jerromyjon said:
MathematicalPhysicist said:
I don't see even the point for more than 3+1 dimensions, but some physicists look for extra dimensions.
No one who only believes in only what they see around them does, because that is all we need to explain our sense of reality.
I would argue that this deceptive argument about out sense or reality implying we live in 3D+1 seems fallacious in the first place.
If i look at what our senses actually does from the point of view of physics and how neuroscientist understand the brain. They actual sensory signals are merely electrical signals conducted via afferent nerves towards the CNS and the brain, and in the brain the information in all electrical signals seeme to be processed encoded in a way that makes predictions of the future accurate and resposive. That is simply the task of the brain from the evolutionary perspective.
So it is clear to me, that our intuitive perception of our world, in particular dimensionality is very FAR from direct. Instead i think the most honest description of the situtation is that that "map of reality", that evolution created for us, encoded in our brain, has AT BEST a holographic connection to actual reality. But this connection might well represent and equilibrium or tradeoff between structural accuracy and dynamical accuracy because the purpose of the BRAIN is not be a truthful map(however one would operationally define that without using another brain?), the purpos is to make the host survive. So an effective map, that is good enough, but easier to make predictions with, will have an evolutionar advantage.
Incidently this insight from how our brain processes input, to produce actions during a race condition that evolutio is, do have parallells to some ideas in physics as well. As we know some of the dualities (AdS/CFT) relate spaces of different dimensionality with each other - BUT sometimes the "COST" of stronger couplings and higher computational costs. And if we thinkg about this just for a couple of seconds, the intuition here is clear why there can be a preference for developing a higher dimensional map. It simpy a "reformulation" and restructuring of a processing task, in order to optimize computational speed. IMO this is right way of using inuition from our senses to understand physics.
This also actually implies that the "actual dimensionality" of our universe might be a matter of perspective! I is actualyl possible that the same universe have different dimenstionality depending on the observer. And - given holographic correspondencs - this is by no means a contradiction.
It may well be another fallacy to think that the dimensionallty "must" be a fixed value. There is in fact NO justified argument for this that i can think of. It is just one part of old conceptual baggage we carry that are not serving us well anymore.
So from a mathematical perspective only, i can't see how there can possible be an upper bound to dimensionality. Mathematics alone can no solve this, as they only guid there are questional arguments like "simplicity" and "beauty". I instead argue that we must see it in the above perspective, and there the "selective principle" is not "beauty arguments" but evoulutionary arguments.
I am simplyfying grossly here, but just to formulate the toy argument to illustrated the idea:
Too low dimesionality of the map, mean the code is very compressed, and the process to infer the future expectation from the self evolution of the map will be one of many computational steps.
Too high dimensioanlity of hte map, will requied a bigger encoding structure (more memory) but it will be more uncompressed, and the computational resources to infer the future evolution from this lower.
So there is somewhere for a given structure and environment encoding a map of its environemnt an optimal "balance" of dimensioanlity thta we should be able to EXPLAIN, rather than put in by hand when we claim to understand this and have the mathematical theory ready.
Our laws and maps may be seen as "optimal codes", taking into account not only the footprint of the code, but also the computation resources to decode it.
/Fredrik
