Cursed Units
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- Опубликовано: 1 янв 2023
- A collection of cursed scientific units.
What If? article: what-if.xkcd.com/11
Dimensional analysis: • Bomb Blast Radius - Nu...
Distance in astronomy: • Father Ted: 'Small' vs...
Pulsar scintillation: arxiv.org/pdf/astro-ph/0111034
Background music was me improvising on a piano.
Some small corrections: the distances between the planets in the graphics should be between their centres, and the wording when describing the pulse delays is backwards at one point.
If you know any other cursed units, share them in the comments! Here's some more (look for the hearted comments to see the original posts)...
Noise in a voltage signal is measured in V/√Hz (volts per square root hertz).
You would expect the amount of data produced by a particle collider over a time period to be measured in bytes or number of collisions, but apparently it's measured in fb^-1, inverse femtobarns, a barn being roughly the cross-sectional area of a uranium nucleus.
Other variations of kWh from commenters: kWh/annum contains seconds, hours and years all mashed together. Also lightbulb power consumption is sometimes displayed in kWh/1000h which, if I'm not mistaken, is Watts. This is probably to avoid confusion with the other use of watts which is to measure lightbulb brightness, which would all be fixed if anyone cared about lumens or candela.
There's an alternative to SI units called CGS, centimetre-gram-second. In CGS, units of charge are derived, and because they really shouldn't be derived there's multiple conflicting standards. One of these is to define charge using the statcoulomb, equal to 1 g^(1/2) cm^(3/2) s^(-1).
Multiplication and division of units is all well and good, but it breaks down when you're working with units on logarithmic scales, like pH, decibels, or stellar magnitude.
Sheet resistance, the electrical resistivity of rectangular sheets of materials, is measured in Ohms per square. Not square metres, not square inches, just square. This is because resistance across a rectangle is proportional to length and inversely proportional to width, so it depends on the aspect ratio but not the size.
A barrer is unit of gas permeability used for membranes and contact lenses, and it is equal to 10^(-10) cm^3(STP) cm / (cm^2 s cmHg). The 4 occurrences of ‘centimetres’ can’t be canceled right away, because they all mean different things. This is now my favourite unit.
Other bizarre combinations of units mentioned by commenters: thermal effusivity is measured in J/(m^2 K s^(1/2)), a Jansky in radio astronomy is 10^(-26) W/(m^2 Hz), and electrical capacitance is measured in Farads which are kg^(-1) m^(-2) s^4 A^2.
A lot of commenters suggested various imperial units. To me these aren’t cursed in a particularly deep way, since they just involve a conversion factor. I’ll give a special shout-out to acre-feet though.
Some people have questioned why I didn't write nm/√nm as just √nm. It's the same reason we don't write the Hubble constant in Hertz - you lose all information about how it was measured and what it represents.
Other commenters explained that the 2 astronomical units is because the distance between the measurements is twice the distance from the earth to the sun. I know that; I’m jokingly questioning why the definition of the parsec doesn’t have the factor of 2 included. 
Наука
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
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
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.
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
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.
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.
"I personally find square roots cursed" ~Pythagorean Cultist, most likely
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 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
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
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
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.)
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?
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
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
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
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.
@@user-mv2nn6rw2w 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.
"I promise this isn't boring"... they say to all of us nerds who just watched a 20 minute math video for humor
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
A long time ago I used translate documents from English to Spanish. More often than not, they were of a techncial 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 Farenheit to Celcius. 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 duelly 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 understant 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
@@XnoobSpeakable there's no such thing as cold but I can work out what's half as warm. Wow its a bit cold.
@@XnoobSpeakable Or for Fahrenheiters, Rankine. Why don't people have names like Macquorn Rankine anymore?
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.
One thing that I always chuckle at is that torque can theoretically be measured in joules.
I hate you
@@suhasguddeti2375 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.
@@suhasguddeti2375 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
I've watched this video more times than I would probably admit, and "Hertz?!" gets me every time. What a gem of a video.
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
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?
My favourite "softcore" cursed unit is the second moment of area, which is often used in engineering and is measured in mm⁴ or cm⁴.
When constructing beams or calculating loads I sometimes think "well, technically we already discovered hyperspace" xD
As a civil engineering student I absolutely love moment of inertia. Such a silly little unit that has so much weight on it
“Millimeters Tesseracted” 🤣
Sort of like how doing 3D matrix manipulations requires a fourth "dimension" just for the equations to work correctly. That's the multiverse showing the way.
Oh good lord, area moments are one if my most hated units, they always seem so damn absurd
in ship stability it also plays a big role.
you grab the transversal moment and divide it by the underwater volume of the ship. this gives a distance. now you add the height of the center of boyancy and substract the center of gravity.
if this value equlas zero, the ship's unstable
@@sethmcnew1093
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.
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
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 .
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.
Ever since I was a little child I was always fascinated with unit cancellations, but never really deeply thought about it. Well, now I've got this amazing video reccomended to me. Awesome.
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.
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
@@QueueWithACapitalQ 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.
A cursed unit I really like from signals theory is the spectral power density unit, which is W/Hz. It is meant to be like that because it's a power divided by a unit frequency, but when you think about it W = J/s, which means actually W/Hz is just a joule, but written in a fancier way.
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
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?
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
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.
For me, I encountered my weirdest units during my Bachelor's thesis. I simulated the die wear during hard turning, and the wear rate was given as [ẇ] = µm³/m. It's basically the volume the tool uses due to wear, over the cutting distance the tool was used
Does this resulting unit correspond to some area of the surface of the die? Intuitively, I'd expect it to relate to a ring of material that is no longer present after wear, when the die is viewed from the side, but I don't know what kind of numbers you'd end up coming up with and whether that'd make sense.
Saying "this video is getting too long" is the RUclipsr equivalent of the Teacher saying "That's outside the scope of this course"
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?
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…
Literally exclaimed out loud at some points in the video. Such good delivery, and while being interesting/educational! Keep up the great work!
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.
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.
@@PeterDercsar 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.
@@PeterDercsar 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.
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
I love this video. Your channel is so small yet so damn entertaining. I love how the piano playing emphasizes some moments. It feels so dynamic and makes realisations a lot more vivid.
I'm also amazed that I understood almost everything and I love how you guide the viewer into such physical conclusions that are, in fact, much more complex in reality.
it's really informative and interesting because one is coming to these conclusions through so simple means such as algebra and converting units, yet so funny through the music, your formulations and your tone and not only visually but also auditively pleasing with all the colors and how the text fluidly morphs and fades.
your channels really deserves more attention wow
this quality begs the question whether your last name is actually newton lol
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 ! 😂😂😂
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.
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.
Love the music in this video, thanks!
Also dispersion is a really useful thing to learn, gonna be using that alot more.
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.
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
I could watch a 2 hour video on this, thank you for blessing me with this cursed knowledge
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
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.
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.
What an interesting presentation on strange units. Loved every moment of it. Thank you.
I came here only to mention how blessed we are that different measurements/units of time are not mainstream.
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
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.
Unfortunately there’s not many people appreciating how ridiculous the unit for pulsar scintillation is, good for pointing it out
One of my theses dealt with pulsar dispersion measures. Thankyou for finally explaining one of the things I couldn't get right in my head, 20 years and 3 professional lives ago.
I have no idea how the youtube algorithm recommended me this video.
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.
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
I loved the atonal song on the background, very on point!
Absolutely love the music design in this video
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.
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.
I really love how well the music is implement
Love the piano in the back to help convey idea's and emotion.
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.
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!
I'd love a part 2 honestly, this video's great.
this was absolutely beautiful. thank you
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 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
I have absolutely no idea what is this man talking about but I'm vibing to it
You explained a lot of concepts very well, good stuff.
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
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
Can we talk about how the background music matched his speech intensity? That music - content synchronization is amazig! Congrats!!
Thanks for including the intuition for why the units cancel like they do. I really enjoyed this video and I’m definitely going to watch more of your stuff.
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
"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
Loved your musical random walk :)
you should make more content like this, i’ve watched this video many times just because there’s nothing else as fun as it on youtube
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...
Once worked with "millitmeters of mercury minuts per liter", now that is one cursed unit!
Great channel! 3B1B vibes. Really cool improvisation, man. Hugely underappreciated, I'm sure.
Just learned about brownian motion and its quadratic variation. Definitely has similar properties to PMD.
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.
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 love how the audacity of these spicy units is accompanied by angry piano noises.
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...
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.
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"?
Wow, you're amazing at explaining things.
This is still one of my favorite videos on youtube!