by igpay on 3/3/22, 10:24 AM with 194 comments
by alchemyromcom on 3/3/22, 8:29 PM
by feoren on 3/3/22, 8:06 PM
Sometimes numbers are for quantifying a pile of things, and 255 and 256 are basically the same.
Sometimes numbers are for cryptographically signing things, and 255 is extremely secure while 256 is completely vulnerable.
Sometimes numbers are for arranging tournaments, and 256 is a tremendously useful number while 255 is super annoying and you should look for another.
Sometimes numbers are stored in a single byte, and 256 (=0) is the friendliest number you will ever know, while 255's words are BACKED BY NUCLEAR WEAPONS.
Sometimes infinity is a useful number, sometimes it's not. Sometimes 1/2 is a useful number (pies), sometimes it's not (babies). Sometimes sqrt(-1) is a useful number, sometimes it's not. Sometimes the sum of all positive integers equals -1/12; sometimes that's stupid.
All of these situations may call for visualizing numbers differently.
by encoderer on 3/3/22, 7:46 PM
I am a successful software developer and I’m terrible at math. To me, 6+3 is not an interaction between two different anything, rather, it’s a key in a hash table where I’ve stored “9” as the value. All arithmetic is rote memory recall for me. I work with complex numbers by just breaking them down into multiple steps.
Now I’m wondering if I should challenge my brain to do this differently.
by ajkjk on 3/3/22, 7:51 PM
Although now that I think about it there is still some element of what's described in this article. There's no visual shape involved in the way I model numbers, but it resonates to think of 7 as "10 with a 3 missing", but also as "5 with a 2 on it". The concepts are built in reference to their closest multiple of 5, and slide between different equivalent forms as necessary in calculations.
By the way, the way I do mental math without images feels like it is using sounds and words for the short-term storage and recall. The language brain seems good at putting something aside for a minute and then bringing it back afterwards with a low chance of error, like repeating something someone just said back to them verbatim even though you weren't really listening.
The one method I am sure _doesn't_ work well for mental math is picturing the grade-school algorithms on an imaginary sheet of paper. For whatever reason it is very error-prone. I once did an informal (definitely unscientific) survey on this (30 or so people IRL plus like 100 reddit users) and iirc there was a strong correlation between "imagining the pen-and-paper algorithm", "being bad at mental math", and "not liking math". Wish I still had the data from that -- all I remember is roughly confirming my hunch that those were related. I also wrote a blog post about this a few years ago (https://alexkritchevsky.com/2019/09/15/mental-math.html) but I wish I had included the survey information in there, it would have been much more interesting.
by hateful on 3/3/22, 6:49 PM
This is the same thing as map reading or what we do in programming. The thing that's disappearing in this comic: https://heeris.id.au/2013/this-is-why-you-shouldnt-interrupt...
I also realized early on that I could count way faster if I fought the urge to say the numbers in my head because the idea of the number would still be there. I started by saying (eh eh eh eh eh) in my head instead of (one two three four five). Eventually you can do things like run your finger across a comb and instantly know how many bristles you passed - that gives you a tactile response for each number rather than the words themselves. If you count by 2s 3s or 5s you can go even faster (which is what the circle is doing in the article). Shortening the "time" axis of the counting.
by chrisstanchak on 3/3/22, 6:27 PM
https://www.youtube.com/watch?v=OPTOCwQoYR4&t=29m23s
This is how my toddlers are learning. It's really good.
by johnatwork on 3/3/22, 6:42 PM
I explained it (poorly) to my wife once and she made fun of me about it. Well until our son told us years later out of the blue that it's how he sees numbers.
by Quai on 3/3/22, 7:41 PM
by yeetard on 3/3/22, 7:18 PM
by teaearlgraycold on 3/3/22, 7:47 PM
by one-more-minute on 3/3/22, 7:19 PM
I'm also curious if you are an unusually quick calculator compared to others you know. Synaesthetes can sometimes turn their condition into a talent, like the famous Shereshevsky who had a photographic memory; every experience was utter sensory overwhelm, making mundane information very memorable.
by pavlovskyi on 3/3/22, 8:48 PM
There is no other feeling in my mind which give me that amount of understading,but it is an understanding which cannot be formulate properly to other person. I feel it as an phenomena which origin started in my mind and grow there for my whole life (which is highly correlated with my introvert pov). Thanks for that thoughts, all best.
by cecilpl2 on 3/3/22, 7:27 PM
The unique thing I think I have is that I visualize long strings of digits as notes on a musical scale. 735 is high-low-middle. I have found I can retain strings of up to 15 or so digits in short-term memory by chunking them into triplets and memorizing them as arpeggio chords, or by their relative positions.
by robofanatic on 3/3/22, 8:20 PM
by vedran on 3/3/22, 11:04 PM
by usgroup on 3/3/22, 9:31 PM
Your sort of just build everything you need out of analogs. It makes me think that if we were not indocrinated into numbers from an early age, we'd end up inventing them as an abstraction to the sort of thing you have to do when you're trying to avoid numbers.
Another one I suggest trying is expressing and exploring linear regression without reference to probability theory.
by duncan_mcisaac on 3/3/22, 11:47 PM
by darreld on 3/3/22, 9:04 PM
by gumby on 3/3/22, 8:44 PM
I remember as a child trying to draw the shape of the number “line” (it curls and twists) and being surprised that I was unable to do so.
This has never seemed to have given me any advantage or disadvantage in learning more complex maths than one gets in primary school. But since so much arithmetic is done in numbers less than 100 (or scaled down to that range) it does make a lot of things easier.
by makach on 3/4/22, 7:06 AM
This is almost how adding, subtracting numbers is taught in schools here. I didn't notice this pattern when was a kid (if this was the pattern back then) but after having sat down with both my kids I can see the pedagogy clearer.
This actually inspired me to keep up with the literature the kids have to go through when they are learning math. I am a little surprised that I find it so enjoyable. There are methods I completely forgot and methods I can grasp easily and add to my existing knowledgebase..
There is always something to learn, even if it is elementary!
by dusted on 3/4/22, 7:51 AM
At the same time, 8 is sometimes a 10 with a notch with room for 2..
Question: Did you find math easy from the beginning of school? I had immense trouble, it just didn't make sense no matter how long I looked at the shapes.. What logic was there behind the 6 shape and the 1 shape together makes the 7 shape..
Do you see negative numberse as different from positive ones, or do you just see them as positive numbers that have to be subtracted? Depending on the context, they're just a subtraction, other times I see them as white and black dots, and when there is equilibrium it is a grey plane of 0, and when add some to the plane, that number of that sign will be visible, for example, you have 0 + 3 = 3 white ones, then you add two black ones ( 0 + 3 + (-2) ) = 1 and the two black ones merge with the white ones and become grey and then you see only the one white one that 's left.. It goes that if you then add two more black ones, ( 0 + 3 + (-2) + (-2) ) = -1 one of the black ones merge with the remaining white one, and there is one black one left on the plane.
I eventually got the basics.. these days, I still prefer using letters instead of the actual numbers, and deal with the abstract instead of the concrete and just let the computer do the calculation if a concrete value is needed.
by tempestn on 3/3/22, 11:19 PM
by trickster_ on 3/12/22, 5:30 PM
by paradite on 3/4/22, 5:38 AM
Wrote about my experience a while ago: https://paradite.com/2017/09/17/bilingual-numbers/
by ChrisKnott on 3/3/22, 8:35 PM
In France, "97" is said "Quatre vinght dix sept", i.e. 4x20+10+7. This is apparently acceptable to the brain as a final answer, there's no way to collapse it to "90+7".
by NylaTheWolf on 3/4/22, 10:00 PM
On a related note, I wouldn't be surprised if synesthesia is actually more common than we currently think because a lot of people who have it think it's normal or never thought anything of it.
by Art9681 on 3/4/22, 1:58 AM
by chronolitus on 3/4/22, 10:41 AM
The consequence is, I don't think there is a 'right' visualization for numbers. You either have an exact model of mathematics in your brain, or you have some approximation thereof, which by definition has to be wrong in some way (but is easier to get / reason about). There is only one true model (if we all agree to use the same axioms, etc), but an infinite amount of approximations, which make them each unique. Fun to think about.
by thekiptxt on 3/4/22, 5:14 PM
by laszlokorte on 3/3/22, 6:42 PM
by rplnt on 3/3/22, 8:25 PM
I see time differently, days of the week, yearly calendar, distance units, temperature. All these, maybe more I can't recall now, visualize different from just numbers. E.g. the year is a loop. If I want to recall a month name, I always see a part of that loop, and the camera is not fixed. I'm fairly certain my mind didn't come up with this on its own, but there were some visual that got paired with it. Same with numbers I suspect, but this one is more obvious.
by Mo3 on 3/3/22, 7:17 PM
by bricemo on 3/3/22, 7:35 PM
by dhosek on 3/3/22, 11:08 PM
by seiferteric on 3/3/22, 10:36 PM
by busyant on 3/3/22, 9:23 PM
"5" and "6" are definitely guys.
The evens tend to be a bit kinder than the odds. Hasn't helped me with arithmetic, though.
by dmccunney on 3/11/22, 6:05 PM
The world we live in is a mental model created by our brains, and the data that underlies the model is supplied by our senses. The model we make will differ depending on which of our senses is dominant.
For example, my primary sense is vision. When I read fiction, I often see pictures in fiction my head. I can be thrown out of a story because the pieces don't fit together, and I find myself saying "You can't get there from here!"
But vision isn't everyone's primary sense. My SO is a good example. She's extremely nearsighted. Without her glasses, anything farther than about 2' from her face is a blur. Her primary sense is hearing. When she asks me a technical question, my first impulse is to grab pencil and paper and draw a diagram. That conveys nothing to her, so I need to find a different metaphor based on hearing to describe the underlying concept.
I corresponded with a chap years back whose primary sense was touch. He felt holes in arguments. And in the oddest case I recall hearing of, there was a chap who could not find his way to the office in the morning. He was not stupid, and was a trained engineer. But testing revealed he was not visual at all. Landmarks conveyed nothing to him. He did have a strong kinesthetic sense. So he was driven from his home to his office in a low slung sports car that transmitted every dip and curve in the toad to the passengers. Thereafter, he could find his way to the office with no problem,. because his body remembered what the drive felt like.
I've spent a fair it of time over the years exploring where people are coming from in discussions. "Yes, I understand what you believe. You've made that quite clear and explicit. My question is why you believe it? How did you adopt this belief? What makes it emotionally satisfying to you?' Belief systems like religion and politics live on an emotional level, and aren't usually amenable to rational argument but cause they aren't rational in origin.
What our primary sense is and how that affects your view of the world my be more critical than you assume. No, you aren't representative, and others may not share your experience.
by gingkoguy on 3/3/22, 11:06 PM
by Razengan on 3/4/22, 3:08 AM
Would they start with 2D numbers (like our “complex” numbers)? Would fractions be the default way of counting instead of whole numbers?
Or something completely different, like thinking of color shades instead of “words” when thinking of numbers as we do.
by visviva on 3/3/22, 7:49 PM
by namelosw on 3/4/22, 8:29 AM
While I'm an analog guy and I'm thinking in geometry. For example, if I sleep 7 hours at 10 pm, I'm getting up at 4 + 1 = 5, (the opposite of 10 is 4 which equals six hours).
by generalizations on 3/3/22, 9:07 PM
[1] https://4.bp.blogspot.com/-Et6_8IvPOW0/VEPMsOiyVAI/AAAAAAAAP...
by yesenadam on 3/3/22, 10:45 PM
Such a fascinating read, thank you! I'd love to read/see more about those other numbers with unique forms, and also features of the way numbers combine. (like the way you described 7+3 or 9+x), I want a part 2! Thanks again.
by armchairhacker on 3/3/22, 11:33 PM
by honksillet on 3/3/22, 8:36 PM
by drivers99 on 3/3/22, 11:22 PM
by EnderShadow8 on 3/4/22, 11:42 AM
by gfody on 3/3/22, 8:33 PM
by virtualwhys on 3/3/22, 8:55 PM
by mbfg on 3/3/22, 11:41 PM
by pjacotg on 3/3/22, 9:37 PM
by bufordtwain on 3/3/22, 10:53 PM
by c-smile on 3/3/22, 11:52 PM
Instead of forms I have color associations with digits.
And I suspect that many people have those...
What is your color associations (if any) with 0,1,2,3,4,6,7,8 and 9 digits?
by kderbyma on 3/3/22, 6:39 PM
7-3 I found interesting because those are modulus complements in base 10
by agumonkey on 3/3/22, 7:11 PM
by gwbas1c on 3/4/22, 4:45 AM
by calculated on 3/3/22, 7:04 PM
by lukaszkups on 3/4/22, 7:56 AM
by autokad on 3/3/22, 11:09 PM
by deltaonefour on 3/3/22, 6:20 PM
Was this learned by him or is this some sort of synesthesia condition?
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