Do You Experience Number Forms ?

[zoobyshoe]

Do You Experience "Number Forms"?

A "number form" is an involuntary chart, of sorts, that pops into some people's minds when they consider things like calendars (months, days), times of day, the alphabet, or even just numbers from 1 to infinity.

These "charts" have their elements grouped rather idiosynchratically from other people's perspective but to the person experiencing the "Number Form" they make absolute sense and seem inevitable. People refer to these charts all the time and visualize them being out in space around them. For some people they're colorless, but for others they are colored and may have some element of motion to them.

"The pattern or 'Form' in which the numerals are seen is by no means the same in different persons, but assumes the most grotesque variety of shapes, which run in all sorts of angles, bends, curves, and zigzags...
...These forms...are stated in all cases to have been in existence, so far as the earlier numbers in the Form are concerned, as long back as the memory extends; they come 'into view quite independently' of the will, and their shape and position...are nearly invariable."
-Galton 1907

These charts are said to be indispensable to the people who experience and use them and they are surprised when they find out everyone doesn't have the same thing going on. In fact, it's estimated only one-in-ten people has them.

I, myself, don't experience this, and I only ever heard about it the first time a couple weeks ago. What's interesting is that, apparently, Feynman had it, and saw colored equations projected into space in front of him.

Any of you have "Number Forms"?

 

[TheStatutoryApe]

I tend to think in visual and spatial terms, I often have trouble getting chess boards and the like out of my head, but I have trouble with numbers. Perhaps my issue with numbers is a lack of perceiving them in a visual/spacial fashion.

 

[zoobyshoe]

I tend to think in visual and spatial terms, I often have trouble getting chess boards and the like out of my head, but I have trouble with numbers. Perhaps my issue with numbers is a lack of perceiving them in a visual/spacial fashion.

Number forms arise specifically from concepts of sequence; months of the year, days of the month, letters of the alphabet, etc. Thinking in visual and spatial terms, like imagining the positions of things in a room, is not the same thing. In Number Forms the position of an element of a sequence takes on a peculiar location in space relative to the person's body.

Here's a quote from one person who experiences them:

"The patterns are very defined, have always been in the same place (and are constantly getting longer as I get older). History is a good example: I cannot think of a period in history (or my past) without simultaneously (but not necessarily consciously) thinking of where it is 3-dimensionally in my mind! For example, the Renaissance is on a curve down to the left of my body. The idea, or thought, and the position are inseparable."

 

[zoobyshoe]

Here's a couple images I found; people's attempt to draw their number forms:

 

[lisab]

I don't think I have this but I do think of numbers visually.

I memorized the multiplication tables as a kid by remembering patterns, not numbers. I remember the pattern of, for example, all the multiples of 6, as they lay on a 10X10 grid in my mind. This is presented in a lot of children's math books and may have been the seed of this idea for me. So for me it's not idiosyncratic, like you describe, but very logical.

 

[DaveC426913]

Wow, what a totally novel and foreign concept. Definitely I'm not one of them.

 

[Jack21222]

Nope, I don't have those. It seems like a type of synesthesia.

 

[rhody]

zooby,

It almost seems obvious now, but do you think Feynman's famous (Feynman diagrams) were inspired by this trait ? Also, I have read more than a few books on Feynman over the years, and his wife would describe him at times as moving his body back and forth, contorting into weird shapes (not spasmodically though) and when asked about it, he would say he was imagining he was a proton or some other subatomic particle, just like Feynman, always the original thinker ! Just imagine, if Feynman diagrams still used by Physicists today were due to his synesthesia, that would be awesome, and newsworthy as well.Rhody...PS I have summed up most of what I want to say for the synesthesia thread, and the afterward does contain some new stuff that everyone following the thread may find interesting, working on it now, will report soon.

 

[lisab]

zooby,

It almost seems obvious now, but do you think Feynman's famous (Feynman diagrams) were inspired by this trait ? Also, I have read more than a few books on Feynman over the years, and his wife would describe him at times as moving his body back and forth, contorting into weird shapes (not spasmodically though) and when asked about it, he would say he was imagining he was a proton or some other subatomic particle, just like Feynman, always the original thinker ! Just imagine, if Feynman diagrams still used by Physicists today were due to his synesthesia, that would be awesome, and newsworthy as well.


Rhody...


PS I have summed up most of what I want to say for the synesthesia thread, and the afterward does contain some new stuff that everyone following the thread may find interesting, working on it now, will report soon.

Interesting idea, Rhody. When I saw Zooby's post with the examples of this, my first thought looking at the stick ones was that they vaguely resemble Feynman diagrams.

 

[rewebster]

they don't look like Feynman's diagrams at all to me---they're more/almost like obstacle paths and/or something out of set theory

 

[lisab]

they don't look like Feynman's diagrams at all to me---they're more/almost like obstacle paths and/or something out of set theory

I probably thought of them because I'm reading QED right now .

 

[leroyjenkens]

I sort of understand what you're talking about. I see calendar days in a line, like a number line, going from 1 to 31, depending on the month, and then right after the 31, another 1 starts the next month. The alphabet is the same way. It's not a weird shape, just a line.

Some of those pictures you posted makes them seem like autistic characteristics.

 

[rhody]

lisa,

I was looking online for examples of Feynman diagrams, and found this: http://www.google.com/imgres?imgurl...ndsp=21&tbs=isch:1&ei=ZqPdS-7SJ4iwtAPg5_CxBg"

Combine the fact that Feynman used to imagine himself a sub atomic particle, affecting and being affected by other bosons (particles) and fermions (forces) around him (with different masses, spins and velocities) and the fact the he naturally was comfortable with colored number series in twisted chains, then it is not too far of a stretch to suggest that all the necessary mechanics or tools were at his disposal to simply remove the numbers and let his branching thought process create the scaffolding. In looking it up on http://en.wikipedia.org/wiki/Feynman_diagram#Alternative_names", it seems Feynman was not the first to invent them though: from the article:

This is a bit off topic but in reading Gell-Mann's, "Quark and the Jaguar" he is a perfectionist to the point of pain when reading his work because he pays such exquisite attention to detail, and writes as if one were reading an English textbook (he was a linguist too, and could speak 4 or 5 languages). I often came away from reading that book with a headache, no disrespect Mr. Gell-Mann due to his style, content and sensory overload he delivers to whatever topic he describes.

Murray Gell-Mann always referred to Feynman diagrams as Stueckelberg diagrams, after a Swiss physicist, Ernst Stueckelberg, who devised a similar notation many years earlier. Stueckelberg was motivated by the need for a manifestly covariant formalism for quantum field theory, but did not provide as automated a way to handle symmetry factors and loops, although he was first to find the correct physical interpretation in terms of forward and backward in time particle paths, all without the path-integral.[1] Historically they were sometimes called Feynman-Dyson diagrams or Dyson graphs,[2] because when they were introduced the path integral was unfamiliar, and Freeman Dyson's derivation from old-fashioned perturbation theory was easier to follow for physicists trained in earlier methods.

Rhody...

 

[Averagesupernova]

I think like this all the time. I've often wondered if anyone else does but hadn't thought of a way to describe it without sounding like a nutjob. This is the first time I've seen it brought to discussion anywhere.
-
I picture the calendar year as an arc. Multiple years (up to 3 or so) are arcs stacked one on top of the previous. However, I don't think of the years going back through history this way. They are 'blocks' like sections of a sidewalk. Different decades have different shades as do different centuries. Different months in the year have different shades associated with them. For instance, January is very bright, but December is dull and gray. Quite a contrast considering they are similar in weather.
-
The alphabet also has various dark and light colored sections in it.
-
Thinking about it, this sort of thing is so familiar to me that a lot of things I am not even conscious of I probably picture this way.

 

[rhody]

I think like this all the time. I've often wondered if anyone else does but hadn't thought of a way to describe it . This is the first time I've seen it brought to discussion anywhere.

Averagesupernova,

Well you can thank Zoobyshoe for it, the serendipidious journey started https://www.physicsforums.com/showthread.php?t=374522", I think you are going to like it... a lot.

Rhody...

 

[zoobyshoe]

It almost seems obvious now, but do you think Feynman's famous (Feynman diagrams) were inspired by this trait ?

Damn strong possibility. Good thinking, Rhody.

Beside what you said about that report from his wife I've only heard the one quote from Cytowic. I don't know where Feynman said that either. The reports of his Number Forms are scarce, I think.

I'm reading Cytowic's Synesthesia, A Union of the Senses and Number Forms aren't classified as synesthesia because they arise from concepts rather than in response to the stimulation of a primary sense. Of course they're considered related to it, though.

Feynman's children are still around. Have to wonder if they have number forms.

 

[zoobyshoe]

I sort of understand what you're talking about. I see calendar days in a line, like a number line, going from 1 to 31, depending on the month, and then right after the 31, another 1 starts the next month. The alphabet is the same way. It's not a weird shape, just a line.

Some of those pictures you posted makes them seem like autistic characteristics.

Funny you say that. Oliver Sacks did a TV special about an Autistic Savant girl a few years back and she had this very elaborate calendar she decorated every day as a sort of journal. It was quite like one of these number forms in that it was rigidly organized in her mind but seemed pretty eccentric to everyone else.

Her special talent was that she painted super-realistic paintings of houses. Very literal, and objectively accurate, unlike her calendar.

 

[zoobyshoe]

I think like this all the time. I've often wondered if anyone else does but hadn't thought of a way to describe it without sounding like a nutjob. This is the first time I've seen it brought to discussion anywhere.
-
I picture the calendar year as an arc. Multiple years (up to 3 or so) are arcs stacked one on top of the previous. However, I don't think of the years going back through history this way. They are 'blocks' like sections of a sidewalk. Different decades have different shades as do different centuries. Different months in the year have different shades associated with them. For instance, January is very bright, but December is dull and gray. Quite a contrast considering they are similar in weather.
-
The alphabet also has various dark and light colored sections in it.
-
Thinking about it, this sort of thing is so familiar to me that a lot of things I am not even conscious of I probably picture this way.

Exellent! This sounds like an authentic number form!

Be very cool if you could photoshop up a calendar to show us how you envision it.

 

[Chi Meson]

Holy CRAP! I thought I was unique!

I have been aware of the weird ladder that my numbers (from 1 to etc) take since 6th grade, and I have never known this to be talked about until now!

Some of the pictures that you showed are similar to my own. I even see various portions of my numberline from different perspectives. Sometimes it helps with quick problems of addition and subtraction, but just as often, it gets in the way, because the damn thing is so irregular.

I recognized it long ago as something that might explain why a savant can do math so quickly, just by essentially looking at the "map" in his head.

Mine starts at zero and goes straight line to ten, looking like a ladder propped agains a low wall. 10 to 20, the ladder turns to the right, and gets steeper. 20 to 30, turns left, and gets steeper still. A bit fuzzy at the 39/40 transition, but the steepness stays the same, and slight zigzags at each ten, but not necessarily the same turn. 100 is like a solid platform (much like zero) from which the same ladder begins again.

After 200, the 100s seem to be a repeat of the 1 to 10 ladder.

The 1000's for some reason, go to the left, at no angle.

 

[zoobyshoe]

Holy CRAP! I thought I was unique!

I have been aware of the weird ladder that my numbers (from 1 to etc) take since 6th grade, and I have never known this to be talked about until now!

Some of the pictures that you showed are similar to my own. I even see various portions of my numberline from different perspectives. Sometimes it helps with quick problems of addition and subtraction, but just as often, it gets in the way, because the damn thing is so irregular.

I recognized it long ago as something that might explain why a savant can do math so quickly, just by essentially looking at the "map" in his head.

Mine starts at zero and goes straight line to ten, looking like a ladder propped agains a low wall. 10 to 20, the ladder turns to the right, and gets steeper. 20 to 30, turns left, and gets steeper still. A bit fuzzy at the 39/40 transition, but the steepness stays the same, and slight zigzags at each ten, but not necessarily the same turn. 100 is like a solid platform (much like zero) from which the same ladder begins again.

After 200, the 100s seem to be a repeat of the 1 to 10 ladder.

The 1000's for some reason, go to the left, at no angle.

Amazing! Do the numbers seem associated with a particular position relative to your body?

Any thing beside the number line? Elements of the calendar, measurements, the alphabet?

 

[waht]

"The pattern or 'Form' in which the numerals are seen is by no means the same in different persons, but assumes the most grotesque variety of shapes, which run in all sorts of angles, bends, curves, and zigzags...
...These forms...are stated in all cases to have been in existence, so far as the earlier numbers in the Form are concerned, as long back as the memory extends; they come 'into view quite independently' of the will, and their shape and position...are nearly invariable."
-Galton 1907

It's weird that it was already studied 100 years ago, and yet today nobody knows about it except probably just a handful of researchers.

 

[zoobyshoe]

It's weird that it was already studied 100 years ago, and yet today nobody knows about it except probably just a handful of researchers.

Well, Cytowic, who is responsible for the revival of interest in synesthesia, figures number forms are incredibly common, that one-in-ten people experience them. So, lots of people know, they just think they're the only one.

Given the # of thread views, though, there should be a lot more people here reporting they have this.

 

[waht]

Here's a couple images I found; people's attempt to draw their number forms:

Here is a PM I sent to Zooby over a year ago:

I've always dismissed that I don't have a photographic memory for this reason. I can flip pages in my head of a book, but they are fuzzy for me to read them. And, I noticed, that if there are gaps, my imagination will fill them with anything.

Like I've wanted to memorize the first 20 digits of pi this way. What happened was I remember a long sequence of numbers. Then I imagine this sequence as a string and wrap it around a cylinder multiple times, or stretch it like a rubber band in my head. I'm almost at the tip of reading the numbers off of this string, but I can't, it's too fuzzy.

 

[turbo]

I experience visual patterns when thinking about time and numbers. Time more strongly than numbers.

 

[zoobyshoe]

I've always dismissed that I don't have a photographic memory for this reason. I can flip pages in my head of a book, but they are fuzzy for me to read them. And, I noticed, that if there are gaps, my imagination will fill them with anything.

Like I've wanted to memorize the first 20 digits of pi this way. What happened was I remember a long sequence of numbers. Then I imagine this sequence as a string and wrap it around a cylinder multiple times, or stretch it like a rubber band in my head. I'm almost at the tip of reading the numbers off of this string, but I can't, it's too fuzzy.

You can see, though, that this is different than a number form. You manipulate this image a lot by act of will. A number form pops up involuntarily and seems like the way it's supposed to be envisioned, despite the fact it's idiosynchratic to that individual. (No two people envision the same number line or calendar, days of the week, or alphabet.)

 

[Chi Meson]

Amazing! Do the numbers seem associated with a particular position relative to your body?

Any thing beside the number line? Elements of the calendar, measurements, the alphabet?

I don't think that the numberline depends on the position of my body, but definitely changes depending on what mathematical operation is going on.

If I'm thinking of the squares, then the line pivots at each perfect square. When counting or dividing by fives, the line folds up along each 5 and 10 like an old carpenter's ruler.

The calender: months look like blocks (much like a calender) descending like stairs, in a straight line, with January always to the left (even in January), and the rest of the year either to the right, or in front. The "new year" is a platform where a counter-clockwise turn is made to start the next year. The calendar descends, but when thinking about the year itself, I shift to the ascending number line.

Which reminds me that the decades of my life have distinct turns. 79-80 takes the sharpest bend, for some reason, with 70s being much steeper and coming up toward my viewpoint, and 80s being very flat after taking a left-turn (but that means going to my right). The 90's turned right and went steeper, and the "twenty-Os" turned left and flattened out again. I'm currently staring down that section and I can "feel" 2011 to my left.

 

[zoobyshoe]

I don't think that the numberline depends on the position of my body, but definitely changes depending on what mathematical operation is going on.

If I'm thinking of the squares, then the line pivots at each perfect square. When counting or dividing by fives, the line folds up along each 5 and 10 like an old carpenter's ruler.

The calender: months look like blocks (much like a calender) descending like stairs, in a straight line, with January always to the left (even in January), and the rest of the year either to the right, or in front. The "new year" is a platform where a counter-clockwise turn is made to start the next year. The calendar descends, but when thinking about the year itself, I shift to the ascending number line.

Which reminds me that the decades of my life have distinct turns. 79-80 takes the sharpest bend, for some reason, with 70s being much steeper and coming up toward my viewpoint, and 80s being very flat after taking a left-turn (but that means going to my right). The 90's turned right and went steeper, and the "twenty-Os" turned left and flattened out again. I'm currently staring down that section and I can "feel" 2011 to my left.

Excellent! Are there any colors involved?

 

[turbo]

Looking back at the 50's and 60's I see a fairly straight uphill grade until about 70 (when I was in college) the then there was a sharp right-turn and various degrees of slope for the next 20 years, then a gradual left turn leading into the 2000s. Still, always up. When I have a memory, I always relate it to that graphic time-line. I didn't create it, but there it is.

Edit: BTW, when I see the graphic during memories I see it from the viewpoint of the present. If I see it during dreams, I see it from the viewpoint of the memory in the dream. It's pretty odd, but that's a firm "rule". I don't make the rules, they are just there.

 

[Chi Meson]

Excellent! Are there any colors involved?

No, now you mention it, there's nothing colorful at all about it. There seems to be some darker and light shades, but that seems to have more to do with the number that I am thinking of or looking for, or the year I am trying to recall. It will "highlight," but I can't say that it brightens or darkens, but seems to "pop out" nonetheless. But, alas, it's essentially monochromatic.

Thinking about color for the first time, I'm trying to actively add color. I tried to make 2008 blue, for example, but it's not sticking. I don't "think" colors very well anyway. My dreams have only muted colors too, if there's any connection there.

 

[rhody]

Holy CRAP! I thought I was unique!

I have been aware of the weird ladder that my numbers (from 1 to etc) take since 6th grade, and I have never known this to be talked about until now!

Some of the pictures that you showed are similar to my own. I even see various portions of my numberline from different perspectives. Sometimes it helps with quick problems of addition and subtraction, but just as often, it gets in the way, because the damn thing is so irregular.

I recognized it long ago as something that might explain why a savant can do math so quickly, just by essentially looking at the "map" in his head.

Mine starts at zero and goes straight line to ten, looking like a ladder propped agains a low wall. 10 to 20, the ladder turns to the right, and gets steeper. 20 to 30, turns left, and gets steeper still. A bit fuzzy at the 39/40 transition, but the steepness stays the same, and slight zigzags at each ten, but not necessarily the same turn. 100 is like a solid platform (much like zero) from which the same ladder begins again.

After 200, the 100s seem to be a repeat of the 1 to 10 ladder.

The 1000's for some reason, go to the left, at no angle.

Amazing! Do the numbers seem associated with a particular position relative to your body?

Any thing beside the number line? Elements of the calendar, measurements, the alphabet?

Chi Meson, Zooby,

This whole exercise is giving me chills, imagine, people are discovering on PF that they may have synesthasia their whole lives and never knew it, that simply blows me away !. Man do I ever love this subject... a living, highly educated, curious group at our disposal to probe and question, hehe, just kidding. I will look for some official documentation on Feynman, I seem to remember if was from James Gleck's book, "Genius: the Life and Times of Richard Feynman". I read it so many times I wore the first copy out and have since lent my second copy, beat up and dog eared to someone at work, I will try to get it back, and do some googling and general poking around in the meantime.

To all, remember Cytowic says that trying to describe what synesthetes perceive is ineffable, and idiosyncratic (no two people experience the same trait the same way, and worse not the same way every time ! Due to external stimulus like drugs, etc... don't get frustrated. The effects can be softer and more intense as well depending on the stimulus and the related area in the brain (lighting up so to speak at the same time).

Rhody...

 

[Averagesupernova]

Exellent! This sounds like an authentic number form!

Be very cool if you could photoshop up a calendar to show us how you envision it.

I'll try to throw something together. I am lousy at drawing 3D and to convey it accurately the lines will need to converge in the distance. I also have a 'zoom function'. LMAO I sound like Kryten in Red Dwarf. Seriously, in time periods that I have studied the same as any other person would have through their school years, I zoom in on various periods to examine them more closely. Looking back on my own life, the lines get converged pretty close together within a few years of my birth. However, if I think about it in a different context, I 'zoom'. For instance, my parents birthdates form a convergence of lines a number of years earlier when I think about the history of their lives. Honestly I didn't know that there was another way to think about it. The lines and blocks that form years go into the future away from me at about 1 to 2 o'clock and slightly upward. 12 o'clock would be the direction I am facing. Obviously, the past goes opposite of the future by 180 degrees.

 

[Chi Meson]

Chi Meson, Zooby,

This whole exercise is giving me chills, imagine, people are discovering on PF that they may have synesthasia their whole lives and never knew it, that simply blows me away !. Man do I ever love this subject... a living, highly educated, curious group at our disposal to probe and question, hehe, just kidding. I will look for some official documentation on Feynman, I seem to remember if was from James Gleck's book, "Genius: the Life and Times of Richard Feynman". I read it so many times I wore the first copy out and have since lent my second copy, beat up and dog eared to someone at work, I will try to get it back, and do some googling and general poking around in the meantime.

I have recognized this as minor synesthesia, but nothing like what I read about. Loud sounds have vague shapes to me, and some shapes make noise in my head, but everything has to be quiet all around me for me to notice.

 

[waht]

Well, Cytowic, who is responsible for the revival of interest in synesthesia, figures number forms are incredibly common, that one-in-ten people experience them. So, lots of people know, they just think they're the only one.

From my point of view, it was impossible to pry out synesthesia on my own. I would note once in a while that some things are in color, but never fully extend that concept outside the box such that there are serious studies revolving around it. I just go with the flow and not think about it, nor think to investigate it. But once the cat is out of the box, synesthesia became pretty quantified in my head as just another process of the brain. It brings closure.

You can see, though, that this is different than a number form. You manipulate this image a lot by act of will. A number form pops up involuntarily and seems like the way it's supposed to be envisioned, despite the fact it's idiosynchratic to that individual. (No two people envision the same number line or calendar, days of the week, or alphabet.)

That's right my perception of it is a dynamic evolution, with few static mental structures. So I guess it doesn't fit description of number forms.

The string with colorful numbers on it can evolve from a straight line to a knot, and then conforms to a string wrapped around a needle, with one end of the string going through the eye, and the other pierced through its sharp point, then bending the whole needle into a circle, and then getting all the numbers dissociate and fly apart from it spinning and rotating. But at this stage it's hard to tell what these number are. Then I think about something else.

 

[turbo]

I don't have a strict synesthesia with numbers because things would get complicated too quickly, but when I was a child, I saw 4 as blue, 2 as red, and 3 as yellow. I don't know why. That happened when I was really young, but to this day, I have a soft spot for squares of 4 and don't have much affinity for multiples of 5.

 

[zoobyshoe]

I'll try to throw something together. I am lousy at drawing 3D and to convey it accurately the lines will need to converge in the distance. I also have a 'zoom function'. LMAO I sound like Kryten in Red Dwarf. Seriously, in time periods that I have studied the same as any other person would have through their school years, I zoom in on various periods to examine them more closely. Looking back on my own life, the lines get converged pretty close together within a few years of my birth. However, if I think about it in a different context, I 'zoom'. For instance, my parents birthdates form a convergence of lines a number of years earlier when I think about the history of their lives. Honestly I didn't know that there was another way to think about it. The lines and blocks that form years go into the future away from me at about 1 to 2 o'clock and slightly upward. 12 o'clock would be the direction I am facing. Obviously, the past goes opposite of the future by 180 degrees.

Galton, I think, says it's very panoramic for some people and you sound like one of them. It's fascinating how three dimensional it is for you.

I have to assure you, no, nothing remotely like this goes on in my mind. "May 2" or even "May" is a bland, isolated concept to me. I experience a small emotional uplift because I associate it with warmer weather, but it is not connected to any chart or even an image of a conventional calendar page. My clock says 5/2 Sun: I may imagine it spoken in my vague inner voice - "Five, two, Sun". And that's it. Maybe a fleeting, very vague, image of warm sunlight on green plants.