Do Mathematical Entities Really Exist?

[baron]

Yes I did wonder about synesthesia. It does sound like it may have something to do with it, although there's still the issue of the calculations themselves, which tend so suggest that the shapes are more than just alternative symbols for numbers, even accounting for the enhanced memory that occasionally goes with synesthesia. Still, interesting stuff.

 

[Kaylee]

Yes, definitely interesting stuff.

Occam's razor dictates going for the simplest answer. We know that blind sight exists, I thought it would be interesting to see if any case history already exists that shows that calculations (or any other thinking process) can be done "unconsciously".

With that in mind, I was curious to see if Tammet had ever had a brain scan done while he was calculating pi.

I wasn't able to get that much information, but I was able to find some information that seems to confirm that there is something to my hunch that "human calculators" perform the calculations unconsciously.
http://www.wisconsinmedicalsociety.org/savant/synopsis_article.cfm

One theory that does provide an increasingly plausible explanation for savant abilities in many cases is left brain injury with right brain compensation.
…
There is emerging evidence that prodigies and savants may share certain underlying mental processes when carrying out their specialized, expert tasks. Event-related potentials (ERPs) can measure very early
components of brain activity, reflecting initial, "pre-conscious" stages of mental processing. This fast, low level "preconscious" mental activity contrasts sharply with that seen when higher level, "executive" functions are accessed during typical information processing. Birbaumer compared ERPs of a "human calculator"— a non-autistic arithmetic whiz — to same age, IQ-matched, healthy controls.46 Compared to controls, early on in the calculating process, the expert calculator showed evidence of "enhanced automatic low-level processing." Studies are now underway with autistic savant calculators to see whether this particular type of early, lower level processing ("without reckoning") is the same as that used by the non-autistic "expert" calculator.

[emphasis mine.]


BTW, here are more links about Daniel Tattum:

http://www.wisconsinmedicalsociety.org/savant/tammet.cfm
(Includes a link to a short video about his abilities.)

His official web site:
http://www.optimnem.co.uk/index.php
(He has an amazing ability to learn languages, and his web site sells tutorials in French and Spanish. An entrepreneur in his 20s! Not bad. )

 

[69dodge]

Yes I did wonder about synesthesia. It does sound like it may have something to do with it, although there's still the issue of the calculations themselves, which tend so suggest that the shapes are more than just alternative symbols for numbers, even accounting for the enhanced memory that occasionally goes with synesthesia. Still, interesting stuff.

What do you mean by "the shapes are more than just alternative symbols for numbers"? Do you think that the number five, for example, really is a clap of thunder, in any meaningful sense? I don't.

Anyway, do all these people visualize numbers in the same way? If not, then that's another reason not to think that, by visualizing numbers the way they do, they're "accessing the underlying mathematics".

 

[Zygar]

What do you mean by "the shapes are more than just alternative symbols for numbers"? Do you think that the number five, for example, really is a clap of thunder, in any meaningful sense? I don't.

Anyway, do all these people visualize numbers in the same way? If not, then that's another reason not to think that, by visualizing numbers the way they do, they're "accessing the underlying mathematics".

Yes. Obviously the underlying mathematic value of thunder is five. Thor loves to throw those sevens down on us, allowing us to bask in the short-lived auditory sensation of fives. That Thor. Such a kidder.

 

[BPScooter]

Well, there is the person of Scriabin, the pianist and composer. He was a "savant" in the old-fashioned way (he studied and practiced) and then later in life expressed, shall we say, eccentric views. He propounded a very well developed musical theory in which each tonal center, "key", corresponded to a certain color and emotional tone. He wrote music along these lines, which is still performed and remembered, mostly by piano players. His life dream was to complete the Theosophist program by creating a piece, to be performed at the base of the Himalayas, in which musical tone, color, and ritual would culminate in a grand transcendent moment. This piece would take several days to develop. He was saying this around 1910, and he called it the "Mysterium".

I'm not entirely sure he was wrong...it might be a worthy goal. But among the musicians, Scriabin is alone in trying to systematize his color/sound experiences and produce real evidence of them. His piano music does describe, in tone, his inner life. At least no other first-rate composer has talked about it so much.

 

[Schneibster]

WOW, did you guys go far afield. Synaesthesia? Scriabin? I mean, I've heard of that stuff, but how on Earth did it ever get into a conversation on math qua math?

As far as general skepticism about the reality of math, I always say, start with the natural numbers. One orange, two coconuts. It pretty much all grows from there, and each different kind of number describes a different sort of situation that some mathematician thought would be interesting, and that we later found out was actually a useful description of something we found in reality. The sole exception to that I'm aware of is tensors, which were invented AFAIK to deal with GRT.

 

[BPScooter]

F major, dude, it's pastoral. Nobody's proved it right or wrong that way yet.

 

[Schneibster]

I tend to like the keys of G minor and C major, but that's just me.

 

[BPScooter]

The only other thing in my field that comes to mind is John Coltrane, the pioneering Jazz musican.

His composition "Giant Steps" walks around the Circle of Fifths (which every student of music theory learns). His performance is staggeringly effortless.

He also appeared to be tapping into a higher bit of thought, he was a Jazz musician, after all. He felt like he was doing something different, there at the end. My take is that he was in full recognition of the fact that he was about to bite the big one, and pushed out a couple more masterpieces before he went. Just from the way he talked about his music. He frankly sounded like he didn't give a poo anymore, and wanted to "go for it."