On Wed, Jul 22, 2009 at 3:41 AM, Brent Meeker<meeke...@dslextreme.com> wrote:
> The way I look at it there is knowledge we gain from perception, including the
> inner perception of logical and mathematical facts.  We make up theories that
> unify and explain these perceptions and which extend beyond what we perceive.

Sounds reasonable enough.

>> In what way, exactly, does logico-mathematical existence differ from
>> quark existence?
> You can kick quarks and they kick back.

So they differ in how we perceive them, and the way we interact with
them.  We experience them differently.

> Certainly many mathematical objects can be illustrated
> because they were invented to describe something we could
> perceive - like spheres or symmetries.

Is that the history of something like Bruno's beloved Mandelbrot set?
I honestly don't know, but your rather broad claim sounds somewhat
weak to me.

> But I don't see how you would visualize Shannon
> information

"H-BloX is a web-based JavaScript application that allows the
calculation and visualization of Shannon information content or
relative entropy (Kullback-Leibler ‘distance’) within sequence
alignment blocks."

So obviously different types of visualizations would be useful in
different situations, and some visualizations might be possible but
not useful at all.  But it would seem to me that nearly anything can
be represented visually in one way or another.

> or strings in ten dimensional space.

Well, given that "strings" aren't logico-mathematical objects, but
instead inferred (though not experimentally confirmed) physical
objects like quarks, I'm not sure what you're saying here.

BUT, since you brought it up, here:  http://bccp.lbl.gov/Images/calabi-grid.gif

> I don't think that's good example. Synesthesia comes from cross coupling in 
> the
> brain of concepts that are usually separate.  I synesthesia were like 
> perception
> then all synesthesists would see the same numbers as having the same color, 
> etc.
>  The main thing that causes us to attribute a form of existence to 
> mathematical
> objects is that everyone who understands them agrees on their properties.

If a race of "synesthetes" had evolved with a common "cross-coupling"
(shaped by natural selection), then they would have a shared
perception of numbers.  Possibly combining the various types of
synesthesia.  So to these synesthetes numbers would have color,
shapes, textures, and spatial locations (using the examples from the
wikipedia article).

When the synesthetes began to develop physics, they would no doubt
notice a correlation between the numeric world and the physical world.
 What kind of conclusions they would draw from the correlations, I've
no idea, but it seems reasonable to speculate that they might be
puzzled in the same way that we are puzzled by wave-particle duality
or the nature of time.  They might even conclude that the physical
world is "caused" by the very tangible (to them) mathematics that
describe it.

So, since we KNOW that it is possible humans to perceive numbers in
this way (from synethesia), then there is no reason to think that it's
impossible to breed it into a population, which would then accept it
as the norm, and who would then have a different view of the reality
of numbers.

>> I think we can say (again, speaking in materialist/physicalist terms)
>> that it's purely an accident of evolution that numbers don't seem as
>> intuitively real to us as chairs, or colors, or love, or free will
>> (ha!).
> But numbers don't cause anything and they are not caused by other things.  So
> it's not an accident.

My point is that we could have evolved with synethesia being a common
condition.  What type of selection pressures would have resulted in
that?  I don't know.  Some survival requirement that is satisfied by
those havin an intuitive feel for numbers I suppose.

I assume your point is that since numbers are acausal, they couldn't
have contributed to those selection pressures in any direct way?  True

> It is more than just perceiving them differently.  For example mathematical
> objects are not located in space or time.  They exist timelessly and in no
> particular place.

Okay, I'll grant you that.  Though it doesn't directly affect the
point I was making.

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