Why We Might Use Different Numbers in the Future
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- Опубликовано: 2 окт 2024
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Creator
Jade Tan-Holmes
Script
Thank you to script writer Simon Morrow for your work on this video.
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Music
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Sources
Excursions Into Mathematics by Beck, Bleicher, Crowe
“What’s in a name?”, which was written by Michael Bleicher
Realm of Numbers by Isaac Asimov
Asimov on Numbers by Isaac Asimov
www.cis.upenn....
rosettacode.or...
Imaginary Number Bases by Philip Herd: arxiv.org/pdf/...
Base 20 was fine until we started wearing shoes
@@WeAreSoPredictable username checks out
@@peelsreklaw You predicted a fantastic joke?
@@WeAreSoPredictable I'm sure that one is a big hit around your middle school lunch table.
@@peelsreklaw It was a big hit at my imaginary tea party at kindergarten last week. We all had a good chuckle, and vowed never to grow up into grumpy old farts who don't like wang jokes. :)
Why y'all so salty lmao @WeAreSoPredictable just made a joke.
Meanwhile in France: let's call ninety 'four twenties and ten'
Abraham Lincoln's famous Gettysburg address starts "Four score and seven years ago" (=87). Was quite common in English too.
Welsh: pedwar ar bymtheg ar pedwar ugain
Pipil: nawpual kashtul-nawi
(quatre-vingt-quinze-quatre)
And then you get Swiss French with "nonante" instead of "quatre-vingt-dix".
Actually, when I count in my head (like seconds or whatever) I always go up to twenty and then start anew while remembering the amount of twenties I counted using my fingers. I do that mostly because the words for the numbers above twenty get quite long (in English as well as in German, my native language) and it takes too much time to actually "think" them.
Correction: 'four twenties ten' there is no 'and'
That Greek "mathematical alphabet" at the time of inception was the commonly used Greek alphabet, a reminder that sometimes additional symbols weren't needed, just additional context.
Braille numbers are similar, they are simply letter symbols with additional context markers
Same thing applies for Roman numerals. Symbols taken straight from the Latin Alphabet.
*Me:* _"Can you calculate the height of that building from here?"_
*Mathematician:* _"Sure. It's 1x."_
Reminds me of the story of a mathematician doing a careers talk for a local school and a student asked "How many digits of Pi have you memorised?"
He thought for a moment, then replied, "Well, one, I guess."
My height is EXACTLY 1.00 Vivek long.
Using a sextant, a laser range-finder and some trig, yes.
lmao
Use quadrature for measurement. It fits in with Euclid.
It's so hard to evaluate the octal and duo-decimal systems because you have to unsee the decimal notation first.
Especially with the fact that numbers have also a phonetic world whose construction is still based on the base-10 system. Like 25 in octal is the number we call "twenty-one" in most western languages, but it's called this way because it is 21 in base-10. Should we actually start calling it "twenty-five"?
@@fluffy_tail4365 You would have to say "octal twenty-five" to make it clear. But now imagine trying to do the same in binary! Or in a base of more than 10 where you would need to devise new language around the extra digits. In hexadecimal, what would be the audible differentiation between 18 and 1A (eighteen or ay-teen), and how would you pronounce C3 (ceety-three, maybe, but that gives you problems with A0-AF v 80-8F again)?
If we had developed our numeric system using a different base then the language would have developed with it. That's going to be something that's quite hard to unlearn now though!
@@stevieinselby You could try "twocty-five" ("oct", "twocty", "throcty", "forocty", "fifocty", "sixocty", "sevocty").
For larger bases, rather than "ay", "alpha"; "cee" becomes "charlie", and so on - and then you can reduce them down to something easier to speak...
Agreed. When I was studying computer engineering we actually used base 16 because it translates so easily back and forth to binary. Once you get over the decimal habits (9+5=D) the arithmetic is actually easier. I was surprised she didn't mention it.
@@danielschein6845 Did you ever come across anything written by Jaron Lanier, I read his book a few years back about how a lot of modern technological systems have become locked into inefficient standards due to the fact that they are so tightly integrated with other systems. This feels like a longer term example of that: It might be that there's a 'better' counting system but we're unlikely to ever use it as societally we're so locked into decimal. I find it a bit hard to tell how seriously he's taken in serious academic comp sci circles as he's a bit of a maverick.
'There are 360 degrees in a circle"
Mathematicians: "We don't do that here"
There are two pies in the circle and they are delicious
Sorry. There is just one tau
That's rad.
But can you eat a tau?
@@AllanDaemon As there is also; the one great Tao.
i thought the music was too loud in the intro but also it was really familiar, then i realised i still had minecraft open
hahahaha
That’s too good
My god. Up and Atom controls our hearts *AND* Minecraft games? Something must be done.
Lol, This kinda sums up the Internet.
This is such a human thing to do, thank you, you made me giggle =)
Your videos were always great, but there's been a noticeably big leap in quality. You're really throwing yourself at this thing. Keep up the good work
Thank you I'm so glad you noticed!
@@upandatom I agree with OP. I really enjoyed this one and am looking forward to the next video. 🥇 🕊❤🤗🙏👉🌻
Drinking Game: Take a shot every time the parchment curls up.
I'm dead bro.
@Smee Self I wish you were with me right now, so we both can be plastered.
This is absolutely not the thing i need to hear right now with my life . . .
_"There are 10 types of people in the world: those who understand binary, and those who don't."_
That's as simple as 1, 10, 11.
"There are 3 types of mathematicians: those who can count, and those who can't."
I bet 2/1 of all people that read that won't get it since they can't even do simple fractions.
"there are 10 types of people in the world: those who understand binary, those who don't, and those who didn't expect this number to be in base 3" I learnt this from Numberphile
lol!
Great video! Surprised you didn't mention hexadecimal though, which is common in computer science specifically because it's a more human-friendly way to interact with binary data
+0x01 for this, hex is used all the time by designers who input RGB colours as hex codes in websites and art programs for example #FF0000 (red) and #808080 (grey). It's a good notation which indicates numbers that have a fixed upper bound space, for example four byte numbers which are always 00000000 - FFFFFFFF and you can see the /scale/ of the number within the bound much more easily than if you used decimal.
I was also going to mention this until I saw your comment. Both octal and hexadecimal work very well with binary systems, being very easy to switch representations. However, hex ultimately wins out because most computers have word lengths that are multiples of 4 bits. And a byte, which is a very commonly used term in the computer world, is simply 2 "hexits", if that's a word. Some calculators are able to do simple (4 function) math operations as well as logical functions in binary, octal, and hex and can convert representations to any of these formats, plus to/from decimal. I once used a calculator that was even able to do floating point operations in hexadecimal. It was useful for my job at the time. The history of math, and math itself, are very interesting subjects.
@@jimbert50 The "hexits" you are inventing are called nibbles (or alternative spellings: nybbles and nybles) :) But I do like the sound of hexit to be honest :)
Hex is just used so available bits don't get wasted.
@@adamkendall997 All representations are a form of information compression. Some are more efficient than others using a given media.
The base 60 was based on counting using the thumb as the ‘cursor’ and the three phalanx on the front of each of the fingers, which gives 4 lots of three =12. This was rallied on the left hand 5 times for 60.
Great to know. Thanks.
Just like jade shows at 8:00
"Phalanges" is the plural.
Technically, that’s not base “sixty” (= 6 x A), which is decimally-coded, but rather base “five dozen” (= 5 x C), which is dozenally-coded. Can’t do base subscripts here so I will put bases in brackets: 60[A]=50[C]. Divide sixty by 2 you get 30[A]=26[C]; by 3 you get 20[A]=18[C]; by 4 you get 15[A]=13[C]; by 5 you get 12[A]=10[C]; by 6 you get 10[A]=A[C]. So the most common divisions of sixty come out “rounder” when it’s decimally-encoded rather than dozenally-encoded. That’s because 5 really isn’t the most important factor, 2 and 3 are more important. So you lead with them by making the top digit 6=2x3.
But using your thumb to count your dozen phalanges on one hand isn’t a trick for base sixty, it’s a trick for base twelve! With two hands, you can count from zero to eleven-dozen-eleven, and then you can stack a coin on the table each time you hit a gross.
Actually, if you use the Korean method known as “chisanbop” you can easily count to 9 using one hand, or 99 using two hands. If you limit yourself to counting 0 to 59 using chisanbop, then you can manage base-sixty counting (decimally-encoded), without unnecessarily turning it into base-five-dozen counting (dozenally-encoded). (Per my previous comment above.)
“You have learned the difference between a mathematical concept and its representation by symbols-many mathematicians never learn that!” - Magnus Hestenes
Representation theory, now that was a hard class oof
Ohhh, now I get it. So even though the symbols, bases and notations we use are arbitrary, the mathematical concepts like addition, multiplication and factorization are more universal.
This leads me to think, just as different civilizations came up with the same basic concepts, something about these concepts are more universal that even Aliens may come up with. It's even more likely to think of these concepts of mathematics than those of languages, since different cultures have come up with completely different systems of writing that use different concepts.
Truly, mathematics is the language of the universe.
@@susmitamohapatra9293 That's why it was used on the voyager spacecraft.
@@susmitamohapatra9293 it's actually deeper than the mathematical operations being something intrinsic to reality (representing a universal idea) but the numbers themselves.
Since a number represents a quantity. The idea of quantization its at the root of all math. (I have one apple. Specifically one.) even decimals (I ate half the apple... I have 0.5 apples) are representative of a concept that goes beyond even ideas. They can be thought to be an intrinsic part of our subjective reality.
Obviously I'm a fan of the Platonic view of numbers.
That boggles my mind. To me, that is such a fundamental concept that I hardly ever even think about it, and it applies to much more than math. Hell, they talk about confusing the map with the territory, and here you're telling me that there are people who confuse the specific printing with the map?!
I, for one, like Roman numerals. (Stewart Francis)
"I, for one, like Roman numerals. (Stewart Francis)"
(Paul G)
""I, for one, like Roman numerals. (Stewart Francis)"
(Paul G)"
(Brigadier Chooch)
How X is ten -tial of you.
“How X is ten -tial of you.”
(Richard Cerasi)
Aye aye, there's two of them now.
I actually invented a new number system and alphabet around when Covid Quarantine began and I just found this video and feel so validated with everything I created. I made it for a fantasy book I’m writing so sadly not sure anyone will ever see it, as I’m not a very talented writer. But it’s nice to know it works in ways other people can easily understand. Thank you!!
What is your number system? Sounds pretty cool!
You can always write a separate blog post or explainer video about it on RUclips. Exposing it won't reveal anything critical about your book's storyline.
I mean that sounds interesting as hell. Im a HUGE fan of fantasy books that get a lil "crunchy" with how stuff works in the universe!
Keep it up! The only way to become a better writer is to keep writing! :)
Is there a blog or a video explaining your number system
Did the numbers "1984" and "42" get selected as nods to SciFi nerds?
LoL
Fiction? What fiction?
Yet truest of true nerds know 42 adjusted for inflation is 47.
@@ThisCanBePronounced Everyone knows that 42 is a multiple of 3 primes and primes are not subject to inflation. Not even into another prime
With how infrequently Michael uploads, I'm just gonna start pretending this channel is VSauce now.
That is the compliment of the century Michael is my idol
Up&Atom and VSauce are different channels. But are they?
.
VSauce music plays.
@@samarendra109
Vsause basically covers everything but up and atom is around math and science
@@upandatom Michael, you, Grant from 3Blue1Brown, Tom Scott, Hank Green, Matt O'Dowd from PBS Space Time, Henry Reich from minutephysics, and Derek Muller - that would be my choice of colleagues to science around.
Of course, I would be the one who provides the coffee.
@@lonestarr1490 You're lucky, in that company I am unworthy to make the coffee.
The assumption I make when I see the number 42 is that it's the answer to life, the universe and everything.
So long, and thanks for all the fish...
hey, thoughty2 here
Like 23?
42 is definitely NOT a random number!
4, 8, 15, 16, 23 and... 42!!
I wonder if Roman numeral X was two Vs back to back.
Holy crap
Don't be silly. No one can handle two Vs back to back. It's way too much Guarana and caffeine.
Try algebra with xv+ iv exp i =xi....solve for x.... lol
Should have used W instead...
Interesting idea! Maybe one day the missing link will be found, which might have been a W, that evolved to X for efficiency reasons. Chisseling an X is way more convenient than VV.
"That said, it seems unlikely that we'd go through all the trouble of completely changing our number system, unless there were some kind of new discovery that fundamentally changed the way we do math."
There was such a discovery, in the twentieth century. It was called the "transistor,",and its importance rivals that of paper. Nonetheless, we didn't change our everyday-use number system. We just developed a minor subculture of technically-inclined people who have basic knowledge of an additional number system (usually represented as base 16, though it corresponds fairly directly with the base-2 system that computers themselves use) that they only use when reasoning about or interacting with computers in a technical capacity.
Boolean algebra and predicate calculus can and were completely represented by logic gates: i.e., wires and switches. That's where base 2, and its more concise cousin, base 16 come from.
Transistors are much more complicated because they can hold multiple voltages, throwing your base 2 number system out the window. Rather than reinvent the wheel, transistors were instead used as a way to shrink the room-sized computers made of copper wire and various switches.
The telegraph is base 2. The transistor is essentially orthogonal to number bases.
@@jessejordache1869 All base systems that are an exponent of 2 are naturally compatible.
A transistor is a automated switch. The only complicated thing about it is the behaviour of electrons in a semiconductor.
@@manuell3505 Um, no. A transistor is more like an automated *valve* . It is a fundamentally *analog* device, capable of letting any amount of current flow (within limits) depending on the voltage present at the base.
In order to build logic gates, and thus binary computers, we deliberately *force* the transistors to swing to either their maximum or minimum output value, switching as quickly and cleanly as possibly between the two.
The most common early applications of transistors were in fields of analog audio and radio, and soon after video (the good old "transistor radio" boom of the 1960s, then compact portable TVs) - all strictly analog technologies at the time.
@@therealpbristow What "um no"? You don't argue anything...
@@jessejordache1869 I see orthogonal in a sentence and I swoon before the face of equilibrium.
Firstly, You completely missed out the representation of zero. Grouping and all is okay but without zero grouping cyclically is difficult. Its actually a very big invention which changes a lot of things. Decimal, binary, Octal, Hex etc are all using it. And simple conversions will fall apart when zero is not there. Secondly, similar to the roman numericals, the spreadsheet columns use a system that don't have a zero and the conversion changes and becomes less intuitive.
Archeologist jade is so ....cool!!!
parthasarathy Venkatadri she got even hotter
@@amehak1922 I always try not to objectify. So let's say she's appealing in all respects.
You failed so hard at not saying hot :)
cos she looks like a cowgirl? :D
all jade are cool
As an old school programmer, I’m still partial to base-16
Base 16 is boring. It's like base-10 but a computer will always pick the hexa-girl you are fancying in the end.
Let's kick it old school and go back to base12!
500 = 256 + 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1
111110100 = 1 1 1 1 1 0 1 0 0
This is because I got confused when I expected to see 500 displayed as 000001010000000000000000
@@aniksamiurrahman6365 What does that even mean, "pick the hexa-girl you are fancying"? Hexadecimal is not boring, it's a fun base to work in. It's also a short-hand for every 4 bits (binary digits).
@@EriknocTDW It means computer circuits can actually read Hex. For decimal, they are just mimicking. Besides, I do read Hex.
Jade didn't mention the hexadecimal system, essential in computer science.
Hexadecimal is basically just a shorthand binary for humans.
it's just used to save space .... probably that's why she did not mention it
@@mathiaslist6705 while that's true... i still do prefer hexadecimal to octal. mainly because 2^3 is a whole lot less nice than 2^2 or 2^2^2
It's because it doesn't fit the balance, going higher then base 10 makes it harder to multiply and divide as the table becomes to large, only base 12 because of it's perfect alignment could be a better option.
@@TinusBruins "too large" is definitely subjective. if anything, i'd argue base 10 is too large too, so why not use base 6 instead? (aka base 12 but better? relevant: ruclips.net/video/qID2B4MK7Y0/видео.html)
(or even base 4!)
but also "perfect alignment" is also arguable. maybe it's ok for factorization and terminating fractions, but other than that it's quite an arbitrary choice imo.
Absolutely loving seeing the beautiful new backdrop (great colour choice) and Indiana Jades. Dusting for those ancient artefacts was awesome! Any truth to Hindu numerals using 10 because we have 10 fingers? As you pointed out, the phalanges divide into 12 and as a kid I was taught to count on the lines on the fingers (giving 16 per hand). Trivia: the duodenum is so named as it was meant to be 12 finger-breadths in size. Oh and thank you for the slooowwww Nebula crawl over my videos haha!
Yep we use 10 because it's the number of fingers! Pretty primitive reason, but luckily 10 works pretty well. Just another system could have worked better. I'm not seeing 16 lines on my fingers...
@@upandatom sorry, that system includes the tips of the fingers
You could do base-14 using your thumb 😄
@@haroldthomas9423 base-14's usefulness would likely be similar to base-10, just swapping out factor 5 for factor 7
@@upandatom If you count lines and spaces on fingers you get 20 per hand. Another number used as a base in some counting systems.
0:30 Tell me about it. Now that I'm getting ancient, it takes me nearly a minute to say my age in unary.
I'm sure you could cut that down significantly. People generally speak at 4-5 syllables a second, so the oldest living person could give their age in around 30 seconds...
Of course, the real trick is knowing when to stop...
@Animator&Fidd1er :-)
@@rmsgrey That's the same problem kids often have with spelling banana.
@@DeclanMBrennan dont you mean banananananananana?
I use imaginary numbers when I give my kids their allowance.
💀
💀
Boltzmann's entropy formula, Euler's identity, Einstein field equations, Schrödinger equation. Are you creating your own Stony Brook Wall?
Btw. this video was 🔥
Well, one thing is clear: we won’t be drawing a martini glass to represent one.
This video gave me hope and then ruined it
Nem party coin unlocked: The Martini
TL;DW version of the video:
"What if we wrote numbers differ... Subscribe to our BS streaming platforms!"
That is because one can not have just one martini.
@@cashaww
It would be "one Martinus" if we could.
I would imagine Roman numerals aren't all that difficult to read once you're used to them. I feel like I'm getting better at them the more I try to read them. A pure positional system may actually be more difficult to read occasionally; that's why we use separators, like in 1,000,000 or short hand symbols, like k and M.
As for different bases, I think base 6 is really good. It is a relatively small base, but not too small, and the multiplication table is really easy. The multiplication table of base 12 is much larger and therefore more difficult. There are also some larger bases that have interesting characteristics, such as base 120 and base 5040, but you have to use sub-bases in order to use them practically.
I taught my eldest son binary at the same time as I taught him to count. It confused the hell out of his grade one teacher. Of course, he became an engineer.
I taught all of my kids in Base Seven; they're basically unemployable. - j q t -
More of an indictment on the teacher and education system than anything. Early years teachers are usually (not always) afraid of math and don't understand what is actually going on.
@@camrouxbg Be fair. They're often _just as afraid and lacking knowledge_ in science and English as well. :)
ha! I did the same thing. I taught our 11 kids binary. Our eldest became an engineer and the others are both rooming together in med school.
@@timobrien2114 I guess that 66% of them don't enjoy math so much
When you apply a 2D texture on a 3D (to 2D transformed) rendering - like for games or vfx, it is helpful to have those textures in squares of 64, 128, 256, 512 or 1024 pixels - so the rendering looks smooth.
Base 16, hexadecimal (0-F) is also widely used in computer programming as it closely correlates to binary but is 4 times more compact
to expand on that: hex has 3 factors: 2,4, and 8. Not as nice as base 12, but it has other advantages, as you stated, such as it's easy relation to binary octets (bytes).
@@honorsprenvg1091
It only takes 2 characters in hexadecimal to express the contents of a byte. (Plus perhaps an optional space for separation.)
A common programming trick for very short machine code subroutines was to encode them into a text string of hexadecimal numbers, poke the characters into the input buffer, and then call the Monitor which was a ROM-based programming tool on the Apple ][ computers skipping the first part where it displays the "*" prompt and awaits a command to be entered, so it thinks that the string was just typed by the user, and it would place the machine code into memory without having to load from a separate Binary program file. It wasn't too bad for efficiency, as it only required 3 characters (or bytes) per byte of code.
It might look something like, "300:5F 69 20 ...". Please do not ask me to remember actual opcodes. But I used to use that trick often back decades ago.
Binary octets? Octal? Base 8? Wouldn't that be a byte (8 bits) is made of 2 4-bit nibbles? 0000 becomes 0. 1111 becomes F.
Base 16 is better especially when using hexadecimals to write webpages with multiple colors and can convert to binary numbers easily.
Hex is awesome, but imagine if it replaced widely used decimal we'd need new words too. Like how would you say "5C% of the 88,4E5,C22 people agree". Fifty-see percent? Lol you can't say ayty-eff for AF b/c too similar to eighty-eff. It's possible, just need new words
It is only useful in binary context (like rgb which is one octet each (octet not octal, for those who are trigger happy about correcting people))
I personally like the Hexadecimal numbering system, it shares some of the advantages of the Duodecimal, and it's a system I'm very used to using from computer programming.
There's 10 kinds of people. Those who understand Hexadecimal, and F the rest.
@@HotelPapa100 There are 10 kinds of people, those who understand binary and those who don't I believe is the original statement.
@@jamesrawlings8493 You're close, there's the other kind who doesn't expect a ternary joke.
Traveller forced me to love hex before I had to use in in programming.
@@sponge1234ify I'm the kind who knows that it works in any base.
She fails to mention that the decimal system came from India and that the key problem with most early number systems was the absence of 0. You can't write 42= 4x10 + 2x1 unless you have a notion of 0 and the understanding that '10' represents something other than '1', even though the '0' on its own represents a null quantity.
Yes . She should have mentioned the importance of 0 .
actually you could because you dont necessarily need a 0 to write a 10 like the roman numerals x which is a 10
@@hxyzazolchak but the 0 was needed for place notation, and that's what makes the base-10 numeral system easy and more digestable in comparison to the tally and Roman numeral system.
@@nin2494 true
She mentioned the mayans. They used 0
I like that base 12 gives you a counter clicker automatically in your hands. Use thumb to count "ones" on left hand by counting joints of fingers, there's 12 of them, use right hand to count dozens same way, when you have a dozen dozens you have a gross, mark down and start over.
With their innate base-8 thinking, I'm expecting octopods to produce some really good music one day. In fact, I'm counting on it.
Base 16 would be better
@@spb1179nah, base 512
@@spb1179 Nah base 6
Like actually, the fractions are a lot nicer
Are you sure it would be base-8? We have four limbs but don't use base-4. We have a total of twenty small appendages at the ends of those four limbs but don't use base-20.
Unfortunately, it's a moot point because octopods can't hear very well.
@@bokkenka We actually have used base 20 many times (see parisian French for a culture and language that still hs vestiges of it).
Stay sane during the quarantine guys!
Stay? Um, y'see, ... before ...
It's not just that duodecimal has more factors - 2, 3, 4 and 6 - but it also has useful "semi-factor" relationships with the numbers 8 and 9 (as 2 * 4 = 8, and 3 *3 = 9 - so though not factors themselves, they are related to factors). The number one less than base - 11, in this case - always has nice arithmetical tricks you can employ (true in any base). 10 is more awkward, but it's two less than base or 4/5ths of 12, so there are tricks. 5 is half that.
So, the truth is, duodecimal does have the most factors, but it's also has a couple of "semi-factors" and, when you get familiar with its use, a bunch of tricks to handle 10 and 11.
Leaving just 7 as the awkward black sheep. That supposedly lucky and magical prime number. Can't do much useful with it.
I mean, we all know and use decimal. It'll do, and we might as well keep on with that, as everything's already working in that system.
But if we were starting from scratch and designing, with some mathematical foresight, how our numbers ought to work, then you should totally go for 12.
(The Babylonians multiplied that 12 by 5 - to get 60 - as that then added 5 to the factors. So every number up to 6 - 1, 2, 3, 4, 5, 6 - is a factor of 60. Thing is, 60 symbols is, I reckon, on the "bit too many" side.12 gets you a nice number of factors - and fairly easily calculated relationships with a few more - without going overboard on the digits.)
No talk of hexadecimal? Why skip that one?
It's far too unruly for everyday operation. A base-6 is really the best anyways
Hexadecimal sucks
Hex is great, and octal is also worth considering
For everyday use having lots of factors, especially of both two and three, is really useful. 6, 12 and 60 pass that test. 16 doesn't but I do agree that it makes repeated halving and doubling easy.
@@eomoran If we can use Base 20, I think we can use Base 16 just fine.
This is the first time I've watched any of your videos and I love the effort you put into making them, this is quality content.
The only issue I have with base 12,16,24 etc numbers is the use of alphabet letters to fill the gap. That would generate problems latter on at mixing alpha with numeric codes. It would be better to come out with different symbols, and there are plenty of them out there.
Yep, I've always thought this too. Maybe dig out some old disused letters like yogh or thorn. Well maybe not yogh, since it looks like 3.
Your props, costumes, and sets make your awesome teaching even better. So fun to watch!
8:20 in the computer programming world, we basically have to retrain ourselves to count in binary and hexadecimal to make arithmetic easier
This was the most frustrating bit of my computer science degree
I still remember the argument long ago that led to an agreement that multiples of 10 would always be read as digits, like 60 being read as "six zero" ... "Sixty? No six dee. I put sixty in and it's not working! Not sixty, six dee. I said sixty! Do you mean sixty or six dee? What are you talking about"
@@Berkeloid0 You'd still get bee and dee confused, and probably cee as well. You're better off using something like NATO alphabet: *alfa, bravo, charlie, delta, echo, foxtrot.* Though in my native Portuguese I tend to use words that we used to quote multiple choice question answers in exams: _água, bola, casa, dado, escola, feixe._
Binary is kind of cool. I think actually twice in my hobby programming, I put a 70-character text string lookup table into my program, so as to tell my number-drawing subroutine how to draw numbers without having to resort to writing a font. My text string had 70 characters, because each digit has 7 segments to draw, and there are 10 possibilities for each digit. 7•10 = 70. As on a squarish-number digital clock, a 1 means to draw the segment, a 0 means to not draw it. So I had "11111010011000011011100111111011010..." well that is the first half of it, for encoding how to draw digits 0 through 4. I sent the number and the x,y screen position to the subroutine, and it separated the digits and drew the number. Note that a "0" uses 6 of the 7 segments so 6 of the 7 first characters are 1s. Imagine how much more code I would have to write, if I had to independently program all 10 separate ways to draw a digit. The lookup table was far more efficient.
Thanks. @4:22 - I have that exact clock! (The black one with 6x2 at the 12 o'clock position) Awesome! It's hanging in my living room, and serves as a genuine nerd badge (of which I have many.) I had the pleasure of going to a private school for 6th & 7th grades. They taught us a whole range of things that were never, ever mentioned when I got back to public school from the 8th grade on! We learned how to create a numbering system (as you discussed somewhat); we learned to diagram every word of complex, compound sentences. I learned to type (that was an elective). I learned about computers & memory storage (microfiche, magnetic spools, etc. - which was also an elective.) I never used any of that knowledge in public school; not once. It's really amazing what kids can learn, and it's sad that we're not teaching them these things. At least there are people like yourself, who are dedicated to learning & knowledge - both for practical reasons, and for their own beauty! tavi.
Warning: This video contains factors of ten! It is not suitable for american viewers!
Paul Paulson i’ll have you know a yard is a very useful unit of measurement ! (it isn’t, we suck lol)
We do use S.I. units metric in science engineering physics..
Maybe we come help you out after this is over ...as we always do.
@@clarkkent1616 well, at least a yard is close to a meter, so it's kinda easy to compare. but you seem to use feet mostly instead of yards, which makes it much more complicated.
Paul Paulson - This is just an ignorant remark about the use (or nonuse) of the Metric System. In fact, Americans use metric units a great deal, and not only scientists. We are far better with metric units than Europeans are with U. S. Customary units.
@@GH-oi2jf That's because no one in the right mind would want to use to US customary units. There's no benefit to do so. It's a weaker outdated system that should have died at least a century ago.
4:15 That pun was so smooth it's just great
Base-12 is easily the best number system imo, plus we already use it for time keeping and its compatible with radial degrees. If metric, or some successor to it, were to be base-12 it would bring all other units in line with time keeping units and have the benefits of 12 being the most divisible smallest number.
And I thought you were gonna talk about peano axioms. Fun fact: Even in late medieval europe roman numerals were sometimes mandated for merchants because they were harder to forge than arabic numerals.
Artifexian also has a great video on a base 20 counting system, that is actually being used. It also makes a lot of maths very easy. The video was called "This is the best counting system" or something like that!
not as good as base 6 tho
The kaktovic inupiaq numbers
ruclips.net/video/EyS6FfczH0Q/видео.html
You could easy use the notation in base twelve (use 4 as sub-base instead of 5 for instance), that'd be like a super saiyan fusion of number systems
If we’re switching to anything in the future I’d bet on hexadecimal - it’s compatible with classical computers, we have symbols assigned & accepted and non-mathematicians use it all the time.
I was thinking about hex but quantum computers could change everything. I guess they are not binary.
base 103 is more efficient, but multiplying is problematic.
Could you please do a more in depth video on a number system that deals with imaginary numbers. I have written several computer programs that have to use them (convert from latitude-longitude to Universeral Mercador Coordinates) and I wonder if there isn't an easier method.
I made a number system that is easily expanded into representing imaginary numbers but it's more a system for math than it is for counting and amounts of things. It's also usable to describe euclidean vs spherical vs hyperbolic space pr atleast 2 dimensional ones (it probably could do more I'm just not very good at math).
But in its most basic form it's similar to the use of i to map out spaces, i presume it might just be a strange way of doing those same things if expanded upon
Nothing sexier on this planet than a smart girl...
@00UncommonSense00
I want to be that microphone 🎤
@@Skyprince27 bruh
8:02 In Sumerian markets/auctions they would display bids by putting their right thumb on one of those twelve places, and the other hand putting fingers for how many twelves. So 41 would be three fingers on left hand (36) and also right hand with right thumb pressed where you wrote 5. Both hands overhead.
Imagine Count von Count counting in binary:
1! One cookie!
1-0! Two cookies!
1-1! Three cookies! Ah-ah-ah!
Todays episode was brought to you by the number e.
Base 2 is cool in the sense that you can count up to 1023 on your fingers (including thumbs). As a plus you also get to make offensive gestures at certain numbers, 4 is the single middle finger and 132 is both middle fingers. Also 6 and 390 for putting the v's up with one hand and both respectively. I've left out the single hand gesture on the opposite hand of course, but I'm left handed and it's easy to work out the single righthanded gestures if anyone can be bothered. Thumbs up 513.
Lmao I haven’t slept since yesterday why am I watching smart
the number system we use is directly derived from devnagari system of India but there is no mention of that,only negative point of the video rest video was fantastic!
Who else really likes Jade’s hat? Every time she wears it in a video I’m always staring at the laces and the grommets they go through.
i like her map of the world @5:06
...and, naturally, the number 42 figures prominently. Douglas Adams was onto something. 😉
6:33 "Which we'll borrow from the English alphabet"
Romans: "are we a joke to you?"
"Yeah lol"
She's maybe American; they are not taught European history in Merica. xD
@@QuantenMagier
She's a Brit
I guarantee it
Yeah
Romans are a joke
That Roman Empire thing
Nothing but a myth
Julius Caesar
Just a figment of someone's imagination
Everyone knows that the English invented the alphabet and spread it to the whole world
The British Empire has existed for 5000 years
@@QuantenMagier Dude, she is Australian!
I saw it somewhere else on youtube. That creative method with numbering finger segments was actually a sumerian invention they would count segments in a right hand with their thumb up to 12 rising a finger in a left hand every time they would start over giving system base of 12 x 5 = 60
I don't know how comfortable I am with this much energy and bounciness in math.
I'm so old, I knew at a glance the number written in Roman numerals! ;-)
It's a simple matter of being used to them. If you use them enough, you'll immediately pick up the groups of numbers that correspond to the powers of ten like *M CM LXXX IV.*
What I felt that she could have done a mention of _romana computatio,_ which was the traditional Roman finger-counting system. Using both hands you could represent any number from zero (yes, zero) to 9 999. It was fairly popular in the _tabernae_ of antiquity down to the great international fairs of the Middle Ages until they were displaced (like the abaci) by the Indo-Arabic numerals in the late Middle Ages. Here is a link to an article which explains _computatio_ in some detail:
penelope.uchicago.edu/Thayer/E/Journals/CJ/47/2/Roman_Elementary_Mathematics*.html
Bet you watched the BBC?
While it's not used as much these days, the American standard for measurements largely is rooted in base-12 and base-16. Easy for fractions, and at certain points the base 12 and base 16 translate to one-another fairly well. This is why a teaspoon is 1/3 a tablespoon while tablespoon and up are x/(n*4).
I don't know why RUclips recommendations brought me here but I'm glad I learnt some fun stuff about numbers.
Beautifully avoided mentioning "INDIA" at all while discussing where the place value number system, the concept of zero or in essence the decimal number system and most fundamental mathematics came from.... Your services to the white supremacist cause shall not go unnoticed 🤣
Circa when did place value number system originate in India?
My favorite alternate base is base 6, it's like base 12 but with better fifths and sevenths, easier arithmetic, it fits on your hands without using finger segments, and the square base (base 36) fits on the 10 numerals and 26 letters, making it easy to compress.
NO READING pnS
Blow your mind: the Roman X is 2 Vs, opposite each other.
Actually, it's the other way around: V was formed by cutting X in half. This video is a great explanation on how Roman numerals originated: ruclips.net/video/Ik4yloCszYo/видео.html
This video got me interested in the quater-imaginary base and .. it's super weird to work in. Addition, subtraction, and multiplication are 'different' but aren't bad. Division, however, that's really tricky. Once you accomplish it, however, you're essentially doing division of complex numbers without calculating a complex conjugate (which is good because I always thought having to take a complex conjugate was kind of silly).
Another difficulty with the quater-imaginary base is that there's no nice way of saying any particular number is greater than or less than any other number. This is what makes division difficult.
Just like how QWERTY keyboard is still the standard long after typewriters, decimal system is going to stay in fashion for as long as there isn't an overwhelming advantage to using something else.
Going back to the keyboard example, I learned Dvorak five years ago and have had no regrets. It is a superior layout for full-size keyboards due to the lessened finger movement, which makes learning it significantly easier. However, since everything was built around QWERTY, and everyone has been trained with QWERTY, the benefits of Dvorak is just not enough to convince the world to switch over.
I get frustrated why nobody mentions the role of Hindu Civilization in mathematics. Modern number system along with trigonometry originated from India. Western civilizations has presented these ideas as 'Original Greek or Roman discoveries.
I've been a big fan of Dozenal (duodecimal) number systems for a while, for the reasons you explained. Multiplication and division can become much simpler in more common situations when calculating from base 12.
Alas, I'm afraid there's already too much of a cultural and infrastructural barrier that prevents us from likely ever making the transition to base 12. A very impactful and widespread change would have to happen in favor of base 12 in order for us to make that leap. I don't think the powers that be in the modern or future world will see the benefits of base 12 to be worth the massive shift in the way the majority of people think about and use numbers.
One last thing I'd like to point out is the distinction between numbers and numerals. Numbers exist in the abstract; they are quantities, independent of the systems used to express them. Numerals, on the other hand, are those systems and symbols. 2 is not a number, it is a numeral. It's the idea of two that is a number; its value or quantity. The value of two can not change, no matter what numerals you use to express it.
This semantic distinction gives us an answer to your question of whether numbers are invented or discovered. Numbers are discovered, because quantities exist independent of our ability to express and articulate them. Numerals, on the other hand, are a human invention. They are the tool we use to express numbers in a way that our minds can interface with more easily.
Finally found an other fan of the Dozenal system. I am prepared to switch tomorrow! But new symbols should be designed for A and B. The reason why so many people stick so hard to the inch unit is because the decimal doesn't have the same nice fractions
"Number vs Numbers." I have but one thumb (base 0?) to give to your excellent answer! Might give an edge to the question of whether mathematics or logic is discovered or invented also - which can take on a slightly theological flavor. I believe that Godel has something to say in that particular matter though.
The last bit is exactly what I came to the comments to say! The reason different cultures have different numeral systems for the same numbers is the same reason they have different words for "rain," it's just a language for numbers instead of other things. Different words (numerals), same concepts.
Hexadecimal system is the way to go. Base 16 so it's an even power of 2. You can represent larger numbers with less characters. Multiplication and division may be a little tough. It's also good for editing save game files.
You should have mentioned Hexadecimal as well. It is used a lot in computer science because it corresponds great with the binary numbers.
Jan Misali has sold me on seximal, which combines the nice parts of duodecimal with the added convenience of a smaller base. I also feel like 6 is just a better fit for the human world than 10. I'm not sure why exactly, but it seems like it's easier to have a handful of six objects in most cases than ten, and the powers of ten grow just so quickly. The only downside is that there's not quite as easy a finger-counting method for six as for ten or twelve, but in the end I feel like that's a convenience we don't need.
Happy to see a video discussing non-decimal bases and explaining some benefits of them. A little sad to not see the inclusion of Senary (base six), as it's my personal choice for best base, but still overall glad this topic is being covered.
(A note about duodecimal finger counting, it's difficult to use it to convey numbers to others, which is a common use for finger counting, and it can also be difficult to count quickly as it requires accurate movements. Senary finger counting works out much more cleanly, as in Senary each digit has six values, 0-5, which can all be represented on your hand by having 0-5 fingers up. Because of this, Senary finger counting works cleanly by having each hand be a single digit, allowing you to count up to 35. It's also easier to do quickly and conveys better to others.)
Memorizing times tables isn't really efficient. Better to have a system that is easy to do the calculation with mentally. I'm not really a fan of the memorization tactic.
We had to memorize times tables in school. That worked great right until someone asked how many hours there are in a year.
I'm old school. In 5th grade, they taught us duodecimal to instill in us the place number concepts. Even in 4th grade, our times table went up to 144 ... 12 × 12. In 6th grade, we traded all that in for algebra.
Thanks for the nostalgia, Jade 😊.
Fifth grade? That's late. We were doing 12 x 12 back in second grade. No wonder kids have a hard time with basic math these day. shesh.
@@sbyrstall - I took algebra 1, algebra 2 and began trigonometry and analytical geometry in 7th grade. What were you doing?
I've taught mathematics. Normal children learn to multiply beginning in 3rd grade, even back in the 70s. A good student might even learn the entire times table (which went to 12 × 12) by the end of the school year.
Save your horseshit scoffing for someone else.
@@sbyrstall That's nothing, back in my day they had us memorize binary to build our own calculators and input systems so we could stack our own program cards, and all that before we were in 1st grade.
Hey jade, you're great! Keep up good work.
If you ever run out of ideas about what videos to make you can always explain what's so interesting about damn rational numbers. Haha
It’s probably a good idea to employ completely new symbols for a duodecimal system to avoid confusion with documentation written in decimal.
Hexadecimal uses the ten decimal digits plus the letters A-F:
A=10, B=11, C=12, D=13, E=14, F=15.
But each hexadecimal digit also represents a group of four binary digits, or bits. Programmers have been using “hex” for over sixty years with no problems!
@@allanrichardson9081 Here's my problem with recycling Arabic numerals. Let's say we adopt duodecimal or hexadecimal. Later, you see "15" with ambiguous or no context.
Is it fifteen or is it twenty-one? It won't happen all the time, but it will happen often enough that we should head it off in this imaginary scenario where the whole world agrees to completely change our numbering system. ;)
Finally a good math video that I was able to understand :).
Binary number system in todays information technology has been chosen because of a technical property: best signal noise ratio = greatest distance between the two states 0 and 1 of their analogue representation = minimal distortion or failure.
That's correct. But still ternary and decimal computers were build before binary became the standard, and those had some advantages over the binary competitors. I wonder if nowadays with modern technology such non-binary computers could be build that could easily deal with a slightly worse signal-noise ratio.
Secret of Decimal number system is ZERO .
"1+1 still equals 2" except in some binary finite fields, where 1+1=0 (xor). although arguably 2=0 in this field, since the only elements are 0 and 1
Or, 1+1=10. When you're a computer.
You forgot NAND and NOR.
2000yrs ago Indians be like: "hold my sanskrit texts on vedic mathematics"
If somebody expects me to watch 2,400 documentaries in 30 days, I’m going to need payment for that.
Why would someone need you to do that?
"thousands of years and inventing and refining" True I suppose, however while the number _system_ is one that took quite some time to develop, but the choice of symbols and base were both poor if you ask me.
I prefer the number system that you can see here postimg.cc/G9JtFzNz It doesn't need to go to dozenal, but dozenal is better so might as well.
Also "zero", "seven" (and eleven for dozenal) should be renamed to a 1-syllable word, as all the others are already 1 syllable. This change alone could save billions of dollars over some years. (granted it will cost far far more to actually implement in the first place)
Fantastic visual symbols! So intuitive :-)
I like the ternary number system for computing...well, the idea anyway. For basic processing it relays tertiary commands (if, then, else) with much less code. Represents positive and negative numbers more efficiently and I am working on how well it can be used to work out Dijkstra's algorithm. Which people tell me isn't the end all be all algorithm, but I'm not sure.
That knot number system looked really interesting. Will need to look deeper into that one.
I like the fact you used the babylonian notation in your thumbnail to represent one. No doubt the representation was amazing too.
Some already use hexadecimal. A base 16 system for use with computer programing of some programs. Counting 1 through 4 and then putting line through is used to keep score in some card games. They can also make switches with more than 2 positions if switched are on dials such as older TV sets or rotary phone also shortwave AM / FM radios switches.
"Numerals", not "numbers". Why we might use different *numerals* in the future. The numbers are the same.
Backwards.
Base 2, and base 8 use a different number line they are different numbers I.e. 10 in binary is different from 10 in octal is different to 10 in decimal.
Same numerals, different numbers.
@@allhumansarejusthuman.5776 Nope. Wrong. I'll just assume that you didn't watch the video. Do you understand the distinction between a numeral and a number? Look at time 2:14. What is on the screen? Is it two different numbers? Or two different numerals? And BTW: you meant e.g., not i.e.
2:08 so you were born in 1984? Or are you an Orwell fan?
Or a fan of the phenomenal 1984 Tull album Under Wraps, which has songs about astronomy and space flight.
LPT: learn to tally on your fingers in binary. With one hand, you can get up to 31, with both hands you can get up to 1023, albeit quite complex at this point.
The amounts have always existed. Mathematics is just the way we represent them.
That sounds backwards. Most numbers cannot be represented in reality, as there are always less amounts than numbers.
It's probably be better to say that numbers don't exist or not exist, and the amounts that correspond to some of those numbers have begun to exist only a relatively short time ago.
What's an amount of i (sqrt(-1)) then?
@@Nickelodeon81
I didn't know i could be the base of a number system. Please, do show me what are the numbers in base-i.
@@NotBigSurprise go to 8:40
@@Nickelodeon81
Fair. I had forgotten about that.
Pissed at youtube for not forcing this channel sooner in my face... Thanks for the video and community that you have built.
Same here, to be honest
The problem with Base 12 is that it doesn't have obvious practical applications that make the switch worthwhile. Base 8 or Base 16, on the other hand, allow easy conversion to and from binary, so either one is useful to computer engineers. Base 16 seems to be the one that took off, probably because it takes up less space on the screen.
9:43 one plus one equals two
Or does it? (Up and atom music starts to play)
one plus one is a phone :D
@@HassanSelim0 hahaha good *one*
One plus one equals three for very large values of one.
When she said each number is associated with a factor of ten, she clearly meant each number is associated with a power of ten.
And really, each *digit* is associated with a power of ten.
Brad Camroux - She said "factor," not "power." What she said is wrong.
Although, as a general statement, using "power," is wrong too, but the specific meaning she meant is correct in the context of recognizing the place relative to the decimal point of each individual digit in a number specifies a power of ten.
A specific "digit" could only be mapped to one of ten powers of ten, so "associating" a digit with all powers of ten is not possible.