58 and other Confusing Numbers - Numberphile 

When I trade with my homies in Minecraft, we refer to 64 diamonds as a stack, so I guess we are counting in base 64?

I’m a simple man, I see Tom Scott yelling at a Klingon I click

He‘s basically giving the first few minutes of an introduction lecture to ethnomathematics, which is a relatively young but fascinating, actual field of study.

"…that's a trillion." Not even that is universal, actually. "Trillion" can mean 10^12 or 10^18.

7:20 useful when you go to the doctor: "Where does it hurt?" - "Near 25, sir!"

The Danish language is actually our best defense against invasions.

7:03 he looks like that old meme

1:58 the normal reaction to Danish for a linguist, obviously

Tom Scott really adds to Numberphile! He really opens my mind to a complete new branch of math. I'd love to see more of his.

imagine someone in papua new guinea watching star trek and wondering what a totally weird numbering and language system the klingons have

I am 17 and I still remember in third or fourth grade I had to learn both the system of naming and writings of numbers called the "Indian system" and "International system" ...on one side you guys have "who wants to be a millionaire" and we have " Kaun Banega crorepati". Edit: just to add, RU-vid also displays views/likes in lakhs and crore here..

"og" means "and" in danish. So when we say 58, we actually say "eight and fifty" :)

A correction and expanding on the Danish counting: The system of using _half_ in fractional numbers was originally quite prevalent (and can still occasionally be found), but in Modern Danish is generally restricted to 1.5, which _halvanden_ (‘half-second’). The logic behind this isn’t, as Tom says here, that you subtract a half, as much as it is that in order to have ‘half of the second’, _you need to already have all of the first_. If you go for a run, for example, and you get tired along the way and walk the rest of the way, you might say that you ran half of the third mile, but then you slowed down and walked home. This implies that you ran the first two miles, _plus_ half of the third one. In Ye Olden Times, a Dane might well say, then, that he ran _half-third_ mile: all of the first two, and then half of the third one. This is exactly how counting in Danish works, except instead of miles, it’s twenties; or rather, it’s _times twenty_’s. The word for fifty, _halvtreds_, is a bastardised and cut-down shorter form of what was originally _halv-tredje sinds tyve_, or ‘half-third times twenty’ (_sinds_ is an old word meaning, essentially, ‘×’, i.e., multiplication; and _tyve_ is ‘twenty’). The same is true of seventy, which is _halvfjerds_ (originally _halv-fjerde sinds tyve_), ‘half-fourth times twenty’; and ninety, which is _halvfems_ (originally _halv-femte sinds tyve_), ‘half-fifth times twenty’. Those all involve fractional multipliers of twenty (2.5, 3.5, and 4.5), so they use this ‘half-Xth’ method. Sixty and eighty, on the other hand, involve non-fractional multipliers of twenty (3 and 4), and they therefore have no need of the ‘half-Xth’ method-they are simply _tre sinds tyve_ ‘three times twenty’ and _fire sinds tyve_ ‘four times twenty’. (It has been joked that, to continue the trend, the Danish word for a hundred ought to be _fems_, but it’s not, because that would just be odd.) Or at least, that’s what they all *were*, a long time ago. Some syllables have been chopped off since then-quite understandable, really, given that ‘78’, for instance, would have been _otte og halv-fjerde sinds tyve_ (‘eight and half-fourth times twenty’), which is quite long. First, the final _‑e_ in all the ordinal numbers (_tredje_, _fjerde_, _femte_) got kicked out (in the case of _femte_, the t got booted along with it). Around this stage, people sort of stopped thinking about the maths behind it and just perceived it all as words for numbers, and they started treating them as single words, rather than phrases-writing them as single words, and pronouncing them with only one stressed syllable. That left us with _halvtredsindstyve_, _tresindstyve_, _halvfjerdsindstyve_, _firsindstyve_, and _halvfemsindstyve_. Eventually, people realised that-since Danish puts the ‘ones’ (i.e., the numbers under ten) first and multiples of ten are always last-every single number that ends with a number in the 50-99 range was pretty annoyingly long and also ended in _‑sindstyve_. Kind of pointless to have half your numbers end in the same three syllables-that’s just useless crud. So those three syllables gradually got shaved off at the end, too. The only thing that was eventually left behind is the initial s in _sinds_: we now have _halvtreds_, _tres_, _halvfjerds_, _firs_, and _halvfems_, which one might semi-seriously transpose as ‘halfthirdt’, ‘threet’, ‘halffourtht’, ‘fourt’, and ‘halffiftht’. This is of course much simpler and much quicker to say, and you also don’t have to worry about the maths behind it-just learn the words. Most Danes, indeed, are quite unaware of this complex history behind the numbers they use every day. Ordinal numbers are still a bit of a problem, though. Danish is less consistent in how it creates ordinal numbers than English, which uses _‑th_ for all ordinal numbers above three: - one to three have their own quirky ones and are irregular; - four uses _‑de_ and a different root vowel; and the d in _‑de_ is not pronounced anymore - zero, five, six, eleven, twelve, thirty, and million (plus milliard, billion, billiard, etc.) use _‑te_, though six is quite irregular, too: _seks_ → _sjette_ - hundred and thousand are the same as their cardinal numbers (_hundrede_ and _tusinde_), although the cardinal numbers frequently drop the final _‑e_ in the singular - seven, eight, nine, ten, and thirteen to twenty use _‑(e)nde_ Back when all the 50-99 words ended in _‑tyve_ ‘twenty’, the ordinals naturally ended in _‑tyvende_, because that’s the ordinal for twenty. In more formal and traditional language (and even in normal, everyday language to some people), they still do. To me, for instance, the ordinal number to go with _halvfjerds_ is _halvfjerdsindstyvende_. That appears ridiculously irregular on the surface, though, and many Danes have come up with simplified ordinals, using the apparently impressionally most common and ‘regular’ ending _‑ende_: _halvtreds_ → _halvtredsende_, etc. I expect in time, these will win out, but to me, they just sound bizarrely wrong, like saying ‘oneth’, ‘twoth’, and ‘threeth’ in English instead of ‘first’, ‘second’, and ‘third’. Congratulations, by the way, if you managed to read all this. You now know more about Danish numbers than you ever cared to. ;-)

A group of Romans walks into a bar. One of them holds up 2 fingers and says "Five beers please".

you lost me at "half thrice times 20"

I would like to give some more information on the Tongan counting system. While it is true that for brevity people mostly just say each digit of the numbers individually so that 771216 is “fitu fitu taha ua taha ono”, that would be pretty confusing since you would have to remember how many numbers were said to know the size of the number. Tongan has words for 10, 100, 1000, and 10,000 (hongofulu, teau, aafe, mano) and there are variants such as 20 and 30 being uofulu and tolungofulu, but these words for multiples of ten are too formal and are usually not used. 771216 would likely be said as fitu fitu mano tahaafe ua taha ono. (if you want to be formal you would say fitu fitu mano mā tahaafe mā uangeau mā hongofulu mā ono) The year 2019 is always said as uaafe taha hiva rather than ua noa taha hiva, for example.

The 'og' in 'otteoghalvtreds' actually just means 'and' :)

I'm an anthropologist, so I really REALLY appreciate this linguistic content on this channel. Just so you know, not only Papua New Guinea (which is really the holy grail when it comes to linguistic and cultural isolates) but also Amazonia has some interesting counting and number systems. They also use the body count system where you go around your body. There is a graduate student doing his thesis on this subject of counting systems in Amazonia at the London School of Economics!

1:42 I'm sorry, did he just push up his IMAGINARY glasses?

Keep Calm and Kling On, probably the only "Keep Calm and..." joke that I've actually thought was funny

"I apologise to Denmark" Welcome to the opposite of a Lemmino video.

Tom referenced the Star Trek: TNG episode “The Chase” when he mentioned all species came from the same ancestor... that’s pretty a deep cut.

@ Star Trek, one of the old pc games they had a Mission involving two ancient races with different numeric systems, base 3 and base 4 and you had to solve a riddle involving 'translating' information between the systems. I found it really cool back then and though what could have been the reason for it.

"We've agreed on Arabic numerals now" - writes a 7 the way many Europeans write 1.

"otteoghalvtreds" or in other words "I have never heard of a functioning number system"

Speaking of fiction: the elves in LotR and Tolkien's other fiction use base six and twelve. The word "Menegroth" (an important city/palace in the Silmarillion) is translated as "Thousand Caves", but probably means (12 times 12 times 12) "1728 Caves" (or, more likely, the word just means a generic very large number to get the point across that it's a big underground palace/city).

1:03 that makes so much sense, I would always think “the Declaration of Independence was signed way more than 47 years before the civil war”

You don’t even need to go so far as China, even in American Sign Language 6-10 are still shown with a single hand.

I want Languangephile or Linguistphile... first video: what's the proper name?

I love how he is so enthusiastic about it, he really brings over the energy

"Super Bowl L" 😂

I love rewatching this video every year or so. It was probably one of the first things to really open my eyes to the weird and wonderful world of linguistics and culture.

Count up to 2047 on just your fingers with one simple trick! CS majors love it, and you’ll hit every possible state your fingers can be in! All you have to do is count in binary!

Reddit discussion: redd.it/2y505w

5:54 Actually in India we group them in twos till Crore and then we group the zeroes of the crore(i.e 1 crore ,10 crore , 100 crore) and we follow the same pattern of twos after that

I have been a numberphile subscriber for over 6 years this is the most intriguing video I've ever seen. Word people doing numbers is amazing. I love this. Thank you.

Tom Scott in Numberphile? How had I not seen this before? I LOVED it!!

"Watch a british guy try to explain crore and lakh" should have been the name of the video. LOL

Awesome video. Love the energy and the genuinity that is transmitted, also how the admiration for the things you explain come across... If that makes sense.... :)

6:05 as a person who did grow up with that system, I find the usual thousand seperator more convenient.

When I was in first grade I learned a system of counting on my hands called Chisanbop. You use the 4 normal fingers of your dominant hand as digits 1-4, thumb is 5 so you can count up to 9 on one hand. the other hand is the same except multiplied by 10. you can count up to 99 on your fingers.

I count my fingers in binary. Since I have 10 fingers with two possible states (down and up), I can count to 1023 on both hands. You could say it's pretty... handy. Note: I can count to 31 on one hand. Just so you don't have to do the math. I consider the states 'down' and 'up' as 0 and 1 respectively, the first finger is 1, the second is 2, third is 4, fourth is 8, etc., and you just have to add up the values.

Otteoghalvtres "that's numberwang! "

I developed my own way of counting on my hands. Right fingers are 1, right thumb is 5. Left fingers/thumb are 10/50. So I can count up to 99 on two hands. I've been doing it that way for years, and it's just second nature/muscle memory for me now.

I have a friend from Norway and when he visited I said I would meet him at 'half 3' - he turned up at 14:30 i.e half of 3 o'clock. I turned up at 15:30 - he was a bit grumpy.

the "og" in otteoghalvtreds means "and"

I've just gone full circle. I was watching Tom Scott's channel. Something interesting popped up in the suggestions, from The Map Men. This led me to a Numberphile video. And that led me back to Tom Scott.

Great video, thanks for putting it together. It was my understanding that Klingon was base 3 until they met other species. They switch to base 10 to keep interactions easy. I think I got that from a Michael Okuda book

So happy to see Tom Scott!!

Watch the words: English: Million: 1,000,000 Billion: 1,000,000,000 Trillion: 1,000,000,000,000 Quadrillion: 1,000,000,000,000,000 German: Millionen: 1.000.000 Milliarden: 1.000.000.000 Billionen: 1.000.000.000.000 Billiarden: 1.000.000.000.000.000 ...and only THEN comes the german trillion (Trillionen). We also use quad and quint but way later because we have 2 "stages" for each of them.

Me: _sees Tom Scott in the thumbnail_ Also me: :O

The thousands separator often confused me because where I'm from, we simply do not use any thousands separator. Sure in textbooks the groups of three will maybe be slightly separated by a little space, but that isn't universal. And when writing by hand or typing on a computer, we leave no spaces, we put no separators, one million is simply 1000000 and that's it. So in fact, not even the very existence of the separators are universal, some don't use any :) Edit: grammar :P

In Greenland we have a very wierd counting system: ataaseq (one), marluk (two), pingasut (three), sisamat (four), tallimat (five), arfinillit (six), arfineq-marluk (second six), arfineq-pingasut (third six), arfineq-sisamat (fourth six), qulit (ten), aqqanillit (eleven), aqqaneq-marluk (second eleven), aqqaneq-pingasut (third eleven), aqqaneq-sisamat (fourth eleven), aqqaneq-tallimat (fifth eleven), arfersanillit (sixteen), arfersaneq-marluk (second sixteen), arfersaneq-pingasut (third sixteen), arfersaneq-sisamat (fourth sixteen), inuk naallugu (twenty, which literaly means 'the whole body' (fingers and toes)). I think it is in base 5, idk.

You can also count with your fingers in base two- it's hillariously confusing to people who don't know what you are doing.

Thanks for sharing. I just found your videos and have enjoyed many of them since yesterday.

British folk: Confused at the lakh crore system Indians when we find out about the darn million system: Head implosion

-hey dude -what? -58 -w-wait, did you said 58? It c-can't be... I'm... I'M SO CONFUSED GAAAAH!!!

There are some videos on RU-vid I just can't stop watching over and over. And Tom Scott is in most of them.

6:07 As someone who grew up there, absolute not. The lakh-crore system gets really annoying, especially at higher numbers

I’m learning Japanese and came across this quite a lot! They use a combination of Arabic numerals and their own script (same as China) and their hand symbols are sometimes different too, a closed hand represents 5 and an open one represents zero, so you count how many fingers are DOWN rather than up (however this is purely for counting, not to show one particular number) Also similar to comma separators, they have a word for 10 thousand so instead of saying million you say hundred ten thousand so some maths is required to just translate the words for numbers.

WTF, I thought you were the programmer/encryption guy. Stop switching majors on me!

In Japan, they have a word for ten thousand, which means that one million is spoken as 100 ten thousands.

This is one of my favorite videos on RU-vid. I am compelled to observe that if you count by the phalanges (the bones of your fingers), you can count to 12 on the fingers of one hand, using the thumb to mark your place. This would also mean that it's much easier to represent thirds and sixths in your number system without repeating duodecimals past the duodecimal point, although fifths become problematic.

I'm from South Asia and grew up with the Lakh-Crore system. In school I thought we used to put two digits in each group in the past, but made the last group three digits long because of the British influence from colonial times. But then I learned it had actually been like that long before the Brits came along.

I can't like this video enough

In switzerland soixante-dix is septante, quatre-vingt-dix is nonante and in some areas of switzerland (not all) there's even a huitante which is quatre-vingt Septante comes from old french setante. Huitante comes from old french uitante. Nonante comes from old french nonante. The spelling of this number hasn't changed.

"We have weirder systems that sscience fiction has ever come up with" There is a series of video games, that shaped pretty much the whole genre of puzzle games, called Myst In it there is a language called the D'ni that comes from a people of the same name, and I think they're fascinating Where Klingon is basically a 1 to 1 from english, D'ni has just nothing to do with it on every scale On the langage side, words aren't just 1 to 1, there is a totally different grammar and syntax system and the alphabet is actually phonetic with 35 different symbols that are a combination of 13 unique line paterns But most interesting of all is their number system that is what I'd call a double base 5 There are 25 symbols that you would use as a standard base 25, which in itself is already pretty unique But the 25 symbols themselves are constructed on a base 5 system : There are 5 base symbols from 0 to 4, and (excluding 0) if you rotate them by 90°, it's like multiplying them by 5 and if you take that multiple of 5 and superimpose it with the symbols from 1 to 4, it acts as an adition So to write 87, you first get 3 * 25 + 12, the first symbol is 3 in 25's place, and the second in the 1's place is 12, written as 2 * 5 + 2

Thank you random video popup at 2AM the morning, I am NOW FULLY awake after this amazing and thought provoking video.

I thought he might also mention how the British used to use the long scale billion (10^12) while America uses the short scale billion (10^9), which is now normal usage in both countries.

58 in Danish: otteoghalvtreds - eight*and*half-third 68 - otteogtreds 78 - otteoghalvfjerds (half-fourth) 88 - otteogfirs 98 - otteoghalvfems (half-fifth)

It is the first video I found on numberphile as much as I watched it that signifies/talks about the concepts from India and Southeast Asia .... And I'm really proud to use the number notation system we use in hindi (because I'm really used to it )... Though I like the sanskrit counting much because it feels a lot easier than hindi as you don't have to learn that much about it... P.S. correct me if I'm wrong at any point ...

Thanks, @Numberphile. Big fan of @Tom Scott.

Oh yeah, Danish numbers, the second biggest _"why haven't they changed yet to something more sane yet"_ I encountered while learning Danish. The biggest is that spoken language is nowhere near the written language.

This is hillarious to watch as a dane :D And yes while we mock the US for their imperial outdated measuring, we silently ignore our horrible number system

Great video content but forget that, this is possibly Tom's best ever performance

Finland doesn’t use a full stop to separate thousands; we use a space to do that, we don’t use a full stop for anything, really. But we do use a comma to separate the decimals. For example: ”1 000,72”. 🇫🇮

Congratulations, you've got all the hand gestures from 1 to 10 correctly!

8:27 "keep calm and kling on" 😂

Worth looking at numbers in Sign Languages as well. Apart from the differences between different Sign Languages (Eg British Sign Language and American Sign Language), there are regional differences within them Eg The number 6 in BSL

I guess someone already mentioned it but there's a novel by Niven/Pournelle called Footfall in which the aliens use base 8 because their trunks branch into 8 digits. Made me think about how decimal, octagonal, hexadecimal and such works.

"Keep Calm and Kling On" Glorious.

I can grasp only lakh and crore. even when I read million and Billion, I convert in my mind to get the scale of the number

We in Slovenia have a logic competition, where one of the four questions is in linguistics. In 2019 (we) kids age 12-13 had to figure out what part of the body corresponds to what number like in the Papua new Guinea language.

Btw speaking of tallying systems that might not help with calculus, I actually use binary counting on my fingers. By using up/down for 1/0, I can count up to 1023 on two hands (2^10-1). I recognize you could push that even higher if you use a halfway-raises finger to enable ternary, but I find that a bit hard to keep up stably.

Base 12 is easily counted on one hand using the thumb to count the joints of the remaining four fingers.

Tom Scott in a Numberphile video. You don't know much this makes me happy !!!

This is definitely not as complicated as the number systems mentioned here, but I find it fascinating that Filipinos--or at least, Tagalogs--rarely use Tagalog words for numbers. We might when talking about things fewer than ten, but more than that, we often switch to either English or Spanish. We use English in casual conversation, but when talking about money, or time, we often use Spanish until we reach a hundred. At a hundred or more, we often use English.

I'm Danish, and I never figured out why the word for "Fifty" is "halvtreds" when the word for "sixty" is "tres" (pronounced the same, and you never see the spelling anywhere). Which would be 30, not 50. I figured they'd simply changed from a sexagesimal to a decimal system, and borrowed the word for 30 to mean 50. And I knew "halvtredsinstyve" was a word, but I thought it was a colloquialism, like "fiftyish". This makes so much more sense... Except for the weird "half" meaning "the next number minus one half". One just gets used to the nonsensical things about language. I'm happy to know that people think Danish is funny. ;)

I enjoyed this video way more than I should have...

One of the most mind blowing videos I have seen since ages.

"The truth, as always, will be far stranger" - Arthur C Clarke

Koreans count in "ten-thousands" or Man- Eok, etc 1.0000.0000,00

The 'Chinese hand gestures' can vary quite a bit depending where you go and who you ask (btw he did them quite well). I believe those originated from accountants and merchants who didn't want competitors overhearing their conversation, so naturally there was no nation wide standards.

Of all Numberphile videos, this was one of the most interesting for me.

Yeah man, love Tom Scott. Even after all these years, his style is on point.

It's so strange that this video came out, i was just pondering this yesterday... I'd say that numbers are universal because they can be converted from any base with 100% accuracy. The same isn't true for words. Numbers retain their meaning forever, as words can change, take on new meaning, and so on. Metric and Imperial is a great example of this, you just need to be aware that a conversion is required. I don't think you can convert any one language to another with 100% accuracy, you will always lose something in the translation. Sometimes it's very minor, other times it's very large. Usually from cultural influences. I'll use jokes as an example of this. You can translate a joke from one language to another, and even with a very accurate translation, the joke can be lost or just not make sense and all you will see are the words themselves, but not the meaning behind them. Again, numbers don't have this problem. As long as you understand the formula you will always understand the translation. With words, you might not even have a counterpart for a foreign word in your language. But with numbers, there is always a counterpart, with maybe the exception of zero and infinity. (you can't convert 0 into roman numerals but you can add it to them) But zero and infinity are a bit of a gray area. 0 by itself is really the lack of a number and infinity is every possible number. (infinity can be hard to define but i try to think of it as the exact opposite of zero) 0 is a very strange number when you think about it, it would sort of be like considering spaces between words to be a word itself. I think i've thought way too much about this... Anyways, i'd love to hear your thoughts on this (or anyone elses) *Edit* Also as an aside. Numbers are much more static. By this i mean.. If you take English and export it to another part of the world, within just a few decades it may become incomprehensible to the people who exported it due to the fluid nature of words... But If you export a number system to another part of the world, it's will change very little. It could have some new additions to it, but it's core will remain intact. The number 1 will mean the same hundreds if not thousands of years into the future. The symbols likely won't change. This isn't universal but it's far closer to it than words ever will be, or should be.

That was a wonderful blend between language and numbers.... nice... this guy is kinda funny

We did come from a common ancestor, that was the most unexpected zinger, cracked me up so hard.

This is fascinating. I think this is my favorite numberphile video

KEEP CALM AND KLING ON