Perception, knowledge, isomorphism, symmetry

[GrowingSmaller]

edit, but fresh posts on previous page.

 

[Bushido216]

Didn't read the thread, but the answer is no.

 

[Naraoia]

My pet idea is that perception is isomorphic to the outside world, possibly even symmetrical.

Aren't isomorphic structures automatically symmetrical? An isomorphism is defined by a pair of structure-preserving transformations between the two, no? And what is symmetry if not the existence of such a transformation between A & B? Or am I totally confusing the terminology?

(Geez, abstract algebra was a long time ago.)

The problem is I am just a layman playing with technical jargon I am not sure how to use. What is a "pet" again?

Good one!

Are you saying that activity in the visual cortex does not resemble activity on the retina?

What does "resemble" mean?

I dunno, I would say that if information is lost in processing, then reality and perception are not isomorphic, because you can't unambiguously get back from the latter to the former.

Wouldn't be the first time I got tangled in mathematical concepts, though...

People who wear "image inverting" glasses (they see everything upside down) will adapt after a few days and be able to see quite normally wearing the glasses.

I've always wondered how they experience the switch. Does the image get blurry and then it's inverted when it sharpens again, like when you pass the focus of a concave mirror? Or do you just wake up one morning and see straight?

 

[Chesterton]

Didn't read the thread, but the answer is no.

I didn't read the thread either, but that's preposterous! The answer is yes.

 

[GrowingSmaller]

Aren't isomorphic structures automatically symmetrical? An isomorphism is defined by a pair of structure-preserving transformations between the two, no? And what is symmetry if not the existence of such a transformation between A & B? Or am I totally confusing the terminology?

I am not sure about the proper use of the term "isomorphic". You are probably right, it's synonymous with "symmetry". My own intuition was that if there is a relation a, b, c in the real world, with a time interval of x between them, then a map a*, b*, c* would be isomorphic even is the time interval were changed to y, because some of the structural relations were preserved..

 

[Naraoia]

I am not sure about the proper use of the term "isomorphic". You are probably right, it's synonymous with "symmetry".

I'm pretty sure that they aren't completely equivalent - within abstract algebra, they are used in different contexts, for one thing -, but as I said, my relevant knowledge comes from four years ago, and wasn't very in depth to begin with

My own intuition was that if there is a relation a, b, c in the real world, with a time interval of x between them, then a map a*, b*, c* would be isomorphic even is the time interval were changed to y, because some of the structural relations were preserved..

Yes, I think, provided that x is transformed to y in a systematic way.