Caveat: I do not have all this connected in some incredibly conclusive mathematical proof way (an impossibility). These concepts below are related semantically, conceptually and process wise (to me) and there is a lot of shared math. It is not a flaw of the thinking that there is no more connection and that I may lack the ability to connect it. In fact, part of my thinking is that we should not attempt to fill in all the holes all the time. Simple heuristic: first be useful, finally be useful. Useful is as far as you can get with anything.
Exploring the space of all possibles configurations of the world things tend to surface what’s connected in reality. (more on the entropic reality below)
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useful basic ideas with logic and programming (lambda calculus)
Propositions <-> Types
Proofs <-> Programs
Simplifications of Proofs <-> Evaluation of Programs <-> Exploding The Program Description Into All Of Its Outputs
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Data Points and Mappings
A data point is either a reducible via Lambda Calculus (a fully determinant/provable function) or it is probabilistic (e.g. wavefunction).
Only fully provable data points are losslessly compressible to a program description.
Reducible data points must be interpreter invariant. probabilistic data points may be interpreter dependent or not.
No physically observed data points are reducible — all require probabilistic interpretation and links to interpreter, frames of reference and measurement assumptions. Only mathematical and logical data points are reducible. Some mathematical and logic data points are probabilistic.
Each data type can be numbered similar to Godel Numbering and various tests for properties and uniqueness/reductions can be devised. Such a numbering scheme should be UNIQUE (that is each data point will have its own number and each data type (the class of all data points that have same properties) will all have identifying properties/operations that can be done. e.g. perhaps a number scheme leads to a one to one mappings with countable numbers and thus the normal properties of integers can be used to reason about data points and data types. It should be assumed that the data points of the integers should probably simply be considered the integers themselves….)
A universal data system can be devised by maintaining and index of all numbered data points… indexed by data point, data types and valid (logical/provable mappings and probabilistic mappings — encoding programs to go from one data point to another). This system is uncountable, non computable but there are reductions possible (somewhat obvious statement). Pragmatically the system should shard and cache things based on frequency of observation of data points/data types (most common things are “cached” and least common things are in cold storage and may be computable…)
Why Bother With This
We bother to think through this in order to create a data system that can be universally used and expanded for ANY PURPOSE. Humans (and other systems) have not necessarily indexed data and mappings between data in efficient, most reduced forms. To deal with things in the real world (of convention, language drift, species drift, etc) there needs to be a mapping between things in efficiently and inefficiently — and the line is not clear… as almost all measures of efficiently on probabilistic data points and “large” data points are temporary as new efficiencies are discovered. Only the simplest logical/mathematical/computational data points maximally efficiently storable/indexable.
Beyond that… some relationships can only be discovered by a system that has enumerated as many data points and mappings in a way that they can be systemically observed/studied. The whole of science suffers because there are too many inefficient category mappings.
Mathematics has always been thought of as being a potential universal mapping between all things but it too has suffered from issues of syntax bloat, weird symbolics, strange naming, and endless expansion of computer generated theorems and proofs.
It has become more obvious with the convergence of thermodynamics, information theory, quantum mechanics, computer science, bayesian probability that computation is the ontological convergence. Anything can be described, modeled and created in terms of computation. Taking this idea seriously suggests that we ought to create knowledge systems and info retrieval and scientific processes from a computational bottoms up approach.
And so we will. (another hypothesis is that everything tends towards more entropy/lowest energy… including knowledge systems… and computers networks… and so they will tend to standardize mappings and root out expensive representations of data)
it’s worth thinking through the idea that in computation/information
velocity = information distance / rule applications (steps).
acceleration etc can be obtained through the usual differentiation, etc.
This is important note because you can basically find the encoding of all physical laws in any universal computer (given enough computation…)
Not a surprising thought based on the above. But it suggests a more radical thought… (which isn’t new to the world)… common sense time and common sense space time may not be the “root” spacetime… but rather just one way of encoding relationships between data points. We tend to think of causality but there’s no reason that causality is the organizing principal — it just happens to be easy to understand.
humans simply connote the noticing of information distance as time passing… the noticing is rule applications from one observation to another.
the collapsing of quantum wave functions can similarly be reinterpreted as minimizing computation of info distance/rule applications of observer and observed. (that is… there is a unique mapping between an observer and the observed… and that mapping itself is not computable at a quantum scale…. and and and…. mapping forever… yikes.)
“moving clocks run slow” is also re-interpreted quite sensibly this way… a “clock” is data points mapped where the data points are “moving”. that is… there are rule applications between data points that have to cover the info distance. “movement” of a “clock” in a network is a subnetwork being replicated within subnetworks… that is there are more rule applications for a “clock” to go through… hence the “clock” “moving” takes more time… that is, a moving clock is fundamentally a different mapping than the stationary clock… the clock is a copy… it is an encoded copy at each rule application. Now obviously this has hand wavey interpretations about frames of reference (which are nothing more than mappings within a larger mapping…)
one can continue this reframing forever… and we shall.
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Related to our discussion:
computation time is proportional to the number of rule applications