The Real (Weird) Way We See Numbers
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- Опубликовано: 7 июл 2024
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Would it surprise you to learn that fish and birds count in pretty much the same way that we do? And that infants can do math? Our animal brains deal with quantities in very specific ways, from quick counts of a few dots to how we perceive larger numbers. This "number sense" impacts our psychology, history, and behavior in the most fascinating ways.
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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.
That's basically the logarithm hypothesis, it's useful for comparing ratios. How is A relative to B.
and THE reason people say it is because these numbers are visual representations. and visually and 'conceptually' they ARE more similar. just not mathematically.
both 11 and 10 has 2 digits and starts with a one, it's that simple.
@@genesises But 99 and 100 differ by a single digit with no digits in common, and the same is true of 9 and 10 -- so if it was "that simple" people would not have a preference on the 9-10 vs 99-100 question. Yet we do.
my brain thought of it less like 99 to 100 vs 9 to 10, and more like 9.9 to 10.0 vs 9 to 10
@terahlunah yeah but the framing in the is that those number pairs are objectively the same distance apart. In a multiplacative world that is basically built out of fractal geometry this rubbed me the wrong way
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.
Yeah, they sometimes avoided IV specifically despite using the subtractive rule everywhere else (9 was always IX, never VIIII) because IV was the first two letters of "IVPITER" (Jupiter, but the I/J and U/V distinctions didn't exist yet.)
@@NovaSaber Not so much a distinction, as a matter of not having certain sounds. No j or soft g i.e. Julius Caesar was 'Yulius Kaiser', and the v, which is a voiced 'F', was used as 'w' or 'U', presumably because they though the 'w' sound was a vowel.
Not just those made during Roman times. Do a Google image search for "tower clock" and-of the ones that use Roman numerals at all-lots of them have IIII.
I had a pendulum clock as a child that had roman numerals and 4 was written as IIII. I always wondered about it.
@@VoidHalothis has always bothered me too. I heard recently that there might be an aesthetic reason for it - the first 4 numbers only contain I's, the second 4 contain a V, and the final 4 contain an X.
With Autism this is different, I am really good at seeing who gets more food even when the difference is close!
The big question is why is any difference in the ability to focus on sense-in-common cause-effect unity-connection not more easily recognized as the absolute consequence of logarithmic condensation-coordination time-timing sync-duration.
Shepards have been counting their flocks just by looking, listening and pictorial correlation of modulo-geometrical numberness for as long as it's known to have been successful hunter gathering.
Think about it. The analysis of QM-TIME Completeness Actuality is the reverse-inverted process that un-sees a coherence-cohesion sync-duration resonance quantization objective-aspect of WYSIWYG flash-fractal re-cognition. What you get is memory association correlation by visualisation, our most natural probabilistic feature.
@@davidwilkie9551 Totally!
@@davidwilkie9551wow. I bet your fun at a party
I'm on the spectrum and I'm terrible with numbers but great with volume. I'm an accomplished butcher and my cuts are clean and precise. I can portion visually by weights or length. I will nerd out on cutting and cooking meat.
@@davidwilkie9551💀
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.
Well said. I agree. Thanks.
How do you deal with money?
@@daysofend typically my money isn't managed with complex equations, which is where the worst of my dyscalculia presents itself.
I don't have any issue doing symbolic manipulations, so I rock at algebra and calculus and so on. But I can't retain math facts and have to rely on my fingers and weird workarounds whenever those pesky numbers show up. In fact, I majored in math, and taught calculus during grad school. I'd just have my students call out the results of any calculations after I set them up while doing problems at the board. Because I always had to go the long way around, I developed a deep understanding of many of the techniques that others could take for granted.
You aint lyin'. My entire educational experience is saturated with "you're so good at reading, we know you're smart. You just hate math because you don't want to do it!" and then having everything I actually WANTED to do yanked out from under me as "motivation" to "stop being stubborn" about math.
The irony in that is that the music lessons would possibly have been helpful to getting my math grades up.
"what numbers are even.. four" really sounds like something Vsauce would say
"... but are they?"
All I'm saying is, I've never seen Joe and Michael is the same room together...coincidence????
Vsauce even has a video on the same topic:
ruclips.net/video/Pxb5lSPLy9c/видео.html
The subtitles says "for" :(
too soon... 😔
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.
Good luck with the dissertation!
Have you considered that musical scores evolved to the point where they are written on groups of only five lines selected from a much larger stave required to cover the full range of pitches? Perception of the patterns written on these lines can be seen rapidly enough to permit sight (instant playing on sight) reading of the music. I think this may be worth a look if you have not considered it already.
Try PhD'ing some writings too. I can understand 3 of your 4 sentence structures.
so......this guy just did your entire dissertation in less time than you did?
@@SoloRenegade You massively underestimate how long a dissertation is. This guy just summarised the intro, the rest of the dissertation still remains.
I once knew a person who was diagnosed with dyscalculia as a child, and he said it was what resulted in his dropping out of school prematurely because it is classified as a learning disability and there was no curriculum to accommodate his needs, but he loved games with numbers like dice and board games, and he was not at all slow at his basic arithmetic. I've also been told a similar condition, dyslexia, is a learning disability, and I've seen someone shut down all their hopes for their future because they were diagnosed with dyslexia, but as a dyslexic myself I know I am not learning disabled because I seem to have zero problem learning things and even seem to learn new things faster and better than everyone around me most times. I just can't perceive printed letters/words/etc. correctly or as easily as other people seem to at a glance. I think the clinical conception of these conditions is wildly missing the mark and incorrectly pegging people as learning disabled and I think it needs to stop until it is studied in greater depth.
I agree. My husband is dyslexic and he's smarter than most people.
A learning disability is defined by the ADA as a neurological disorder that causes difficulties in learning that cannot be attributed to poor intelligence, poor motivation, or inadequate teaching, and it does recognize both dyslexia and dyscalculia as learning disabilities. Whether they should or shouldn't be classified as such, they do cause difficulties in learning in terms of reading/writing and math. The issue is, it doesn't differentiate difficulty with learning in general from difficulty with learning in a specific field, nor the reason why. Besides, a person with dyslexia could be the best writer known to man, it might just take them longer to recognize the words and put them on the page. Some dyslexic people have a very wide range of vocabulary, but struggle to use those words in context or spell them correctly. With that said, I believe disability more-so refers to the conditions and environment around us making it significantly harder (or impossible) to do things. For example, left-handedness used to be seen as weird, or an ailment, rarely a handicap, and they'd often be forced to write with their right hands. Then, we started accommodating them with left-handed desks, left-handed bows in archery, etc. Thankfully, we also moved away from those horrid L-shaped desks and plain rectangle desks have become a lot more common (though I have no clue whether left-handedness played a part in that). However, left-handedness is a lot easier to accommodate and far more common than most disabilities. I wouldn't expect a teacher to make an entire different learning curriculum to suit one dyslexic student (possibly including different assignments, an excuse from spelling tests, extensions on assignments, etc.), but maybe that's the problem. Grades are not a good measurement of intelligence at all, but colleges see them as such, so why shouldn't a dyslexic person be excused from spelling quizzes? Better yet, they take the quiz and have it handed back so they are still learning, maybe take a spelling quiz of a lower grade level if needed, but it doesn't count towards a grade. As an autistic person who also has ADHD (both classified as disabilities, but not learning disabilities), different conditions and a different environment where my sensory needs are met and I'm not graded on participation would help me and my learning immensely. Again, they aren't learning disabilities, but they do affect my learning *because* of the conditions surrounding me. It's up to every individual with a classified disability whether they want to consider themselves disabled or not, though. The main issue is the stereotyping that happens when someone is diagnosed with a disability. Like you said, it can really discourage people from pursuing education, which is a huge problem since neurodivergent people (autism, ADHD, dyslexia, and dyscalculia are all neurodivergencies) are some of the most intelligent people out there, generally more-so than neurotypical people in my experience. These are the people we *need* to be teaching students, researching cures, etc. Take Temple Grandin- her autism is precisely why she was able to make such big strides in the agriculture field when no one else couldn't because it changes the way she perceives the world (which we need to stop assuming is a bad thing).
Graph paper saved me. Putting the numbers in little boxes helped me with my dyscalculia
@@pixpixi Well, that's great; however, I attended this Jr. College where the Head Psychologist, Dr. Wheeler told me that I had brain damage and all learning disabled people have this damage too! Years later, I realize that the CAPD I and others were labeled with is simply a different way my brain stores information! I figured this out after decades of frustration with feeling inept and low IQ. One day I just couldn't shake the idea that I was intelligent despite my so called learning challenge! That person also told me that I was unorganized and that she was because she could see the big picture in a drawing she showed me! Ugh, how grandiose of that woman!!!!
I have number dyslexia. Not with words but that might be because I taught myself to read.
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.
I also have dyscalcula, but nobody would diagnose me because they "didn't have the resources".
I had always discounted myself as stupid because I couldn't do math. By the time I realized the issue I was already an adult, so I went back to school to re learn math.
But it's been difficult for me, there's a lot of math trauma built up and I had missed a lot of foundational work. It takes me about 3x the amount of time to complete a problem.
I also hope modern kids have improved diagnosis techniques, and better resources available in approaching problems.
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.
Also remarkable is that in proto-Indo-European the numbers are only declined up to four and then they become invariable, a feature retained in for example Icelandic or (more or less at least) Greek.
Quite interesting. You should send your fact to the QI elves (fact gatherers of a BBC tv show).
@@kellydalstok8900 There is a good wikipedia article "Slovak declension". Citation: "A particular case is associated with three distinct groups of numerals associated with nouns:
1 (one) - nominative case singular, for example jeden dub (one oak)
2, 3, 4 - nominative case plural, for example dva duby (two oaks)
0, 5 and more - genitive case plural, for example päť dubov (five [of] oaks)"
I do not know what QI elves are, never seen the show. Feel free to inform them.
That's amazing
Interesting! Arabic has three cases: for 1, for 2 or for more (singular, dual, plural)
1 fish, 2 fish
3 fish, 1 school.
1 school, 2 school, 3 school, 1 university.
1 fish, 2 fish, red fish, blue fish?
one little, two little, three little, indians.
ninety-nine bottles of beer on the wall
99 luft balloons
Damn, I just found out I'm a robot
Well done, Deckard. How's the Electric Sheep?
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 !
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?"
Rhythmically it does indeed seem four is the most our brains can comfortably handle as an indivisible unit. Dividing a measure into five is only done rarely and gives a bit of a weird feeling as if there is an 'extra' beat every measure, while measures divided into six, eight, nine and twelve are processed as multiples of smaller groups of three or four beats.
@@hydrocharis1 Trying to do a 5:4 polyrhythm with my hands is _way_ harder than doing a 4:3 polyrhythm (with its infamous "pass the god damn butter" mnemonic).
A cousin who explored Indian music turned me on to Ravi Shankar once counting out something like 23(?) beats in the rhythm of the piece he played on sitar...
It's good to have a guide when venturing to strange and foreign lands... :-)
@@hydrocharis1 here it just comes down to exposure, what you are used to. 5/4 is not inherently complicated than 4/4 - we just like to think it looks like that through a mathematical lens. actually 'feeling' rhytms is not mathematical.
@@rustycherkas8229 Not long ago I played Sgt. Pepper’s on my phone while babysitting my 2 year old grandson. As soon as Within You Without You started playing he came over to listen intently, and when it ended he went back to his toys. I think he liked it being so different.
this explains why in most countries phone numbers are divided by parts that consist of 3 or 4 digits.
here in Spain it is common to say in groups of 2, except the first 3. like 123 45 67 89
I'd like to see a source on that, but it's plausible.
@@gigaherz_same in my city in Massachusetts USA
@@ginnyjollykidd have you ever tried to remember a 10 digit phone number without the hyphens? not as easy as you think unless it's like a phone number you've remembered for years
The same goes for bank account numbers.
Did you know that 4 in roman number clocks is iiii (IIII) and not iv (IV)?
They didn't have locks back then :P
"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 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!!
So, would you please share a link to your work here?
I'd like to read it too! 😊
Jumping on the train of people who would love to read the thesis if you're willing to share it!
Crickets....
You will find it under the name "External representations for learning and comparing energy consumption", on the theses HAL science platform (fr). Not sure I can post a link here. Quite the opposite. Thanks for the interest!
It's like I always say, there are 3 types of people in the world: those who can count, and those who can't.
There are 10 kinds of people.
Those who understand binary,
and those who don't. 😁
@@WarpigA23Binary is base 2, and it shows numbers only using 2 digits. 1, 10, 11, 100, 101, 110, 1000.
@@JoelDaAmazingGD In binary 2 is represented as 10 hence the joke. Really kills it that's I have to explain it 🫠
@@skyking469 I got the joke, I was just elaborating to people who didn’t by counting
There are only two types of people: those who count and those who do not count.
7:35 my smart brain immediately raised the issue of right hand bias.
I so love that you addressed that right away!
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.
0:33 My brain counted 7 until you said 8, then I had to go back and double check...
Im still counting 7 huh...
oh ok continued the video lol
i thought it was 6 😔
Same here. Instantly when Joe said 8, I was calling it an error on his part. Turns on he did it on purpose.
I counted 6 😅
Yeah, I saw 7, but I saw it as 5 and 2.
*"There are FOUR lights!!!"* 😏
Calm down, mr Picard.
@@MeesterG 😉
These four words always give me goosebumps instantly.
@@DeltaNovum 🪿
Shaka when the walls fell
So, on the segment dealing with "which is larger" ending ~8:35, the instructions of which button to push (left or right), could be phrased as "when u see a number, push either the left or right button. If you pushed the left as the larger one, continue to push the left for the larger and the right for the smaller ones". This would help to disambiguate the effect from a naïve subject's hearing and understand the test's instruction from the actual cognitive function believed to be about the numbers. ...might be fly poop in the pepper, unless one is interested in the possible connections between the instruction and the act, but it would also serve to show things in simpler context of the author's central idea and means supporting it.
Thanks for bringing us this great content!
I like your thinking but I think that phrasing is pretty complicated and brings in questions of whether they are going to try to guess which one the researcher thinks should be smaller.
Maybe just come with two wireless buttons labeled large and small then right before the test starts ask, "Ok, do you want the button for smaller on the right and larger on the left or the other way around?"
@@petergerdes1094 Much better because it allows the subject to deal with these kinds of choices early on, so they can be put to rest and pose no further distraction to the primary task of interest.
Thank you so much for enriching my vocabulary! I am enjoying the new muchness of available words a lot! ;)
11:15 " babies clearly understand that 1 plus 1 does not equal 1" ... someone tell that to terrence howard
Ah but that’s what he thought in the womb. Then he remembers progressing beyond all human comprehension of symbolic mathematics at both the quantum and computational levels - at least in terms of the planck length vibrational wave-width.
He does mental math--you have to be mental to follow that math.
can someone explain this joke?
@@lastyhopper2792 Terrence Howard a few years ago did an interview with Rolling Stone where he explained that he never believed that 1x1=1 and insisted that it equaled 2. He and his girlfriend even made 3D models to try to demonstrate this. He also doesn't like the Pythagorean theorem. Luckily, you don't need math to be an actor.
I don't like when you say it's been proven to be right. But everything was subjective. You kept saying what numbers feel closer together. One of the reasons I love math is because there is no feelings 🤪
As Terry Pratchett's trolls count: one, two, many, lots.
Grammatical number wise I believe these would be singular, dual, paucal and plural.
also he's my favorite author. His footnote aboit the relatavistic pazuma being the fastest creature on the disk was hillarious!
I'm at a party this weekend and apparently I am going to drink a LOT of re-annual wine because I already have the Hangunder of a lifetime.
@@carlchapman4053 i call heinekin "backward ls beer" because i get hung over dr8nking itblong before i get drunk.
One too many lots? :P
Love the Disc World Series. I've read little else since I discovered it in 2019. Sadly, I'm almost out of books. 😞
Prisoners use a smart visual system to keep track of time (count days).
They use vertical lines (I, II, III, IIII) for 1, 2, 3, 4. For five, they add a horizontal line across 4 vertical lines (IIII). For 6 through 9, they add vertical lines to the symbol for 5.
So, to count any large number, a reader first counts the number of fives, multiply by five, and then add the remaining vertical lines. For example, 23 would be written as 4 units of fives plus 3 vertical lines.
Of course, this is space-inefficient, but less labor-intensive for stepwise counting. Each day, the prisoner adds a vertical line and every fifth day he adds a horizontal line. Remember, prisoners have plenty of time but limited space.
This system could be improved by borrowing from our present way of counting in tens, by using columns. To simplify, let’s use 2 columns: the left column keeps track of the number of sets of fives, while the right column represent the number of days fewer than 5.
Now, 23 can be symbolized by 4 vertical lines to the left, plus space, and then 3 vertical lines to the right: IIII III
It would still be space-inefficient. So maybe adding a symbol for 5, say one horizontal line (-) and a symbol for 10, say 2 horizontal lines (=) and using columns. Now, 23 would be ==III and 29 would be ==-IIII
Now we’re getting closer to the Roman system of counting 😅
It's called tallying. It wasn't invented by prisoners
@@bororobo3805 In Finland it's called "tukkimiehen kirjanpito", literally "logger's bookkeeping". Possibly because the lines resemble logs in a flume.
Note on dyscalculia; it is not a struggle in *understanding* numbers, rather it is a struggle to mentally keep track of multiple values simultaneously. Give me a calculator and I am an absolute whiz; I can solve, modify, find values using complex formulae and statistical analysis. However, if you ask me to divide 66 by 3 in my head, you'll be waiting a while.
It is just as a dyslexic person doesn't struggle with the inherent meaning of words, rather they struggle with their physical representation and format.
When I multiply I visualize a grid of dots with an x and y axis. Visualization is way easier than math.
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.
it's the ratio of the numbers compared to one. 99/100 is closer to one than 9/10.
Expanding on that, it feels to me like the effect is in how we understand what "close" means. I wonder if the effect would change if you instead asked "which two numbers have more numbers between them?"
If anything, it's probably more interesting that an investigator would think the "correct" measure of "closeness" is the absolute size of the interval between the numbers, rather than any other reasonable way of defining it.
@@AD_AP_T They all have an infinite amount of numbers between them
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 😄
Interesting! May I ask: How do you draw a number line (or x-axis of a Cartesian coordinate system)? Increasing to the left, or to the right?
@@sharonminsuk in theory, if we want to keep it 100% consistent in Arabic, then yes; even graphs and axes would be right to left. However, there's a big trend in math and science to adopt Latin-based notation for numerals and variables.. etc. Even if the text book is written in Arabic
@@abdalrazzakyousef4168 I figured as much. That's interesting though, because it means that your number line and your written language go in opposite directions. And that suggests that, since you score better with the "smaller" button on the right, that it's not so simple as just a spatial representation of numbers, but that instead, there's crosstalk between language and number sense. Pretty intriguing.
@@sharonminsuk exactly 💯. Similarly, if I visualize a calendar week, for example, it would be on a horizontal line, but the first day of the week is on the right, then the next days follow it to the left
@@abdalrazzakyousef4168 Correct me if I'm wrong but I heard that Arabic numbers still go from left to right, it's just that you don't say "onehundred-twenty-three", you say "three-twenty-onehundred". Is this right?
Fascinating video that connects a lot of concepts for me that I had familiarized with before. Very cool.
You did a drive by with that dyscalculia name drop. Please do a deeper dive into that.
99 and 100 feel closer because they are closer by percentage. 99 is 99% of 100, whereas 9 is only 90% of 10.
ratios
But why would people say 9 is closer to 10? As opposed to saying 11 is closer to 10(which it is)?
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
Yup, that's partly what they mean by us thinking logarithmicly. We see big percentage changes easily, smaller ones take effort to differentiate.
Given 9 dots vs 10, and 99 and 100, we'd fairly quickly say there is a difference in the first two, whilst we wouldn't notice a difference between 99 and 100 at all.
@@fatsquirrel75 isn't he talking about the numbers specifically? and not amounts of things.
@@genesises I think the idea is that for numbers 1 - 3, we think of amounts of things in discrete integers, but stuff 4 or 5 and up, we start to think of them more logarithmically (percentage wise?). The integer difference between both 8 to 9 vs 98 to 99 is 1, but 8 - 9 is a 22% difference, while 98 to 99 is a 2% difference. In the wild, something going from 4 to 5 is a significant difference, but 100 to 101 barely means anything, so our brains, and many animals' brains, don't care about it as much.
Something funny is that I've done 3d graphics for almost 38 years, and i noticed my brain reacted very differently to those mental exercises, it would've been very interesting to make a study on people in the 3d insdustry, animators, graphic designers, and people doing ultra speed reaction sports such as f1 pilots or pool players that basically do instant calculations of magnitudes in fractions of miliseconds, thousands of times per minute, for extended periods of time.
3:30 Strange I had no trouble at all with these large scale dot comparisons and got them all right instantly. I always knew I had a weird brain.
Same here! In every question I either knew/guessed the correct answer or chose the opposite of the norm. This was without pausing the video at all. I wonder if there is any cause or meaning behind this!
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..
She sounds like a smart lady💖
This is how I quickly verify the number of players on a hockey team! (I scorekeep rec league hockey).
6 on the ice, 7 on the bench, that means 13 total. The roster says 3, 6, 9, 12, 13. We’re good.
When I count large quantities, I always count three triplets and add one to make it 10, then three triplets and one to and so on: 3-3-3-1, 3-3-3-1, 3-3-3-1, 3-3-3-1... The number of tens plus the lefover is the final result.
Interesting. My brain is binary-I once weirded a bunch of people out when standing by a failing bank machine in a crowded student union building. I commented “programmers, huh?” and got blank stares in response. Evidently nobody else was able to notice passively that it retried exactly 256 times.
Of course, that's based on an audio stream, not a visual stimulus. Threes are easier visually, for, I think, good mathematical reasons.
@@samuela-aegisdottir That is not a bad system...
I don't see numbers, I smell em. Safe to say I failed maths because I couldn't read the textbooks
you failed. not because you couldn't, but because you could.
That stinks.
did.. you try smelling the book?
A whole new meaning to scratch and sniff
My middle school math book was...fragrant 🙄
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.
Interesting. That sounds similar to the experiences of some mathematical savants.
Great Counting Crows reference at 12:41. Well done.
I CAN ONLY COUNT TO FOUR! I CAN ONLY COUNT TO FOUR!
You must be a drummer! 🥁 🤣
@@mal2ksc As a drummer, I do not count at all. I play by "feel". I never counted anything when playing, even complex polyrhythms like 17/8.
Me count so poor.
Me too! Somethings wrong with me. Somethings got to give.
Your edumacation has faild you
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.
And this kind of goes without saying, but we were taught the inverse: you can expect to be able to hold a defensive position up to a 1:3 disadvantage. (I'm from Finland, we train primarily for defense and not offense.)
This was 1 of the most interesting videos you've done.
IIII is 4 strokes. IV is 3 strokes and you only have to take your pencil/brush off the paper twice. Not only is it easier and saves ink (which mattered when ink was expensive to make) and the glyph is narrower. Plus if anyone has less than good eyesight III and IIII can be difficult to distinguish in the middle of text.
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!
😅
It had the same shape as the 6 from before, which I counted as 3 and 3, but there was something more, but only a little more, and my brain thought.... 7? But it wasn't 100% confident.
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
The fact that that they were mirrored images (one were just missing two dots) made it a bit easier. 🙂
I found this video deeply fascinating, thank you 🙌🏼
For many years I was thinking about the experiment with number cards he showed in the beginning of the video, never knowing the name of that experiment, and this is the first time I hear about them here!
Chinese notation: 1 comet, 2 comets, 3 comets, window, guy kneeling on skateboard
Bridge, ladle, legs, cliff, cross
Cinese time units: 999 incense sticks!
No,田( tian ) is window
@@Ivyjiang823 No, 田 is a rice field. And thats even its actual meaning.
四 does also look like a window, (while its probably meant to represent an open mouth.).
@@mathis8210it looks like curtain to me
This video fills the Vsauce void
this video screams an old video by Michael :(
@@redsalmon9966 ikr, was constantly thinking of it myself too!
I miss the old style of vsauce videos.
IT DOES
SOOOOOOOOOO VSAUCE. I LOVE IT
This is genuinely super interesting to me on many levels! 🤩
This may explains: "Two beans, add two more beans" results in "four ... and that one"
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.
And when they have exactly 4 they have to throw one away?
@@molybdaen11 There are no exact definitions. In some cases, quantities as large as 6 were considered few, and quantities as small as 3 were considered many. It varies from person to person, and it seems to depend on the items that are being discussed.
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).
By that logic, IIV would be a reasonable equivalent for 3.
I am very proud of myself for getting every dot question correct, even on 1.5 speed!
At some point or another I figured that the fastest way to count objects is by grouping them into 3/4/5s and adding them up so that helped a lot.
For the large scale differences (e.g. 90 vs 100) It was mostly guesswork based on density.
ding ding ding! I do the same.
Large groups of objects I'll do: 3 3 4 or 5 5 (if it's obvious), to group into tens in my mind, enabling me to count really fast, then add the sub-10 at the end.
For example, my wife will get me a large box of strawberries (typically 40 to 50), I'll count them all (using 3 3 4 or 5 5) then divide by number of days left so I take the same number each day. My family are astounded that I can count them all in a few seconds without going 1, 2, 3, 4, 5, ...
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. :)
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)
Interesting, I was a fan of the animated movie as a kid but I have never read the book. Looks like I'm going to have to give it a read.
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
Thar pun at the end though....!
I got every one of the trivias correct immediately and confidently, and now I'm over here googling how to know if I'm a counting savant
I was able to compare the no. Of dots pretty quickly and easily and the button test where you choose larger or smaller, I was able to it quickly and accurately with smaller at my right side
Does that mean I am weird
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.
If 1 is half of 2 then the difference between 1 and 2 has to be 50%. Half of something is always 50% no matter how large or small it is. 200% is basically twice the amount, 200% of 2 would be 4.
The difference between 1 and 2 is 100%, the difference between 9 and 10 is 11%.
I think we simply calculate the percentage by throwing the smaller number over the bigger one. 1/2=50%, 9/10=90%, 90%>50%, therefore 9 is closer to 10 than 1 is to 2. I think even with the smaller numbers of 1-4 we’re still doing the same thing, just much faster because we’re often presented with them on a daily basis.
The difference between 2 and 1 always seemed like less as compared to 1 and zero. I recall my young mind pondering this at several single-digit ages. Still do!
Every example so far I've had no problem, until doing the button task - but I recognized the issue for me with that wasn't comparing the number but the physical action in a foreign method, no kidding flipping it at that point was slower, I required more mental processing to unlearn the first task and learnt he new one - I'm also high and have ADHD...
Re: 8:40 I was training on a psych study where people had to answer by hitting the 1 and 2 keys with their left hand. I found the processing to be really slow because that made the middle finger #1 and the index #2. This seems counter to the hand crossing not messing up the left-right number line.
Mr. Jones predicts A Long December! That crow knows how to count.
That was awesome. It tickled my brain
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.
actually, there is no correct way to do roman numerals
you could absolutely just write IIII but the way we do it, is the "optimum" way of writing it down, the least "characters" written, the real romans and others did NOT follow the same "rules", in fact, how they wrote their numbers was ALL OVER THE PLACE
5:50 I think this can also be explained by the spesifics of the numeral system. To distinguish between the options, one may ask which number feels closer to 9 out of 8 and 10
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.
naw, before it crosses the threshold it's just a clump of cells and therefore can't know things /s
to me it's also kind of a ridiculous idea
@@genesises And yet people still think this way. Tell someone about a problematic (or just unusual) behaviour a kid has and they will always assume it's the parents' fault. While nurture does have a large role in shaping habits, many things related to the personality are innate. That is to say, often behavioural issues are the parents's fault, but sometimes the child genuinely is the reason.
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.
ruclips.net/video/qkfBXPAiZ_0/видео.htmlsi=fS4S9TTiBmSWn7cK
In music we tends towards 4 beats. 3 and 2 beats are also common but 5 and over are less so. And even on those there is a subdivision using 2s and 3s.
I am dyslexic and dyscalic, and for anyone who doesn't know, these disabilities never go away. It doesn't matter how many skills or coping mechanisms I have, its always there.
I find language and math fascinating, and I am convinced that the only reason we can manipulate math the way we do is because it is adapted language to describe a real aspect of the world. "Number sense", to me, clearly has a distinct evolutionary pressure to exist and it doesn't surprise me that these many different types of animals have this ability. I also think that there is a big reason for my disabilities and it is a struggle to grasp these abstract concepts to the real world (im open to being wrong about this, i have other ways i can think abstractly so its not necessary a good theory). There have been several studies done on people with learning disabilities and there is a lot to suggest that our brains literally work differently and that we have strengts in other ways. Problem solving, creative thinking and the ability to stop small detailed differences are a few things I'm good at. Why this doesn't translate to language I have no idea, because there are clearly these components within it, but they just dont match up. Its very strange.
I love that you always wake up my curiosity. THANK YOU!
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)
yep. I think it is partially because both are prime. and, 37 and 73 are both prime.
Yea amazingly I caught myself sliding towards 37 when thinking up a "random" number. Like, 4 is even, 5 is nice, gotta use 7 ... hold up.
4:41 Love the use of the Dutch angle there.
Super interesting. I did this as an experiment in high school and it's not just the number. How you lay them out has a huge impact. Random is hardest. Next is what I think I called "non-traditional" patterns. So some sort of pattern, like two rows, or in a circle. And by far the easiest what I called "traditional patterns." The two I used were intersections of shapes (three dots laid out like a triangle, 4 on a square) and dice layout, by far the easiest. My belief was that people read the dice layouts as symbols similar to our western numbers. No counting or processing, just "reading" it.
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.😁
I taught geometry. Now my very smart son cannot memorize arithmetic facts but dyscalculia is not studied like dyslexia. Learning disabilities are not covered by insurance here either.
@@trerubinsy6250 I had big issues with geometry. I did calc, linear algebra, stats, diffeq, and more.
@@boomergames8094 Was it the visual aspect that threw you off? Usually geometry is the only one people do get, as there is at least a picture to go along with the stupid problems teachers invent. There are great reasons to do each of the other more interesting subjects you listed, but many times when they are taught, you don't get those. You may be able to sense my thoughts on the US education system.
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.
with the left button vs right button experiment, did they ever do a group where the participants STARTED OFF with big numbers on the left side, before switching? because there can be some mental delay just trying to remember that the direction's changed.
i have dyscalculia! rarely hear anyone mention it or know what it is, so thank you! i cannot comprehend big numbers. anything larger than 1000 feels the same: it’s just classified as “a big number”.
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.
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.
Maybe because they typically have so many that they don't bother keeping track of the exact number?
Do you know exactly how many friends you have? I bet you can list them though.
I agree with the "how many friends you have?" approach. Probably they just don't have a reason to count them.
@@juanausensi499 I'm not sure about that. What counts as a "friend" is a bit fuzzy, and I think that if I used a wide enough definition that I couldn't instantly put a number to it, that would also be the point at which I would have trouble listing them systematically.
@@gcewing A friend is somebody you intentionally contact for the pleasure of his/her company. If you just interact with someone you like because your daily routine puts him/her in front of you, that's not a friend.
In every one of these tests I was able to pass them instantly... The initial dot counting test, aced without hesitation. The 50 vs 52 dots one? I didn't know how many dots but I instantly knew which one had more dots... etc etc etc...
This video just proved to me that I have some sort of an objective look in life. It proves to me that I sure can see in more than two colors at once. Thanks for the video.
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 😌
i could feel myself thinking and my eyes moving when the 5 and 6 dots came up. bc I one-by-one counted 6 and went back to double check 5 by counting when I realised I had some extra time lol.
Excellent video! I'm a very skilled mathematician, but I never understood people's innate "number sense", or perhaps the lack of it!
That Counting Crows reference was top tier. You deserve some Hard Candy. 😉
Beat me to it. Well played with Hard Candy, by the way.
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)
We're all visual.
@@JohnPretty1 I hear some people are not. I cannot conceive of it myself, but some people are not visual at all.
I'm going to guess that we all have varying degrees of it, and I've always been extremely visual. I used to make things appear in front of my eyes when I was younger. Never had an imaginary friend, but if I wanted to see it, I could flip a switch and turn it on. I completely lost this ability as a teenager around 17 or so. By that point, I had to concentrate extremely hard for things to appear, but even if I did, I couldn't maintain the focus for very long.
Now, I know for a fact that teenagers don't normally have that degree of imagination, and I know for a fact that some people...somehow... are not visual at all. And some people can smell numbers. My point is that we're all different and our own experience of life does not align with everybody else's.
@3:54 on the dots, i think the colour chosen for background plays a part, the red dots are harder to see against the red background, this makes seem like theres more dots, because we are asociated dots with red and the purple on the bottom has more red, more red equals more dots. @3:34 has a similar effect of the bootom is more blue, the dots were blue and i got that one faster then the yellow dots were the differences was much larger.
"Dyscalculia" sounds like Dracula's estranged cousin
isnt it just about density?
Right, that's what I was thinking. At some point we switch to counting by density, which is still inherently different form of thinking and fuzzier than counting precise numbers
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.
8:59 Glad you touched on right-to-left cultures, that was my hypothesis
I was being all serious furrowing my brow and listening to the video, then you hit us with that counting crows joke and I laughed so hard I had to rewind 45 seconds to hear what I missed.
i learned this when i was looking for specific lego pieces based on number of 'nubs' as a kid
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!"
8:50 - I had my fingers interlocked on top of my head while "pushing the button" and got them all "wrong". Weirded me out, lol!
2:19 Ancient Chinese people also used tally marks for 4 and 5, just extending the pattern (long marks on top and bottom, shorter as they reach the middle)
This is a very cool episode, thank you!
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"
Yup, en.m.wikipedia.org/wiki/Pirah%C3%A3_people
@@jonathanwoodvincent well they seem to fall into that category but their situation sounds a bit different from the people I recall hearing about.
I think the tribe I'm referring to are these people
en.m.wikipedia.org/wiki/Munduruku
Though it could be some of the kids that I grew up with 🤣
@@Philrc ah, so it is..thank you. Wonderful