Do You Experience Number Forms ?

[fuzzyfelt]

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"?

That is a good question for the number formers here. I’m not one and also have trouble thinking of numbers at all.

I’ve read that this sort of question is a topic of interest regarding synaesthesia, and may be related to which sense or mode evokes the experience.

In "Synesthesia- A Window into Thought, Langauge and Perception”, Ramachandran and Hubbard, regarding synaesthetes, and not necessarily number formers, Roman Numerals and dot clusters were not effective in evoking the experience, with exceptions. Also tactile and auditory stimuli were ineffective unless visualisation also occurred, leading to the summation that it is vision and not concept triggering the experiences mentioned.

In another text describing synaesthetic script rather than numbers, or number forms, experiences were evoked by one and not another script in bilinguals, for an interesting example, a first language, English, didn’t evoke any experience, whereas a second language, Hebrew, or Hebrew script, did. I think I’ve read this is consistent with an idea from lesions, that different languages may be mapped in different regions.

http://books.google.co.uk/books?hl=...q=ramachandran hebrew second language&f=false
(last paragraph, page 446)

 

[billiards]

I wonder whether Jean-Robert Argand might have experienced this phenomenon?

 

[EnumaElish]

http://books.google.co.uk/books?hl=...q=ramachandran hebrew second language&f=false

Wow, quite a read!

I may not have number forms, but FWIW, I visualize climatic seasons in color (winter = white, spring = greenish bluish whitish, summer = orange glow, fall = rust) -- no big surprise there. Perhaps more notably I see days of the week in color: Monday = blue, Tuesday = yellow, Wed. = red, Thu. = dark blue, Fri. = off-white/beige, Sat. = white, Sun. = orangy red.

 

[Chi Meson]

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"?

That's an interesting question, and the answer for me is "no they don't change."

I learned Spanish cardinal numbers at the age of seven, and got into Roman numerals at 8, and also learned numbers through twenty in French, Japanese, German and Greek. In all cases, the numbers, regardless of the language, and regardless of their form, all sit in exactly the same space on the number form (I'm still stoked by the fact that it has a name!).

 

[zoobyshoe]

(I'm still stoked by the fact that it has a name!).

And, despite, or to spite, the fact I was trying to keep Cytowic's classifications in order, he has gone and changed them on me in Wednesday Is Indigo Blue. Number forms have been upgraded to a form of synesthesia, and:

"These objectified three-dimensional sequences are commonly called 'number forms', although more precisely the phenomenon is called 'spatial sequence synesthesia'. Formally we note it as sequence -> location."

p.109

So, all you number formers may now refer to yourselves as synesthetes having "spatial sequence synesthesia".

 

[fuzzyfelt]

Wow, quite a read!

Oops, I should have mentioned the information I used was from the last paragraph of page 446. :)

 

[fuzzyfelt]

That's an interesting question, and the answer for me is "no they don't change."

I learned Spanish cardinal numbers at the age of seven, and got into Roman numerals at 8, and also learned numbers through twenty in French, Japanese, German and Greek. In all cases, the numbers, regardless of the language, and regardless of their form, all sit in exactly the same space on the number form (I'm still stoked by the fact that it has a name!).

That is a fascinating answer! If no one form or language alone is uniquely associated, does it beg the question, what does seem strongly associated with the experience?

 

[Chi Meson]

That is a fascinating answer! If no one form or language alone is uniquely associated, does it beg the question, what does seem strongly associated with the experience?

I don't know if this answers your question, but when I think of a number, the location on the form is what I associate it with. When the location "pops out," there is no numeral or name on it, only its position.

So regardless of what language I "think" it in, or which numerals, a 3 is a three is a tres is a drei is san is a III is a trois; they are all the same number that comes after 2 and before 4.

I also noticed that the astronomical numbers cause a sense of of disturbance in me because they simply cannot "find a place on the form." They are only numerals. If it is a number like
53,000,000,000,000,000, I can say "fifty three quadrillion." The "fifty three" initially jumps out, but then evaporates when "quadrillion" comes in. I have a vasensation of staring off into the distance, but here I am not sure if it is my projection, or simply "zooming out too far."

"Billions" is the last order of magnitude that can hold onto a position, and perhaps that is because I learned of "billions by the age of seven (when there wer 3 billion people in the world).

 

[EnumaElish]

So regardless of what language I "think" it in, or which numerals, a 3 is a three is a tres is a drei is san is a III is a trois; they are all the same number that comes after 2 and before 4.

This reminds me of the "kiki/bouba" experiment described in Ramachandran & Hubbard (http://books.google.co.uk/books?hl=...q=ramachandran hebrew second language&f=false, p. 457) -- relative geometric forms were found to be associated with relative sounds, regardless of language.

In Chi's case, cardinal magnitudes are associated with spatial positions, again regardless of language.

 

[rhody]

I don't know if this answers your question, but when I think of a number, the location on the form is what I associate it with. When the location "pops out," there is no numeral or name on it, only its position.

So regardless of what language I "think" it in, or which numerals, a 3 is a three is a tres is a drei is san is a III is a trois; they are all the same number that comes after 2 and before 4.

Chi,

This begs the question then, what if you were to study say French again, and the names of numbers 1 - 20 were changed from what you originally taught yourself and commited to memory would the location as you describe it above be the same as the original position of 1 - 20 ? In other words once the official words and locations are assigned in nearly life, can a new association break the one that you sense synesthestically now ?

Example: For the number 2, if Deux were replaced with Daix, and you believed that Daix is now the official number two would it still occupy the same place in your position space ? Does the new sound of the word keep it from occupying the same space ? What if Diux were used instead, which is closer to the original word Deux ? Is it the shape and number of letters that helps establish the location, just the sound of the word, or the combination of them together ?

Additionally, is tagging the meaning of Deux = 2 = etc... another factor in establishing where it appears to you synesthetically ?

Rhody...

 

[Noja888]

This thread is a very interesting read. I never knew number forms existed in a sense like this. My memory is very visual but I have no number forms. Many times back in high school I have recalled a page out of a textbook in visual memory. From my mental picture I could come up with enough information to pass the test/quiz. If I was lucky I could read some of the words from the page out of my head - but this was very rare. If someone is talking, mental images of whatever they are saying appears - which can be good or bad depending on the subject.

 

[zoobyshoe]

In some forms of synesthesia it's clear that a concept is triggering the sensory experience.

For grapheme -> color synesthesia Cytowic says:

"...what happens when a synesthete looks at foreign letters written in non-Roman scripts such as Hebrew, Arabic, Cyrillic, or Chinese? Typically the newly learned shapes are not accompanied by a color experience. As Cassidy C writes, 'They look like little black shapes on a white background. They have no color effect whatsoever.' But most synesthetes report once they have learned a language (even as an adult), the new graphemes take on colors. Often there is some correlation between the sound of a letter and it's associated color in both alphabets."
...Indigo Blue p.67

So this strongly indicates that it is the concept of a letter, not it's shape, that is the operative property.

"It now seems clear that for the majority of synesthetes it is the concept inherent in the grapheme that induces color - not the visual shape itself. To demonstrate this, note that capitalization and font style generally do not change an induced color: j, J and J all evoke the same synesthetic color."
p.75

This dependence of the color on the concept in grapheme-> color synesthesia seems to translate to a dependence of the position on concept with a number form, as described by Chi Meson: the position is held by the concept of 2 or the concept of 45, not by the sound of the word used to symbolize that concept verbally. Therefore switching languages doesn't affect his number form.

 

[Chi Meson]

Chi,

This begs the question then, what if you were to study say French again, and the names of numbers 1 - 20 were changed from what you originally taught yourself and commited to memory would the location as you describe it above be the same as the original position of 1 - 20 ? In other words once the official words and locations are assigned in nearly life, can a new association break the one that you sense synesthestically now ?

Example: For the number 2, if Deux were replaced with Daix, and you believed that Daix is now the official number two would it still occupy the same place in your position space ? Does the new sound of the word keep it from occupying the same space ? What if Diux were used instead, which is closer to the original word Deux ? Is it the shape and number of letters that helps establish the location, just the sound of the word, or the combination of them together ?

Additionally, is tagging the meaning of Deux = 2 = etc... another factor in establishing where it appears to you synesthetically ?

Rhody...

It's more as though the location is the fundimental concept of the number itself. Any way of describing a number is translated into its location on the form. Any variation is projected onto the location. If I learned the numbers in any new language, as I learned the equivalent to 17 for example, It would project directly to the "17" location, and not exist as a translation of the English language "seventeen."

To try to say it another way, "17" is a concept independent of the language, and the "definition" is visual, rather than textual. I think I'm figuring this out as I'm saying it. It's quite exciting!

 

[zoobyshoe]

It's more as though the location is the fundimental concept of the number itself. Any way of describing a number is translated into its location on the form. Any variation is projected onto the location.

The "concept" of a number is not quantity, but location. Pretty fascinating.

 

[rhody]

It's more as though the location is the fundimental concept of the number itself. Any way of describing a number is translated into its location on the form. Any variation is projected onto the location. If I learned the numbers in any new language, as I learned the equivalent to 17 for example, It would project directly to the "17" location, and not exist as a translation of the English language "seventeen."

To try to say it another way, "17" is a concept independent of the language, and the "definition" is visual, rather than textual. I think I'm figuring this out as I'm saying it. It's quite exciting!

Chi,

I only have one comment that both you and I have expressed numerous times,

Holy Crap !

Rhody...

P.S. This thread and the one on synesthesia supplies all the elements of a great learning exercise, exploration, wrong turns, dead ends, debate, clarification, surprise, amazement, and a willingness to keep digging. If I were a college student committed to the study of biology or neurology, this would inspire me for sure.

 

[fuzzyfelt]

I don't know if this answers your question, but when I think of a number, the location on the form is what I associate it with. When the location "pops out," there is no numeral or name on it, only its position.

So regardless of what language I "think" it in, or which numerals, a 3 is a three is a tres is a drei is san is a III is a trois; they are all the same number that comes after 2 and before 4.

I also noticed that the astronomical numbers cause a sense of of disturbance in me because they simply cannot "find a place on the form." They are only numerals. If it is a number like
53,000,000,000,000,000, I can say "fifty three quadrillion." The "fifty three" initially jumps out, but then evaporates when "quadrillion" comes in. I have a vasensation of staring off into the distance, but here I am not sure if it is my projection, or simply "zooming out too far."

"Billions" is the last order of magnitude that can hold onto a position, and perhaps that is because I learned of "billions by the age of seven (when there wer 3 billion people in the world).

That answers my question brilliantly, thanks!

I’d mentioned before, that a strong association with a particular form, which I guess was Arabic numerals, had conjured colours, and had led to the idea that a strong association with a concept would be dismissed in that particular example. Interestingly that isn't case here, and it seems you have also discounted nominal and aural stimulus.

I was wondering if instead then, the trigger was indeed conceptual. I understand it must be extremely difficult to isolate an influential part of a thought process. That you describe an experience elicited by a learnt, cultural concept is brilliant!

To rephrase you, I hope this is right- the concept of number/units, rather than any image or sound, elicits a spatial and visual (sequentially linear and formal) positioning, although limited by magnitude.

I’ve found a few papers about whether in cases studied, the link is between number/units and a matter of position (a location in a sequence) or a matter of magnitude (ordinality/cardinality- I think?) in some and not others or whether both properties are required to some degree, and these papers all seem to contradict one another! So your description of your experience is impressive. I'm not sure how it fits, but it seems to fit well. It is a fascinating insight into the minds of those “gifted with a strong tendency towards schematisation” (Flournay), or into numeracy cognition, these sorts of things.

Here is one-
http://www.unicog.org/publications/HubbardRanziniPiazzaDehaene_NumberSpaceSynesthesia_Cortex2009.pdf

 

[WiFO215]

To rephrase you, I hope this is right- the concept of number/units, rather than any image or sound, elicits a spatial and visual (sequentially linear and formal) positioning, although limited by magnitude.

I don't know about Chi, but I'd agree that's what happens to me. Whether I do Sanskrit, Hindi or Tamil, the numbers' place is the same.

 

[WiFO215]

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.

I don't know, Zooby. I can't 'feel' the numbers in any unconscious way. I just know they're there when I need to use them.

 

[fuzzyfelt]

I don't know about Chi, but I'd agree that's what happens to me. Whether I do Sanskrit, Hindi or Tamil, the numbers' place is the same.

That is great! I'm relieved to hear it! :)

 

[Chi Meson]

To rephrase you, I hope this is right- the concept of number/units, rather than any image or sound, elicits a spatial and visual (sequentially linear and formal) positioning, although limited by magnitude.

I’ve found a few papers about whether in cases studied, the link is between number/units and a matter of position (a location in a sequence) or a matter of magnitude (ordinality/cardinality- I think?) in some and not others or whether both properties are required to some degree, and these papers all seem to contradict one another! So your description of your experience is impressive. I'm not sure how it fits, but it seems to fit well. It is a fascinating insight into the minds of those “gifted with a strong tendency towards schematisation” (Flournay), or into numeracy cognition, these sorts of things.

I'd say that's right. This is not exactly what I'd always understood as "synesthesia." For me, numbers have absolutely no color nor sound.

Everything seems to be spatial to me. Music also conjures spatial forms. I remember in a 6th grade art class, we all had to "paint what the music sounds like." While I suspect I was the first person to understand what the teacher meant, I had the hardest time of anyone. While others were making these static, abstract paintings, I was trying to figure out how to paint something that wouldn't stop moving and swirling.

And in retrospect, it seems that the lack of color made things difficult for me, too. I don't do color so well.

But the visual aspect of music always seemed to be a fairly common sensation, is it not?

 

[zoobyshoe]

This is not exactly what I'd always understood as "synesthesia." For me, numbers have absolutely no color nor sound.

"Synesthesia" has never been limited to color and sound. Cytowic became famous for describing a man whose sense of touch was triggered by the taste of food. This was so important to him that he cooked according to how the food "felt" to his fingers, and on his arms and face. Rhody posted a comprehensive list of known pairings in the synesthesia thread:

https://www.physicsforums.com/showpost.php?p=2704648&postcount=102

Regardless, this association of concept with an automatic sensory reaction has only recently (sometime between 2002 and 2008) been promoted to being regarded as a form of synesthesia: Spatial Sequence Synesthesia, as I mentioned (At least that's what Cytowic asserts. I don't even know what that means: did all the synesthesia researchers have a conference call and take a vote? I dunno). I personally never heard of number forms until Rhody linked to a video of Cytowic lecturing at a book signing in which he talks about what's discussed in Wednesday is Indigo Blue a couple/three weeks ago. Anyway it makes perfect sense to me that you could have a number form, have heard of synesthesia, and still not connect them in your mind.

 

[rhody]

Chi, anirundh215,

Let me get this straight then, if you picked up a new language and committed to memory and then used the numbers, no matter what their form they would be in an ascending ordered space, in their proper position (in your mind's eye so to speak), correct ? (except for truly large numbers in the billions range and beyond as you mentioned previously (Chi))
Is the same true for you anirundh215 ? Are you multilingual in math as well ?

Second, Chi, can you easily switch from one language to another with numbers, if so, do the numbers spatially occur next to one another (shared in hierarchical space) or in their own separate space ? anirundh215, if this applies to you same question as well.

I invite you both to watch this http://www.ted.com/talks/lang/eng/arthur_benjamin_does_mathemagic.html" of Arthur Benjamin, a mathemagician: fast forward to 10:40 where he attempts to square two 5 digit numbers. He uses words to help keep track of intermediate calculation values and then retrieves the number from the word association (at 14:15, 77862 becomes cookie efficient), he uses 3 or 4 word to number associations in order to arrive at the correct answer.

Listen carefully because he runs through this very quickly. After watching this short segment, if either of you does math with large numbers in your heads, do you use number -> word association, then back from word -> numbers to arrive at the correct answer ?, or a different method due to your synesthetic hierarchical spatial organization with numbers ? In other words if you do higher math problems in your heads, how do you do it ?

Rhody...

 

[Chi Meson]

Chi, anirundh215,

Let me get this straight then, if you picked up a new language and committed to memory and then used the numbers, no matter what their form they would be in an ascending ordered space, in their proper position (in your mind's eye so to speak), correct ?

yes, that's correct.

Second, Chi, can you easily switch from one language to another with numbers, if so, do the numbers spatially occur next to one another (shared in hierarchical space) or in their own separate space ? anirundh215, if this applies to you same question as well.

the same number, no matter whatever the language, or form (Roman numerals, tally marks, written out, or numerals), the same number is always in exactly the same location.

Listen carefully because he runs through this very quickly. After watching this short segment, if either of you does math with large numbers in your heads, do you use number -> word association, then back from word -> numbers to arrive at the correct answer ?, or a different method due to your synesthetic hierarchical spatial organization with numbers ? In other words if you do higher math problems in your heads, how do you do it ?

Rhody...

I can NOT do higher order math in my head. I teach physics, and even the basic algebra that I have been teaching for ten years, the easiest possible stuff, I still need to write it out to be sure. The number form is a liability for math skills.

 

[zoobyshoe]

FYI, everyone, Rhody just unearthed a fascinating new form of synesthesia:

https://www.physicsforums.com/showpost.php?p=2714867&postcount=121

 

[Chi Meson]

Here's another thing I've just considered:

decimals and fraction have no place on the form. This could be why I have a more-difficult-than-it-should-be time with wrench sizes. I have to pause and think, for example to figure out which size socket is larger than 3/8 , for example. I have to translate everything into "16ths."

There is also NO PLACE for PI!

Another problem is that 1.75 meters is not in the same place as 175 cm. So the scale of the unit has no bearing at all on the position. This means I must absolutely ignore the damn thing when doing math, but it still clouds my numerical intuition.

 

[rhody]

Chi,

When you said:

I can NOT do higher order math in my head. I teach physics, and even the basic algebra that I have been teaching for ten years, the easiest possible stuff, I still need to write it out to be sure. The number form is a liability for math skills.

A fair question to ask then is, do the spatially separated hierarchical numbers help, hinder, provide distraction, or are merely a curiosity (pets, as zooby fondly refers to them) to your everyday activities.
Have you every used them for anything, and if so what for ? Bookkeeping, reminders, things like that... ?

Rhody...

 

[zoobyshoe]

Here's another thing I've just considered:

decimals and fraction have no place on the form. This could be why I have a more-difficult-than-it-should-be time with wrench sizes. I have to pause and think, for example to figure out which size socket is larger than 3/8 , for example. I have to translate everything into "16ths."

There is also NO PLACE for PI!

Another problem is that 1.75 meters is not in the same place as 175 cm. So the scale of the unit has no bearing at all on the position. This means I must absolutely ignore the damn thing when doing math, but it still clouds my numerical intuition.

Number forms do not indicate high mathematical ability or deficiency, nor do they seems to be correlated with any specific intellectual talent or mental dullness. However, the automatic positioning of integers can interfere with more complex mathematics, such as algebra or calculus, as in the wayward numbers of the student cited above. "For one thing," notes Marti, "they are not evenly or consistently spaced. There is also some fluid or jelly-like movement to them." Magnitude can also be problematic because, for Marti, 6 is physically the highest number in her visual representation. Therefore, 6 and numbers containing 6 have the highest degree of magnitude. In other words it does not "make sense" to her that 11 is "larger than" 6 or that 234 is "greater than" 66. To her, magnitude comparisons are literally physical: when she thinks of someone older than herself she looks "up," whereas younger people are seen not "down" but "in back" of herself.

"...Indigo Blue" p.28

I can empathize with this number former. I had a great math crisis right off the bat in first grade when the teacher was teaching us to write and understand numerals. She called on me and asked which was "greater", 2 or 3. I hesitated. She said, "I mean which is larger." That didn't help at all. Reverting to some size estimating skill I didn't know I had, I pondered and determined that the numeral 3 was probably larger in size than the numeral 2, and gave that as my answer. "Right", said the teacher. I remained completely confused about the relevance of the physical size of the numeral to anything and really couldn't understand why she asked about it.

 

[Chi Meson]

Chi,

When you said:

A fair question to ask then is, do the spatially separated hierarchical numbers help, hinder, provide distraction, or are merely a curiosity (pets, as zooby fondly refers to them) to your everyday activities.
Have you every used them for anything, and if so what for ? Bookkeeping, reminders, things like that... ?

Rhody...

I think I went over all that earlier in the thread. In short, it is useful for simple addition and subtraction. I stated earlier that I can fold the form like an old carpenters ruler when playing considering multiples of fives, but after consideration, I think that is a spatial invention that I built way back long ago. Using the "fives" number form feels different than the "natural" one.

The greatest use is in remembering simple quantities, some dates, and I am punctual to a fault.

 

[zoobyshoe]

(pets, as zooby fondly refers to them)

That wasn't me, that was Jim McNamara and his "whatever-they-are eelights":

https://www.physicsforums.com/showpost.php?p=2703729&postcount=58

 

[fuzzyfelt]

I'd say that's right. This is not exactly what I'd always understood as "synesthesia." For me, numbers have absolutely no color nor sound.

Everything seems to be spatial to me. Music also conjures spatial forms. I remember in a 6th grade art class, we all had to "paint what the music sounds like." While I suspect I was the first person to understand what the teacher meant, I had the hardest time of anyone. While others were making these static, abstract paintings, I was trying to figure out how to paint something that wouldn't stop moving and swirling.

And in retrospect, it seems that the lack of color made things difficult for me, too. I don't do color so well.

But the visual aspect of music always seemed to be a fairly common sensation, is it not?

I have the same problem with the name, and think “atypical intra-modal and cross-modal binding” is better, and I’m interested in how atypical it is. I hope not to detract anything from the verifiable, incredible experiences like those described in this thread, nor from a difference between such actual percepts in some and a bound ‘feeling’ in others, and then perhaps further differences in others generally, but to your question at the end- combining aspects of the arts is common, including combining vision and music. (However, not necessarily always involving the modal binding like that being discussed here, and also not as common as, say, seemingly normal cross-modal facial recognition, I guess.)

Painting music is a usual exercise, and, interestingly cross-modal painting often involves a line a bit like yours. I remember the first time we were asked to do this, we were asked to paint “pain”. We weren’t told, but it was expected we render pain as something intrusive upon an otherwise untroubled line, the line representing temporal progression in space. Fortunately, I ( I was the only one, too!) did think to use such a line, but unfortunately, my line spiralled inward, for various reasons I had, which lessened the impact and so wasn’t deemed successful enough.

If it is interesting, I think rather differently, and do do colour. As mentioned before, I don’t do measure and I think there are a lot more practical things to do than colour! I understand you find your spatial experience hasn’t been so helpful, but that it helps with memory, and I imagine it helps possibly with a feeling of conversancy? I can’t imagine what impact not doing colour would have, but guess it is like a pronounced absence of the things I just mentioned when regarding colour?

I’d like to ask more about the musical-spatial form, and for that matter, croesoswallt’s colour-musical tone diagram, but don’t wish to stretch the OP too far.

Maybe a quick question for croesowallt- does it mean that you have perfect pitch?