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.
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.
@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
Interesting technique I learned in the Army. When scanning ground always scan from right to left. Was told to do this because if you scan from left to right you are more likely to skip something because your mind skips things when you read.
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.
@@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.
It is not only numbers. Both lightness and loudness intensities are also perceived in ratios. That is why logarithmic units (e.g. decibels) are used to describe perceived intensities.
Perfectly matches with a commonly shared opinion among physicists when it comes to counting things: 1, 2, 3, many. Many usually means "let a computer deal with it".
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.
@@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.
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.
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.
@@SoloRenegade You massively underestimate how long a dissertation is. This guy just summarised the intro, the rest of the dissertation still remains.
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!!
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!
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.
As someone with less than stellar eyesight reading this comment while leaning back in her chair, I can indeed confirm that those are hard to disambiguate :P
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.
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.
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.
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).
@@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!!!!
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.
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.
Wondering, does this also work for blind people? Visually 10 and 11 feel more similar than 9 and 10 because 10 and 11 are more similar (two symbols vs one). 99 and 100 feel more similar than 9 and 10 because 99 and 100 are visually more complex, have more symbols, thus more important, hence I'm more likely to choose them as relevant to any kind of ambiguous question.
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.
@@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 🤪
2:42 That doesn’t automatically follow. It is a pattern that could’ve equally emerged, because it’s quicker to write a different symbol than 5 strikes. Not because the brain understands it more quickly.
It is worth acknowledging that in ancient China, before the Spring and Autumn period, four was written as 亖 and it was not standardized to write 四 until the Qin dynasty. The modern character for four is thought to be descended from a character representing nostrils or breathing. I was taught that these characters were homophones, and it became commonplace to write 四 instead of 亖 for the express purpose of not confusing it with 三, and the original character was replaced with 呬 after its meaning changed to be four.
@@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
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.
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.
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, ...
Started doing it while learning card tricks as a kid and never understood why people don’t do it as well. Grouping allows you to manipulate larger numbers by considering them to be the same unit.
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!
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 😄
@@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?
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..
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.
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.
@@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.
Maybe it's just because I'm so used to our current way of writing numbers, but to me, a number like 12,345,678.098,765,432 would be extremely confusing to read.
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.
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.
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.
Yeah I also have dyscalculia and dyslexia so I get this. I’ve always had a really good number sense, and been great at mathematics on a conceptual level. I’ve just been a little slow with computation.
I don't know if I have legit dyscalculia but my issue seems to be that my brain tries to interpret numbers as letters or words rather than sums. It takes a while for me to "translate" them into their numerical values so any calculation requires more mental processing than it probably should. By the way, I just tried to divide 66 by 3 in my head and it went like this, verbatim: "I have no idea what the answer is, but let's divide 66 by two instead because that's easier. That's should be 33, I'm pretty sure. So I have two 33s. Now if I subtract half of... Actually, scratch that. Let's subtract a third of 33, because that's easier. That's eleven. If I add together the two elevens from each 33, that's 22. If I compare that to what I have left of 33, turns out that's also 22. So, the answer should be 22."
@@RelativelyBest Thats proportional math. Its faster than regular computation, and is what really good mathematicians start with. I always calculated by removing the ends (47 - 22, 40 - 20, 7 - 2) and divided by a brute force method like that, finding any near multiple I could. I am terrible at math and hate it, but I am in awe at what it can accomplish.
@@pauldeddens5349 Interesting. I was always so bad at math in school I never learned any actual methods, so I end up doing whatever seems easiest to me. At once point I basically reinvented pi trying to work out the circumference of a circle, because I never made it far enough to learn about it. A friend of mine, who _is_ very good at math, found that amusing.
That is exactly the logarithmic "fuzzy" representation Joe talks about later on in the video. It's not just our number sense either. Most of our senses work logarithmically. But even that's not entirely accurate. For scales that are very, very far out of our normal realm of experience (say the size of atoms on the small end or the size of galaxies on the large) even a logarithmic sense of numbers isn't quite fuzzy enough for our brains to intuit and we just lose track of the concept of scale entirely. You _might_ be able to intuit the 384,400km distance to the Moon by thinking in terms of say, 85 coast-to-coast road trips across the US, especially if you've made that trip before (and even then you'll probably measure it in units of time rather than distance), but you have absolutely no concept of how far away Pluto is, or even Jupiter. There are videos on RUclips of people making to-scale "models" of our solar system and ending up with Pluto being halfway across a city when the Earth is only a few meters away from the Sun. Just wildly out of the scope of human intuition. And that's still within our solar system. The scale of our galaxy, never mind the entire universe, can only ever be understood through math and measurement. Intuition will never suffice for numbers that big, no matter what tricks our brain tries to pull.
0:33 umm yeah that's seven lol... interestingly enough, as soon as it flashed, I was caught off guard by you saying eight cuz I could tell quickly, it was not.
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!
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)
There's a related concept in the book- "tharn". When a rabbit has too much to think about, their brain shuts down entirely. There's a psychological model that the human brain has its own "hrair limit" of about four to seven, and if you try to hold more concepts than that you drop all of them, you go tharn.
Okay, honestly at first I was trying my best to get everything right and try to “fight” against what you were saying, but then as soon as you brought up people writing from right to left thus their number line increases to the left- I have no words except that my mind is blown. I physically and mentally cannot imagine a right-to-left as easily as a left-to-right. Even thinking more just typing that out because it’s not natural at all to me. Paused to write this comment- will update on more mind breakage. Update - I need MORE KNOWLEDGE.
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!
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
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.
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.
"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.
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.
I wondered about animals and counting when our cat had kittens. There were times when she seemed to count them, and she always knew when one was missing.
Ducks and other birds do a similar thing. They watch their babies swim through the water and onto the shore, one ... two ... three ... four. If they have more than four, they stop "counting" and keep going up the bank. I've also seen it with cats/ dogs / any animal that has litters, really. The "runts" get left behind.
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.
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'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).
I don't believe that there are any such languages in use today, but I wonder if someone whose native language was written boustrophedonically would show no difference in the right/left measure.
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.
@@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.
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.)
@@Ivyjiang2326 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.).
Thank you for the mention of dyscalculia in your video. It's helpful for people to be aware that dyscalculics don't have that same innate sense for numbers, including the ability to subitize (see small quantities without counting individual dots), as most of the population.
Unsure if this is related, but at 7:12 you point out that we think logarithmically, we also perceive volume this way too. That's why guitars have logarithmic potentiometers rather than linear because it feels more natural for the volume curve.
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)
@@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.
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.
I remember this concept has been beautifully explained before in other famous mathematics channel. The concept of "numerosity" and "Extracting numerosity" si given there
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
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.
@@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.
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.
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.
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!
Before I became Japanese Language Teacher, I was assistant of some of them, thus I interacted with university students. One of them said she had dyscalculia. She didn't have much troubles with Japanese, understood quite well grammar, pronunciation and writing. She wasn't an eminence, but neither a challenged student. However, when she had to say numbers in Japanese or write them... The dyscalculia affected that too! Our native language is Spanish, and yet, her troubles with numbers traslated into Japanese. It was a very peculiar experience.
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.
The fact that you partition 7 into 3+4 is exactly the message of the video: you can't deal with it directly. So I'm not sure you're getting any better at recognizing numbers directly. You're just getting better at partitioning.
@@LilFeralGangrel Now that I'm re-reading it, it appears I did misunderstand OP. Apologies, my brain must have merged OP's message with a previous comment.
I saw the seven dots as a pentagon and an unattached pair, but I've learned to "chunk" in groups of five (and when counting up dice pips, ten) because it keeps the multiplication a lot simpler.
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.
@@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.
I used to work in pharmacy as a tech. When we were hiring people we had to test them to see if they could just "see" up to five. The way he said most people can just see to three. It was the number one disqualifier, more than background checks.
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!
1. I legit found a website where you can type 2 numbers and it will tell you which is larger. B. Switching the larger and smaller buttons wasn't a problem for me. I'm the type of person who can read backwards, upside-down, and upside-down and backwards. I write with my left hand but my right hand is dominant. 27. Everything else for me is spot on.
@@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 🤣
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
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.
@@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.
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'.
@@boomergames8094 Here's an example in polish language: 1 cat - 1 kot 2, 3, 4 cats - 2, 3, 4 koty 5, 6... cats - 5, 6... kotów many cats - wiele kotów Seems that's a common pattern among Slavic languages.
I worked at a factory where counting up to 12 at a glance became necessary, and what I found was that I was able to accurately recognize groups of 3 super easily, 4 through 6 were fairly easy, and after that, I would split them into sub-groups. So, if something had 11, I would see a 5 and a 6, or else 3 3s and a 2. Which subgroups things got sorted in was based on their orientation. If there were clear triangles or squares visible at a glance, those would get grouped as 3s or 4s. I was interested in this, so I tested it with my friends and found that I could count coins at a glance accurately up to 12, while my friends could only do 5 or 6. I'm willing to bet if I'd worked at a factory where I was expected to count 24 or more, I'd have improved, but I'm sure there's a limit.
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!
@@boomergames8094 Yea, for me numbers up 6 have "shapes". 1 is a dot, duh, 2 is a line, 3 is a triangle, 4 is a square, 5 is a crossed box, 6 is two rows of threes. Then I hit 7 and completely fall apart.
![Eminem - Fuel (feat. JID) [Official Lyric Video]](http://i.ytimg.com/vi/t5H_CewqpKA/mqdefault.jpg)
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
Interesting technique I learned in the Army. When scanning ground always scan from right to left. Was told to do this because if you scan from left to right you are more likely to skip something because your mind skips things when you read.
So true
You might also say that going against the flow encourages your mind to work harder at processing more things.
I wonder what you should do if you speak both a left-to-right language and a right-to-left language. I don’t, but it’s an interesting question.
Your eye naturally goes to the top right when looking at something. It’s why logos often appear there and marketing info is designed based on this.
Cool - makes sense! I'll try to remember this trick.
Hmmm, I wonder if it's worse for people who learned sight-reading (vs. phonics), too.
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)
It is not only numbers. Both lightness and loudness intensities are also perceived in ratios. That is why logarithmic units (e.g. decibels) are used to describe perceived intensities.
Perfectly matches with a commonly shared opinion among physicists when it comes to counting things: 1, 2, 3, many.
Many usually means "let a computer deal with it".
😅
similar to the rabbits of Watership Down
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.
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 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!
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.
This is a perfect explanation! Thanks!
Logic, who would have known.
I thought the same thing about III and IIII being hard to differentiate.
As someone with less than stellar eyesight reading this comment while leaning back in her chair, I can indeed confirm that those are hard to disambiguate :P
@@malachi-I know. We’re still reinventing the wheel in 2024 everyday on RUclips
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.
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.
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.
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.
4:10 if you’re talking about an image of dots, a computer can do it *quickly*, but writing a program to do this is not trivial.
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.
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
No it's not... it is exactly the same... one unit.
It is very important to quickly account for which Sibling has more sweets
Wondering, does this also work for blind people?
Visually 10 and 11 feel more similar than 9 and 10 because 10 and 11 are more similar (two symbols vs one).
99 and 100 feel more similar than 9 and 10 because 99 and 100 are visually more complex, have more symbols, thus more important, hence I'm more likely to choose them as relevant to any kind of ambiguous question.
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
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 🤪
2:42 That doesn’t automatically follow. It is a pattern that could’ve equally emerged, because it’s quicker to write a different symbol than 5 strikes. Not because the brain understands it more quickly.
It is worth acknowledging that in ancient China, before the Spring and Autumn period, four was written as 亖 and it was not standardized to write 四 until the Qin dynasty. The modern character for four is thought to be descended from a character representing nostrils or breathing.
I was taught that these characters were homophones, and it became commonplace to write 四 instead of 亖 for the express purpose of not confusing it with 三, and the original character was replaced with 呬 after its meaning changed to be four.
"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... 😔
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.
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.
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, ...
Started doing it while learning card tricks as a kid and never understood why people don’t do it as well. Grouping allows you to manipulate larger numbers by considering them to be the same unit.
yayy! i also figured out that, counting on multiples of 3 or 4
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!
Glad to know I’m not the only one.
Same here.
Same. I am putting this down to my autistic brain. Could be other neurodivergent people answer these differently too
Same here, also autistic.
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?
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'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.
This had me thinking: thats why there's a comma every 3 digits. But then why don't we mark decimals every 3 digits
clarity,
Maybe it's just because I'm so used to our current way of writing numbers, but to me, a number like 12,345,678.098,765,432 would be extremely confusing to read.
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💀
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.
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.
Yeah I also have dyscalculia and dyslexia so I get this. I’ve always had a really good number sense, and been great at mathematics on a conceptual level. I’ve just been a little slow with computation.
I don't know if I have legit dyscalculia but my issue seems to be that my brain tries to interpret numbers as letters or words rather than sums. It takes a while for me to "translate" them into their numerical values so any calculation requires more mental processing than it probably should.
By the way, I just tried to divide 66 by 3 in my head and it went like this, verbatim: "I have no idea what the answer is, but let's divide 66 by two instead because that's easier. That's should be 33, I'm pretty sure. So I have two 33s. Now if I subtract half of... Actually, scratch that. Let's subtract a third of 33, because that's easier. That's eleven. If I add together the two elevens from each 33, that's 22. If I compare that to what I have left of 33, turns out that's also 22. So, the answer should be 22."
@@RelativelyBest Thats proportional math. Its faster than regular computation, and is what really good mathematicians start with.
I always calculated by removing the ends (47 - 22, 40 - 20, 7 - 2) and divided by a brute force method like that, finding any near multiple I could. I am terrible at math and hate it, but I am in awe at what it can accomplish.
@@pauldeddens5349 Interesting. I was always so bad at math in school I never learned any actual methods, so I end up doing whatever seems easiest to me. At once point I basically reinvented pi trying to work out the circumference of a circle, because I never made it far enough to learn about it. A friend of mine, who _is_ very good at math, found that amusing.
99 and 100 feel closer because they are closer by percentage. 99 is 99% of 100, whereas 9 is only 90% of 10.
But why would people say 9 is closer to 10? As opposed to saying 11 is closer to 10(which it is)?
That is exactly the logarithmic "fuzzy" representation Joe talks about later on in the video. It's not just our number sense either. Most of our senses work logarithmically.
But even that's not entirely accurate. For scales that are very, very far out of our normal realm of experience (say the size of atoms on the small end or the size of galaxies on the large) even a logarithmic sense of numbers isn't quite fuzzy enough for our brains to intuit and we just lose track of the concept of scale entirely. You _might_ be able to intuit the 384,400km distance to the Moon by thinking in terms of say, 85 coast-to-coast road trips across the US, especially if you've made that trip before (and even then you'll probably measure it in units of time rather than distance), but you have absolutely no concept of how far away Pluto is, or even Jupiter. There are videos on RUclips of people making to-scale "models" of our solar system and ending up with Pluto being halfway across a city when the Earth is only a few meters away from the Sun. Just wildly out of the scope of human intuition. And that's still within our solar system. The scale of our galaxy, never mind the entire universe, can only ever be understood through math and measurement. Intuition will never suffice for numbers that big, no matter what tricks our brain tries to pull.
@@joex9865since 11 is larger than 10 it feels further away from 10 to me. "Closer" implies "closer without going over" in my head.
1:31 a light emitting stone tablet?
Stone Tablet P7 Pro Ultra
0:33 umm yeah that's seven lol... interestingly enough, as soon as it flashed, I was caught off guard by you saying eight cuz I could tell quickly, it was not.
*"There are FOUR lights!!!"* 😏
Calm down, mr Picard.
@@MeesterG 😉
These four words always give me goosebumps instantly.
@@DeltaNovum 🪿
Shaka when the walls fell
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. 😞
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.
There's a related concept in the book- "tharn". When a rabbit has too much to think about, their brain shuts down entirely.
There's a psychological model that the human brain has its own "hrair limit" of about four to seven, and if you try to hold more concepts than that you drop all of them, you go tharn.
Okay, honestly at first I was trying my best to get everything right and try to “fight” against what you were saying, but then as soon as you brought up people writing from right to left thus their number line increases to the left- I have no words except that my mind is blown. I physically and mentally cannot imagine a right-to-left as easily as a left-to-right. Even thinking more just typing that out because it’s not natural at all to me. Paused to write this comment- will update on more mind breakage.
Update - I need MORE KNOWLEDGE.
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!
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. 🙂
Damn, I just found out I'm a robot
Well done, Deckard. How's the Electric Sheep?
ikr
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.
1, 4, 3, 5, 2, 6. (I think. This is posted before much more of the video has happened.)
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.
So we can add touch to sounds, sight and imaginary representations as exhibiting this. Also, I wonder where braille fits in?
"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.
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.
Did you know that 4 in roman number clocks is iiii (IIII) and not iv (IV)?
They didn't have locks back then :P
I like this channel because it answers questions I didn’t know I had
I wondered about animals and counting when our cat had kittens. There were times when she seemed to count them, and she always knew when one was missing.
Ducks and other birds do a similar thing. They watch their babies swim through the water and onto the shore, one ... two ... three ... four. If they have more than four, they stop "counting" and keep going up the bank. I've also seen it with cats/ dogs / any animal that has litters, really. The "runts" get left behind.
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.
ya i counted 6 and knew he played a trick when he said 8.. but still got it wrong :D
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'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.
@@EdgarRoock- I have seen that notation, too
If the smaller number is left of the larger, subtract
Thus, IIL is 48
8:59 Glad you touched on right-to-left cultures, that was my hypothesis
I don't believe that there are any such languages in use today, but I wonder if someone whose native language was written boustrophedonically would show no difference in the right/left measure.
You did a drive by with that dyscalculia name drop. Please do a deeper dive into that.
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.
It seems like it should cut off at 5 since beyond 5 you're adding another hand if you use fingers as a general metric that humans consistently carry.
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.)
SO: Who leaked the info to the chimpanzees??
You'd think chess would have the same belief. Probably wasn't invented by monkeys though 😂
@@greegorygrimlee5487 chess was definitely invented by monkeys...
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
@@Ivyjiang2326 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
Thank you for the mention of dyscalculia in your video. It's helpful for people to be aware that dyscalculics don't have that same innate sense for numbers, including the ability to subitize (see small quantities without counting individual dots), as most of the population.
Unsure if this is related, but at 7:12 you point out that we think logarithmically, we also perceive volume this way too. That's why guitars have logarithmic potentiometers rather than linear because it feels more natural for the volume curve.
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)
@@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.
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....!
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.
He’s read Stanislas Dehaene and read the quanta magazine article on this
I remember this concept has been beautifully explained before in other famous mathematics channel. The concept of "numerosity" and "Extracting numerosity" si given there
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
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 🙄
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.
This makes it more understandable how spatial reasoning task performance has been found to correlate with mathematical task performance too!
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.
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!
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 😌
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
Before I became Japanese Language Teacher, I was assistant of some of them, thus I interacted with university students. One of them said she had dyscalculia. She didn't have much troubles with Japanese, understood quite well grammar, pronunciation and writing. She wasn't an eminence, but neither a challenged student. However, when she had to say numbers in Japanese or write them... The dyscalculia affected that too! Our native language is Spanish, and yet, her troubles with numbers traslated into Japanese. It was a very peculiar experience.
The way the dots are arranged matters a lot, if evenly counting them is far faster
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.
The fact that you partition 7 into 3+4 is exactly the message of the video: you can't deal with it directly. So I'm not sure you're getting any better at recognizing numbers directly. You're just getting better at partitioning.
@@terahlunahyou seem to be making assumptions on OP's part. Where did they imply that they were better with larger numbers?
@@LilFeralGangrel Now that I'm re-reading it, it appears I did misunderstand OP.
Apologies, my brain must have merged OP's message with a previous comment.
I saw the seven dots as a pentagon and an unattached pair, but I've learned to "chunk" in groups of five (and when counting up dice pips, ten) because it keeps the multiplication a lot simpler.
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.
I love that you always wake up my curiosity. THANK YOU!
Great Counting Crows reference at 12:41. Well done.
As someone with synesthesia with numbers this was fascinating.
That Counting Crows reference was top tier. You deserve some Hard Candy. 😉
Beat me to it. Well played with Hard Candy, by the way.
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.
Mr. Jones predicts A Long December! That crow knows how to count.
That was awesome. It tickled my brain
I used to work in pharmacy as a tech. When we were hiring people we had to test them to see if they could just "see" up to five. The way he said most people can just see to three. It was the number one disqualifier, more than background checks.
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!
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!
i learned this when i was looking for specific lego pieces based on number of 'nubs' as a kid
11:15 "one plus one doesn't equel one" Terrence Howard would disagree
Infants are better at simple math than Terrence Howard.
Oh shoot not that guy
I swear this is the same video in a parallel uni.
All of this makes me feel like its all about the ratios between things.
1. I legit found a website where you can type 2 numbers and it will tell you which is larger.
B. Switching the larger and smaller buttons wasn't a problem for me. I'm the type of person who can read backwards, upside-down, and upside-down and backwards. I write with my left hand but my right hand is dominant.
27. Everything else for me is spot on.
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 🤣
@@Ana_crusis ah, so it is..thank you. Wonderful
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
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.
7:35 my smart brain immediately raised the issue of right hand bias.
I so love that you addressed that right away!
Also yes! I absolutely manage numbers via a mental construction of a number line, and a graph.
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.
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'.
What's that? Can you elaborate some? Thanks.
@@boomergames8094 Here's an example in polish language:
1 cat - 1 kot
2, 3, 4 cats - 2, 3, 4 koty
5, 6... cats - 5, 6... kotów
many cats - wiele kotów
Seems that's a common pattern among Slavic languages.
I worked at a factory where counting up to 12 at a glance became necessary, and what I found was that I was able to accurately recognize groups of 3 super easily, 4 through 6 were fairly easy, and after that, I would split them into sub-groups. So, if something had 11, I would see a 5 and a 6, or else 3 3s and a 2. Which subgroups things got sorted in was based on their orientation. If there were clear triangles or squares visible at a glance, those would get grouped as 3s or 4s.
I was interested in this, so I tested it with my friends and found that I could count coins at a glance accurately up to 12, while my friends could only do 5 or 6. I'm willing to bet if I'd worked at a factory where I was expected to count 24 or more, I'd have improved, but I'm sure there's a limit.
I am no longer going to call it math class. Its now muchness class... i like that better.
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!
I like your excitement re: knowing this!! (!!)
I can do 5 easily, and 6 most of the time. I think this comes from rolling lots of dice. Lots.
@@boomergames8094 Yea, for me numbers up 6 have "shapes". 1 is a dot, duh, 2 is a line, 3 is a triangle, 4 is a square, 5 is a crossed box, 6 is two rows of threes. Then I hit 7 and completely fall apart.