Do You Experience Number Forms ?

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Number forms are involuntary mental visualizations that some individuals experience when thinking about sequences like numbers, days, or months. These forms can vary greatly among individuals, often appearing as unique spatial arrangements or colors, and are considered essential by those who have them. It is estimated that only about one in ten people experience these number forms, which can resemble a type of synesthesia. The discussion also touches on Richard Feynman, suggesting that his visual thinking may have influenced his scientific diagrams. Overall, the phenomenon of number forms highlights the diverse ways people conceptualize numerical and temporal information.
  • #91


Chi Meson said:
It's extremely obvious though, when I play the game "Set." Finding cards with combinations of color, quantity, shading and shapes... it's freaking cacophonous

Can you find any patterns by sound if you know what sound to look for? or is the noise just random?
 
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  • #92


rhody said:
Just a quick question, when you say quiet, you mean like quiet with no background noise, or quiet in your state of mind ? You mention repetition, like it doesn't happen at first but only when you relax, and the sensation starts to flow ? Do you notice it more intense when the room is quiet and after you are really tired or have been drinking ? (that is if you do drink ?)

Finally, can you cause it to vanish at will, and if so, what thing or combination of things remove the sensation ?

Rhody...
I'm trying to separate what actually happens from what I think ought to happen. I am trying hard not to project here, but it is clear that the easiest way to get this to stop is to start concentrating on it. To get it going, I need to concentrate on something else.

So by quiet, I did mean "externally quiet." But as I also need to be in a state of concentration, I guess I also mean "internally quiet." Such as assembling a model or putting together a design from a building toy. K'nex for example. I'd be looking through the big box for 24 small green rods from a colossal assortment of other shapes and colors. So I'm sorting and picking, and about halfway through I'd be aware of the sound of the piece I was collecting. Also when a single, peculiar piece is needed, I can find it fairly quickly and I know it's the right piece because the shape and sound matched that of the one in the picture-instructions.

I don't drink much anymore, but in recollection, I don't think that it enhances the sensations. The same for being tired. Since both of these situations are going the wrong way from "state of concentration," I'd have to say that concentration is key.
 
  • #93


zoobyshoe said:
Well, the researchers are saying 1 in 23 people has some form of it! (Synesthesia, I mean.)
That still seems like an overestimate to me. Though, if my friend's experience is typical, we may simply not hear from all the people affected by it since they either 1) don't realize what they experience is not normal or 2) don't want to share their experience out of fear of being considered abnormal.

You ought to invite him to post and describe it.
I would, but he's pretty busy with raising a kid and now getting back into a musical career. He also recently shared that musical notes also have colors to him. So, yeah, I'm also very curious if using multiple senses has helped him learn these subjects more than those of us who haven't used these associations to learn these subjects.

Wow! I just realized highlighters are part of their plot to take over!

LOL! We were in school when highlighters and colored inks were first being marketed (aside from red ink, of course). He was part of my lab group then, and we all had lots of fun with highlighters and competed for who could get the highest grade over 100% in the class (each exam had an extra credit question). It was actually very useful to me, even if others cringe at the abuse of highlighters. I used to go through my notes and highlight content very systematically. Each color meant something different for me. Nowadays, I couldn't even remember the significance of colors to give an example, but I have seen this with my med students too. Some of them really struggle their first year when they try to do like their classmates and take notes on their computers. For them, I've found that they are usually the students who took notes in multiple colors as an undergraduate, and do very well when I simply suggest that they ignore their classmates and go back to using colored pens to take notes in class.
 
  • #94


zoobyshoe said:
I found it, in the chapter called "It's as simple as One, Two, Three..."

The chapter is kind of remarkable because you see that Feynman was a natural neurologist. He discovered neuro-psychological testing, from scratch, all on his own.

What Do You Care What Other People Think p. 59

I know this is a long shot, but is it well established now that Feynman had synesthesia based on this reference? At least Gleick was pretty sure of it.

Feynman is quoted talking about this also in another book, No Ordinary Genius. He's highly alert to the fact that no two physicists are speaking the same language, and the "linguistic" differences are due to the fact each processes very simple things in different ways. Feynman felt he always had to "translate" himself, and that other physicists were usually not even aware there was a language problem, erroneously assuming that everyone thought the same way they did.

Wouldn't this be also true of other great speakers, teachers or story tellers? Can't think of a non-physicists off the top my head, but Neil Degrass Tyson seems to have this ability. He can explain what a black hole is to an 8 year old, and yet many adults find the same explanation fascinating, and thrilling.
 
  • #95


Moonbear said:
Some of them really struggle their first year when they try to do like their classmates and take notes on their computers. For them, I've found that they are usually the students who took notes in multiple colors as an undergraduate, and do very well when I simply suggest that they ignore their classmates and go back to using colored pens to take notes in class.

Most of my notes look like pages from children's coloring books. Just couple of days ago, I bought a new 12 color uni-ball pen set. My notes and calculations are in black, and then I circle, box, underline or connect various parts of my work with lines, and curves of different colors. Sometimes I shade them too.
 
  • #96


waht said:
I know this is a long shot, but is it well established now that Feynman had synesthesia based on this reference? At least Gleick was pretty sure of it.

waht,

I mentioned this before, I believe James Gleick was aware that Feynman was unique in many ways described in previous posts. I don't believe he was aware that Feynman had what Cytowic defines as synesthesia because Gleck published his book in 1992, while Cytowic first published his in 1993, so unless he knew him there would be no way for him to be aware of synesthesia. See my original comments about Feynman in post #53.

Rhody...
 
  • #97


I haven't followed this thread closely, so maybe this has already been discussed. But does it have to always be numbers?

A woman I used to work with had a grandson who was about 4 or 5 years old. She had all his "masterpiece" art work on the fridge, of course, including several that featured the alphabet. She noticed that for each alphabet, every letter was a different crayon color, and it was always the same sequence of colors! He'd made these sequences over a very long period of time, and rarely in the kitchen where he would have been able to see his old ones to follow the pattern.

Also not sure if it's pertinent, but the kid was in the process of being evaluated for autism. I have no idea how that came out, though.
 
  • #98


lisab said:
I haven't followed this thread closely, so maybe this has already been discussed. But does it have to always be numbers?

A woman I used to work with had a grandson who was about 4 or 5 years old. She had all his "masterpiece" art work on the fridge, of course, including several that featured the alphabet. She noticed that for each alphabet, every letter was a different crayon color, and it was always the same sequence of colors! He'd made these sequences over a very long period of time, and rarely in the kitchen where he would have been able to see his old ones to follow the pattern.

Also not sure if it's pertinent, but the kid was in the process of being evaluated for autism. I have no idea how that came out, though.

Lisa,

From the synessthesia thread, my https://www.physicsforums.com/showthread.php?t=393977&page=6" colors can apply to quite a few things:
1. Mingling of two or more of the sensations (sight, sound, touch, taste, smell) in a cross modal fashion. Most commonly reported is color and hearing. Rarer types: page 232 from Dr Sean Day's study of 365 cases, all in percentages:

Note: The first group are grapheme associations, the rest, rarer still are mingled sense sensations:

colored time units: 19.2
colored musical sounds 14.5
colored general sounds 12.1
colored phonemes 9.6
colored musical notes 10.4
colored tastes 6.3
colored personalities 4.4
colored pain 4.4 (woah, I would like to hear from someone with this trait)
colored odors 5.8
colored temperature 2.2
colored touch 1.9

As you see my note above: I would love for someone who experiences colored pain to describe it, I imagine though, they would only experience it if they were sitting quietly reading and then something fell (without them hearing it) and bopped them on the head, or other part of their body.

Funny, you should mention color stimulation, I was going to ask about color pain eventually anyway, thanks, you beat me to it.

Rhody...
 
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  • #99


waht said:
I know this is a long shot, but is it well established now that Feynman had synesthesia based on this reference? At least Gleick was pretty sure of it.
It's not established at all. All there is is one quote that sounds very much like he's describing a synesthetic experience. Cytowic, for reasons unknown to me, has decided to declare Feynman had a number form. There's really no indication I can see that he did. If anything,the quote indicates he had a bit of Teslavision, like you.

Wouldn't this be also true of other great speakers, teachers or story tellers? Can't think of a non-physicists off the top my head, but Neil Degrass Tyson seems to have this ability. He can explain what a black hole is to an 8 year old, and yet many adults find the same explanation fascinating, and thrilling.
It's not a matter of being able to explain yourself to an untrained person. Feynman realized no two physicists are talking the same language. He had to both translate what they were saying to his tongue, and then what he was saying into theirs. At the same time he'd try to teach them some of his language.
 
  • #100


lisab said:
I haven't followed this thread closely, so maybe this has already been discussed. But does it have to always be numbers?
A number form can be formed around anything that is a sequence, including the alphabet. Cytowic mentions a woman who has a number form for the relative heights of people she knows, for relative shoe sizes, and for relative salaries. Many people seem to have them for the calendar and the hours of the day.
A woman I used to work with had a grandson who was about 4 or 5 years old. She had all his "masterpiece" art work on the fridge, of course, including several that featured the alphabet. She noticed that for each alphabet, every letter was a different crayon color, and it was always the same sequence of colors! He'd made these sequences over a very long period of time, and rarely in the kitchen where he would have been able to see his old ones to follow the pattern.
This sounds more like Grapheme -> Color Synesthesia than a number form, but it depends on whether the letters have a consistant, but idiosyncratic positioning relative to each other.
 
  • #101


zoobyshoe said:
Does this mean 1 week = 7 boxes? Therefore each box = 1 day? Or something else?

Also, you said the boxes were thin. Can you estimate a ratio of height to length? Is the longer dimension horizontal or vertical?

I get the fact there is an involuntary grouping by seven that seems to serve no purpose, but I am trying to imagine what an individual group or box looks like and what's in it. Like, I'm asking myself: "Is one 'box' a tall, skinny column of seven consecutive numbers stacked on top of each other"?

The boxes are tall and thin, but I cannot measure the dimensions of the box no matter how good your scale is. It's somewhat fuzzy and that's all I can say. If you look at the numbers, I can tell you that 200 is "above" the 100 line of boxes and 800 is also "above" the 200 line. But this isn't any sort of above or below that you can see on a day to day basis. It isn't like you look up and see 800. There is just an obvious sense of 800 "below" 1000. This sense of above and below also fuzzes out after a certain number range. For "large numbers" (~million) I can't see anything. I can "zoom in" and do the math here, i.e. if the addition to large number is in the non-fuzzy region. I can just forget the million and "bring back" the boxes.

I've used a lot of quotes above, but all those words in quotes aren't what they mean generally. I'm just hoping I don't sound like a bloody fool, but this is the best I can explain this stuff. In a previous post, I added there was no above and below. I meant that there wasn't an above and below in a 'local' region.
 
  • #102


I'm interested to know how those who don't consider themselves to have numberforms manage to perceive abstract concepts.

I wonder if you could elucidate the degree of "realness" these things have.

This is a significant point, the forms seem possibly more real than anything I see with my eyes, yet their physicality is incomprehensible. How real are they for others?

How do those of you who consider yourselves to not have these forms perceive of say, the time of day? If someone says I'll meet you at 7:30 pm I imagine a time darkening with the day and somewhere high above my head, the morning is situated within my belly. Does a non-numberform-experiencer just see a clock? If so, that clock must be situated somewhere in relation to the personage surely? Or is it within?

I do have a strong feeling however that these forms are at learned at a very young age while the mind is still developing and is less inclined to attribute beliefs and reasonings to the world, however certain people are more susceptible to it, full blown synesthetes being the extreme end. The numbers, for example, may be grouped in a way that they were learned. 1-10 were learned together first, then the concepts of 11 and 12 are introduced, then the incline towards 20 is brought to our awareness, then the patterns which seem to be perceived in accordance with the 20s, 30s, 40s etc. are similar as their relation to one another required a similar teaching method.


The most information you're going to find is most likely in the book Wednesday is Indigo Blue. Amazon has it. I'm reading it now and the authors pay a good amount of attention to number forms.

I shall be purchasing it, sounds like a good read.

I have a friend who also experiences forms, he also has perfect pitch which he attributes partially to colour associations with notes. I'll link him to the thread and see if he wants to pop in and discuss it.
 
  • #103


The boxes are tall and thin, but I cannot measure the dimensions of the box no matter how good your scale is. It's somewhat fuzzy and that's all I can say. If you look at the numbers, I can tell you that 200 is "above" the 100 line of boxes and 800 is also "above" the 200 line. But this isn't any sort of above or below that you can see on a day to day basis. It isn't like you look up and see 800. There is just an obvious sense of 800 "below" 1000. This sense of above and below also fuzzes out after a certain number range. For "large numbers" (~million) I can't see anything. I can "zoom in" and do the math here, i.e. if the addition to large number is in the non-fuzzy region. I can just forget the million and "bring back" the boxes.

This is a great description, when I try and map out physically the shape of numbers or anything it doesn't seem accurate, it can only be experienced in it's fullest and most clear form in very temporary, unintended moments. Thinking about numbers will instantly draw up a form, but if one begins to consider the form itself, it disappears, or at least becomes a corruption of itself?

So is it safe to say you also experience a 'fourth dimensional' element to these forms? A within-ness and a point in space being simultaneously in two places?
 
  • #104


Forms for a keyboard and beginnings of number system I just drew up.
 

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  • #105


This is a general comment to all contributing in this thread, the subject of synesthesia and in particular "Number Forms" whether experienced as a synesthestic (by Cytowic's current definition) or in general, without obvious external stimulus. I believe there is much to be learned from observation and rigorous scientific experiment by experts, we are just scratching the surface, even in the face of everyone's ineffable and incongruous experience, unique to each individual.

Would anyone out there care to venture an educated guess as to the nature of what that might be ? A new underlying principle in agreement with or perhaps shattering to the agreed upon definition and validation of quantum mechanics as we know it ?

From the descriptions expressed of Number Forms it seems (to me at least) that there is some inscrutable (for the moment hehe) principle at work.

Rhody...
 
  • #106


croesoswallt said:
I'm interested to know how those who don't consider themselves to have numberforms manage to perceive abstract concepts.
This is a good question. I can't speak for anyone else but in my case I "perceive" concepts because they are automatically hooked directly to an emotion. In most cases these "emotions" are subtle, barely consciously perceived.

I experience nothing "sensory", nothing visual, tactile, auditory, gustatory, nothing involving any of the normal senses. There are no charts, no visuals, no positions in space, no sense of motion. Wednesday is distinguised from Thursday in my mind primarily by the extremely slightly different emotional reaction I have to it.

If you ask, I can free associate on the concept "Wednesday", and a huge archive of memory snatches will come up that are attached to Wednesday, per se; as a day of the week. When I casually think of Wednesday, what I'm doing is lightly grazing the tip of that archival iceberg, and a small distinguishing emotion is felt.

The same goes for numbers, months, letter of the alphabet, all that: they evoke a very subtle emotional reaction which is the tip of the iceberg of the number, month, letter of the alphabet "archive" of the memories I have that are associated with it.

It's not completely accurate to say this isn't "sensory" because emotions obviously cause physical sensations, but these sensations are peculiar to "emotion" for me and don't involve anything I can identify as a normal "sense". They are "feelings" in my torso. I suspect they indicate changes in blood flow, breathing, muscle tension, etc.
 
  • #107


croesoswallt said:
This is a significant point, the forms seem possibly more real than anything I see with my eyes, yet their physicality is incomprehensible. How real are they for others?
That's the thing: I can't tell. It's been impossible for me to get a feel for the degree of sensory vividness attached. 100% vivid would mean there is no difference between it and reality. The schizophrenic who lives in my building says the voices he hears are 100% vivid: no different than the way my voice sounds to him. Same thing with people who have musical hallucinations. When they start having them they assume without question the source is a radio or CD player someone left on, and they spend a lot of time trying to find where the hell it is: 100% vivid.

Number forms and synesthetic experiences rarely seem 100% vivid from the descriptions, so I have a hard time grasping what the experience is like.

My other response may help synesthetes understand what isn't understood, although other non-synesthetes should try to describe their manner of mentally dealing with concepts as well. I have no idea if I'm typical.

I do have a strong feeling however that these forms are at learned at a very young age while the mind is still developing and is less inclined to attribute beliefs and reasonings to the world, however certain people are more susceptible to it, full blown synesthetes being the extreme end. The numbers, for example, may be grouped in a way that they were learned. 1-10 were learned together first, then the concepts of 11 and 12 are introduced, then the incline towards 20 is brought to our awareness, then the patterns which seem to be perceived in accordance with the 20s, 30s, 40s etc. are similar as their relation to one another required a similar teaching method.
One hypothesis is that we're born with all senses linked and experience multimodal synesthesia up to about six months of age. As we develop the connections are pruned back. Synesthetes would represent people whose connections became fixed before they were pruned to the "norm". This makes sense, (but it's just a hypothesis at this point).
I have a friend who also experiences forms, he also has perfect pitch which he attributes partially to colour associations with notes. I'll link him to the thread and see if he wants to pop in and discuss it.
That'd be nice.
 
  • #108


croesoswallt said:
Forms for a keyboard and beginnings of number system I just drew up.

I can't help but notice quite a few of the tones have the same color. Then Gb and F# are the same, but Eb and D# are as opposite as possible: complimentary colors. Also F has alternate colors? Are these the colors of keys or of notes?

Your number line is mysteriously bifurcated at the start, from 1 -12. 10 exists on an anomalous connecting "rung". What's that about?
 
  • #109


anirudh215 said:
The boxes are tall and thin, but I cannot measure the dimensions of the box no matter how good your scale is. It's somewhat fuzzy and that's all I can say. If you look at the numbers, I can tell you that 200 is "above" the 100 line of boxes and 800 is also "above" the 200 line. But this isn't any sort of above or below that you can see on a day to day basis. It isn't like you look up and see 800. There is just an obvious sense of 800 "below" 1000. This sense of above and below also fuzzes out after a certain number range. For "large numbers" (~million) I can't see anything. I can "zoom in" and do the math here, i.e. if the addition to large number is in the non-fuzzy region. I can just forget the million and "bring back" the boxes.

I've used a lot of quotes above, but all those words in quotes aren't what they mean generally. I'm just hoping I don't sound like a bloody fool, but this is the best I can explain this stuff. In a previous post, I added there was no above and below. I meant that there wasn't an above and below in a 'local' region.
This may or may not help you to describe some of this:

There is a sense you have that you may not know you have, which is called "proprioception". This is like the sense of touch (pressure sense) except it is internal, and it is sometimes characterized as the "internal sense of touch", but the very important function it serves is to tell you where your body parts are located relative to each other. It is, somewhat more accurately, the "sense of body position".

You can prove you have it by closing your eyes and "feeling" the position of your body. You should be able to describe the position of every limb, finger, toe, everything, without having to look and see where they are. You can move any limb and immediately know the new position, again without having to look. With your eyes closed you can assume any posture you want, put your arms straight out to the side, or straight up, or straight out in front of you, or bent at the elbow, and you will always know where they are without having to look at them. You can just "feel" where they are.

The reason I'm explaining that is because I'm wondering to what extent any of the "above" or "below" relationships of any of the numbers in your number form seem to be "sensed" via proprioception.
 
  • #110


I experience nothing "sensory", nothing visual, tactile, auditory, gustatory, nothing involving any of the normal senses. There are no charts, no visuals, no positions in space, no sense of motion. Wednesday is distinguised from Thursday in my mind primarily by the extremely slightly different emotional reaction I have to it.

If you ask, I can free associate on the concept "Wednesday", and a huge archive of memory snatches will come up that are attached to Wednesday, per se; as a day of the week. When I casually think of Wednesday, what I'm doing is lightly grazing the tip of that archival iceberg, and a small distinguishing emotion is felt.

The same goes for numbers, months, letter of the alphabet, all that: they evoke a very subtle emotional reaction which is the tip of the iceberg of the number, month, letter of the alphabet "archive" of the memories I have that are associated with it.

I imagine that most if not all people will experience these 'memory snatches' you describe so well. I suggest they are an indication of the internalization process we all go through at a young age. Relating this to what you said about infantile multimodal synesthesia, I think it is reasonable to suggest that synesthesia is developed in order that those who struggle more with abstract concepts create a system to help them understand. So maybe the more elaborate a synesthete's graphemes are, the harder they initially found it to grasp abstract concepts. Could this possibly relate to autism?

On the other end of the scale and your 'minimalistic' emotional responses, I think that these are probably universal but for a synesthete these responses are expanded to encompass something spatial or chromatic. There could well be people who have absolutely no method or association of which to speak, whose weeks and months are instantly processed without any perceivable 'middle-man' of emotional response or numberforms. Could this also be related to autism?

What I'm digging at is the possibility of a synesthesia scale on which everyone is placed in accordance with the level of ordering they use for addressing abstract concepts.
 
  • #111


I can't help but notice quite a few of the tones have the same color. Then Gb and F# are the same, but Eb and D# are as opposite as possible: complimentary colors. Also F has alternate colors? Are these the colors of keys or of notes?

This is partly due to the limitations of my understanding of customising colours on paint (!) but indeed I see a lot of green, though they are all different shades (Eb is mintier, G is deep foresty). I don't know how far your theoretical music knowledge extends but the accidentals (sharps and flats) are referred to as being enharmonic, they sound the same (theoretically) but their name and role is dependant on whether you're in a sharp or flat key. For this reason, I think of a different colour for most of the enharmonic accidentals, depsite their sounding exactly the same when isolated.

Gb and F# both act as the turning point in the cycle of fifths (cycle of keys), neither is often used and they are interchangable as reading them is equally challenging - they both have 6 of their respective accidentals. I think that my mind has come to use grey to represent the ambiguity and equality of that note.

These colours represent both the feel of individual notes and keys I associate with them. When i think of the note C in the key of F or G it is yellow, but when It will be slightly tainted with the colour of the key it is appearing in. F seems both green and orangey red, and maybe a brown colour between the two. I could choose a secondary colour for several notes, F just happens to be one I'm more undecided on.
Your number line is mysteriously bifurcated at the start, from 1 -12. 10 exists on an anomalous connecting "rung". What's that about?

This bifurcation is representative of a sense of movement, but perhaps more importantly it is a poor visual representation of the dual nature of that line of numbers. 1-10 seems to be traveling in two different directions simultaneously, but ending at the same point which is after 12. The rung at 10 is a 'cap' of sorts, an important milestone where the diverging pathways come together, yet they are still not totally reunited until 13. 11 and 12 roll into one number, they share a similar character. Hard to explain! I'd ideally draw a few more double helixes.
 
  • #112


croesoswallt said:
I think it is reasonable to suggest that synesthesia is developed in order that those who struggle more with abstract concepts create a system to help them understand.
This seems to make sense in the case of number forms; one could suppose they're an attempt to grasp concepts, but when you get into pairings like taste -> touch or sight ->sound, you can see that there is no abstract concept that needs to be struggled with. A second sense is just inexplicably triggered along side the first.

Cytowic has a couple pages about autism in the book I mentioned . He calls it "the opposite of synesthesia". His argument is that various kinds of tests show that autistic people demonstrate far less neuronal "cross talk" than normal, while a synesthete has far more than normal.

Number forms don't seem to be "developed": people can't tweak them or improve them. They're not "inventions" with a purpose. They seem, as far as I can see, to just happen somewhat haphazardly. In most cases reported in this thread they don't seem to be a helpful thing to have. Cytowic reports cases of calendar and clock number forms that seem to be helpful, but no number lines that have been of benefit.
 
  • #113


croesoswallt said:
This is partly due to the limitations of my understanding of customising colours on paint (!)
Ah! Paint is a horrible graphics program. Maybe someone will lend you a photoshop disc. There are also some free ones online that are better than paint. Photoediting programs often have a large graphics capability compared to Paint.

The rest of it made more sense as well.
This bifurcation is representative of a sense of movement, but perhaps more importantly it is a poor visual representation of the dual nature of that line of numbers. 1-10 seems to be traveling in two different directions simultaneously, but ending at the same point which is after 12. The rung at 10 is a 'cap' of sorts, an important milestone where the diverging pathways come together, yet they are still not totally reunited until 13. 11 and 12 roll into one number, they share a similar character. Hard to explain! I'd ideally draw a few more double helixes.
The verbal explication helps understand the graphic. I can see it's still too ineffable to completely articulate.
 
  • #114


When doing simple addition and don't want to think abstractly (or from memory), I count the "limbs" on digits 1 through 5. For example, I visualize 3 as ≡ and count the limbs, top to bottom, as "one, two, three." So, 9 + 3 = "ten, eleven, twelve" = 12.
 
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  • #115


EnumaElish said:
When doing simple addition and don't want to think abstractly (or from memory), I count the "limbs" on digits 1 through 5. For example, I visualize 3 as ≡ and count the limbs, top to bottom, as "one, two, three." So, 9 + 3 = "ten, eleven, twelve" = 12.

How does that work for 2, 4 or 5?
 
  • #116


DaveC426913 said:
How does that work for 2, 4 or 5?
With 2 you count the beginning and end and ignore the "corner".

With four you count the two "corners" and the beginning and end.

With 5 you count the beginning, end, two corners, and promote some point on the bottom backward C to a corner.

I know exactly what he's talking about, I used to do this too. In fact, I once invented a new system of numerals to make this obvious and easy. 6,7,8,and 9 all had their respective proper number of counting points in this new, improved system. However, no one was interested.
 
  • #117


In my visual system, 2 is sort of two hand movements, one continuous (think of writing ? without the dot) and _. But essentially I've come to see 2 as = without a diagonal connector, just like I see 3 as ≡ and ignore the vertical connector.

Four is:
/_|
...|
(just ignore the dots, they are the typographical equivalent of 'blank space" in PF edit window).

5 is:
._
|_
._|

I had no idea others might have the same or a similar system, and it's good to know so. I see that zooby's system is more advanced than mine; I never took it beyond 5.
 
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  • #118


EnumaElish said:
In my visual system, 2 is sort of two hand movements, one continuous (think of writing ? without the dot) and _.

Four is:
/_|
...|
(just ignore the dots, they are the typographical equivalent of 'blank space" in PF edit window).

5 is:
._
|_
._|

I had no idea others might have the same or a similar system, and it's good to know so.

Oh, I get it. You're (sort of) counting the motions it takes to write the numeral.

Yes, it's interesting to see someone else came up with something similar.
 
  • #119


The only numeric form (in the OP sense) that I can think of having is the circle; it pops up when I visualize trig problems.

Another question is, whether number forms change when one switches languages. If the number "ten" is yellow and one step northeast of a green five, does the same apply to "dix" or "diez"?
 
  • #120


Another question is, whether number forms change when one switches languages. If the number "ten" is yellow and one step northeast of a green five, does the same apply to "dix" or "diez"?
Hmmmmmm. I dunno.
 

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