Towards a new theory of information kinematics

[John Bernier]

TL;DR Summary

A new theory of the motion of bits, memory locations, and information regions is devised with Sierpinski topos theory.

The physical world is highly parallel; many things are happening side by side simultaneously. This is true not only at the macroscopic scales that we can see but as far as we know down to the subatomic scales. This is referred to as the principle of locality [1], which states that an object is influenced directly only by its immediate surroundings.

This concept of locality says that for one thing to influence another, something, such as a wave or a particle, must travel between them, carrying the influence. Einstein's special theory of relativity limits the speed at which such influences can travel to the speed of light, c [2]. As a consequence, the universe is like a highly parallel causal web of influences that travel between one another at no more then the speed of light [3].

With the universe so intrinsically based upon the principle of locality and the laws of relativity, from the smallest scales to the highest that we can see, the sequential model of computing, which posits the old idea of 'universal time' is a completely unnatural match for reality [4]. This has become a problem as we try to make computer programs run on multiple cores [5].

The one concept we have that stands out is motion. A comparably natural metaphor for computing then is dataflow: the flow of bits of information around from place to place. Dataflow is like a different kind of motion, moving around bits of data instead of particles, and it has mathematical laws which we might call information kinematics. In turn, this information kinematics will hopefully lead to a style of computing that is more in tune with physical realities.

I intend to address the foundations of information kinematics using highly abstract mathematics. Using a branch of mathematics called topos theory, we devised a new theory of how information flows around an information system. This work is most similar to the prior work of Hartmanis and Stearns on information flows [6].

References:
[1] Wikimedia Foundation. (2023, January 19). Principle of locality. Wikipedia. Retrieved January 26, 2023, from https://en.wikipedia.org/wiki/Principle_of_locality

[2] Wikimedia Foundation. (2023, January 25). Special relativity. Wikipedia. Retrieved January 26, 2023, from https://en.wikipedia.org/wiki/Special_relativity

[3] Wikimedia Foundation. (2023, January 19). Causality (physics). Wikipedia. Retrieved January 26, 2023, from https://en.wikipedia.org/wiki/Causality_(physics)

[4] Selwood, D., (2012, July 18). Does the world need a new programming language? EEJournal. Retrieved January 26, 2023, from https://www.eejournal.com/article/20120718-language/

[5] Programming parallel computers is difficult. (n.d.). Retrieved January 26, 2023, from https://www.cs.cmu.edu/~jurgend/thesis/intro/node2.html

[6] Hartmanis, J., & Stearns, R. E. (1966). Algebraic structure theory of sequential machines. Prentice-Hall.

[7] Khedker, U., Sanyal, A., & Karkare, B. (2017). Data Flow Analysis: Theory and Practice. CRC Press.

 

[PeroK]

Don't forget about quantum mechanics!

 

[John Bernier]

Don't forget about quantum mechanics!

Action at a distance in quantum mechanics is indeed spooky.

 

[PeroK]

Action at a distance in quantum mechanics is indeed spooky.

Well, no it isn't. Einstein was wrong about that.

 

[anorlunda]

I can't find a definition of "information kinematics."

However, information in Physics is restricted to the same speed of light constraints as the motions of massive and massless particles and the propagation of fields.

 

[Wrichik Basu]

we devised a new theory of how information flows around an information system.

Congrats! Can you please link to the peer-reviewed published article?

 

[John Bernier]

Congrats! Can you please link to the peer-reviewed published article?

Its too early for this article to be peer reviewed yet. But the (not yet peer reviewed) article is in the attachment. Go ahead and review it yourself or send it to someone you can. I've sent it to a couple of local professors, but its not their specialty. I tried Olivia Caramello (a famous topos theorist) but that was only a couple of days ago and I haven't heard back yet. I think you just got to be patient? Peer reviewing takes time, potentially months even. In the mean time I am ready to answer any and all questions: any input on the concepts involved is welcome.

 

[Dale]

Its too early for this article to be peer reviewed yet.

We don’t provide any form of pre-publication evaluation or support. I have closed the thread until it is actually published