The Real (Weird) Way We See Numbers 

One reason people might say 99 is closer to 100 than 9 is to 10 is because there is only about 1% difference between 99 and 100 while there is an 11% difference between 9 and 10.

"what numbers are even.. four" really sounds like something Vsauce would say

One little addition: Romans did actually use both IV and IIII to represent 4. Most sundials and sculptures made during the Roman Empire actually use IIII instead of IV.

oh hey! I'm getting a whole PhD in this! this is what my research is all about! I'm going to have to use this video to easily explain the first 80 pages of my dissertation to everyone the rest of time.

1 fish, 2 fish 3 fish, 1 school.

My native language (Slovak) has different plural cases depending on the amount of things. Two, three and four "things" have a different word than five or more of the same "thing". Singular, plural 2 to 4, and plural from 5 and more. This messes up many translations of various programs that are programmed with either one singular or one plural word when displaying a result. In all cases so far they are grammatically incorrect. Like "items in basket". English has just two cases: item and items. Slovak (and other Slavic languages) has three cases: item, items up to 4 pieces and items of 5 pieces or more.

I wrote a PhD thesis about this in 2017! There's so much more stuff to discover in embodied cognition. A fascinating subject that really contrasts with our cultural representations of how human minds work. Nice to see this in a Be Smart video!!

As Terry Pratchett's trolls count: one, two, many, lots.

It's like I always say, there are 3 types of people in the world: those who can count, and those who can't.

Speaking of babies and counting, at home we listened mostly rock, pop, and jazz in 4/4 time. I once played "Take five" from Dave Brubeck which is in 5/4 and my son (about 3 or 4 at the time) was like "what is happening here?"

As someone who has struggled with dyscalculia my whole life, thank you so much for the validation. It's really hard when teachers tell you just to practice to "do the math faster" and then accuse you of making things up when you say you have dyscalculia. Maybe you could do more videos on learning disabilities? There are so many that people don't know about and the human brain is a wonder.

Reminds me of Watership Down. The rabbits in the book can count to four, but any number greater than for is represented by the same word (hrair). There's a character named "Fiver" because they were born in a large litter, but their untranslated name uses hrair (Hrairoo, with the modifier meaning it's a "small" thousand). It's also in the name "Elil-Hrair-Rah" (prince(rah) with a thousand(hrair) enemies(elil), with "enemies" really just meaning "predators" because rabbits)

0:33 My brain counted 7 until you said 8, then I had to go back and double check...

this explains why in most countries phone numbers are divided by parts that consist of 3 or 4 digits.

11:15 " babies clearly understand that 1 plus 1 does not equal 1" ... someone tell that to terrence howard

The difference between 1 and 2 is +200%, the difference between 9 and 10 is +10%. Maybe we tend to make comparisons in a relative way instead of an absolute way, because they're more useful in the vast majority of situations.

*"There are FOUR lights!!!"* 😏

I'd like to point out that we feel as if 99 was closer to 100 just like we find it easier to tell which number is smaller and greater between 90

00:33 I have to say I'm proud of myself. I paused the video after the dots disappeared and before it went on and told myself “those don't seem like eight points”. Then rewinded it and replayed it until the dots had disappeared, paused again and said to myself “those must be seven, not eight, unless I didn't see an extra dot”. I finally checked and there were seven points, as Joe later showed us. That happened to me because I quickly saw a group of four and a group of three, I'm not a computer. Although I'm hyperlexic and autistic, and maybe a synesthete, so maybe that was related. Who knows! 😅

Damn, I just found out I'm a robot

My grandma taught me to count in threes. She used to work at a printing press and had learned it there, counting stacks of things. She said that human eyes detect three things much about as fast as two or one. If you know the multiplication table of three intuitively, you can do one (threes), two (threes), three (threes) etc. at the end you multiply by three or do it along the way, 2,6,9,12.... (easy for anyone i think at least to 18, and that is probably 80% of usage cases covered, how often do you need to count stacks higher than that..). Add one or two for the leftovers and you are done..

Chinese notation: 1 comet, 2 comets, 3 comets, window, guy kneeling on skateboard

Also it's real obvious to me that 99 feels closer to 100 than 9 to 10 because we don't think about absolute difference, we think about relative difference. The relative difference between 99 and 100 is much smaller than 9 and 10.

I've noticed that beginning musicians and dancers sometimes are resistant to 3/4, stubbornly adding the fourth beat no matter how many times 3/4 is demonstrated. Then there's the song I wrote in 7/8 (shades of Brubeck), which always seemed to elicit a breath to serve as the eighth beat. Hard to fight that. Very interesting discussion here. Think I've found a new rabbit hole!

99 and 100 feel closer because they are closer by percentage. 99 is 99% of 100, whereas 9 is only 90% of 10.

8:20 As a native Arabic speaker, I have scored better when the "Smaller" button was on the right. Even after all of these years I've been heavily using Engish and German, deep down in my brain, there is still a bias towards a Right-to-Left text orientation 😄

That Counting Crows reference was top tier. You deserve some Hard Candy. 😉

Most amazing fact about the Alaskan Iñupiat notation shown in 2:20 (also known as Kaktovik notation)? It's not ancient like the others but it was invented in the early 90s by middle schoolers, guided by their math teacher, in Utqiagvik (formerly known as Barrow), Alaska. From there, it started to spread. Then in 1996 the Commission on Inuit History Language and Culture officially adopted the Kaktovik notation and in 1998 the Inuit Circumpolar Council recommended its use in Canada.

I don't see numbers, I smell em. Safe to say I failed maths because I couldn't read the textbooks

I CAN ONLY COUNT TO FOUR! I CAN ONLY COUNT TO FOUR!

9:17 as soon as I heard 3 and 7 I get reminded that statistically, humans think that 3 and 7 are the most random numbers between 1 and 10 (Veritasium)

i learned this when i was looking for specific lego pieces based on number of 'nubs' as a kid

There is a language in the Amazon basin called Pirahã. It is notable for missing many common features that almost all other languages have, such as colour or certain common verb tenses. Another thing the language lacks is numbers. There are two terms for quantity, which basically translate to 'many' and 'few'. Although there is some variability, generally speaking, amounts smaller than 4 are considered few, and amounts larger than 4 are considered many.

I thought the group with 52 vs 50 was pretty obvious but I'd have to be tested on a lot of different sized groups to see if that held up or if it was chance

Little children (under six, I think it was) don’t recognise there are an equal number of M&Ms if one row has more space between them, they’ll think the longer row has more. The same goes for cutting two identical cookies in fewer or more pieces; they’ll think that the cookie divided into more pieces is bigger, even if they watched them being cut. ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-qkfBXPAiZ_0.htmlsi=fS4S9TTiBmSWn7cK

Interesting thing about chimpanzees only attacking with a 3:1 advantage in numbers is that there's a rule of thumb in military planning saying that one should attack with a 3:1 advantage in numbers.

I feel like you held back on a lot of puns... I can't quantify it, but I have a fuzzy feeling that there were a lot less of them :D

Mr. Jones predicts A Long December! That crow knows how to count.

I used to watch brain games in my childhood but nowdays we don't watch tv. Felt so good when i realised i am still exploring science by your videos 😌

Interesting! In my language nouns have different plural forms for quantities of 2-4 and 5 or greater. You would also use the latter form if you wanted to say 'many'.

This video fills the Vsauce void

Radio Lab had an episode years ago about numbers and how babies count in logarithms, but forget it once they’re being taught the decimal system. Seems like you can’t completely erase everything, which explains our intuition regarding large numbers and distances. Regarding the Right handed writing systems and preferring small numbers on the right - as a Left handed person with a maternal language that is written right to left -I still envision numbers from left to right.

7:35 my smart brain immediately raised the issue of right hand bias. I so love that you addressed that right away!

I love that you always wake up my curiosity. THANK YOU!

Apparently if you ask people from some indigenous languages (mostly researched in the Amazon) "how many kids do you have" they don't know. If you ask them to LIST their kids, oh they very very much know.

I'm reminded of a tribe I read about somewhere years ago who's counting went up to about 3 or 4 . Apparently they went " 1 2 3 4 many"

Great Video, loved it. more videos like this would be nice.

Interestingly, and possibly (I'd wager *probably* imho) related: we think of time durations logarithmically as well. With attention (flow) held constant, children tend to think 5 or 10 minutes is a long time, while adults do not. Likewise, when you think back on older memories, the duration of those events seems to feel shorter as you age. Like, a single lecture when I was in college may have felt like a full class's time (which it was), but now thinking back, all of my college years collectively feel like just a blink. We consider durations effectively as a percentage of our entire remembered collection of life events -- approximately, as a percentage of our current age. Which leads to a logarithmic perception as that age increases.

Time-stamp 14:10 My twin sister has dyscalculia and dyslexia. Yet, she made it all the way through Calculus in high school with A's and B's. Her checkbook, on the other hand, is a jumbled mess because she reverses digits and messes up the resulting calculations. She majored in art and photography in college, while I majored in math. Perhaps, someone will find this interesting.😁

First time I got high, I could visualize these very distinct crystal shapes- and each shape was hyper specific to the color I was trying to picture. Green had a dramatically different shape than red vs blue. I couldn’t stop being surprised by how accurately the shape for the color would return. I still feel these crystal shapes sometimes just by thinking about color, and I don’t even partake.

"you're physically comparing [numbers] in space" When I was severely developmentally dyscalculic as a child, this was one of the only visualisation tricks that actually helped me. Stop trying to turn numbers into some abstract idea, and imagine them as physical objects inhabiting a physical number line. My brain literally couldn't process abstract number concepts, but seeing them physically in front of me in the form of objects allowed me to understand what the numbers represent.

I've always thought that IV is written like that in Roman numerals because it corresponds to how one would show it with their hands (the whole hand, minus the thumb).

9:08 my Hebrew teacher once read the word “push” backwards from the inside of a glass door and pushed on a pull door.

Love this! I also think that we have a ‘gravitational pull’ to small numbers because they are what we interact with every minute, hour, day, always. Our lives revolve around small numbers.

isnt it just about density?

The reason why I feel 99 and 100 are closer is because I'm visual; in my head, I instinctively picture 99 or 100 "indiscernible things" crammed in a space, but by contrast, 9 or 10 in the same space has more room to spread out. So they're closer because in my brain, they're physically closer distance wise (even though that's not true nor does it make sense)

I recall an anecdote, from an assortment of courses in my undergrad, that cited a general pattern among numberless cultures. And, the general rule was something like: "1, 2, 3, more than 3." I wouldn't even be surprised to learn that these observations were the initial inspiration points for the various psych studies referenced in the video.

"Dyscalculia" sounds like Dracula's estranged cousin

This is a very cool episode, thank you!

11:15 "one plus one doesn't equel one" Terrence Howard would disagree

I have dyscalculia. It started with being diagnosed with dyslexia first and they didn't understand dyscalculia at the time, so my dyslexia was targeting and I overcame that no problem and even excelled in writing, while I still have a hard time with any math. It's not that I don't understand the concept of numbers, it's that my brain gets foggy and can't place the numbers. It is just like when dyslexic people try to read and the numbers kind of go everywhere on the page, except that is happening in my head, on the "page" in my head where I am trying to envision the numbers to do math. I really think that if dyscalculia was more understood when I was a kid, it might have been able to be corrected, I still struggle with it, and all though I know I am not stupid, math is a big part of IQ tests and markers of intelligence. Being in honors English, creative writing AND special ed math and never getting past algebra in high school is a weird duality, lol. The only 90% I ever got on a math test was Geometry. I hope kids who have this now get the help they need.

Thank you for the Counting Crows reference!!

I will note that the comment about people thinking babies are just a blank slate is actually a new idea in and of itself. It originated with Locke's Tabula Rasa in the 18th century. Prior people always assumed that things like math were naturally ingrained into us.

This is the crow epistemology and the triple integration theory of Objectivism

2:05 Some places do use IIII as 4. My grandfather was a clockmaker, and we have about a dozen old pendulum clocks in our house, and of them, 5 use IIII rather than VI (though all of them use IX rather than VIIII).

I dunno why (all your vids are excellent) but i found that one super interesting. Thank you ❤️

Play enough games like Big Brain Academy that have you practice comparing quantities of increasing size and decreasing proportional difference, and you'll develop a partitioning reflex. It's not hard to group a collection of dots into sets of 3-5 that appear in recognizable arrangements. For example, parting out a 5-pip die face or a "house" (connect the dots to make a square with a triangle roof). When you showed 7 dots the first thing I saw after it appeared was a 4 + 3 as a quadrilateral and a triangle.

Me: "That wasn't so bad. A previous job trained me to count things really fast." Joe: "But once we get to eight dots . . ." Me: "There were EIGHT dots? Maybe I'm not as accurate as I thought!" Joe: "Just kidding. There were only seven dots in that last one." Me: "VINDICATION!"

Thank you so much for enriching my vocabulary! I am enjoying the new muchness of available words a lot! ;)

so I do have to split big numbers into smaller groups to count properly, but funnily... when you talked about 8 dots, I didn't have enough time to _actually_ count, but I still had a moment where I was like, "that looked like only 7... but he said 8, so I must be wrong"

I’m no longer a virgin. You’re my first…Patreon. Make it worth it buddy 😂

I tasted 3 once. It tasted like blue which sounds like saline. And saline sounds like the sky. Had an ablation and it gave me harcore synestheshia.

At 3m52 I feel the effect is IN PART due to the background color that is closer to the ball color and diffuses into what seems a higher number of dots. I'd have preferred to look at it without the distraction. Fascinating, thanks !

I absolutely LOVED that video!

In the studies, have they done a comparison between mathematicians and non-mathematicians? Do mathematicians see numbers more accurately?

More evidence that my brain isn't "normal", not that that was ever my aspiration.

For apes that evolved to survive on the African plains, being able to quickly and distinctly count out upto three items - whether prey animals, predators, allies, foes or edible items - makes sense. Anything beyond that makes sense to quantify more by a sense of quantity rather than by exactly numerical quantity.

This was 1 of the most interesting videos you've done.

this episode was sponsored by the number 4

The ability to read small groups of dots (or lines like tallies) really fast is called subitizing! The specific fraction that makes 3 and 4 or 9 and 10 difficult to differentiate is called the Weber Fraction! The approximate number system is just called the Approximate Number System! Reacting to small numbers faster on the left and big numbers faster on the right is called the SNARC effect!

Thank you Joe, for teaching me something new today!

This makes me feel so much better about having such a hard time with mental math of large numbers. Without seeing the numbers, they all just kind of blend together in my head.

1, 2, 3, brain.exe has encountered an error

*stares in dyscalculia* Yeah, numbers are not friends. Words are everything, but numbers... ugh.

8:50 It is funny because even if we associate bigger numbers with the right side, the way we write numbers is the complete opposite. 523 - the 5 which means 5 times 100 is on the most left side. And the smallest factor which is 3 is on the most right. But if we would write 523 as 325 we would need to read it from right to left then anyway. Weird indeed. Maybe the cultures who say smaller is on the left is "more right".

This is fascinating and fantastic. Part of my job is teaching data visualization, and I always teach people that-when possible-try to have fewer than five series. I know I've seen studies on this, but this was very affirming to what I instruct. And now I can borrow your references. :)

Great video!

Money is that way not because of logarithmic thinking, but because you can combine smaller ones to make bigger. You don't need 175 bill when you have 100, 50, 20 and 5. You don't need 375 bill when you have 200, 100, 50, 20, 5. It's just not practical to make these intermediate bills.

Meanwhile, me with autism: Wait, what? You normal people can't recognize 7 dots at 2x video speed? Most of these examples didn't apply to me. But then, I have a very strange connection to numbers. I memorized 1000 digits of pi in middle school just because I was bored one day.

I work with Flow Cytometry. I look at groups of dots all day for work. It was incredibly easy to tell which group of dots was larger and I got it correct each time in less than a second.

The real way we see numbers The way we see real numbers The real way we see real numbers The imaginary way we see numbers The way we see imaginary numbers The imaginary way we see imaginary numbers The real way we see imaginary numbers The imaginary way we see real numbers

Nice video, but it also feels like a song costantly close to doing a drop, but never actually doing it lol

I remember an article, many years ago, about this problem. But it was in the context of marbles in your pocket. You can recognize up to three instantly, but four and up, you need to count.

1 is a dot 2 is a line 3 is a triangle (usually) 4 has many shapes

This is genuinely super interesting to me on many levels! 🤩

Great subject!

terrific video, very interesting.

I recently learned how the Mayan vigesimal number system works. IMO it's awesome because it only uses two different symbols which makes it very easy to do additions and subtractions. I also think it would make it easier to quickly compare numbers.Btw, they build their numbers from bottom to top. Wonder how they would've done in the left/right button test.

2:45 we also say 1st 2nd and 3rd but then it’s 4th 5th 6th etc

Did you know that 4 in roman number clocks is iiii (IIII) and not iv (IV)?