There's a Big Difference In How Your Brain Processes the Numbers 4 and 5 (sciencealert.com) 81
Longtime Slashdot reader fahrbot-bot shares a report from ScienceAlert: According to a new study [published in Nature Human Behavior], the human brain has two separate ways of processing numbers of things: one system for quantities of four or fewer, and another system for five and up. Presented with four or fewer objects, humans can usually identify the sum at first glance, without counting. And we're almost always right. This ability is known as "subitizing," a term coined by psychologists last century, and it's different from both counting and estimating. It refers to an uncanny sense of immediately knowing how many things you're looking at, with no tallying or guessing required.
While we can easily subitize quantities up to four, however, the ability disappears when we're looking at five or more things. If asked to instantly quantify a group of seven apples, for example, we tend to hesitate and estimate, taking slightly longer to respond and still providing less precise answers. Since our subitizing skills vanish so abruptly for quantities larger than four, some researchers have suspected our brains use two distinct processing methods, specialized for either small or large quantities. "However, this idea has been disputed up to now," says co-author Florian Mormann, a cognitive neurophysiologist from the Department of Epileptology at the University Hospital Bonn. "It could also be that our brain always makes an estimate but the error rates for smaller numbers of things are so low that they simply go unnoticed."
Previous research involving some of the new study's authors showed that human brains have neurons responsible for each number, with certain nerve cells firing selectively in response to certain quantities. Some neurons fire mainly when a person sees two of something, they found, while others show a similar affinity for their own number of visual elements. Yet many of these neurons also fire in response to slightly smaller or larger numbers, the researchers note, with a weaker reaction for quantities further removed from their numerical focus. "A brain cell for a number of 'seven' elements thus also fires for six and eight elements but more weakly," says neurobiologist Andreas Nieder from the University of Tubingen. "The same cell is still activated but even less so for five or nine elements."
This kind of "numerical distance effect" also occurs in monkeys, as Nieder has shown in previous research. Among humans, however, it typically happens only when we see five or more things, hinting at some undiscovered difference in the way we identify smaller numbers. "There seems to be an additional mechanism for numbers of around less than five elements that makes these neurons more precise," Nieder says. Neurons responsible for lower numbers are able to inhibit other neurons responsible for adjacent numbers, the study's authors report, thus limiting any mixed signals about the quantity in question. When a trio-specializing neuron fires, for example, it also inhibits the neurons that typically fire in response to groups of two or four things. Neurons for the number five and beyond apparently lack this mechanism.
While we can easily subitize quantities up to four, however, the ability disappears when we're looking at five or more things. If asked to instantly quantify a group of seven apples, for example, we tend to hesitate and estimate, taking slightly longer to respond and still providing less precise answers. Since our subitizing skills vanish so abruptly for quantities larger than four, some researchers have suspected our brains use two distinct processing methods, specialized for either small or large quantities. "However, this idea has been disputed up to now," says co-author Florian Mormann, a cognitive neurophysiologist from the Department of Epileptology at the University Hospital Bonn. "It could also be that our brain always makes an estimate but the error rates for smaller numbers of things are so low that they simply go unnoticed."
Previous research involving some of the new study's authors showed that human brains have neurons responsible for each number, with certain nerve cells firing selectively in response to certain quantities. Some neurons fire mainly when a person sees two of something, they found, while others show a similar affinity for their own number of visual elements. Yet many of these neurons also fire in response to slightly smaller or larger numbers, the researchers note, with a weaker reaction for quantities further removed from their numerical focus. "A brain cell for a number of 'seven' elements thus also fires for six and eight elements but more weakly," says neurobiologist Andreas Nieder from the University of Tubingen. "The same cell is still activated but even less so for five or nine elements."
This kind of "numerical distance effect" also occurs in monkeys, as Nieder has shown in previous research. Among humans, however, it typically happens only when we see five or more things, hinting at some undiscovered difference in the way we identify smaller numbers. "There seems to be an additional mechanism for numbers of around less than five elements that makes these neurons more precise," Nieder says. Neurons responsible for lower numbers are able to inhibit other neurons responsible for adjacent numbers, the study's authors report, thus limiting any mixed signals about the quantity in question. When a trio-specializing neuron fires, for example, it also inhibits the neurons that typically fire in response to groups of two or four things. Neurons for the number five and beyond apparently lack this mechanism.
Depends on the "shape" (Score:3, Insightful)
If objects are arranged roughly in the same way they appear on a number die, I GUARANTEE you that people can instantly count five or six.
The human brain is pictoral and excels at categorizing pictures. We know what the picture of "four" looks like, and we also know what "five" and "six" look like if they line up with the expected pictures.
Re:Depends on the "shape" (Score:5, Insightful)
If objects are arranged roughly in the same way they appear on a number die, I GUARANTEE you that people can instantly count five or six.
The human brain is pictoral and excels at categorizing pictures. We know what the picture of "four" looks like, and we also know what "five" and "six" look like if they line up with the expected pictures.
The paper is about different neural encodings for different quantities of things. I don't have access to anything except the abstract paragraph so I don't have details about what (or whom) they studied and how. I'm not here to bravely defend the study against nay-sayers.
I can say that 5 pips on a standard die is probably processed more like a glyph, like the roman numeral V and the Arabic numeral 5, than it is processed like a scattering five objects. Which would make the point irrelevant to the study.
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Re:Depends on the "shape" (Score:5, Interesting)
What seems curious to me is that in a number of languages, numbers up to 4 are handled differently than numbers from five and onward. For example, in Icelandic, there's a series of declensions for the first four numbers (across 3 genders times 4 cases (12x), with #1 additionally across singular vs. plural (24x)). But once you get to five and beyond, there's no declension whatsoever - all nuance gets lost. It leads to a joke:
"An immigrant walks into a store. In broken Icelandic, he turns to the shopkeeper:
"Má ég fá fjórir banana?" (May I have four (masc. nominative plural) bananas?)
"Ha?" (What?)
"... má ég fá... fjórum banana?" (... may I have... four (dative plural) bananas?)
"Ha?" (What?)
"... fjögur? Fjögurra? Fjórar?" "... four (neuter nominative plural)? Four (genitive plural)? Four (feminine nominative/accusative plural)?)
"Ha?" (What?)
"...." "... Okei, má ég fá FIMM banana?" (Okay, may I have FIVE bananas?)
"Já, gerðu svo vel!" ("Sure, here you go!")
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I guess to jump into a different linguistic family, from another language I'm learning, Ukrainian... for counting most things, declension stops after 3... but for some things it stops after 4. For example, counting hundreds, it's:
(STO, one hundred).
(dviSTI, two hundred)
(trySTA, three hundred)
(chotyrySTA, four hundred)
' (p'yatSOT, five hundred)
(shistSOT, six hundred)
(simSOT, seven hundred)
(visimSOT, eight hundred)
' (dev'yatSOT, nine hundred)
Everything
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Many languages consider 2 to 4 to be different to 5 and up, and such grammatical peculiarities are everywhere.
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+[-->-[>>+>------.>>>+.>>..+++[.>]>>>+
(I admit, I copied it from Wikipedia.
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The early arabic numerals were outright just n line segments in a pattern, at least up to 4. Probably 5-9 originally were too, but that's just too many I guess.
Re: Depends on the "shape" (Score:2)
This. Exactly what came to mind as I read this
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Yeah, me too. That wouldn't be counting, it's pattern recognition.
You can prove it to yourself by putting the pips in a non-standard fashion and surprising people with it during a dice game...compare their reactions to what you get with standard dice.
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Pretty sure that's what they are doing when they look at numbers 4 and under as well. They aren't counting, it's pattern recognition. It's just that the amounts of patterns is much less with 4, and gets exponentially higher as the numbers go up. I'm sure when people estimate quickly they are breaking things down in smaller groups of let's say 4 as well, and just adding them up.
Re: Depends on the "shape" (Score:4, Interesting)
You should see the studies on primates related to this. They absolutely blow away humans on their ability to see a set of objects and duplicate the number and positions in a fraction of a second.
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I saw a documentary on this as well. Very interestingly they discovered chimpanzees all literally have perfect photographic memories - almost as their brains lacking a language center is more of a tradeoff than the obvious limitation it seems to be.
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You should see the studies on primates related to this. They absolutely blow away humans on their ability to see a set of objects and duplicate the number and positions in a fraction of a second.
I could do better if they used potatoes instead of apples in the example.
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Huh, I had also been about to post something like: "I can subitize up to 6, you insensitive clod!" but I hadn't considered that 6-sided dice might be why I can do that. Now I wonder if the board games we grew up with as children more often featured dice with more sides, if that might have been able to raise our brains' limit for this.
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Probably that's because a 6 on a standard die is represented by a 2x3 pattern. I also can recognize 9 items as 9 items if they are in a 3x3 grid. Recognizing 7 or 8 is much harder. But I think for higher rows/columns I need to count. I don't know if I can do 4x4 without counting rows/columns
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Now I wonder if the board games we grew up with as children more often featured dice with more sides, if that might have been able to raise our brains' limit for this.
I used to work with a guy who spent some time 'proselytising' the use of flash cards for children in their early years. The basic idea is that you create a (large) number of cards with a (varied: 1 to ~30) number of objects 'scattered' on it, with the number written on the back. You briefly show the card to the child, and say the number. Next card. Next card. Five minutes a day of this, every day during their language and number formative years, and they gain the ability to instantly 'recognise' quantities
Re: Depends on the "shape" (Score:2)
It depends, you can process numbers of objects up to 9 or 10 because you see groups of 3 or 4 regardless of shape and then just add and multiply really fast. Iâ(TM)m sure itâ(TM)s a split second slower but not sure you can measure it consistently. It also depends on the objects, smaller and uniform objects like screws are very hard to start grouping once it exceeds 6 or 7.
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If objects are arranged roughly in the same way they appear on a number die, I GUARANTEE you that people can instantly count five or six.
Oddly enough, nerds are fumbling through their D&D die bag wondering exactly what common representation of the number five you're referring to.
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Some people. Sure.. And I admire those who do.
It's like how some people can add and subtract without thinking.
It's not a skill that has ever really 'clicked' with me. I'm... not young and I still add/subtract on my fingers.
If someone is playing dice, I can see that it's a high or low number, I remember 'one' dot as 'lowest' and 'two full rows' as 'highest' but unless it's only those two extremes, I need to count to work it all out.
Re: Depends on the "shape" (Score:2)
Not really that hard, imagine the numbers from 0-10 as a sectioned line in your head then slide up and down that line for the numbers. You can do this very quickly starting right to left and you only have to worry about carryover once in a while, which you put in your locus.
Re:Depends on the "shape" (Score:4, Insightful)
And you would be wrong. Recognizing a configuration you new in the past had 5 or 6 of s thing in it is not the same as "instantly counting them". This is, incidentally, a reason we have scientists and we do not let everybody just contribute to science. We expect things to come with proof, not half-assed guesses.
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If objects are arranged roughly in the same way they appear on a number die, I GUARANTEE you that people can instantly count five or six.
The human brain is pictoral and excels at categorizing pictures. We know what the picture of "four" looks like, and we also know what "five" and "six" look like if they line up with the expected pictures.
The human who learned how many sides are on a six-sided die before...why are they looking at "six" instead of the known object that is a six-sided die? The human who learned what a duck looks like, would instantly recognize that object as a duck, not "two" because they come with two feet.
The human brain does categorize; and a six-sided die is a six-sided die. Not simply "six". The drunk brain would argue beer bought with plastic rings is what "six" looks like. The mechanic brain would argue an inline-6
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Although, from an old story on Radiolab, babies and toddlers don't understand the concept of numbers, and even some societies that don't have mathematics might not have good concepts of counting even up to ten. But they do seem to underastand logarithmically. That is, 1 is easy. Then "a few", "a lot", "a huge amount", etc. So telling the difference between 1 and 2 is easy - 2 is twice as large; but the difference between 8 and 9 is not so much, since 9 is only 1/8th larger. With toddlers, they may know
I can't count, you insensitive clod! (Score:4, Funny)
I only have words for one, two, and many!
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ooo, since I have words for zero, one, two, a few and many I'm clearly some better than you...oh wait I don't know how much "some" is. Nevermind.
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Re:I can't count, you insensitive clod! (Score:5, Funny)
I only have words for one, two, and many!
According to Baldrick (from Blackadder), it's "one", "two", "three", "some".
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See you Blackadder, raise you Watership Down.
According to the truer-than-I-thought epic tale of rabbits and their interspecies relationships, rabbits can count to four - any number above 4 is "hrair" (many). Now this study comes along and says this applies to humans as well, is Watership Down cited as a source?
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Re: I can't count, you insensitive clod! (Score:4, Funny)
Re:I can't count, you insensitive clod! (Score:4, Funny)
I only have words for one, two, and many!
It was only a dream, Bender. There's no such thing as two.
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Trolls count to Many.
One, Two, Three, Many,
Many-One. Many-Two, Many-Three, Many-Many,
Many-Many-One, Many-Many-Two, Many-Many-Three,
Many-Many-Many-One, Many-Many-Many-Two, Many-Many-Many-Three,
LOTS.
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Well, with this discovery you can probably give yourself credit for Zero, One, Two, Three and Four before going to Many.
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Is this why communists have such a hard time with 2+2=4?
They seem to think 2+2=5 for some reason.
Woktards
When dealing with capitalist scum, we always add your big guy's take.
Re: This may explain woketards (Score:2)
Of course, only recently counted the thumb. (Score:2)
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Of course, there is a state change and the brain switches to a new algorithm at 5. For a significant amount of humanity's development we used our thumb to count. Once we discovered 5 and assigned it to the thumb we needed a new system, that however does not mean the old "wiring" goes away. You can see little kids learning to count using the old wiring.
The preceding is completely fabricated, made up, false, a lie, bs, etc. I just wanted to do my part polluting chat gpt. Looking forward to someone turning in a paper at school with the preceding. ;-)
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Unnecessary, I checked online and confirmed that the counting system used by rabbits in "Watership Down" only goes up to four - any number greater than four is "hrair" (many).
This may have already happened, I'm sure chat gpt has been exposed to that book.
Wrong subject (Score:2)
This is not about the numbers, i.e. doing math. This is about a concrete situation where you are presented with a number of objects, i.e. essentially image processing and image content identification.
They should also study 7 and 9 (Score:4, Funny)
People are a bit scared of 7, naturally - because 7 ate 9.
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We cannibals worship 7, you insensitive but tasty clod!
Of course they're different (Score:2)
Four gets a rising emphasis, five is just an afterthought.
https://www.youtube.com/watch?... [youtube.com]
I see ... (Score:2)
THERE ARE FOUR LIGHTS! (Score:4, Funny)
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I don't have access to the paper, but it's likely they're using an MRI scanner.
Probes only allow the detection of activity in the immediate vicinity of the probe. An MRI allows the detection of activity anywhere in the brain, so it's commonly used in studies like this.
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Okay, but how do they get enough resolution to see individual neurons firing? Or do they happen to be and/or fire in isolation such that monitoring the general vicinity is sufficient?
Reflected in language? (Score:5, Informative)
The book "Alex's Adventures in Numberland" by Alex Bellos talks about this. There is a difference in the way we treat numbers 1, 2, 3, possibly 4, compared to numbers 5 and above. The author suggests this is reflected in number systems. Roman numerals start I II III and there are two alternatives for four, IIII and IV. In Chinese too the first three numbers are groups of lines before it changes with four. Our Indio-Arabic glyphs for 1, 2, 3 also originate as one, two, or three lines joined up.
I would suggest that case endings in Slavonic languages might be another indicator. For two, three, or four of something you use the genitive singular (roughly: "three of apple") but then for five or more the genitive plural is used instead. (Things may get muddy when dealing with compound numbers like forty-two where you could use the same case ending as for two.)
What other languages or writing systems have a change between 2,3,4 and larger numbers?
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Icelandic (and I think Fareoic) has a big difference between of the first 4.
There is also something like a word like "both", but for three and four.
https://ielanguages.com/icelan... [ielanguages.com]
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What other languages or writing systems have a change between 2,3,4 and larger numbers?
Romanian has singular ("one apple"), 2-19 plural ("five apples"), and what I would call "20+ plural" ("54 of apples"), but that pattern repeats itself somewhat, for example "100 of apples", but "105 apples", never "105 of apples". But we have "120 of apples" because the last two digits are above 19.
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This is useful also for understanding animals. After all, we know many animals, common housepets like dogs and cats included, can count to a basic degree. Some animals are 0, 1 and many (that is, they know the absence of something, the presence of one thing, and two or more things). Of course, other animals have the ability to count higher.
This is usually discovered by showing the animal a counted number of say, a treat, then handing them the treats one by one. If you're short, they actually do indicate and
How many... (Score:2)
How many fingers am I holding up Winston?
Four. I suppose there are four. I tried to see five. I wish I could.
This appears in some languages (Score:2)
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At first, I though another frivolous FA but the whole thing is very interesting after further analysis.
Another poster has asked how they analyze data from the neurons, which was one of my concerns:
https://science.slashdot.org/c... [slashdot.org]
Anyway, if you go along with the vision of the neuron network theory, you are suggesting that the network could have adapted because of Slavic languages ways to express things, correct? This brings an interesting question anyway about their samples.
In the end, it doesn't really mat
That's the way my dog counts (Score:3)
one, two, three, four, bazillion!
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And rabbits. one, two, three, four, hrair
Numbers | Radiolab Podcast (Score:1)
Give it a listen for more science on what we're born with vs. what we learn about numbers
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My daughter's experience (Score:2)
Back when my kids where be evaluated for school, one of the tasks was counting stacks of objects. The instructor had stacks of random things set up on the table. My daughter replied to each as the instructor pointed: 14.... 9....12... all without counting. Fast forward to today - we NEVER play SET (https://boardgamegeek.com/boardgame/1198/set) with her because she still has that ability to see objects and counts quickly. As soon as a card would be flipped she'd say SET and always be right. I suspec
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Five requires a thumb (Score:2)
Four fits on your fingers, five requires a thumb.
You read it here first.
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So, the Viking Counting Method (Score:2)
Should be extended to 1, 2, um, 3, er, 4, many, more, hell of a lot, and I surrender" (not stopping at 3).
Lost count again (Score:2)
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20% difference, right? (Score:2)
20% is a big difference, for sure!