Why We Might Use Different Numbers in the Future
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- čas přidán 17. 04. 2020
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Creator
Jade Tan-Holmes
Script
Thank you to script writer Simon Morrow for your work on this video.
simonmorrow.com
Music
www.epidemicsound.com/
Knot Numbers - en.wikipedia.org/wiki/Tangle_...)
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.edu/~matuszek/c...
rosettacode.org/wiki/Balanced...
Imaginary Number Bases by Philip Herd: arxiv.org/pdf/1701.04506.pdf - Věda a technologie
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'
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 CZcams. 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
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.
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.)
'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.
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.
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 =)
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 . . .
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!!
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. 🥇 🕊❤🤗🙏👉🌻
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.
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.
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.
_"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!
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.
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.)
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: czcams.com/video/qID2B4MK7Y0/video.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.
“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?!
4:15 That pun was so smooth it's just great
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))
You are so engaging! You've giving us such great, fun, and informative lessons. Thank you!
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.
amazing video really. the process you took to explain the needs for better number systems was awesome, even already knowing a good little bit of number history, this video showed a nice different view.
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
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?
"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.
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.
Wow! This is like TOO good. I'm familiar with most of this info already, but you cover it so well. Plus I did not know about the imaginary number base, so I def learned something new. I feel like this is so dense with brilliance and happens in such a flash that the average person who is unfamiliar with it will totally overlook some remarkable items e.g. the easy to count base-12 on fingers. Regardless, just wanted to gush a bit about how great I thought this was. Instantly subscribed for more well taught concepts. Thanks for making this!
Boltzmann's entropy formula, Euler's identity, Einstein field equations, Schrödinger equation. Are you creating your own Stony Brook Wall?
Btw. this video was 🔥
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.
Amazing video! It is so interesting, well written and explained!
Wow, you are really great! Thanks for the great quality content!
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
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.
Keep up the goodwork! Looking forward the mentioned video on Nebula.
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.
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.
Your props, costumes, and sets make your awesome teaching even better. So fun to watch!
I use imaginary numbers when I give my kids their allowance.
💀
💀
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
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
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.
Thank you for the great video! 🙏🏻
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.
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.
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
czcams.com/video/EyS6FfczH0Q/video.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
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.)
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.
Great video. I taught different base systems to a group of junior high students and it blew their minds. I taught them hexadecimal as well because it was an engineering lecture. I think hex is a good contender for a switch because it bridges the gap between binary engineering and seeing things at a glance. Great work describing all this.
Excellent video as always. I would love to see a follow up video on the Tangle mathematics system, or any other number system based on knots cord or string.
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.
All the props you use make your videos way more entertaining. Keep it up 👏👍
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.
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.
That knot number system looked really interesting. Will need to look deeper into that one.
Great video to think about. Really enjoying your content so far. I’m hopeful for better solutions and tools into the future.
Stay sane during the quarantine guys!
Stay? Um, y'see, ... before ...
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.
I’d love to see the results of the added fx you would do with your red camera.
I think this was the video I discovered your channel with.
Keep it up.
Good on ya.
Very good video
Relaxing voice and rly deep think trough implication is also easy thx
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).
I really like your new filming studio, awesome job!
Thank you very much!
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.
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.
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.
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
@@ishxyzaak 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
When learning musical harmony, I rewired my counting circuits to use base-12 (duodecimal). It was convenient to have one symbol per pitch class. C as 0, C# as 1... A as 9, Bb as T, B as L. (being an english speaker Ten and eLeven were chosen instead of the customary A and B, it would have caused confusion when switching back and forth between duodecimal and tradition note names. After a few days, it was easy to quickly reckon that moving up 7 semitones (distance) from Ab was Eb (8 + 7 = 13) or work out in real time that G# Mixolydian starting in the 3rd octave is { 38 3T 40 41 43 45 46 48 } or simply { 8 T 0 1 3 5 6 8 }. This also worked well when intervallic relationships were considered (the distance between adjacent notes in a scale < 2 2 1 2 2 1 2 >. There were a few mental glitches afterwards when working in base ten for everyday math ($16 + $11 does not equal $25) but now switching back and forth is 2nd nature.
I would love to see you do more philosophical videos. I love science and philosophy equally!
But it seems only science is for free, for philosophy we are supposed to pay. I wonder about the philosophy behind that.
I think how many numbers you can represent with "decimals" or whatever you call the point for some fractions is important, and for that having only prime factors is important. So that leaves base 6, base 10, base 14, etc, and I think base 10 compares pretty well for those, although base 30 could be quite good as well.
I had the same idea of comparing number systems two years ago. However, I argued that 6-base is the best because I also included easy division as one of the factors. The factors i used for testing the (m-base) number system were:
1- The difficulty of comparing numbers which is measured by ln(10)/ln(m).
2- the difficulty of multiplecation mesured by counting the irregular numbers in the multiplication table.
3- the difficulty of devision measured by the sum of the inverses of the prime factors of m (without repetition).
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.
nice production! set changes, wardrobe changes, props! CAKES! :) this one took some work.
Brilliant vid about a fascinating topic. Number symbology is one of those things we don't think about enough, but should.
This raises the question of whether some number base is more natural than others, mathematically speaking. For example, there are formulas for directly determining the n'th digit of pi in hexadecimal (base 16) and binary (base 2), but we have not found one in base 10.
Edit: A few references.
See Bailey-Borwein-Plouffe formula and Bellard's formula for more details on that.
@wubs23 Base e. :)
You should have mentioned Hexadecimal as well. It is used a lot in computer science because it corresponds great with the binary numbers.
It was the Sumerians who created the base 60 number system.
This was later borrowed/adopted by the Babylonians.
The reason for base 60 is that it makes division,ratios(i.e. geometry + trig),etc much easier than decimal and much more precise because 60 is divisible into many factors thus leading to precise answers that decimal can only dream of.
I really appreciate your efforts...
Thank you
Jade's soothing voice was all I needed now. Thanks!
I wasn't going to like this comment... until I got to the end of the video, and got the connection. :)
"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.
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.
youve basically gone over a lot of the stuff ive read about base systems from wikipedia when i was bored lol, great video
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
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
Since fixed base number systems, regardless of whether we use different tally marks or a positional system of numerals, are about the idea of repeatedly multiplying a constant base to a number and then add another number, having a limit on how many similar numbers you may add before carrying over to the next place (342 = (3*10 + 4)*10 + 2 e.g.), i have been toying with the idea of a number system based on exponentiation from a constant base, and otherwise summing, also having a limit on how many similar terms you may add without carrying over.
So we can have a number that looks like 3*10^0 + 5*10^(2*10^0) + 8*10^(4*10^(7*10^0)) + 6*10^(9*10^0 + 8*10^(1*10^0)) for example. Which might be written as 3,5{2},8{4{7}}},6{9,8{1}}, or we may use a two dimensional notation in order to show the difference between summing and taking (a multiple of) the base to the power of a sum.
All exponentiations terminate in 0 eventually so we don't need to write that part. Also we never need to use the numeral 0, but we need to use sums of very mixed things, and have sums in the exponents recursively.
This will still work in any base, so in base 2 exponential we would have the first natural numbers (except zero) as
1 1{1} 1,1{1} 1{1{1}} 1,1{1{1}} 1{1},1{1{1}} 1,1{1},1{1{1}} 1{1,1{1}} etc
where 1{1} is 2, 1{1{1}} is 4, 1{1,1{1}} is 8, 1{1{1{1}}} is 16, 1{1,1{1{1}}} is 32, 1{1{1},1{1{1}}} is 64, 1{1,1{1},1{1{1}}} is 128, 1{1{1,1{1}}} is 256, 1{1,1{1,1{1}}} is 512 etc.
In base 3 exponential we would have 1 2 1{1} 1,1{1} 2,1{1} 2{1} 1,2{1} 2,2{1} 1{2} 1,1{2} 2,1{2} 1{1},1{2} 1,1{1},1{2} 2,1{1},1{2} 2{1},1{2} 1,2{1},1{2} 2,2{1},1{2} 2{2} 1,2{2} 2,2{2} 1{1},2{2} 1,1{1},2{2} 2,1{1},2{2} 2{1},2{2} 1,2{1},2{2} 2,2{1},2{2} 1{1{1}} etc
where 1{1} is 3, 1{2} is 9, 1{1{1}} is 27, 1{1,1{1}} is 81, 1{2,1{1}} is 243, 1{2{1}} is 729, 1{1,2{1}} is 2187, 1{2,2{1}} is 6561, 1{1{2}} is 19683 ... while 1{1{1{1}}} is 3^27 = 7625597484987 etc.
Of course this number system notation would only be particularly useful if we found pretty straightforward ways to add, multiply and hopefully exponentiate such numbers. Adding them is mostly straightforward, although it's a little bit tricky when we must carry over. Multiplying them makes it necessary to sum over all terms we get by multiplying two sums, although multiplying two such terms is merely the same as adding their exponents and multiplying their digit multiplyers, of course we need to carry over sometimes as well.
42 is better displayed as (4x10^1)+ (2X10^0)
And 42199 is (4x10^4)+(2x10^3)+(1x10^2)+(9x10^1)+(9x10^0)
This notation allows us to change the base with ease.
Any base 2 number is always going to be a better base, 2,4,8,16,32,64, etc
I like the fact you used the babylonian notation in your thumbnail to represent one. No doubt the representation was amazing too.
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. ;)
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.
Thanks. Nice explaination
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
Finally a good math video that I was able to understand :).
Wry nice production (props, etc.). The work shows!
Gosh, you are so easy to listen to and watch- and to follow - thank you! (PS - I will have to watch again a couple of times to REALLY understand, but that's because I'm old and slow, and you're young and quick - but I love your programmes) Old Pete x
The base 12 system has a lot of advantages about fractions.
1/3 wouldn't be an infinitely recurring decimal like 0.3333..., but actually 0.4 (because a third of 12 is 4).
1/4 would be 0.3 and 1/5 would be the first one being a long decimal 0.2497... but it's not as commonly used as 1/3.
1/6 is short again (0.2 instead of 0.1666...)
I think that dozenal is actually worse in fractions than decimal.
Yeah, it can write 1/4 as 0.3, but it isn't really necessary, because if base is even, then 1/4 will always be written with 2 digits maximum, because it's just a half of a half.
1/3 in dozenal is 0.4, and in decimal it's 0.(3), which is worse than dozenal, but still pretty good. Because it's just 3/(10-1), it's just 1 digit recurring. Every fraction of 9 can be represented as one digit recurring.
In dozenal 1 recurring digit is a fraction of B (decimal 11). You still can write 1/11 as 0.(09) in decimal tho, because it's 1/(10+1). Similarly, 0.(0B) in dozenal is 1/11 (decimal 13).
But 1/5 is absolutely awful now, it's 0.(2497), you just can't use it anymore.
Dozenal makes thirds, fourths and thirteens be written a little simpler in cost of absolutely destroying fifths. It's just a bad idea.
Also, there's a base that makes thirds easier while making fifths possible, it's base six! Actually in it you can write sevenths as well. 1/5=0.(1) and 1/11=0.(05). I think this is the best base in fractions that is smaller than tridecimal, which is base 2*3*5.
But then 1/5 doesn't have a non-terminating expansion.
@@KrasBadan thirds and fouths are like a hundred times more common than fifths, so I think that's fair. Especially for thirds
@@huawafabe the thing is that it's already pretty simple to write thirds and fourths. Two digits and one digit recurring. In dozenal it's one less digit for fourths and isn't recurring digit for thirds. But it's 3 more digits recurring for fifths. 5 is the third most common prime, so while not being as common as 3, still really important. Decimal makes it possible to write both of them relatively simple and dozenal chooses only one. And yeah, it's more common, but not nearly a 100 times.
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!
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.
Hexa-decimal system is so common in the software world (bit-splitting is easier due to the use of base-16 (2^(2^2)=2^4=16) system. If that's not compact enough, base-64 encoding is more compact and very popular in the web-technology world. Same in bio-informatics and genetics world (e.g. base-4 (DNA/RNA bases) and base-64 (codons => amino-acids/proteins) from genetic-code (transcription/translation and gene-expression etc.) to protein-folding problems (Check out Alpha-Fold ML).