWh/1000h = 1W
Watt do you mean?
I needed to pause for a second when you revealed that the Hubble constant can be measured in Hz. That is truly cursed
It makes sense from Hubble´s law: v = H*r. r has unit meters, so H needs units s^-1 to give v the units m/s.
the moment i saw inverse seconds i had to pause the video and take a breather. funniest shit ive seen all week
i mean this is basically the frequency in which the universe expands, similar to how an APR interest rate would work, since %growth is unitless so it’s just 1/time as well
I just assumed that it was the "red shift" offset. Like, the Hubble constant is how much (on average) redder the light from other objects in the universe are compared to their true color.
It made my head hert
The sun appears to move through the sky at a rate of 15 minutes per minute.
Earth revolves 360° around its axis in 24 hours. 360° is 21,600 arc-minutes. 24 hours is 1,440 time-minutes.
Your 15:1 arc over time is itself a fine "cursed unit."
@@robertarvanitis8852 First one about the bird poop is malformed. Does not take into the account size of poop and
I could lay in my backyard and get pooped on or go to middle of the arctic sea and never get pooped on.
I see bird poop on my car almost every day. And I see many cards in my hood with bird poop. So clearly we are not waiting 195 years per poop.
You're taking the average of "never" and frequent and providing a useless and meaningless number.
Rate is (360×60)/(24×60)
Or, 15
@@robertarvanitis8852 it's rotates ig not revolves
So just 15 then lmao😂
The craziest unit I’ve ever worked with is an Erlang, which is equal to 60 minutes per hour. You read that right. It’s used by telecommunications engineers to describe the capacity of trunk phone lines (i.e. between exchanges) to carry multiple voice calls simultaneously. If you group 10 regular phone cables together, it will have a capacity of 10 Erlangs. Long live engineering.
I guess you could use it to measure the rate at which time flows in different gravitational fields?
Every 60 seconds a minute passes in Africa
You could call that a dimensionless number (ratio of spoken time to real time, or (usually average) number of calls at once) if you wanted to. I think there are a lot of numbers like this you could rewrite with "cursed" units for clarity if you wanted to.
So just 1, basically
@@EdKolis seems possible, but only if you fix the hour to 1 earth hour
I've seen in the notes of a friend of mine attending a urbanism class the unit "people/dumpster", which was used to measure how many people would be served by a single dumpster in a particular area. The first time I saw it I found it very funny, I read 500 people/dumpster as 500 people crammed into a single dumpster
That is indeed very funny 😂
But wouldn't this just assume that all users of a single dumpster would generate an equal amount of garbage each?
@@Gabsboy123Considering how many US cities suffer from trash overflow, I would assume that this measurement does _not_ take people who create more trash into account.
@@Gabsboy123It sounds like an average. For every random person with a dropshipping business putting tons into the trash, there's a vegan committed to making no trash. They balance out eventually, especially if we're talking about a group of 500 people.
Person per toilet is even more complicated. There's a whole equation needed, it's also split per gender with up to 2/3 of male toilets being converted to urinals which makes it even more annoying
My favorite is s^-1 / s^-1, where the units don't actually cancel.
(One is a frequency, the other is an _angular_ frequency, and so is off by a factor of 2pi.)
In general, anything involving radians is 'fun', because people declare it to be unitless and then omit the unit, and then get really confused.
This always annoyed me, because degrees and radians are definitely units, and by declaring their unitlessness, it's easy to get confused when reading about models in papers where you're not familiar with the field's standards as to whether they're talking about radians or degrees. This issue comes up a lot in crystallography modelling, where the angle standard in physics is radians, but in measured X-ray diffraction data, it's degrees, and models either choose one or the other.
The same happened here with the gravitational constant at 9:30. Google covered it wrong. It went from 1/s to Hertz and multiple the unitless constant "revolution" without stating it. So, converting back to 1/s would introduce the 2pi or 360° factor incorrectly.
@@AimeeColeman ° is the symbol for degrees and rad for radians. Isn't it pretty standard to write rad/s for angular velocity?
It's dimensionless, not unitless.
@@朕是神 Indeed!
I've watched this video more times than I would probably admit, and "Hertz?!" gets me every time. What a gem of a video.
How can the "thin tube of fuel" be so simultaneously cursed and brilliant at the same time?
do you also see all the cars passing by led by their own fuel line now? :D
It's like trolley wires but made out of dinosaur juice lol
crossectional consumption rate.
It makes perfect sense. You are just using a different more roundabout way of measuring the flow rate of fuel to keep it running.
That tube is also predestined and shows where you will go due to time travel. For more information, watch the documentary "Donnie Darko"
The most cursed unit I came across in my physics degree was for the frequency spindown rate of a pulsar, measured in seconds per second (or, every second, how many seconds longer each rotation of the pulsar increases by)
If the spindown rate of the pulsar was accelerating, you could measure that in seconds per second per second. How many seconds per second slower the pulsar is spinning every second.
@@TotallyDapper I feel like we could throw "seconds" as an angle measurement in there too, somehow.
@@DuetJaylongitude/latitude seconds are equivalent to arcseconds but measured and represented as seconds, so yes
Janky if you convert it is J/s/m^2/Hz, and so s=1/Hz, it remains only J/m^2.
When I did this, my supervisor wasn't happy.
Ah the good old Pdot. Dispersion measures for pulsars are another weird one.
The musical companionship to the monologue is frickin' amazing. I noticed it early on, but at the random walk, I decided I had to comment on it
I love it when music does this it's great
Lol I am looking at the comments for this with the video paused at the random walk moment
@@SmashCrunch I gotchu, 16:01
same, this is crazy
@@thatoneofficialpianist Background music was me improvising on a piano. he said this in the description
Back when I was an astronomy grad student (c1990) one of my professors told us "a barn megaparsec is a teaspoon". I quickly responded "That can't be right - maybe 0.6 teaspoons?"
The reasoning being: I knew a parsec was 3 x 10^something meters, a teaspoon was 5 ml = 5 x 10^something m^3, and a barn was 10^something m^2. So taking on trust that the powers of 10 cancelled as he claimed, there was still a factor of 3/5 left over.
A bit later, I showed him on my shiny new HP48SX calculator, which could attach units to quantities and do conversions, that multiplying a megaparsec by a barn and converting the result into teaspoons indeed gave a result of about 0.6.
That HP48SX's units functionality was absolutely wonderful for an astronomy grad student.
I'm an Astrophysics undergrad student (and researcher), and I've got my HP-48GX on my desk next to me!
@@HobbitJack1 Back in the day, I wrote a program to turn the top five rows into a giant CST menu. It was very handy for keeping all the odd units and constants astronomers use close at hand.
@@michaelwoodhams7866 Absolutely! It's super useful.
This is an incredible story, thank you for sharing
Just did the calculation (on my 48GX!): One barn-megaparsec is 0.62604tsp.
There's an XKCD comic with a cursed measurement resulting from unit conversion. The unit is meters and Randall Munroe called it the "Oily House Index (OHI)".
He noticed that real estate prices are stated in dollars per area while oil prices are dollars per volume.
By cancelling these two units against each other, you get the OHI measured in meters. He then graphed it over time and some economical events even showed up (housing crisis, oil crisis, etc).
The "intuitive" representation of the OHI would be: if I sold a piece of real estate and bought crude oil from that exact amount of money, how high could I fill the property with the oil I bought?
Its absolutely lovely and the corresponding comic is one of my absolute favorites.
That's amazing
That's comic #2327 for those curious
so the constant value of this would be OHIo?
You know, that actually makes sense.
You know, that actually makes sense.
A long time ago I used to translate documents from English to Spanish. More often than not, they were of a technical nature. And often I had to review and fix someone else's work. One day I had to review someone else's translation of some very specialized industrial paint. The work also involved converting from customary units to SI. The original instructions indicated the lowest and highest temperatures at which the paint could be applied. And these had been properly converted from Fahrenheit to Celsius. But there was another important parameter provided by the instructions. For the first 24 hours after applying the paint, the ambient temperature should not fluctuate by more than 20F°. This had been duly converted to -6.7C°. So "for the first 24 hours the temperature should not fluctuate by more than -6.7C°". Whoever did this did not have a technical mind and did not understand that the 20F° referred to a relative change and not an absolute temperature. The correct value was about 11C°. The temperature should not fluctuate by more than 11C° over the first 24 hour period.
This reminds me of the basic issue of people having trouble with things like 30 or 0 degrees F being cold, so what is twice as cold??? But really we compare those to the reference 'room temp' where we are comfortable, not the numerical 0 (and I suspect the relationship is rather nonlinear to boot).
So in your problem, they needed to know the difference in temperature from 0-20 degrees F, which meant calculating both and subtracting, or if they understand that this is a scaled difference, all they actually had to do is multiply by 5/9 since C and F differ by a constant ratio, plus an offset.
duly
This confusion would all be solved with kelvin
@@Xnoob545 there's no such thing as cold but I can work out what's half as warm. Wow its a bit cold.
@@Xnoob545 Or for Fahrenheiters, Rankine. Why don't people have names like Macquorn Rankine anymore?
The most cursed units I've seen are "Hertz per dioptre". The dioptre comes from optics, measuring the optical power of a lens, and it's equal to an inverse meter. So, Hertz per dioptre is (s^-1) / (m^-1), which is speed if you flip the fraction to eliminate the negative exponents.
The speed of what is frequency per optical power measuring? I could conceivably see this unit in a graph that tracks the optical strength of a lens depending on light frequency in Hertz. Diopter is the inverse of the lens’ focal length, so it's focal lengths (of a lens with a certain optical power) per period (of light with a certain frequency) in this context.
@@adiaphoros6842 length → width, span; travels → goes, fares, wends
Beer's law similarly has (M^-1)(cm^-1) for the molar absorption coefficient. k in a third order reaction would be (M^-3)(s^-1)
@@adiaphoros6842 Brace yourself, because this answer might shock you.
This is a unit for the speed of ANYTHING with a velocity.
(s^-1)/(m^-1) = m/s. "Inverse seconds per inverse meter" equals "meters per second", which is a pretty common general unit of speed in physics.
@@emmeeemm It can’t just be anything, since the context of the units needs to be considered. In this case, the context is optics because “(light) frequency” and “optical power” are commonly used units. So, in that context, the speed of what is being measured?
5:40 Oh yes! I have taught physical chemistry at the university for quite a while, and dimensional analysis got very important pretty often. Students would divide quantities instead of multiplying, getting completely nonsensical results; but just evaluating the units of everything can reveal the error. I am glad my physics teacher back in high school drummed this into us relentlessly.
It's a great sanity check on any sort of ad hoc calculation from physical measures in daily life.
For example, my wife and I live off grid, and we're going to be upgrading our domestic propane system end to end in the coming year. We will have to rethink the consumption rate of our appliances and determine the capacity of lines to supply them.
Even before we get to drawing up a consumption budget, it's very helpful to think about the units of measure. Appliances here may be rated in either peak BTU/hour or equivalent Litres/hour, or more rarely kJ/h or Watts, as well as thermal efficiency. Line capacity will be a function of cross section and pressure, also possibly taking length into account. Tankage is rated by either weight or volume.
So already there's a comfortable sense that peak L/h can be the common currency in drafting the budget and sizing the lines and regulators and tanks. We haven't cited a single number, and yet we have a good preliminary grasp of what we'll be talking about when we get together with the gas fitter. No doubt there will be some regulatory constraints, the need to work within standard pipe sizes and whatnot, but we have an easy conceptual framework to make sense of all that.
It may also be that the trades have a preference for converting directly between particular units. That can seem cryptic at first encounter, but already having a dimensional analysis makes it much easier to follow. In short, it's an extremely valuable form of literacy.
This is what I keep telling the second semesters I'm supervising for 2.5 ECTs: Solving this homework is simple:
Step 1: Google every formula that might be relevant and note it down
Step 2: Figure out how to get from what units you start with to where you want to end up
Step 3: Calculate the unit to make sure you don't end up with a hamster whose mass is measured in km²/C
Step 4: Calculate the order of magnitude and ask yourself "Does it make sense for this hamster to have a mass of a few 10^36kg?"
Step 5 (optional): calculate the numeric value
It's amazing how many chemistry and physics problems can be reduced to just "dimensional analysis" and I used to try to impress that on the students in my chemistry recitation sections. What does the problem give you? Mass. What does it want you to find out? Volume. What do you know that relates mass to volume? Density. Boom, problem solved, the rest is just arithmetic.
@@lucykitsune4619 km²/C is a beautiful unit arrangement
As a physicist I passed physical chemistry thanks to knowing dimensional analysis (and rate equations). Still no idea of the chemistry.
By far my favorite cursed unit in electronics is Ohms per Square. It's used to measure resistance of flat copper planes (such as in a printed circuit board). It turns out the length and width of the square cancel out, so the square is unitless. Any square you draw on a copper plane will have the same constant resistance regardless of size.
the thickness of the copper is the only remaining variable.
Wait, so that means that you want as few squares as possible, in order to minimize resistance? 🤔
Are those Parker squares or city squares? :)
@@MrNicoJac Pretty much, yeah! If you have a long thin trace it'll have higher resistance because you have to draw a bunch of tiny squares in series to cover it. A thicker trace means each square covers more of the distance since both the length and width can expand to fill the wider trace, and thus the overall resistance is lower for the same length of trace.
Yesss !
Just today I had to redo some of my older experiments for a paper involving a four probe sheet resistance and I was just thinking about what an actual bullshit 'Ω/sq' is, and then this video pops up on my way back ! 😂😂😂
The music adds a lot of value to the presentation here. It's cool that the topic is interesting enough, but having an inherently emotional component validate the audience's interest in a topic, in particular by matching a reasonable emotional understanding, kept me hooked in. Sort of like helping you suspend your disbelief, but without the disbelief because the thing in itself is science.
It really feels like an unnamed goose from an unnamed game will come and steal the text on the screen... and maybe a bell
Mr. Rogers' Neighborhood
I thought it was a tad too loud, distracting me from the voice.
what's the piece's name
The random walk section was funny
Dimensional analysis kind of saved my butt in high school physics and even some college physics. When you understand unit multiplication, I find it WAY easier to remember equations. Sometimes you can derive unit breakdowns in the exam and get a eureka moment which makes you remember the equation from your studying.
It's insanely helpful. I'm studying physics and I do that all the time.
I did this in high school physics too. I was in AP calc at the time, so rather than spend time studying, I used calculus on the tests to re-derive the equations from dimensional analysis, because that way I basically only had to remember calculus which I needed to do for my other class anyway.
Dimensional analysis turns out to be a nontrivial part of our understanding of *quantum field theory*, so this feeling never goes away even at the highest levels of physics :p.
Same here, it saved me in a lot of tests cause I couldn't remember the equations so I would just derive the equations based on the units
In a dynamics test I had forgotten the formula for final velocity given distance and acceleration so I used dimensional analysis to recreate it on the spot. I did however forget the 2.
My father used to say: "always check the units". It helped me being a bit above average in my physics courses at university. Keeping the units in every step helped me not to be too lost in my own calculations.
Your examples are fantastic, thx !
One of my best teacher got mad when he realized we weren't taught to think in units when solving equations "It makes it so easy!" he yelled. I've been checking my units all the time since then but gotta admit that getting in the game late can be veeeery confusing like when juggling with angular speed in rad/s... o.O and finding out that basically radians aren't real... or having to prove to myself in a middle of an exam that a Joule is a W/s so a Watt is a kg.m^2/s... Not the most efficient way to solve something I should have prepared instead of playing skyrim
Yep, retain units throughout and always write conversion factors out as longhand fractions like in Randall's example at the beginning. Can't go wrong then.
I mean you can, you can always go wrong, but at least it won't be because you didn't write down units.
Conversion factors come in clutch, I write them out always, otherwise I make some dumb mistake like saying 1 day is 3600 seconds and the entire calculation from then on is wrong
I once saw (in an old technical report from Oak Ridge National Lab) thermal conductivity written in units of BTU/hr/ft/°R, and I still haven’t recovered.
°R?
@@carlosvasquezjr92I presume it's degrees Rankine (Fahrenheit offset so 0°R is absolute zero)
It's actually crazier than that. Thermal conductivity is usually expressed in BTU*in/(hr*ft^2*°F). That is, the number of BTUs that will conduct through a material that is 1 inch thick, 1 foot square, and has a 1°F difference in temperature between the hot and cold side in 1 hour.
@@yableckiI hate that
Actually, both °R and °F are a very colloquial way to write that part of the unit. Technically correct would be R (without the ° symbol), i.e. just Rankine, as that signifies a temperature difference on the Fahrenheit scale (the same way a temperature difference on the Celsius scale would be K, Kelvin, without the ° symbol).
°R (with the degree symbol) would be an absolute temperature with its zero point at "absolute zero", the lowest temperature possible. It's the same with the Celsius scale, where °K would be an absolute temperature with its zero point at the lowest temperature possible.
And both °F and °C never go without the degree symbol, as they're both absolute temperatures, never temperature differences. (However, with a zero point at a physically silly - but useful in practice and more tangible for human consumption - temperature.)
As an astronomer I am delighted to see the cursed units of the Hubble constant featured. Also, the 2 AU distance between measurements in January and July is resolved by taking half of the angle between those two measurements. The January and July measurements make an isosceles triangle that you then slice in half to make right triangles. This phenomenon of apparent position change is called parallax!
Since you like cursed units, here is a cursed unit of volume: (Hubble Length*Acre/(Barn ^ 1/2) *(1 gallon)^(1/6)* (1 rod)^(1/2)/(1024)^16) ~ 2 cu in.
And you can raise it to the 1/6th and divide by Milliparsecs squared, and pass an Earth Day as a duration to get a different, very fast growing Earth Days per square root ~1.1 in. per Milliparsec squared. A cursed unit you could use for... cooking checking... using solar panels and a goofy hourglass setup.
Yeah, units get really cursed if you want them to.
Whence, parsec: *par*allax distance per arc-*sec*ond
Do we account for the fact that we're in an elliptical orbit around the sun? Theoretically, the January/July measurement would be a little different from say a March/September measure.
@@joshuaychung Well, I would assume they only take measurements in the months where the earth is 1 AU from the sun. Makes you wonder why AU is a unit when the earth’s distance from the sun is not always the same depending on where it is. The ellipse is probably not that big of a difference.
@@fury_blade9303AU is the radius of a perfect circle with the same year length .
I can't remember any cursed units, but I gotta comment on how excellent the piano accompaniment was. The discordant sounds when you mention something confusing, the dramatic build-up as you build up to a conclusion, the sudden stop when you drop a surprising fact! Top-notch.
it's so bad
Don't forget the step up and step down when talking about the chance of the diffraction changing and the piano music being a musical random walk when talking about random walks!
He didn't even touch the planck equation
It definitely adds a great touch, reminds me of how Untitled Goose Game uses its soundtrack
One thing that I always chuckle at is that torque can theoretically be measured in joules.
I hate you
@@mguddeti Except Torque isn't a form of work? Is It? It can't be... "Work" is Energy, It's the result of the action of a force inducing deplacement. The units are the same but the thing they measure isn't.
For Work we consider the distance travelled by the object because of the force applied to it, If the object doesn't move It didn't recieve Energy. (unless it deforms or warms up or emit light or wathever ^^')
But for Torque, we consider the distance from the force application point to the center of rotation of the object. Torque exists without displacement. you can apply a Torque without spending energy if nothing happens to the object.
And this "rotational Inertia" equation is kinda misnamed because it's simply newton's second law F=ma applied to rotation it doesn't measure rotational energy. "Rotational kinetic Energy" does E = 1/2 * I * w^2 but Yes, this again has the same unit, Joules xD
@ReySilverskin you truly are evil hahaha
I'll keep using N.m for torque
Here’s a proof for those wondering:
Torque => F * d => ((kg * m) / s^2) * m => (kg * m^2) / s^2 = Joules.
Here’s the proof using the rotational inertia equation:
Torque => Ia => (kg * m^2) (rad / s^2) => radians are unit-less so => (kg * m^2) / s^2 = Joules
However, even though it’s possible to measure torque in joules, it doesn’t have the same intuition as energy, as torque is just the rotational version of force, which just by chance has the same units as energy, but it shouldn’t be thought of as that.
@@mguddeti Rotation energy is another form of energy, as with kinetic or potential energy etc…
For extra fun, rotate or move fast enough that you need the lorenz transforms…
I mean most of those implication arrows (=>) should just be equal signs. "Implies" or "=>" is used when you have two statements, such as x = y => x+1 = y+1 rather something like 1 => 2-1
in chemistry, pH is the negative logarithm of the concentration of protons in a solution, and concentration is basically the number of particles in a volume. most equations using pH aren't that cursed, but i was never really able to figure out an intuitive way to understand the dimensional analysis of the henderson-hasselbalch equation
It comes from the fact that strictly speaking, generally the concentrations of protons in a solution is in fact quite low, so of course you're dealing with negative powers of 10
Hence, to make pH a sensible unit, and to reduce the scale in such a way as to be interpretable, you first take the logarithm, but that's a negative number, and you can't HAVE negative scalar units, so you then negate it.
If there's enough protons in solution to suggest that there is indeed somehow one mole of loose protons per liter of solution, AKA 1 M, or pH = 0, or there are somehow so few protons per liter of solution that there's one mole of hydroxide ions instead, then the solution is likely so caustic as to be nigh-on uncontrollable without highly specialized and study equipment, thus handily explaining why pH is generally not measured once you go below 1 or go above 14.
Ultimately, it only really works because 'concentration' can be a dimensionless constant - Number of Protons per Number of Total Particles (mol/mol). The issue is that we measure concentration as mol/L. The only way to make that dimensionless so that the logaritm can log it without issue is to have an implied scaling constant of 1 L/mol on that concentration (instead of pH = -log(a), you have pH = -log(ka), where k = 1 L/mol). If we were to rescale this so that we were measuring concentration as mol/mol (dimensionless), we introduce a new scaling constant is the volume per mole of the solution (pH = -log(kma), where a is now our dimensionless concentration, and b is the mol/L of the solution, while k = 1 L/mol), and so varies based on the solution. Since most acid/base work is done in liquid water, 1 mole of water is 18 grams, which is 18 mL liquid water, so b = 1 mol/0.018L = 55.6 mol/L or so.
Rewriting so as to only have one scaling constant, we have pH = -log(na), where a = concentration in moles per mole, and n ~= 55.6 dimensionless, for no real reason except to keep the final answer (also a dimensionless value) consistent with the existing pH scale. In theory, you could redefine pH to not need that constant - the constant factor only serves to shift the final number by about 1.74ish. A 7 pH would end up being a 'pH' (normalized to mol/mol) of 8.74 or so, which is less pretty, I guess.
Which variation is 'more right' comes down to which option makes it easier to compare activity in different kinds of solutions (not just water). In this case, mol/L sort of makes sense as a 'how much activity by volume of liquid', but on the other hand, chemistry is done stoichiometrically, so you're more likely to want to know how much 'activity by mole of solution' you have, I would think. On the other other hand, 'activity by volume' is probably more readily accessible to a non-chemist, so is more comprehensible to the layman. So I don't really know.
pH = - log(mol / L) = log(L) - log(mol)
Considering L = 10^-3 m3, we can write:
pH = log(10^-3 m3) - log(mol) = log(10^-3) + log(m3) - log(mol), therefore:
pH = 3log(m) - log(mol) - 3
the explanation I received is that there is an implicit "unitary concentration 1 mol/litre" inside of the logarithm or something like that.
This is to cancel out all units, since logarithms (and trig functions) cant have units in their arguments.
Specifically in logarithms and exponentials, it's always a ratio of something against something
Excuse me, the pH wasn't measured by the activity of a component in the solution?
Noise (density) of electrical components e.g. operational amplifiers is usually given in nV/sqrt(Hz).That's my all-time favorite.
still it quite makes sense.
Is it similair to the dispersion mensioned in the video? As in how many volts of noise are generated in a certain bandwitch?
so... nV√(s)?
Hello there fellow EE. I was looking for this one
That made me laugh.
In university, I had some work that was calculated in minutes per hour. We were doing a group project on how many toilets a building needed, estimating the time of a trip to the toilet, estimating the nukber of people in the building and estimating the number of toilet trips per day to try and estimate the amount of minutes of toilet usage per hour. One model had 2650minutes/8hours which became 331.25minutes/hour and then further simplified to 5.5208minutes/minutes.
incredible lmao
Couldn't you just interpret this as 5.5208% of work time spent on toilet breaks?
@@chemtrailsmoker9852 I guess that's one way to interpret it. Although we mostly wamted to work with it to model theideal number of toilets for the building. I think it was something like 1 toilet per 20 people, plus an accessible toilet on every floor.
@@toast99bubbles im no maths geek but this gave me a good laugh!
Do I interpret correctly, that you do not have enough toilets?
Urologist here, when I calculate the risk for prostate cancer on a patient, I measure the density of PSA. That number is obtained by dividing the PSA (ng/ml) and the prostate volume (cc or grams). The unit therefore can be expressed is in the unit ng/(ml · g) and that can be simplified into ml^-1 or ng/(ml · cc) which is ng/ml^2 or ng/cm^6
Mass per square volume is truly heinous
omg, another square volume. I use dbZ, which mm^6 per cubic meter. It's a radar thing.
I just love how, when you were talking about random walks, you were also playing a hexatonic random walk on the piano! Great soundtrack, clear explanations, 10/10!
10/10! is a very low score...
@@MB-yf4lt 100% is low?
@@khandmo 10 divided by 10 factorial (10!) is 3628800, so 10/10! is about .00000276, or .000276%, which is very low.
@@khandmo If i told you your mom is a 1 would you take offense?
@@khandmoJoke went over your head
Can we appreciate the music in this video? Like, I've genuinely never seen someone have reactive, living music that plays with and compliments the video, rather than a few standard, unchanging backing tracks. It's so creative, I love it!
I absolutely love it aswell. Wonderfully done.
Yeah I noticed that too
@@kasperlindberg179same
106th like 1d ago
@@kasperlindberg1791st like. Also hi from 3 hours ago lol. I was probably still playing chess with a librarian.
I remember the first time I thought about how strange unit cancellation is was when I learned that you can measure rainfall as either liters/meter², which is basically (0.1 meter)³/meter² or 1/1000ths of a meter, or 1 millimeter. So if you're expecting five millimeters of rain, that's just five liters per square meter of ground it's falling onto. Super obvious in retrospect, but it confused the heck out of me as a kid.
which incidentally is how you can "easily" measure rainfall: put out a 1m^2 pan outside, and measure how high the water is in the pan at the end of rain. in your example, it would be 5 milimeters. in fact, because of unit cancellation, you can see that any pan would have 5 mm of water on average.
So thats what that means, i thought they left some sort of rain catcher out and measured how much it filled, which always confused me as to how small of a number it was
@@Queue3612 That's exactly what you do, but you do not measure how much it fills but how *high*. That way you do not have to specify how big the container is.
@@Themoonisachees damn. I went and wrote a comment saying that measuring height is container agnostic, only to read the last line when I was done >_>
On the other hand, if you don't have a ruler but you have a scale the size of the container matters
Wow. I never thought about that.
I stand by this statement with 100% confidence, this is the best video on RUclips. I can watch it so many times and it never gets old. This needs to be a series…
The bit about fuel consumption has an interesting update with the transition to electric cars:
The specific energy consumption of an electric car can be given in kWh/km, which translates to 3600 kJ/km = 3600 J/m = 3600 Newtons. And it has a neat interpretation: It's the average force (air resistance, friction etc.) holding your car back over the distance of the trip (some overhead for onboard electronics notwithstanding).
This explanation feels wrongs. The energy efficiency of a car does not only depend on external losses like air resistance. In fact, air resistiance and frictions can be considered constant, depending on the actual car design and implementation details.
@ but these resistances change with different driving conditions (speed, headwind, ...). I would also expect electrical and mechanical efficiency to change with variables such as temperature.
@ That's why it is not an explanation but rather an interpretation: Assuming that all losses were created by air resistance then it would have the exact force of your energy consumption.
@@MrHankeyYT I think it's a valid explanation too. Those newtons are the total forces the engine needs to overcome, including air resistance, wheel friction, and also internal resistance of the engine itself.
At that point it's just an aerodynamics value.
My AP physics teacher once told us a story about how one student would always write his test answers with ridiculous units just to make our teacher check the conversions to make sure he got it right.
After beginning E&M and encountering the unit of "Ohm" for the first time, and him telling us "1/Ohm" was allowed to be written as "Mho", I got inspired to do something stupid just for fun.
Long story short, after consulting the year's worth of notes to find the right connections, I found that all units can be written in terms of "Mho", with my favorite example being meters.
c^2s/KgMhom=m, or Coulumbs squared seconds per Kilogram Mho Meter is equal to meters. The part about this both my friends and teacher thought was the most cursed, was the fact that meters appears its own definition of itself, which is just plain stupid.
I never had a student do that, but my solution would be to call the student to my desk and have him explain what his unit meant and why he used it.
1/Ohm is Siemens... But I like Mho better.
I. e. c²s/kgMho = m², i. e. m = c sqrt(s/kgMho). So you can actually avoid that the meter appears on both sides.
Nowadays the "mho" is known as the siemens.
Let's be completely honest. Meter IS derivative of itself, which was tied to physical world occurrences to have ability of consistently reproducing value within laws of our universe.
Any measurement value is such, because it relied on people defining it in the first place and there were no good ways to create absolute measurements back then.
And, as meter is one of the key values, as everything can be tied to meter, it is reasonable to assume you can actually derive meter or second from combinations of basically any existing metric values as well.
Unlike SI, CGS does not have a separate unit for charge. Instead it has the statcoulomb, a derived unit equal to 1 sqrt(g cm^3)/s. To add to the cursedness, it's not dimensionally consistent with the coulomb. The conversion factor depends on the context of the quantity it's measuring.
CGS is an entire cursed unit system in the first place
Better than having to use vacuum permittivity and permeability constants. Makes dimensional analysis a whole lot easier.
Hardly any reason to ever convert charge itself, anyway, and CGS is consistent with SI on stuff like Energy.
@@TimothyRE99 That's like saying working with g the gravitational field strength is tedious. Constants in physics having units is nothing new.
I remember too many problems where cgs helped cut through the tangle and clarify the problem to think it’s completely useless. That said, the statcoulomb is pretty cursed.
@@Saturnius But why use an extra constant when you don't need to?
There's a reason natural and Planck units exist.
In materials science, fracture toughness is measured in MPa/sqrt(m). If you account for the fact that Pa are N/m^2, you can end up with the unit N/m^3/2, which I’ve always found to be super cursed.
Finally, an outlet for the weirdest unit I came across in college. Sheet resistance, the measurement of electrical resistance of thin films of uniform thickness, uses a unit that is so cursed it has stuck with me for nearly a decade at this point, that being "ohms per square". This unit is referred to as such because, while bulk resistivity is measured in ohm*meters, which is actually stated as ohm*m^2/m (ohm*area/length), you then ALSO divide it by its sheet thickness, giving you straight ohms again. However, to designate the maddening process you've been through, it is designated as "ohms per square". Link here for more reading: en.wikipedia.org/wiki/Sheet_resistance
I'm doing PEM fuel cell research and this unit was pissing me off to no end until I finally figured out wtf it means...
I LOOKED AND IT'S AN ACTUAL SQUARE LMAO
Holy fuck there's Ω/ロ notation for it. (The square I used here is a Japanese letter I cba looking up a square symbol)
Electrical/electronic engineers are masters of using cursed units to designate stuff, at this point I've abandoned any hopes of ever doing a proper dimensional analysis and just look at the formula long enough until I'm convinced the units _probably_ line up lmao
you have the same in the resistance of heat of materials, isntead of metres. its hard really hard but the same
After our physics teacher taught us about dimensional analysis in school, I never had to remember all these many complicated formulas again. It felt like enlightenment! I only remembered some basic formulas (F=m*a etc.) and in every test I simply derived the more complicated formulas again. It made everything so much easier!
same. i just follow the units
This is what I teach to my students! Stop memorizing and just practice dimensional analysis until you're confident with it. It'll help you actually understand the relationships between the values.
@@marmaladetoast2431 me too. Although I sometimes forget dimensionless factors like 1/2 or 2Pi...
My friend in college forgot ohms law during an electronics test. He used a few of our phisics 2 formulas to derive it. I still don't know if he was right or just got lucky, the prof wrote a bunch of question marks then circled ohms law on the formula sheet. (Yes he was being completely dumb)
@@nicholasreale7998 * physics
Saying "this video is getting too long" is the RUclipsr equivalent of the Teacher saying "That's outside the scope of this course"
Permability coefficient Pm which is: 10^-13(cm^3*STP)(cm)/(cm^2*s*Pa). Ohh and STP is 101,3kPa.
The unit is from material science, seen in the book Callister
Material science? 💀 I wanted to study that ngl XD
You made the next vid, replace Pa with cmHG
A rule of thumb in surveying is that the elevation of a horizontal line of sight changes by 8 inches per mile-squared. This turns out to be the reciprocal of the diameter of Earth.
Oh I know that unit from back when I used to look at flat earth videos for fun lmao
The elevation drop is pretty much "the same number" in SI, for once(!), namely ≈ 8 cm/km². That's because, in the spirit of this video, (1 mi² × cm)/(1 km² × inch) = 1.02 ≈ 1, dimensionless.
@@sternmgThat’s an amazing coincidence!
@@flerfbuster7993 Is that where they get that from? Flat Earth is the only context I have ever heard that.
Matt Parker did a video on that and he obtained the same number
I really like how you use music/sound to help the video more. Its not just background noise, it really fits
flying over the comments i just thought "Uhm, Music divided by Sound, now thats weird..." until my brain broke out of this spiral of madness.
No. It's really fkn annoying.
@@BibleBlack667 to each their own
@@vedantsharma6206 Indeed
In my nuclear education (I promise this isnt that boring) we had to do a lot of unit conversion, and to teach us how to do them well we had a sheet of obscure units broken down into their metric derivatives. Basically on that sheet was the "Miner's inch" and it became a meme between the boys because, y'know, yeah... If you were curious, its a measurement of volume/time.
How much a man can........ If you catch my drift😂
@@thebiggaklipa It'd be crazy if it also depended on the mass of what ever caused the 'enlargement' too.
We use miles per gallon in the UK but due to the unique way the Imperial system works, it’s not the same gallon as the Americans use. This means there are roughly 1.2 gallons per gallon.
the metric system - my beloved - has a stroke rn
For my cursed unit I'm gonna go with a plain old meter... USED FOR TENSILE STRENGTH OF A MATERIAL. I don't remember the exact equation, but basically it answears the question of "how many meters of a wire made form a specific material would it take to deform plastically under it's own weight". It's quite nice for aerospace science and other science branches where weight is important, because it combines strength properties with density of a material.
Strain = Change in length / length. Thanks A-Level Physics for ruining my life.
In every engineering setting I’ve encountered, we’ve used the Young’s Modulus, aka modulus of elasticity which is in units of stress, ie GPa or psi
@@pushatsinfrared strain is a dimensionless unit?
@@nanamacapagal8342 Yes, it is.
@@nanamacapagal8342 Yes
"Volts per square root hertz" often pops up in audio amplifier specs. My understanding is that this is fairly common when dealing with power distributions. Same thing for shock and vibe testing where power spectral densities are specified in units of G^2/Hz as a function of Hz.
That unit is often used to work with thermal noise, so what I get from it is that sqrt(unit) is expected to show up whenever dealing with probabilities (such as noise or random walk in the video)
You beat me to it. Another cursed unit in the audio world is decibel. I mean think about it, it is a ratio so no unit isn't actually needed and we always use it in its deci(1/10th) form no matter the context; it is even common to see mdB used which is like saying microcentimeter. To make things worse, it is also common to reference off standards that are just assumed and not always agreed on. So in an audio system, you might have amp gain measured in db(log scaled input voltage/output voltage) feeding into a speaker which produces db/V(but in this case, db is the log scaled ratio of volume vs a standard sound[20 micropascals]) as well as a signal-to-nose-ratio(SNR) which is also measured in dB(log scaled signal/noise).
It wouldn't be so cursed if people didn't insist on using dB as both a method of comparison(what it mathematically is) and a unit(by comparing against unofficial standards).
@@Amir_404 I want to measure using the unit bel now
@@thecodeking91 ah, bells are a unit of house buying currency in Animal Crossing
My parents had to ask what comedy show I was watching when I kept laughing and wheezing at this video. The silence pause after you introduce each cursed unit is phenomenal, it's like you have to stop for a few seconds to massage your temples and be like 'ugh this again' before continuing. Instantly liked and subbed, I need more of this.
I think the music is also a big part in it. It fits every moment very well and amplifies the comedic value
Unfortunately, too many people mistake this video for a serious science video. I'm giving him the benefit of the doubt in assuming he meant it to be humorous, because it is certainly not serious science.
This video has been on my youtube suggested list for some time and finally I decided to watch it today...
YT algorithm was right!
Not only I really enjoyed the video but also I realized that I had the same questions and reactions myself about these cursed units. Good work.
megaJansky per Steradian (10^-26W/m^2/Hz/sr) is a particularly cursed one I found while working on a power radiometer for radio astronomy. A jansky corresponds to the power per telescope dish area per hertz (flux density) and steradians the observed circular arc of the sky (rads^2)
That does seem pretty Jansky
None of these words sound real lmfao 😂
That’s the new Final Fantasy end boss’ final form.
I had forgotten about the Jansky 💀
"it's a perfectly cromulent word"
If you could only remember one thing from high school physics, it should be dimensional analysis. It's gonna be useful for the rest of your life.
So many little problems in life can be solved with a dimensional analysis exercise in like 10seconds. But when you do that people think you’re a god damn wizard or something
yeah we never had that. Maybe that's why I like learning about this stuff, because I hated most everything else in school and this didn't get ruined
facts
The best use of dimensional analysis imo is to find out that you modeling the whole thing wrong, especially when working with imperial vs SI distances raised to powers, etc.
My highschool physics and chem teachers 100% drilled dimensional analysis into our heads. I'm pretty sure they colluded on that fact. Also, for AP chem, the teacher would randomly ask students question about ions if he saw you in the hall and tally the total right/wrong answers to buff or nerf his curve for the final exam 🤣. People took it very seriously as his class was super hard.
I really love how the piano music follows the story! It adds so much!
YES!
Can’t believe it’s improvised
It really is an incredible feature
Wanted to say this too incredibly well done!
props to the music in this video!!!! It very well ties together the background ambience with the words being spoken. I particularly love the example of the random walk in the section on PMD
the most cursed units for me are inverse centimeters, which are used for a sort of frequency because they're the inverse of the wavelength, but they're called wavenumbers and have a factor of 2pi thrown in, and they're also used for energy because you can convert a wavenumber of light to an energy in joules or eV pretty easily, and then physical chemists get excited and start just doing literally every single unit in inverse centimeters
Spectroscopists are a plague. I had to recall that RT thermal energy was roughly 200 cm-1 and that it corresponded to the much nicer 25 meV to remember the "conversion"
I wholeheartedly agree. Inverse centimeters are absolutely terrible. Luckily for me, nm is the standard for the near-IR so we get to work with beauties
and it is a _named_ unit. 1 cm^-1 is a kaiser. Visible is from 13 kilokaisers to 26 kilokaisers. Just think of 10kK as an inverse micron...
The way you use music in this video (and I presume, in your other videos too) is perfect. Music is often used and made with a sort of standalone role, as if the whole purpose of it is to just listen to it. Sure, in movies, games, theatres and a lot of other form of art it plays a role of enchancing the emotion, but so rarely it is used in learning processes for that purpose. Using it like you did here is precisely what we often overlook in how we learn things. And it is crucial that you didn't just use some off the shelf piece but actually made it like a soundtrack for this particular video. This is just great and I appreciate it very much.
Especially when it got to the random walk bit and the music turned into stepwise staccato notes! It was all so good
Yeah, how did he do that? Is he a pianist in addition to being an engineer.
I personally found it extremely distracting and pretty annoying. It's cool and all, but imo this is the kind of content I want to be focusing on the presenting material , and the music is consistently pulling me away from that (as I'm a musician so I'm subconsciously analysing it as it goes along, and each time it changes (which happens when the info is changing in this vid especially), my mind goes to that for a couple seconds; I have to either fight that impulse or rewind the video a lot as a result...).
@@99jdave99 to each their own, I guess. As you are a professional musician and automatically focus on music more then the main content of the video I'd say it's more of a compulsion than a normal way to perceive such stuff. Some people of different professions can't de-focus from their field when they find it's footprints in other types of content, or when someone talks about something completely different. Don't take offense, I truly mean nothing bad, but there are a certain type of scientists, that can't help but tell you why and how some piece of science fiction is not realistic, and how they should've made it differently, as if they cannot enjoy sci-fi without constantly thinking about their work. It either means you are extremely passionate about your stuff, which is good and you'd most likely be able to give it more of your time than others, or there is a problem in how you view your profession. I don't know if it is a term in English, but in Russian we say it's a "professional deformation". And to be professionally deformed is to carry over some traits and particular views on things that are useful and ubiquitous in your field into other spheres of your life, where those traits are usually problematic to you or your surroundings.
In my photovoltaics lecture I really hated kWh/a (Kilowatt hours per year). The justification, which kinda makes sense, is, that you can see from the unit, that the value you are looking at signifies energy generated (or consumed) averaged over a whole year (with its different seasons etc.). Still, it seems stupid to me to have a time unit divided by a time unit.
That's even worse than kWh (energy * time^-1 * time). This one's energy * time^-1 * time * time^-1.
@@suomeaboo sooo.... J/s?
wait that actually makes perfect contextual sense...
@@suomeaboo well the unit makes sense culturally, we get our electricity bill yearly ( more or less you pay some estimate per quarter but it is always corrected at the end so doesnt matter), now on that bill it states you used e.g. 2500 kWh, therefore for a solar panel it makes sense to know how many kWh it generates per year to quickly figure out how much money you would save per year and if it is worth it. (of course for solar panels there are other factors and costs like batteries and stuff since you probably arent using all the energy during the day and so on)
The EU energy efficiency labels (for some products, like displays) are even weirder: the average consumption is stated as xyz kWh per 1000h. Weird way to write it consumes xyz watts...
The reason for kWh at all is because it makes accounting easier. Take the wattage in KW, multiply by the price of electricity, you have your hourly cost.
Can we talk about how the background music matched his speech intensity? That music - content synchronization is amazig! Congrats!!
I just finished my first year in a university Particle Physics degree and I have a great addition: magnitude - a measure of brightness . This comment will only discuss apparent magnitude (so distance between observer and body can vary), absolute magnitude (M) is a measure of apparent magnitude when the body is at exactly 10pc away.
The Greeks originally classed stars in 6 magnitudes, the brightest were m=1 and the dimmest were m=6. They aimed for each grade in magnitude to be merely twice as bright as the previous grade. Nowadays we've quantified magnitude into the formula: m = -2.5 log(F) + c. F is the flux (W m^-2) at the star's surface and c is complicated... The result of this modern equation is that if star A has magnitude 7 and star B has magnitude 6, that means star A is 2.5 times dimmer than star B.
However, since we have more advanced apparatus for observing the sky, more stars have been discovered which are brighter or dimmer than the original 6 grade system (m = 1 to 6). This leads to very bright stars having a magnitude of 0 or even negative numbers! Alternatively we can have very dim bodies with magnitudes near 20.
To make all of this worse, you need to consider that to observe something, you are detecting wavelengths of light that body is emitting. With this knowledge, let's discuss what c is in the magnitude equation. Consider some bands of light: U, B, V, R, and I. Ultraviolet, blue, visible, red, infrared. Different bodies may be brighter in some bands than others e.g. a star may emit more infrared light and thus have a smaller magnitude in the I band than the V band. The variable 'c' in the magnitude equation must be chosen such that it is m=0 across all bands. For most of my exam papers, the star chosen was Vega. Once you have chosen a reference magnitude/body, all subsequent calculations must use the same c if you want to compare any of them to each other. The result is an incredibly cursed, negative, non-linear, dimensionless system of measuring brightness. Could we not just have used the candela or something?
The funniest part of this whole story is that this convoluted system was made exclusively to be convertible to a brightness ranking from antiquity, which is so far removed from us that modern astronomers probably don't even know it other than as some thing that used to exist.
(Disclaimer, I don't have a particle physics degree or much knowledge of luminosity related stuff lol)
If we wanted to make a measure related to how much light you would detect at some distance maybe we could use photons per square meter at 10 parsecs or whatever distance of the star. After looking up how many photons hit one square meter of the Earth's surface which is apparently 3.8*(10^21) photons, I divided by 4.25 trillion (10 parsecs' worth of AU squared) to get 900 million of the Sun's photons inciting on a square meter sheet at a 10 parsec distance from the Sun in any given second, or an absolute magnitude for the sun of log 8.95 photons/m^2, and in my hypotherical scale stars would range from around magnitude log 6 (1000 times dimmer than sun, lowest bolometric luminosity I found for red dwarfs) to mag log 15,5 photons/m^2. (~5 million times brighter). Fairly complicated explanation but the photon is an absolute unit, so at least that much isn't arbitrary.
Edit: After looking it up, it appears that the original figure of 3.85×10²¹ photons I encountered comes from people calculating how many photons of green light (which is what light the sun emits the most) would equal the 1400 joules of energy per second that a square meter of ground receives in the Earth, so my scale is in relation to 500/550 nanometer wavelength photons in specific, which keeps in a good deal of cursed-ness is kept in the details of my hypothetical brightness scale as that would mean my scale which is supposed to be for absolute and relative magnitude apparently has a bolometric correction effect built into it because it's measured in terms of Sun-like green photons.
and you didn't even mention that that flux is subject to another weird unit cancellation: W m^-2 = kg s^-3 !
@@frogflint4371 that unit must have a very ugly interpretation, if it has one at all lmao
clear your doubts and read it again, you must have failed
@@frogflint4371 that one is hilarious. it does kind of illustrate the dishonesty of these tricks though. a joule of thermal energy per square meter of pizza per second is coherent. converting a joule of thermal energy to a kg of... something times a square meter of something else per square second is dodgy as hell, and canceling a square meter of undefined something-else with a square meter of pizza is just outright fraud.
I had a similar experience when we tried out ChatGPT 4 and asked it to calculate something for us. It kept referring to pressure as "meters", but the answer it got was correct. When we asked it why it uses meters are pressure, it said that it uses "meters of water" as a pressure unit...
reminds me of mmHg which is a written abbreviation for millimetres of mercury: a measurement used to record blood pressure:
If I remember right, you have a U shaped tube that's closed on one end, and open on the other, and you apply the pressure to the open end, and the pressure you measure is how far the water level on the closed end moves. We used inH2O as units in one of my labs
But that unit in that context would be incomplete. It would need to be water colum in meters under earth gravity. Because water pressure dpening on depth is connected to the gravity of the object it´s on, or in short, the weight of it.
That is absolutely a unit! I work with a lot of natural gas generators for my job, and frequently take pressure readings. Natural gas runs in most houses ~ 1/4 of a PSI, or .0172 bar. To be more precise, we use the unit “inches of water column”
It’s amazing you can get enough power to run 20 houses at once with less pressure than is at the bottom of a glass of water
Not that strange tbh. I see pressure measured as height of a fluid column pretty regularly
As someone who majored in both engineering and piano as an undergrad, I absolutely love this backing track!
This guy is a genius. He explains as good as it gets and meanwhile makes piano music that goes with the feeling of what he is saying. Subscribed.
The unit barn (b) which is 10^-28m^2, which is still used as a unit for a cross sectional area of a target, usually used in the creation of new elements where barn came from the phrase "couldn't hit the broad side of a barn"
The more cursed version of this is that particle accelerator data collection is measured in inverse femtobarns
barn/b is just arn
there's also a BarnMegaparsec which is a unit of volume. its the volume of a prism with base area of one barn and height of one megaparsec, used to measure the volume of space that a particle of cosmic radiation traverses in its long travels.
@@pr0hobo It's about 3.08 milliliters.
physicists sometimes takes jokes a bit too far lmao
Weirdest unit I encountered was the Fracture toughness constant, which has [MPa m^0.5] as units
And at the same time [N m^-1.5] which is so cursed when you convert some millimeters to meters for the stress.
I used to despise the entire field of Fracture Mechanics because of MPa m^0.5… Until I had to start playing with T m^0.5 (Tesla root metres) in my Honours thesis…
One cursed unit I hated at uni was the barrer, often used in membrane engineering. As defined, 1 barrer = 10^-10 * [( cm_STP^3 * cm ) / ( cm^2 * s * cmHg )]. When the units are so awful, we have to invent new ones to try and handle it!
cmHg? Not mmHg like normal people? Or mmmHg like vacuum people?
@@tykjpelkit's the alto clef of barometry
@@FelineBlender we dont like the alto clef
Similar to permeability (of rock samples, for instance) which is measured in m^2 when expressed in SI units. Since the values in m^2 are usually unwieldingly small, the Darcy or even millidarcy is more often used, one Darcy being about equal to 10^12 m2
@@klaasbil8459 and even smaller than the Darcy is the Barn, clocking in at about 100 square femtometers. It’s used in nuclear chemistry to measure the cross section of individual nuclei. And it’s not even a physical cross section, it’s a probability measurement!
"Dimensional Analysis" got me through several midterm exams, and I didn't even know what it was called!
Ever since I heard about about kWh for the first time i was obsessed with it since I found it to be so dumb. I didn't find anyone else getting annoyed by it until now. Thank you for finally discussing how absurd it is
Consider also the "kWh/a" (a=annum=year) that others have mentioned or "TWh per annum" that I described in my comment. It's a total farce, and harmful.
Thank God I have a friend in a random internet stranger. I always said that it is stupid to first you divide by time only to multiply with time later. Did we not learn to shorten down fractions? How can a math / phys teacher ever accept an answer given in kWh?!
From an engineering perspective, a power plant is more concerned about average power consumption over time. If a factory needs to run 8 hours a day and consumes 1600 kWh, then it will consume an average of 200KW of a plant's bandwidth. These conversions are of course doable in Joules, but it's a lot cleaner and easier to reason with if you just stick to kWh rather than converting to and from Joules all the time.
It's also why lightyears/light-seconds is a thing: (300e8 m/s) * years is the same as 9,46e15 m, but in astronomy it's convenient to have a measure based on relativistic speed since it's a commonly desired conversion.
tl; dr it's a convention borne from conversion convenience
I have a Masters degree in physics and absolutely detest that unit. I also teach high-school physics and it is quite difficult to help students understand it, which I honestly cannot fault them for.
Really if you think about it, there's a very simple reason why things have ended up this way. It's the one variable that doesn't comply with the SI prefixes in the whole thing: time. That's it. 1 Watt for 1 second is exactly 1 Joule. 1000 Watts for 1000 seconds is exactly 1 MJ. But the issue is that 1000 seconds is a completely arbitrary 16 minutes and 40 seconds. Instead we use 1 hour, which is 3,600 seconds, which is why we end up with the 3.6 factor from kWh to MJ.
It's all because we never got around to metrifying time. Which tbh is understandable because our circadian rhythm and the sun doesn't give a shit if 86.4 ks is an awkward amount of time.
Moral of the story: mixing metric units with non-metric units is cursed.
I remember in my engineering class we had an answer to a problem measured in "dozens of slugs per day", slug being the SAE unit of mass. That was an interesting result
The old school hackers will be familiar with the "jargon file" (you can still look it up on the internet). It refers to, amongst others, deliberately arcane units like nanoparsec per milliforthnight, roughly an inch per second.
@@olmostgudinaf8100Or Barn-Megaparsec, which is a volume of roughly ⅔ of a teaspoon
It gets weirder when you realize that a dozen slugs is called a blob. So your answer was in units blobs per day.
@@dillonryan285 That is awesome. I don't even think our engineering teacher knew that
I used to work installing optical fiber and not only do the cables have impurities, they also end up being installed in all kinds of crazy ways with a lot of bends which also scatters light. Fiber being as fast and consistent as it is even with all those things working against it is really cool.
8:30 the 2 is because 1 au is the distance from the earth to the sun (radius of orbit), but the second reference point isn’t the sun, it’s twice as far away - specifically, on the other side of the sun, or twice as far away (the diameter)
Bro he knows.
my math teacher once said: "science is just guessing, just really really smart guessing". and its the most funny, yet accurate thing ive ever heard from any teacher
You got half right. Guessing is the hypothisis. Proving it is science.
@@bipl8989 You got it wrong. Doing stupid shit is stupid shit. Once you start writing it down it becomes science. Simple.
@@bipl8989 Half right (so maybe we are down to quarter right now?) Yes smart^2 Guessing is the hypothesis, Science is proving it wrong, and Confidence in the hypothesis increases the more times competent people fail to prove it wrong. Only in mathematics can we prove the hypothesis (aka assertion/conjecture) is correct.
@user-xh9pt8zu2l
No, the original commenter is correct. You see nothing can really be proved regarding the really world since there is always some uncertainty in the accuracy of our observations. Therefore science isn't about proving things exactly, just finding patterns that match reality very well. You can see this in how new developments in science often overwrite previous theories, such as newtonian mechanics vs gr
@@bipl8989 You can't prove anything in science, only disprove
Not the most cursed unit I've encountered, but strain is worth mentioning.
Put simply, if you put a material under tension (or compression) it will expand (or contract). For the tension case, the ratio of the material's new length to its old length will usually be some number very close to, but slightly larger than 1. If we subtract 1 from this number, we have a measure that starts at 0 when you apply no force and increases linearly for a little while (for "normal" materials). This measure is strain. If you consider the units, you have length/length, which is unitless, so subtracting 1 from it isn't nearly as insane as it might look. But then you find that it's not uncommon to report strain in units of mm/mm or inch/inch.
I'm reminded of radians, which are technically unitless, but in practice are written as "rad", because it makes the bookkeeping easier.
i thought radians were also technically distance/distance, since its defenition is the length of a part of the circumference of a circle devided by the radius of the circle.
i know you would never write an angle like m/m or smth, but i thought it was funny that both of your mentioned units could be defined by this m/m
They're only unitless if you're only considering fundamentals as "true" units.
the torque distribution unit is pretty cursed as well: Nm/m
this type of stuff i usually just dont mind understanding because its just a matter of keeping things tight lol
"How many mm/mm?" Is a question that could kill a robot honestly
The most cursed unit I've ever had to work with is Rankine, where some very old documentation on refrigeration used Rankine for all of it's temperature references. Rankine is the Kelvin of the Fahrenheit scale. R°=F°+459 and some change.
That's super cool :)
Wait what there is K for F?
personally I think we should call this scale "Melvin"
@@nekomi_chsure, why not? It wouldn’t be as useful cause Fahrenheit isn’t used in science much but the same rules would apply to F as C
I have to deal with legacy NASA documents (and engineers) for launch vehicle certification. Rankine rankles.
Hi, 3rd year engineer (i am very stoopid tho im a civil) For the Hubble constant, wouldn't've it be 2 Au because 1 au is the distance from the earth to the sun and they measured from. . . both sides of the sun? Like, the june and july "points" and the distant object "point" make an isosceles triangle. They convert it into 2 right triangles by splitting it down the middle, and in the process dividing the "base" of the triangle by 2.
This new "base" is an averaged distance between the earth and the sun (the earth is closer to the sun in the winter or summer i forgor which tho) and this difference gets accounted for with the average (the average (i would assume) is why they waited 6 months to go 180 deg around rather than 3 months and only go 90 deg around).
Aaaanyways, following the process backwards now, we have 3 points to start with. 1) the distant object 2) the telescope, and 3) the sun. We know the average distance between the earth and the sun (base), we know the angle (measured angle divided by two (isosceles triangle to right triangles)). NOW we can figure out wtf the distance from us to the body is .
Hope this helps and sorry if anythings wrong, i study frames and dirt not space, but this jus feels like a big trig problem.
For the first question. It is measured as 1 au but the only suitable way of measuring it is by using 2 au. Kind of like how speed is measured in km/h but during short distances and short time, we can measure it using m/s and then convert.
There are a few papers on the fractal nature of some day-to-day objects, like paper balls. We use this experiment for our undergrad students to learn log-log linearization. What is interesting is that you find the mass is proportional to the diameter^n, where n is a real number between 2 and 3 for paper balls (usually around 2.3). Then, since M = k*D^2.3, the unit for k is kg/m^2.3, which is some sort of "fractal density".
🥇👏👏🥇👏❤️
Is that related to the Hausdorf dimension?
So, paper balls are 2.3dimensional?
@@Xnoob545 yep!, your grade for the class is A+
@@Xnoob545 not quite. If you find that MODELLING them as a fractal gives you some insight, of course you can do it, but the fractal dimension for a "crumpled" 2D object (theoretical sheet of paper) will be greater than 2 but less than 3. (It approaches 3 as the paper ball approaches being a solid ball.) We can also see that if you have a line that is a fractal. Lines are 1-dimensional but once you make a fractal line it kind of starts to fill up area. The furrier and crazier it gets, the more area it fills up, and we say its dimension is increasing. A maximally furry fractal line would approach being a solid sheet of something, so approaches being 2D.
POV: You are solving a physics problem and see GPa for the first time as a unit of tension
I hate that I understand this joke.
Pascal as a tension unit? What?
Funny, in engineering I encountered GPa as a unit of stress 🙃
@@harrygenderson6847 man, thinking of my studies in engineering is putting me under 4.20 GPa
@@seesaw41 A tensile stress unit. Usually it is MPa for stress, and GPa for Young's modulus, since that's the order of magnitude we generally expect for these concepts.
I did my master´s in theoretical physics, so for the last few years I mostly used natural units, to the degree where you tend to forget that there even are units involved. But if you think about it, a unit system where hbar = c = 1 is incredibly cursed if you try to convert back to SI (but nobody ever does that).
Currently I am writing a paper about that because I love the cursed physics and math behind such stuff
Even though I understand why people would want to use natural units (or other units which simplify their customary work) I find dimensional analysis so useful for ensuring you get the right answer that a system where you tend to forget the units seems like it would make certain types of mistakes way easier to make.
Some engineers I've worked with tend to do similar things where they routinely normalize their equations to make things unitless or they just ignore units while calculating and attach them at the end. It also feels similarly error prone.
I had a crazy teacher who wore dark glasses (tim buc 3) luckily I was still able to finish my doctorate in rocket science, meaning jet engine internals: thermodynamics and fluid dynamics.
I remember a funny answer on physics stack exchange about the conversion back to SI units which described how god might convey to Noah how much wood to buy for his ark but I can't find the link unfortunately.
@@doctorbobstone Yes, you want units to help you verify your algebra, even when you don't actually have units in this formal system; e.g. radians. In one of the Lockdown courses (I don't recall if it was Brian Green or Sean Carroll) he get to Natural Units, and then keeps going to Planck Units. Just like Time is equal to Space (length) once you eliminate the conversion factor of c, you can remove units entirely, as everything is either equivalent to Energy or inverse Energy.
Fuel consumption of an excavator is measured in liters per cubic meter, which is dimensionless.
And it doesn't get better if you use an electrical engine, because then you have something like joule per cubic meter, which has the dimension of kg m^-1 s^-2, which is Pascal :P
Jan Misali made a video where he derived a new set of standard units that were pretty cursed. Like instead of distance and time he used units of velocity and frequency with the speed of light c and middle C (256ish Hertz). But all the math works out.
You can to a lot of convoluted bullshit with math. In part that is also where math becomes pretty fun, because it can feel like magic to take some seemingly random stuff and pull something that you wouldn´t think by guessing could be calculated out of it. Makes you feel a bit like a wizard.
I like slugs, "A slug is defined as a mass that is accelerated by 1 ft/s2 when a net force of one pound (lbf) is exerted on it." I just remember opening up an old textbook and it talked about how the some 60's jet weighed about 900 slugs and being a little sleep deprived I just burst out laughing on the quietest floor of the library.
Isn't a slug a generalization of g?
No. A slug is the imperial unit of mass. It is "equivalent" to a kg since they are both units of mass in their respective systems. The pound is technically a unit of force but it's also used as a unit of mass (lbf vs. lbm) since people who work in imperial units tend not to be quite so pedantic. But then again metric people tend to use kg as a unit of force as well as a unit of mass. After all, when is the last time you heard someone give their weight in Newtons?
A mass of 1 slug weighs g pounds (32.2 pounds) just like a mass of 1 kg weighs g Newtons (9.81 Newtons) on Earth at sea level.
My favorite unit is horse power hour, but slugs are cool too
@@pjl22222 People don't measure their weight in Newtons because it changes constantly depending on your velocity and frame of reference. They just say weight when they mean mass. But in certain situations where the distinction matters (eg, climbing) people really do measure their actual moment to moment weight in a system in N and kN.
@@Barnaclebeard Unless you're leaving the surface of the Earth your weight isn't changing more than a miniscule amount that is probably less than the precision of the scale being used to measure it.
If you want complicated SI unit, most of the unit in electronics are absolutely horrible, like the Farad (for capacity of condensator) : F = 1 m−2. kg−1. s4. A2
But whatever units you have, the dimensional analysis is the same, so if you think the farad's horrible, that's not SI's fault.
@@rosiefay7283 I m not sure of what you mean exactly
And then there's V/sqrt(Hz) for noise levels (???)
@@markmarketing7365 Noise units are definitely cursed. All consequences of defining noise as the “power” in a 1 hertz bandwidth. The worst is it’s not a real power, but the power spectral density of the noise signal, so it’s V^2 / Hertz. Oh you want a unit that lets you compare amplifiers? Ok plot V/sqrt(Hz), divide it by the gain A(f), integrate over all frequency, and then turn it into the RMS voltage of a fictitious input voltage. 🎉
i think the idea of "capacitance" is just so abstract that the units can't help but be ugly
This is absolutely fantastic. I love the dynamic music. It reminds me of the excellent video essay on the music of Wii tanks (I know it sounds silly but trust me, this is a massive compliment). The music was certainly custom made for the video, and it's great. Subscriber well earned!
A cursed unit that immediately came to my mind is the reactivity from nuclear reactor physics because it is (somewhat commonly) measured in 1$ or 100ct.
If you wonder why: A nuclear reactor can be in different states. These basically describe if the amount of nuclear fissions happening at a time is stable increasing or decreasing. For example a reactor being critical means the the amount of reactions stays the same over time (good). Then there is the supercritical state, which means the amount is increasing (not always good but necessary to power it up). The supercritical state corresponds to a reactivity of more than 1.
However: There are two kinds of supercriticality, one which is easy to control (nice) and one which is impossible to control (bad things happen). Both have a reactivity larger than one but for the nice supercritical state it is maller than another variable (often called beta). Since beta is not constant it's good practice to divide the reactivity by it and define a new reactivity. With this new reactivity the "Nono-zone" corresponds to a value larger than one (very easy to remember). But now the problem arises that these values are both without any unit at all and bad things may happen if ever some reactor operator doesn't know if his colleague was talking about one reactivity or the other. So the one which should never go beyond a value of 1 was simply assigned the unit of 1 Dollar (1$) because Dollar is not otherwise used in physics as a unit.
So a Dollar is just the number 1? Why not just call it "unit"?
Why not use %?
Units of currency are cursed to begin with, just due to grammar. The dollar sign is supposed to go before the numeral, as in $1, but if you're using cents the cent sign goes after the numeral, as in 100¢
The smoot is a unit of length originally defined as the height of Oliver Smoot, a student at MIT. In 1958, the length of the Harvard Bridge in Boston was measured using Smoot as a unit, with the bridge being declared to be 364.4 smoots plus one ear.
Or minus! It did say (initially) "364.4 smoots +/- 1 €ar" (I know that's the EUR symbol- I just couldn't find an epsilon symbol)
Imagine how cursed it would be to have "e" as an exponent, and Pi as a log base
log functions are all identical save for a constant scaling factor, so a log base of pi would probably be a *more* useful interpretation than a natural log combined with a scaling factor involving both e and pi
XKCD has got you: "If you ever find yourself raising log(anything)^e or taking the pi-th root of anything, set down the marker and back away from the whiteboard; something has gone horribly wrong."
@@christianullrich2923 there's an xkcd for everything
Finna have a brain aneurysm
@@trevorx7872 Is there an XKCD for "there's an XKCD for everything"?
The 2 factors in quite simply. Basically, as the base of the triangle doubles, the vertex angle doubles as well. So a parsec is equivalent to the height of a triangle with a base of 2 au and a vertex angle of 2 arcseconds.
can't an AU cubed be converted into a year squared per (inverse, maybe) kilogram?
Electron-volt really does deserve a spot here.
Especially as you can convert any unit to eV and eV to any unit. That was proven in the 00s. The immediate result was half the science and engineering students started converting everything to furlongs per fortnight.
@@eekee6034 what do you mean "any unit"?
@@ExodiumTM any unit of measurement. grams, metres, kelvin, seconds, metres per second, any others I can't remember just now, and any unit that can be converted into these.
@@eekee6034 I searched it and didn't get any relevant results?
@@ExodiumTM Search results can be pretty bad these days, especially for uncommon knowledge which sounds like commonly known things, if that makes sense. I'm not sure what tips to give. I can't find anything myself today, but I'm too tired to look properly.
As a meteorologist, units of reflectance are a little funny, mm^6/m^3. It takes on a log relation whenever people use it so it comes out as dbZ, where db is decibels and Z is the reflectivity factor.
dragon ball Z
Goku is a loud one...
For weird dimensions, look at fractals, there is a snowflake with a dimension of 1.2619. For weird units, look at Planck units, where you set G=kb=h/2π=c=1, and then derive how to write down length in terms of these units. Momentum has sqrt(hbar c^3/G).
Fractal dimension is weird because it describes the curviness of a curve rather than something easier to describe like length or weight.
@@Sauvenil kind of like how calculus (kind of) measures the rate of change of the rate of change....
@@slateslavens And the rate of change of the rate of change of the rate of change.
I love how the music during the random walk part feels like a random walk itself
Let's not forget that a lot of SI units are now pegged to Planck's constant. So now you can have everything also mixed in with Joule-seconds
I feel like there's a way to a fully all-encompassing equation beyond the standard model somewhere there, but I just can't see it.
@@standard-carrier-wo-chan well you arent einstein I guess
Planck's constant in general is one of the most bizarre numbers I've seen. For how weird it is it somehow ties in with many physics equations.
@@standard-carrier-wo-chan If you can figure it out though we'll throw you a cool party, promise!
My favourite single SI unit is the becquerel, which is defined the same as the Hertz (1 becquerel = once a second), but for things that aren't cyclic. 1 Hz is once per second on the regular; 1 Bq is randomly, but once a second on average. (It's used to measure radioactive decay rates, which are random.)
No, in civil engineering for flood resistance, you plan for a variety of potential floods, such as a once-in-40-years flood. Since floods are not clockwork, this means something like "the typical/average worst flood you'd expect to see in 40 years". So the figure "once-in-40-years" converts to 0.8 nano-becquerels.
It gets worse.
Consider the units hertz-second and bequerel-second. Multiply 1 Hz (once per second) by 1 second, and you get 1 per. Per what? It's not specified.
Similarly 1 becquerel-second is "1 on average, at random".
Now let's say my street is 2 kilometers long and has about a thousand potholes in it.
That makes a pothole rate (not frequency as they're not evenly spaced!) of 0.5 pothole-bequerel-seconds per meter.
Instances of an event measured in hertz-seconds.
Estimated instances of an event measured in becquerel-seconds.
It's supposed to make sense but it just hurts to look at
Once worked with "millitmeters of mercury minuts per liter", now that is one cursed unit!
That was SUCH a well-put-together presentation in all ways! My favorite cursed unit is Specific impulse, Isp. Essentially a whole bunch of units get cancelled out until the final dimension is 'seconds'. That's it 'seconds'. Super unintuitive. Sometimes its better to NOT cancel everything out...