The Nugget Algorithm
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- čas přidán 23. 06. 2019
- The Frobenius Number -- also called the McNugget Number -- is the highest number you can’t make out of two integers that have a greatest common divisor of 1. This late 19th-century math quirk was examined by Ferdinand Frobenius and expanded on by JJ Sylvester, but it came to public consciousness by examining the impossible orders of McDonald’s McNuggets in the United Kingdom.
Poring over the possibilities of ordering chicken nuggets might seem like a trivial affair, but the concept of the Frobenius Number appears in important aspects of real life. It’s the beginning of thinking about optimization in certain areas, like the coin-based currencies we use worldwide. What denominations of coins are best mathematically? Which combinations fit best with how humans actually think and live?
And that’s how we started thinking about whether the United States could need an 18-cent coin.
By looking how we can combine nuggets and how we utilize coins -- including a “greedy algorithm” that helps us select the method in which we make change -- I found that sometimes the most optimal mathematical way of doing things just isn’t the right fit for how we navigate the world.
** LINKS **
How To Order 43 Chicken McNuggets by Numberphile
• How to order 43 Chicke...
Chicken Nugget Numbers by DataGenetics
datagenetics.com/blog/august22...
Jeffrey Shallit
cs.uwaterloo.ca/~shallit/pape...
What This Country Needs is an 18 Cent Piece by Jeffrey Shallit
cs.uwaterloo.ca/~shallit/Pape...
Formula For the Frobenius Number In Three Variations
web.iitd.ac.in/~atripath/publi...
** VSAUCE LINKS **
Vsauce2 Links
Twitter: / vsaucetwo
Facebook: / vsaucetwo
Hosted and Produced by Kevin Lieber
Instagram: / kevlieber
Twitter: / kevinlieber
Podcast: / thecreateunknown
Research And Writing by Matthew Tabor
/ tabortcu
Editing by Aspect Science
/ @tommocarroll
Huge Thanks To Paula Lieber
www.etsy.com/shop/Craftality
Select Music By Jake Chudnow: / jakechudnow
#education #vsauce2
Missed the perfect opportunity to use the dipping sauce packet as a substitute for the word 'sauce' in the outro logo.
if he put it in a v shape it would be 10x better
@@gorneth8313 no because it's not the S A U C E
@@Platinum_XYZ But then...
*the V is made out of sauce*
lol
@@gorneth8313 it will be a V-sause
=D
Can I get some Vsauce to go with my 43 McNuggets?
That will be 69 dollars
@@Joe-kp5yr and 63 cents
$1.02
ew
*Vnuggets
The limit is 412
“Man paralyzed after eating 413 chicken nuggets”
Dont forget he was local
And he was specifically from Florida.
@@matthewallen9072 Yes this is how math works
WHAT IN THE NAME OF HYLIA
homestuck
Manager: Oh just give him one extra nugget, jeez.
yay free
That feeling when you get an extra nug is like no other
Oh pwease give me a Vsauce too *PWEASE*
@@therealspookspeak yay
If you did this 43 times with a manager that didn’t find the extra nugget a big deal, you could would buy 43 meals and get 1 free
"Taking you Pickake swinging side to side"
chicken nugget and a biscuit song
*_Kevin is truly a man of culture_*
Aw man...
Good thing it’s not a fortnite pick axe
bruh he watches corlson religiously
sgop gdtting lieks
*PICKAKE*
The video should be titled “How to torture McDonald’s staff”
"I'd like 43 nuggets, please."
"That's not a menu item."
Better to do this is to wait until your order is bagged to ask for "no salt"
Ever just get an extra nugget? Like, you order 6 but they accidentally give ya 7...
Mcdonalds employee here
43 nuggets don't torture staff because a basket of nuggets have around 42 nuggets and we can drop two baskets at the same time.
No salt is only a huge issue when we are really busy unless you talk about no salt fries.
You get an extra nugget if we are busy and the person is just throwing nuggets in.
If we get 43 nuggets we just gonna give you 4 10 boxes and a 4 box with only 3 nuggets but you'll be charged for 4 anyways
Did I stutter?
McDonald: Welcome to McDonald, how may I help you?
Kevin:
69th like
@@maze7050 no one care
@@maze7050 nice
Kevin: You actually can't...
@@kapyness nobody asked
*starts talking about 16 different coins*
Cashier: *Sweats nervously*
Mom: What are you watching
Me: *optimal nugget, momther* 👁️👄👁
Optimal nungenet consumption
I’m crying lmao
nugget *F R O 🅱️ E N I U S*
Nebelniek playing Minecraft on youtube
👁️👅👁️
i thought you said McMother for a second
I just realized this goes against French laws against Forced Sale
Basically for common products and foods you cannot be forced by packaging to buy more than you want (exception being discount sales), that's why in French stores you'll often see people pulling soda cans out of 6 packs as the law allows us to do so.
So if I order 43 Chicken McNuggets and they tell me I need to buy 44, then I can sue them for forced sale and probably win!
There are countries you can't rip up six-packs? In Germany that is quite normal actually. I wonder if we have a law like that too
I doubt it would work like that. It's the same in a lot of countries. And I also doubt you can buy 1 nugget. There probably is something for that
If that law would generally allow everyone to rip open packages, you could buy half a bag of flour? Or is it just common practice to be allowed to buy individual bottles in civilized countries?
Sue for 1 more nugget
@@SchwachsinnProduzent another american here, that's not what they mean as they mean individual packaging
Me: Can I have 43 nuggests?
McDonalds: Wait thats illegal
4 nugget box: sad chicken nugget noises
You can get 43 chicken nugerts in the UK but not with just the 6, 9 and 20 boxes. Happy meal nuggets have 4
9 + 9 + 9 + 6 + 6 + 4 =43 he was correct with saying any combonation of 6, 9, 20 can not make 43.
but can you order 4.281
Aaron the video came out about a decade ago
@@mrleaf6055 no it didnt
@@mrleaf6055 are you in 2029?
@@MasterofBeats yes I am . But I'm time traveling to the past to warn my fellow humans that in August 2029 the moon is going to explode
Some dude asked me something like this while I worked at a McDonald's. He asked for like 21 nuggets. I just marked it up as 20 piece and gave him an extra nugget.
Lots of good luck will come to your life for that
That was nice of you. I would've charged for a six piece and give him one. Saved the company 5 nuggets, and get super special promotion.
beeing bold is the way to go.
And then you got caught doing that and that's why you no longer work there? :D
@@silkwesir1444 why would they get fired for one extra nugget
0:20 - I see you’re a man of culture Kevin. Great work!
u stole.this comment from above
meeter beeter u meant to say best minecraft song
man its cool to think that all these mathematician's got together to get back at mom by figuring the impossible amount of nuggets for her to buy
As silly as this sounds these videos have changed my life. I was never able to understand mathematics as a child now I am rocking it. Thanks!
No one:
Vsauce: WHAT IS THE HIGHEST NUMBER OF CHICKEN NUGGETS NEEDED TO CONFUSE THE MCDONALDS CASHIER
its Vsauce2.
CL4P-TP #69 It’s still vsauce
@@DrizzyGames or is it
Georgejr Pangan WHAT IS VSAUCE?
@@DrizzyGames when is vsauce
Vsauce2: says there are 4 coins
Half dollars: _sad coin noises_
he did say 'common", there's a dollar coin too
Sakajeweea $1 coins tho
i was once given a dollar coin instead of a quarter in my change at the checkout at the grocery store.
Based Yoshi probably because When the worker was given that coin from another customer, there was no place for it in the cash register, so they just put it in the slot for quarters since they are otherwise the biggest coin, and when they proceeded to give you your change they mindlessly picked up the coin without looking thinking it was a quarter, from muscle memory.
laughs in $50 gold coin
In Bulgaria there are 0.01 , 0.02 , 0.05 , 0.10 , 0.20 , 0.50 , 1.00 and 2.00 levas
(1$≈1.72levas)
Wait, you guys don't use euros yet? Lithuania went to euros in 2014 I think, but before that we had Litas (LT) which had same denominations as levas:) I kinda miss Litas, but sometimes I forget that we even had it:D
Good on Bulgaria for keeping their own system of currency.
9:17
"It turns out that sometimes what's best for math isn't best for everyday life."
No! I refuse to believe that!
In 1870 french milit- *No Stop*
Vsauce 1: cool math and science shit also mind field
Vsauce 3: Cool science applied to pop culture and video games
Vsauce 2: THE CHICKEN MCNUGGET NUMBER
HarryV Renegade angel vsauce 1: *Cancled*
So basically Vsauce 2 is the best
So true
chimken nunget
Or: Vsauce 2: the science of MEMES
Oh my! Is that a 47¢ coin I see lying on the ground!? Today's my lucky day!
Props for using the cent-symbol. It's not right in plain sight anymore.
¢
@@HollywoodF1 ¢
¢50 > .50
Q: "Is 1-2-5 the best for everything?"
A: "No. In music it's 1-4-5."
he said in mathematics in the video lmao
@@yerwan5799 Plenty of people have made the argument that music is a form of math, but either way, you're missing the point of the joke.
how about 2-5-1?
2019 and I still like all the hidden clips you layer into the videos.
Me: Mom, can i get 73,212,907 nuggets
Mom: yeah sure!
Mom: they didnt have 73,212,907 nuggets so i got you 73,212,908 nuggets
Stonks
That mom is a legend.
Because she got the nuggers
73,212,906
But, mom! I wanted 73,212,907
T O O M U C H ! ! !
Me: Tries to stump mom with an order of 43 in the UK
Mom: Orders 45 and eats 2.
Me: Pikachu face.
+VagueReferenceHere We can actually do it, now, since we have packs of 4 nuggets for Happy Meals!
9 + 9 + 9 + 6 + 6 + 4 = 43
@@cosmicjenny4508 Numberphile?
@@cosmicjenny4508 Y not 20 + 9 + 6 + 4 + 4, it's much simpler
+Konnos Vatamidis Because that’s the one I copied from the Numberphile when they first said it.
“You wanna make things difficult for her cause she cancelled your realm subscription”
if that isn’t me-
Mom: here is you’re chicken nuggets!
Me: let me tell you something
*says everything in the video
Interestingly on topic here - there is a chicken tender place (Laynes in College Station, Texas) that prices all of their meals, sides, and drinks in such a way that with tax (of 8.25% here in Texas), the total of your meal will always come out to end in a combination of a quarter (.00, .25, .50, or .75). It makes paying with cash super easy and you only ever need bills and quarters - no dimes, nickels, or pennies.
A buddy and I had a debate/thought experiment back in our college days (longer ago than I care to admit) about getting rid of change entirely. This could be done at the register by just rounding the amount to the nearest dollar. He argued that store owners might price their wares so it would always round in the favor (e.g. $1.51), but I argued that it would it would be difficult (thought maybe still possible) to create a price system for multiple items that would still be in the store owner's favor.
I postulated a better system where the cash register would take the final price and use a random number generator to decide whether to round up or round down. (e.g. $1.99 would round to $2 with probability 99/100, but would round down to $1 with probability 1/100.)
I feel like electronic transactions are making this conversation less and less relevant.
It is actually a feature in australia that the sales tax is built into pricing, so most things you are generally paying like $8.76 but the sales tax brings it up to an even $10.
@@mistriousfrog This is how it should be done, I'll talk to my aussie pal about it
I can't believe many countries don't do stuff like this. It is literally basic math and you need very few changes. Just prohibit certain prices and make rounding fair so it goes both up and down. Now you have a more efficient system where you can eliminate low-value coins
@@kevinjohnson4531 Not so sure whether I would like not knowing what I will pay in the end and I wouldn't like gambling in every transaction either. For some people a chance of 0.05 of paying an extra $1 could ruin their day or mess with their calculations.
And without the gambling the store owners would have to price their wares to round in their favor. To an extent that they can never be screwed, because every loophole would be exploited by customers. You buy 2-3 items at the store and would pay $4.75? Let's get some free chewing gum on top. It would be dumb not to do that and I am not even talking about people going into the store calculating every item price to get the best out of it.
You just want to buy a bread roll from your bakery? It now is either free which screws the bakery or more likely needs to cost $1.
I would agree that the difference between a single cent or two (and maybe even 5) at the end of a transaction is so insignificant that we could get rid of everything under 5ct. Very cheap items (e.g. screws) are already calculated with fractions of a cent. So if you buy 100 screws it could still be 100x2.75ct and only the overall price would be rounded to the next 5ct.
But the difference between paying 1ct and $1 is way bigger and does make a difference for the customer and the store owners.
I’ve been waiting for the Vsauce 2 and CaptainSparklez crossover for so long, and now that it has finally happened, I can say that it has definitely been worth the wait.
i definately concur
Who?
Ever heard of the CZcams CaptainSauce?
Someone post this on the CaptainSparklez subreddit.
@@bertberw8653 ahh, the new generation of the youtube viewers
well technically , if you had 100 different coin types , each having a denomination of every possible change combination possible , it would further decrease the 'avg coins' needed for any and all change scenarios to a mathematically startling 1 . you will never have to search for combinations and you will always have the best solution for any 'greedy problem' you may have .
but as explained outstandingly by kevin , this 'highest mathematically efficient' method will be 'poorest socially efficient' method .
i loved this video .
I absolutely love how he put a revenge by captain sparkles reference in there
You know what's more efficient than 3 18c coins?
1 54c coin
Ya if we a coin for every number 1-99 we only have 1 coin per transaction. Big brain.
@@Drogon7102 *ban coins*
@@Drogon7102 IF WE HAD 1 CREDIT CARD WE COULD MAKE ANY TRANSACTION WITH 1 CREDIT CARD
@@Xnoob545 the floor is made out of floor
"You've been grinding in the mine all day with your pickaxe swinging from side to side."
_CaptainSparklez wants to know your location_
*_Satan wants to know you are location_*
@@thealbinotadpole2878 ew go away
Shiny sylveon M.L.G. *I WANT TO KNOW YOUR LOCATION*
The Albino Tadpole thanks for correcting
I want to know who uses a pickaxe by swinging it side to side?
Nugget can definetely make his Nugget cave with those warm and soft nuggets
What I love most about math is that things that often seem pointless with out current knowledge, often become very important with new technological advances. For example, the tailor and maclaren series seem useless beyond being neat, but with the invention of computers, they have become extremely useful. This is because it is much easier to program a formula (such as anything using sin, cos, or tan) if you expand it to the point of repetition with one of the aforementioned series expansions.
Iron: iron nuggets
Gold: gold nuggets
Diamond: mcnuggets
emerald: wheat nuggets
Redstone: dust nuggets
dirt: wendy's nuggets
After nether update: netherite nuggets
@@jan_sipiki DAYUM SON
Clicked on this video by accident, but y’know... happy little accidents
Welcome! Follow us down the rabbit hole of magical new perspectives on science!
I smell a Bob Ross quote.
Good job.
Good.
Job.
I relate
Felix culpa is what you can call this experience, to sound fancy
@@heathenfire fancy
I watch this guy all the time and he normally amazes me, but this time he broke my brain. I never thought chicken McNuggets would be so confusing
Thank you for the video! All of you friends are super awesome!
I liked the video just because of the minecraft meme at the beginning
*because
@@OutstandinglySteve *beecuz
I LIKE
*Vsauce2 music* I liked this comment becuase I liked this video becuase of the minecraft meme at the beginning.
@RayRexDex wiat waht ddi yuo say
"Vsauce! Kevin here."
All of Michael's viewers: *You weren't supposed to do that.*
Lol
RunningAmpharos I like ur name
It is funny
I watched this entire video waiting for him to take a bite of nuggs.
There was no other reason.
Instructions unclear, accidentally stuffed 43 chicken nuggets down my friend's throat. He's asleep now, what should I do?
Well you're wrong. Half of the time you order 10 but get 9.
zeek Maybe the cashier was hungry. Or you were so hungry you didn't even realize you ate one or two.
@@Sillytake1705 that's what my dad says when my cheeseburger is half beaten
I once ordered 6, got a box of 9 but there were 10 in it
@@yeetusmcgeetus4946 That cheeseburger prolly deserved it for talking back.
@menohe everybody gangsta till the cheeseburger starts talking.
Me: I would like 42 nuggets
McDonalds: thats illegal
Me: I would like 43 nuggets
McDonalds: *aNYthInG eLsE?*
Pretty sure you got your numbers mixed up
Me: can I have sauce?
Mcdonald's: sure what sauce?
Me: Vsauce
Mcdonald's employee from Czechia: (｀∇´) "yes"
@RunningAmpharos did you miss the bit in the video where it said that 42 was possible? o.O
Some counterfeiters make $18 bills, but are unsure of where to pass them off. They decide to try at a hillbilly's store in backwoods West Virginia. They go in and nervously ask for change on one of the bills. The cashier happily says "Sure! Would you like three $6's or two $9's?"
Here In Australia, we have a 5, 10, 20 and 50 cent coins. We do also have a dollar and two dollar coins, but I feel like the cents were more relevant, also, in notes, we have 5, 10, 20, 50, and 100.
Isn't it weird, that the notes are 5, 10, 20, 50, 100 but the cent coins are 5,10,25,50? In Germany we have 1,2,5,10,20,50 Cents (other Euro countries started to remove 1 and 2) The Euro coins are 1,2,5(only for special occasions),10(collector pieces made out of silver), The notes are 5,10,20,50,100,200,500 (I think 500 doesn't get printed anymore, somehow it was more or less only liked by Germany). It feels more consistent.
Australia was smart to eliminate the penny. Here in the U.S. you always end up with tons of them and they are basically worthless. I literally don't think there is anything you can buy for less than 5 cents so we should eliminate it as well and just round to the nearest 5 cents. I believe Canada is phasing out their penny. They also replaced their 1 and 2 dollar notes with coins. We have tried the $1 coin here multiple times and it never takes off, nor does the $2 bill. Personally, I would also like to see us go to a $1 coin and $2 bills and get rid of $1 bills.
I'm glad after showing the optimal coins, you explained why theoretical efficiency doesn't always translate 1:1 to real life. It helps make people sound more well-rounded and knowledgeable about these kinds of things.
Vsauce2 sang the CaptainSparkles Parody at the start.
A man of culture I see
"And you cant order 73,212,907 nuggets"
" *NO* "
Missed the opportunity to replace "sauce" with an actual sauce box
Personally, I tend to hand over smaller denominations of coins and bills first so that my wallet is thinner
Before watching video: Aw a Vsauce video about a "Frobenius", I guess I won't understand anything
After: nüget
nüget
nüget
nüget
ñüğəţ
nüget
In school I got a math problem about this involving 3 and 20, couldn’t figure it out because this equation didn’t seem to work
After watching this video for 3 times, I finally understand this.
Kid: "I want 31 nuggets! I bet you can't get me that many, mom!" 😝
Mom: *buys 32 nuggets and eats one*
Kid: .....
I would like this but it's on 69 likes and I don't want to ruin that
im pretty sure vsauce just became a giant meme now LMAO
did you vsauce micheal in d!ng he is the meme
Have you watched a VSauce video since 2014 @midlowreborn ??
i've been subbed to vsauce since the start LOL, but in 2017/2018 they started memeing around more
yes yes vsauce gamer meme
midlowreborn hes been a meme for years you normie
I've always been bad with math so thanks for all your videos
I love the reference. So much that I'm gonna cry
What a delicious thought experiment! Always love seeing a Vsauce upload in my feed.
fEED
45 nuggets? I see we have an amateur here
Fawks Masters you can get 45 🤨
Rhys Davies 0:02
45th like on this comment I would say I'm above average.
Dan Doom above and beyond, my friend. However, to be fair. i was the first like on the third comment. Not to mention the fact im the 4th comment and first like of the aforementioned comment. 1st like 3rd comment = 4, 4th comment 1st like = 5. 45, 45. I guess in a way, we are all special, except the OP, screw that guy
I wanted 69 nuggets :(
This is highly relevant to the E series of preferred numbers.
The starting example hit closer to home than it should have...
God I fucking love when you put the abstracts of proofs in your videos. And the fact that you are delving into computer science and displaying it in a way that other people find interesting. It makes my brain tingle. You don't know how nice it is to see someone articulate concepts we study in the degree at a level that others will understand and be captivated by. It allows me to show friends and actually have a dialogue, and show them a look into what computer science is, rather than the void of mt dew and hacking that they perceive it to be. Thank you for everything. Much love.
What kind of child-exploiting scenario are we talking about here, where the mom buys nuggets for her mining son?!
@Ala File Well, can't argue with that.
Considering the inconsistency in the number of nuggets I get vs what I am suppose to get I conclude that any combination is possible.
0:43 reminds me of the time a friend and I decided we would like to have, and I quote "a ridiculous amount of chicken nuggets"
we wanted 2) 50 piece nuggets... they claimed they didn't have them. I sweet talked them into figuring out the cashier side of things and told them we will begrudgingly accept
that broken into 20's and 10's or whatever it was at the time.
It was like we robbed the chicken nugget vault and ended up with only small bills.
PS all nuggets were eaten... mine was eaten later but my friend actually ate all of his in one sitting.
wow, Jeffrey Shallit? he was my algorithm prof at university of waterloo
*_mother, i have consumed nugget._*
*_i need more nugget._*
*_GIVE ME MORE NUGGET MOTHER_*
No, I wont
James Gruber *DON’T MAKE THIS HARD MOTHER*
ShubbyShabaas *anime face and avengers theme plays with huge earrape*
*HIDES NUGGET*
But we have nuggets at home.
Nuggets at home: 🥔
It sounds like nugget is saying that. (Kindergarten game)
Why is the opening premise so relatable?
when working drive through and asked for 37 nuggets, I just told the customer that a 40 nuggets (2 20 packs) would be cheaper than any other combination of nugget sizes to get closer to 37.
The larger nugget sizes are (typically) by far cheaper than the smaller ones so it was normally easier (and cheaper) to round up a weird size to something that can be purchased with the bigger packets.
... there was a stage at my store where two 3 packs of nuggets were cheaper than a 6 pack.
I’m gonna take the diamonds over the chicken nuggets
We ain’t living that greentop life
I love Skyrim
SWN-001 Bass
YOURE BREATHTAKING
wtf is a greentop
Sick.. but what happens if the cashier just puts an extra nugget in the box for you.
"This conversation never happen, if you get what I'm saying"
Thanos: “Impossible”
This takes the word hungry to another level.
Fun fact: in Hungary the cost of minting 1 Ft (forint / HUF) was around 4 Fts when it started to lose value against the Euro. Until then we had 1 Ft and 2 Ft pieces. At that point the national bank decided to stop producing coins below 5 Fts, and since then the whole country is using prices rounded to 5s and 10s. And yes, if something costs 99 Ft, you pay 100, but buy 3 at the same time and you can get away with 295.
I so want the curiosity box, but it's almost 5000Rs in India.
That's just too much
Vedraj r.m street shitter
Mc Nuggets are made from organic, British chicken.
*Or are they?*
since when are nuggets only in Britain.. your own country is not the centre of the world
Forget2BHuman I was just quoting a part from our country’s advertisement. I could of used any country but I was just using the ad that I was familiar with :)
You can absolutely mathematically optimize for the stated "daily use" case. Just count the number of arithmetic operations a human has to do to figure out the change and weight each by a time. Then weight some time for dispensing each coin. Sum and minimize that number.
Electronic engineering uses preferred numbers although for a different reason. For example, the E12 series is 10, 12, 15, 18, 22, 27, 33, 39, 47, 56, 68 and 82. There are other series including E6, E24 and E96. They can also be scaled up and down by factors of 10, 100 etc.
These are geometric series with similar ratios between each adjacent number, guaranteeing that you can find a value within 20%, 10%, 5% or 1% of a desired value without needing a huge number of different values.
1.) Introduce a fully customizable McNugget box
2.) Sell at a slightly higher price per nugget
3.) ??????????
4.) *_P R O F I T_*
that would be quite easy to do...
just put the current prices on a graph, figure out a fitting formula and then automatically determine the price that way. needs an upper limit after which the price does't drop further. they could even use the same boxes they use now (maybe add another huge size, like 50), and do "greedy packing" of the ordered Nuggets into those.
The problem is that most humans are using a decimal system, even when other systems like the duodecimal system (base 12) are much more usable.
Yeah, but we have 10 fingers, so it goes back to simplicity
@@Chermaid we could use a 10-bit binary system
@@Chermaid Kind of off-topic, but I wanted to mention that human languages do not necessarily always use base 10. (Ok scratch that "kind of" off-topic, this is definitely off-topic. But bear with me, because I think people who watch these sort of videos would find this interesting.)
First of all, languages spoken by primitive civilizations may not even have a true counting system. Think about it, languages spoken by tribal people who live a hunter's life, hardly ever need to count above 4-5. AFAIK, it's not uncommon for such languages to lack the ability to express any number higher than those. Some cannot even express those numbers properly.
I once read that some languages express high numbers via naming body parts. So a "head" might be 15, a "right shoulder" might be 26 and so on. If I remember correctly, these languages can often express numbers up to roughly 30. I don't how common this is though.
Now of course, once the civilization advances, a more complex system is necessary. This is often (always?) done by a base system. However, even then base 10 isn't the universal choice. According to what I've read, the most common choices are 8, 10, 12, 20. 10 is pretty obvious, it's the total number of fingers. Although it definitely isn't universal, if memory serves, it is the most common. And 20 should be the second most common, though again, that's if I remember correctly. It's been a long time since I last read about this. 20 comes from counting both the fingers and the toes. Ancient Mayans used a base 20. Among base 8 and base 12, I'm not sure which is more common. Base 8 comes from counting the gaps between the fingers, rather than the fingers themselves. Base 12 is a bit more complicated. It comes from using your thumb to point at the knuckles of the other fingers. There are 4 other fingers with 3 knuckles each, resulting in base 12. Also as mentioned earlier, base 12 is actually easier to use, but I don't know if this had any significant effect on the number systems found in the world's languages.
A language may also have sub-bases. English has sub-base 20, as numbers between 10 and 20 have special names, though these are also connected to base 10 (fifteen is obviously just five-ten). Eleven and twelve are exceptions to this. Therefore, English also has a sub-base 12. These are no longer base 10, but if I remember correctly, they actually come from Proto-Germanic "one-left" and "two-left".
However some languages can have different systems. Certain languages for example, have base 5, clearly connected to the number of fingers on one hand. This is however unusual, probably because of how small it is, resulting in many digits. (25 would be expressed as 100 in a base 5 system!). Babylonians used a base 60 system (yeesh). The most natural sub-bases for such a system would be base 5 and 12. You can count to 12 on one hand as I explained, and then use the other hand for counting to 5. However Babylonian system seems to use sub-bases 6 and 10 instead (at least in writing). If I remember correctly, these are the people responsible behind 1 hour being 60 minutes, and 1 minute being 60 seconds.
Don't trust me too much though, my memory is a bit blurry, it's been quite some time since I last read about this. I've read this on Wikipedia, but which page exactly, I don't know. Speaking of which, Wikipedia itself shouldn't be too trusted. Anyone can modify it, and while they do check if people have given their sources, I have seen stuff on Wikipedia that were definitely wrong and/or didn't give any sources. So if someone with better sources could clarify this, I would be glad. Thank you.
Also thank you, the reader, for reading all this, even though it's completely unrelated to the video. You must be a great nerd! I would like to know you! (lol)
@@KineticManiac wow that was a lot. It's pretty interesting learning where a lot of the most popular numbering systems came from. I don't really remember what this vid was about (and am too lazy to watch again haha) so I'll just say props to you for taking the time to share your knowledge of the subject. Impressive!
@@KineticManiac the base 60 system isnt that complicated, you have 3 bones in each finger and each finger has 2 sides. 3*2*10 = 60. for the thumb you can count the palm or back of your hand. so its actually quite convenient for ancient peoples who didnt have any type of calculators and counted on their hands. oh and im an artificial intelligence programmer lol
This was really nice.
I can’t believe it. I’m actually having fun learning
This number is made with only 70% inorganic material
0:17 Ahh, I see you're a man of culture aswell
Ikr
No
Lol
Lol
I wrestled with something like this a while ago when my roommate and I were trying to think of the domain of possible football scores
Those calculations also likely assumed that you always had enough of every denomination of coin to optimize the transaction. However, if you were to implement the 16 denomination system, the likelihood of not possessing every denomination coin during a single instance rises drastically, making things less efficient.
Assume you are in the drive through.
Easy fix: 2 boxes of 20, and 1 box of 6
The cashier accidentally drops 3 on the ground between the window and the car.
43
Ad : Can you hit the skip button? This is-
Me: skips ad
Kevin: Vsauce! Kevin here
THIS IS A SIGN
i love this man
I'm watching CZcams and eating chicken nuggets and then I see this video
perfect timing
I always appreciate your quirky presentations of interesting math topics (although the chicken nuggets made me a bit hungry, processed as they may be). Also, thank you for reminding me of the word "anaglyph." :-D Peace, Shan
0:57 I honestly wouldn't have noticed
My heart raced as he started to say SIDE TO SODE
I don't understand this man, but I still wanna watch his content
0:58 probably spilled vsauce lol
3:22 I want somebody to order 73,212,907 Chicken McNuggets just for.. y’know.. the memes.
That'd cost you $16,092,196.96, but if you have a lower social credit score it may cost more.
@@xijinping5937ni hao, wo renshi gaoxing!
It's interesting how different nations have different coins.
Australia used to have 1c and 2c coins until somewhere in the late 80's early 90's. People were collecting them and cashing them in since they were being made obsolete. Now, Australia has the 5c, 10c, 20c and 50c coins left. Unlike USA, with it's $1 and $2 notes, Australia uses coins. Apart from that, we have the same as USA in notes - $5, $10, $20, $50 and $100, but made with a different material, so if it gets wet, there is very minimal damage done to the notes.
Similar to Canada, except for the 50 cent coin, which I believe is only minted for coin sets now and is uncirculated.
problems I noticed that he eventually sort of addressed:
>how easy is it for the average person to count change in their head without using multiples of five?
>would I not rather have some of the most valuable coins and more of the less valuable coins, than only a couple of middling value coins, as I can use the higher value coins for more transactions?
>at this point, just digitize all currency to let computers use exact change calculations, which we're already working on