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How many other 'mathy' people with aphantasia have trouble 'thinking like a cartoonist'? (And how many people with aphantasia are naturally 'mathy'?) Read Blak

by Agamus 5y ago

How many other 'mathy' people with aphantasia have trouble 'thinking like a cartoonist'? (And how many people with aphantasia are naturally 'mathy'?) Read Blake Ross' post for a better sense of why this method simply does not work for many people who are more comfortable with abstraction.

mathstuf 5y ago
I have aphantasia. For reference, until 2019 or so I thought things like mental imagery and mind palaces were just metaphors and my memory for such things was poor (even after seeing Sherlock put his mind palace to screen). As you can tell from my username, I am mathematically inclined (4th in the state in MathCounts, 2nd place team, a 5 on the AP Calc AB exam in 10th grade, and 5 on the BC exam the next year despite not having a math class that year[1]). I'm actually decent at the folding nets problems ("which cube matches this unfolded pattern?") as well, but I suspect my methods just don't match how those that can visualize and manipulate those visualizations do it. As for the article at hand, there's no real difference to me in terms of what I get out of it (the cartoon gives me a slight smile, but good caricatures usually do) as I only remember the "gist" of such images anyways. I can easily recognize it as the Married with Children actor, but I couldn't begin to verbally describe it in any useful way for even a cartoonist to make without looking at it at the same time (barring "it's a well-known actor": "it's a male face…surprised or 'deer in the headlights', some stubble if any facial hair, short messy hair"). I feel like on some level the aphantasia it is helpful. Namely when expanding some concept such as "equality" to "equivalence" to allow such things as "sum of all natural numbers is -1/12" or modular equivalence relations because I can just replace "is" with "can be treated as" without much mental work. Someone who has a visual representation of such things may have trouble "uprooting" such understandings to plant them in richer soil (a metaphor for which I have no trouble using despite not having a picture of such a thing handy). Do you have a link to the Ross post? [1] Having finished Honors Calc in 10th, I instead tripled up on science classes my junior year and went to a local college for math my senior year.
- auto 5y ago
  This is interesting, and I'm curious if I could pick your brain a bit. I don't have the math accolades you do, but got through all of grades school math (up thru Calculus) with ease, as just "one of those kids who are good at math", and got my B.Sc. in math without much fuss. I consider myself on the opposite end of the spectrum from someone who suffers (is blessed?) from aphantasia; I can muster up not only a mental image of just about anything, but really recreate any sensory experience (although it has a dullness to it) in my head. This was obviously a huge part of math for me growing up, and as a professional SWE for over a decade now, something I still lean on heavily. What I'm wondering is, how different really are our methods for reasoning about mathematical things, especially the shape rotation/unfolding you mentioned. Do I get to the solution via the mental visualization of the process, or perhaps do you and I perform a similar non-imaged subconscious process of unfolding, but I just "check my work" in a way. If that were the case, I'd argue aphantasia is an advantage, as you're not bothering your brain with unnecessary work. This is all handwavey speculation of course, but I've always found this stuff super interesting.
  - mathstuf 5y ago
    > I consider myself on the opposite end of the spectrum from someone who suffers (is blessed?) from aphantasia One distinct downside is that I'm queasy around other people's blood or gore. I can't watch visceral movie scenes for too long or visit some science exhibits (that I'd otherwise enjoy) because of it (at least this is my suspicion). My problem is that because I can't visualize a discussion about, say, amputation, my mind grafts the description onto me and things go downhill from there. However, I was able to watch some small procedures on myself just fine because I could see that it was OK (though I still cannot watch my own blood being drawn). > I can muster up not only a mental image of just about anything, but really recreate any sensory experience (although it has a dullness to it) in my head. Yeah, I don't have anything to compare that to. I recall "gists" of things through feelings and notions rather than anything I'd call "sensory". I cannot recalls scents or tastes all that well and even sounds get muddled up very easily (I have a very hard time finding a rhythm, melody, or other patterns out of music though I can usually pick out instruments while listening; "tap out this song" detectors never worked well for me because I would tap nearly every note and lyric syllable, not some "core" pattern from it). Some interesting side effects of this include a blank stare while I think about a list of items when someone asks something like "what is your favorite food or drink?". The answer sometimes changes depending on whether I remember "everything" too. Even "what do you think about your travels to X?" brings it up because I have to first conjure up the feelings associated with that travel, remember the big events in that timeline, and then put it into words for the answer (hoping I didn't miss anything). > What I'm wondering is, how different really are our methods for reasoning about mathematical things, especially the shape rotation/unfolding you mentioned. The first thing I notice is that I do not "unfold" the possibilities at all; I turn it into a logic puzzle. I focus on one face that is in "most" of the images and look for contradictions with the net by focusing on one or two vertices of that face. Some rules come out of this like "two steps in one axis is an opposing face" and if you see those two symbols on one possibility, it's obviously not a candidate. It also works fine for the harder versions where the symbols on the face are right, but rotated incorrectly to the facing edge. This usually gets you down to one candidate and you can move on to the next one while your hand is filling in the bubble. I suspect (but have no actual experience with it as most of such tests are on cubes) this scales up well for even octahedra and dodecahedra (but starts to fall apart trying to keep the order/orientation of the 5 items around a vertex for an icosahedron or when the possibilities do not share many symbols from their view because that greatly slows down the method). Giving "adversarial" nets where the answer is actually based on two distant legs of the net that I need to actually mentally fold multiple edges also likely stymies my strategy because I have to think "star circle square" as I walk the edges and cannot just "snap" a picture of the sequence as a gestalt as easily. I took part in a research experiment recently where they have some 3d shapes made of cubes rotated around a vertical axis and ask "are these two objects the same or mirror images of each other". I obviously don't have the answer key, but I felt that I did really well except when mirror images were rotated 180° from each other. I don't know if I have an explanation for that (usually I realized my mistake right after answering). > If that were the case, I'd argue aphantasia is an advantage, as you're not bothering your brain with unnecessary work. I think a major difference is in working memory. What you might be able to "freeze frame" as a collection, I have to extract out the distinct parts and remember them more individually. Sometimes I can "find" a pattern and gestalt that way which tends to stick quite well (like I do for my wife's phone number or a friend's phone number I saw a pattern in once he got it), but most things are just rote memorization. For example, "star square circle" could just be "decreasing side counts" and just using recognition to determine membership later versus "star circle square" which is more likely to be 3 working items. If they are also colored, that doubles the work for me right away as they otherwise don't have any color association to me.
ginnungagap 5y ago
I have aphantasia and I'm doing a PhD in math. I draw on paper when I'm trying to visualize something, but the area I work in is quite abstract and very often the images are huge oversimplifications that give some intuition, but on which one shouldn't rely too much. I agree that the suggested method doesn't sound like a good approach at all to me
djmips 5y ago
Everyone here, including the original poster has, I believe, made a mistake of thinking the article meant to literally visualize a problem like a cartoonist. The cartoon caricature is only meant by analogy. Possibly a blind spot for those with aphantasia, but the thesis of this article isn't centered around literally visualizing something but capturing some salient points, perhaps exaggerated and not technically correct as an initial way of starting to explain a mathematical concept. It's perhaps unfortunate that the analogy chosen was difficult to understand or sidetracked people that have trouble with the process of making a cartoon caricature.
- necovek 5y ago
  I am self-diagnosed with aphantasia :), but I understood the desire of the article to simplify by exaggerating most prominent features necessary for a given context, similar to what cartoons do (though I implicitly assumed they simply meant a "caricature" as opposed to any "cartoon", though I haven't looked up if my understanding of the specifics matches actual definitions of those words). So definitely not a blind spot for those with aphantasia. Still, the article does an extremely poor job of showing how that is done well, thus fails in getting the point across. Even the cartoon of a person example sticks out to me as not amplifying a feature, because I don't see the jaw line as a feature in the original face at all. If anything, I see non-existence of that jaw line in the original photo. As such, it's a great model for the article: bad caricature, just like all the bad math examples below.

by Agamus 5y ago

mathstuf 5y ago

I have aphantasia. For reference, until 2019 or so I thought things like mental imagery and mind palaces were just metaphors and my memory for such things was poor (even after seeing Sherlock put his mind palace to screen). As you can tell from my username, I am mathematically inclined (4th in the state in MathCounts, 2nd place team, a 5 on the AP Calc AB exam in 10th grade, and 5 on the BC exam the next year despite not having a math class that year[1]). I'm actually decent at the folding nets problems ("which cube matches this unfolded pattern?") as well, but I suspect my methods just don't match how those that can visualize and manipulate those visualizations do it. As for the article at hand, there's no real difference to me in terms of what I get out of it (the cartoon gives me a slight smile, but good caricatures usually do) as I only remember the "gist" of such images anyways. I can easily recognize it as the Married with Children actor, but I couldn't begin to verbally describe it in any useful way for even a cartoonist to make without looking at it at the same time (barring "it's a well-known actor": "it's a male face…surprised or 'deer in the headlights', some stubble if any facial hair, short messy hair"). I feel like on some level the aphantasia it is helpful. Namely when expanding some concept such as "equality" to "equivalence" to allow such things as "sum of all natural numbers is -1/12" or modular equivalence relations because I can just replace "is" with "can be treated as" without much mental work. Someone who has a visual representation of such things may have trouble "uprooting" such understandings to plant them in richer soil (a metaphor for which I have no trouble using despite not having a picture of such a thing handy). Do you have a link to the Ross post? [1] Having finished Honors Calc in 10th, I instead tripled up on science classes my junior year and went to a local college for math my senior year.

auto 5y ago
This is interesting, and I'm curious if I could pick your brain a bit. I don't have the math accolades you do, but got through all of grades school math (up thru Calculus) with ease, as just "one of those kids who are good at math", and got my B.Sc. in math without much fuss. I consider myself on the opposite end of the spectrum from someone who suffers (is blessed?) from aphantasia; I can muster up not only a mental image of just about anything, but really recreate any sensory experience (although it has a dullness to it) in my head. This was obviously a huge part of math for me growing up, and as a professional SWE for over a decade now, something I still lean on heavily. What I'm wondering is, how different really are our methods for reasoning about mathematical things, especially the shape rotation/unfolding you mentioned. Do I get to the solution via the mental visualization of the process, or perhaps do you and I perform a similar non-imaged subconscious process of unfolding, but I just "check my work" in a way. If that were the case, I'd argue aphantasia is an advantage, as you're not bothering your brain with unnecessary work. This is all handwavey speculation of course, but I've always found this stuff super interesting.
- mathstuf 5y ago
  > I consider myself on the opposite end of the spectrum from someone who suffers (is blessed?) from aphantasia One distinct downside is that I'm queasy around other people's blood or gore. I can't watch visceral movie scenes for too long or visit some science exhibits (that I'd otherwise enjoy) because of it (at least this is my suspicion). My problem is that because I can't visualize a discussion about, say, amputation, my mind grafts the description onto me and things go downhill from there. However, I was able to watch some small procedures on myself just fine because I could see that it was OK (though I still cannot watch my own blood being drawn). > I can muster up not only a mental image of just about anything, but really recreate any sensory experience (although it has a dullness to it) in my head. Yeah, I don't have anything to compare that to. I recall "gists" of things through feelings and notions rather than anything I'd call "sensory". I cannot recalls scents or tastes all that well and even sounds get muddled up very easily (I have a very hard time finding a rhythm, melody, or other patterns out of music though I can usually pick out instruments while listening; "tap out this song" detectors never worked well for me because I would tap nearly every note and lyric syllable, not some "core" pattern from it). Some interesting side effects of this include a blank stare while I think about a list of items when someone asks something like "what is your favorite food or drink?". The answer sometimes changes depending on whether I remember "everything" too. Even "what do you think about your travels to X?" brings it up because I have to first conjure up the feelings associated with that travel, remember the big events in that timeline, and then put it into words for the answer (hoping I didn't miss anything). > What I'm wondering is, how different really are our methods for reasoning about mathematical things, especially the shape rotation/unfolding you mentioned. The first thing I notice is that I do not "unfold" the possibilities at all; I turn it into a logic puzzle. I focus on one face that is in "most" of the images and look for contradictions with the net by focusing on one or two vertices of that face. Some rules come out of this like "two steps in one axis is an opposing face" and if you see those two symbols on one possibility, it's obviously not a candidate. It also works fine for the harder versions where the symbols on the face are right, but rotated incorrectly to the facing edge. This usually gets you down to one candidate and you can move on to the next one while your hand is filling in the bubble. I suspect (but have no actual experience with it as most of such tests are on cubes) this scales up well for even octahedra and dodecahedra (but starts to fall apart trying to keep the order/orientation of the 5 items around a vertex for an icosahedron or when the possibilities do not share many symbols from their view because that greatly slows down the method). Giving "adversarial" nets where the answer is actually based on two distant legs of the net that I need to actually mentally fold multiple edges also likely stymies my strategy because I have to think "star circle square" as I walk the edges and cannot just "snap" a picture of the sequence as a gestalt as easily. I took part in a research experiment recently where they have some 3d shapes made of cubes rotated around a vertical axis and ask "are these two objects the same or mirror images of each other". I obviously don't have the answer key, but I felt that I did really well except when mirror images were rotated 180° from each other. I don't know if I have an explanation for that (usually I realized my mistake right after answering). > If that were the case, I'd argue aphantasia is an advantage, as you're not bothering your brain with unnecessary work. I think a major difference is in working memory. What you might be able to "freeze frame" as a collection, I have to extract out the distinct parts and remember them more individually. Sometimes I can "find" a pattern and gestalt that way which tends to stick quite well (like I do for my wife's phone number or a friend's phone number I saw a pattern in once he got it), but most things are just rote memorization. For example, "star square circle" could just be "decreasing side counts" and just using recognition to determine membership later versus "star circle square" which is more likely to be 3 working items. If they are also colored, that doubles the work for me right away as they otherwise don't have any color association to me.

ginnungagap 5y ago

I have aphantasia and I'm doing a PhD in math. I draw on paper when I'm trying to visualize something, but the area I work in is quite abstract and very often the images are huge oversimplifications that give some intuition, but on which one shouldn't rely too much. I agree that the suggested method doesn't sound like a good approach at all to me

djmips 5y ago

Everyone here, including the original poster has, I believe, made a mistake of thinking the article meant to literally visualize a problem like a cartoonist. The cartoon caricature is only meant by analogy. Possibly a blind spot for those with aphantasia, but the thesis of this article isn't centered around literally visualizing something but capturing some salient points, perhaps exaggerated and not technically correct as an initial way of starting to explain a mathematical concept. It's perhaps unfortunate that the analogy chosen was difficult to understand or sidetracked people that have trouble with the process of making a cartoon caricature.

necovek 5y ago
I am self-diagnosed with aphantasia :), but I understood the desire of the article to simplify by exaggerating most prominent features necessary for a given context, similar to what cartoons do (though I implicitly assumed they simply meant a "caricature" as opposed to any "cartoon", though I haven't looked up if my understanding of the specifics matches actual definitions of those words). So definitely not a blind spot for those with aphantasia. Still, the article does an extremely poor job of showing how that is done well, thus fails in getting the point across. Even the cartoon of a person example sticks out to me as not amplifying a feature, because I don't see the jaw line as a feature in the original face at all. If anything, I see non-existence of that jaw line in the original photo. As such, it's a great model for the article: bad caricature, just like all the bad math examples below.