A big evolution

Version 0.1e; June 24, 2014. This work is in its utter infancy, more metaphysics and speculation than proper science. I'm working on software to model universes (or parts thereof) as described below at multiple scales, some of which is published peer reviewed scientific research.


Summary

We present a comprehensive and consistent meta theory of universes. The Universe is an infinitely expanding information theoretic bitstring encoding its own grammar and parser that progresses as a big evolution rather than a big bang going through a step function in a recursive fashion. The big evolution posits similar principles identified in biological evolution such as mutation and natural selection, and universes (and portions thereof) may be evaluated in terms of homology and analogy. The big evolution refers to constant dynamic equilibrium of interacting particles (bits of information) contained in a universe as specified by chaos theory [1]. The laws of complexity thus followed the laws of physics.

A universe is a quantum relative universal computing device that evolved to encode its own grammar and parser described by the recursive equation:

U(t) = 2 * U(t++)

U is the recursive step function that operates on itself to generate its corresponding component universe bitstrings. Recursion is thus postulated to be the fundamental process by which things happen in nature. As U recurses on itself, it causes an evolutionary expansion like a balloon inflating except at each step there's also an evolutionary process of variation of selection happening at the same time. The goal here is to model the organisation of information that occurs by this process, rather than deal with its material aspects.

In more formal terms, a universe is a digital computing device encoded in the form of a bitstring that includes both a grammar used to generate it and an interpreter to compile and execute it. Our Universe is a Universal Turing Machine encoding a grammar that describes quantum and relativistic physics interpreted (compiled and executed) by a corresponding automaton (in the case of context-free grammars, it is a push down automaton). Summing and concatenation are interchangeable operations in and by bitstrings universes where a given universe variable (opcode) consisting of i bits (the bitindex) is represented by the number 2^i and its value is equal to the bitstring encoded by i-1 bits.

This model is a superset of all string theories including M-theory and loop quantum gravity. (It is left as an exercise to the reader to figure out why and how this is the case. :)

It follows logically that a theory of everything would not only explain and unified quantum mechanics and relativity but also would be completely self contained, consistent, and explain itself. As with string theories including M-theory this model does not make new predictions that lend themselves to falsification (in general, any theory of everything has this problem).

In terms of mathematical logic, all the string theories and any other theory that unifies quantum mechanics and relativity are equivalent. The bitstring theory or model says that a digital computing device encoding a push down automaton is provably equivalent to a universal Turing computing machine. The model implies that our Universe can be simulated in a digital computing device with the von Neumann architecture, which is consistent with the development of modern computers from quantum mechanics. The model also indicates that the mechanics of quantum objects illustrates the limits of Gödel's Incompleteness Theorems.

Most importantly, the bitstring model indicates that all objects and problems in nature are recursively enumerable substrings that can be interpreted (compiled and executed) by a push down automaton encoded by the universal Turing machine or digital computing device. This statement is made with accepting the fractal-based nature of the universe, or more simply, by understanding that if our universe could be simulated using computing devices of the type used in the year 2014, then it (the statement) becomes a tautology.

If we think of the universe as akin to computing devices, then the issue of hardware vs. software becomes a matter of state. When a modern computing device is constructed and an operating system and associated software run on it (which is essentially one big program) to achieve a specific outcome, we cannot say the outcome is achieved by one or the other alone. When trying to model universes, the distinction becomes meaningless as it does in formal computing science (i.e., the universal Turing machine is an abstract machine that can run any type of a program, including one that specifies a modern computing device's operating system). The hardware and software are viewed as being the same in the bitstring model: the hardware represents the abstract bit object and the software specifies the information content (or arrangement and interactions) of the bits.


Conventions


Model

A conceptual framework for creating and manipulating bitstring universes is now presented. If the description of this framework is not clear, then reading how it is implemented may help with clarity.

Information theoretic component

The physical component


Implementation

It is one thing to specify a conceptual model, but it is another to say how it will be implemented. We don't know how it is implemented in nature, though we can guess. Since we're working in a digital computer, and since I'm writing this out in English on the Web, for simplicity's sake there are some implementation details that I'll specify. This just means that these issues are separate from the model itself and should not be confused.

Examples

These are the first opcodes and their corresponding bit strings representing primordial baby universes.

t = 000 = 0 or time 
e = 001 = 1 or energy             (or <= 0 time)
m = 010 = 2 or mass               (or <= 0,1 time or E/2)
d = 011 = 3 or dimension/position (or <= 0,1,2 time, energy, mass)
x = 100 = 4 or position x         (fill at number of steps (address) where speed of light is a constant in our universe)
y = 100 = 5 or position y
z = 101 = 6 or position z
f = 111 = 7 or count of steps (i.e., gives frequency/wavelength) relative to position (or <= 0,1,2,3 time, energy, mass, dimension)

The number of steps in a given universe is the universe's Gödel number.


Features


Retrodictions

The model agrees with what we know about quantum mechanics, relativity, and indeed, all of what physics which can be rightly termed "laws" (i.e., they are unlikely to be wrong, in our universe at least). That is, it makes retrospection predictions.


Predictions

prospective

Mappings

Abstract

Anything that involves a duality can be thought of as a related metaphor. In general, all dualities can be mathematically shown to be equal to one another by the means of the Gödel bitstring numbering. This applies to various theoretical, natural, life, and applied sciences such as mathematics, chemistry, biology, medicine; as well as fiction in the form of movies and music.

Indeed, in terms of philosophy, metaphysics, and epistemology, the Gödel equivalences set up the way described above, the distinction between concepts like "real" and "imaginary" becomes as irrelevant as the distinction between space and time. Thus the concept of choice itself is an illusion.

Delving into mythology just a bit, the concepts of good and evil, god and the devil, the fundamental elements of fire (radiation), earth (matter), wind (currents), water, are related metaphors. Dualities occur as a result of recursion which represents the 0 (off) or 1 (on) states. Recursing on 0 gives you 1 == {0}. Recursing on 1 gives you 2 =={10}. Recursing on 2 gives you 4 {11}. Reading this right to left gives you the strings "42" and "420".

In fact, there's a self consistent feedback loop/pattern being established here and one can see a Gödel mapping everything. This makes sense since a theory of everything should not only be able to predict itself but it should also predict why it took us the time it did to get there. This is why transparency and openness is illuminating". Even an extremely loaded metaphysical/epistemological statement like that within the quotes relates/maps to statements about quantum physics and optics can be written down as a bitstring. Heck, it actually already is if you're reading this online. The Gödel number for it is 9223372036854775807. This is the same way Gödel's Incompleteness Theorem was proven, by encoding a self-referential statement in number theory/mathematics. The encoding process lets you give meaning to understanding the nature of a paradoxical statement (paradoxical only within the system).

With this model, Platonic space could be thought of as metaphors that have a Gödel mapping between them. Quantum physics and relativitistic physics are essentially isomorphous groups. This doesn't mean humans can't be stupid. Stupidity and ignorance are states in a system.

          1 | 0          (state bit)
         on | off        (state bit)
   positive | negative   (state/direction bit)
         up | down       (direction bit)
  clockwise | counterclockwise (direction bit)

     opcode | operand    (pair bit)
   variable | value      (pair bit)
    integer | real       (pair bit)
   exponent | mantissa   (pair bit)
          h | c          (pair bit)

     energy | mass       (state bit)
      start | end        (state bit)
       time | space      (direction bit)
  frequency | amplitude  (direction bit)

       wave | particle   (energy/mass pair bit)
     motion | rest       (time/space pair bit)
   discrete | continuous (h/c pair bit)
    quantum | relative   (h/c pair bit)
      small | large      (h/c pair bit)
mathematics | physics
information | entropy
       life | death
        new | old
 
       good | bad
      light | dark
     genius | stupidy
  happiness | sadness
    freedom | slavery
      bound | unbound
      real  | illusion
     causal | coincidental
     choice | no choice

Mathematics

Number theory is a branch of pure mathematics dealing with the study of integers. All integers are factors of prime numbers and in a similar fashion give rise to rational numbers.

In 1931, Kurt Gödel proved a statement of the form that consistent axiomatic formulations of number theory includes undecidable propositions. Corollarywise, such formulations cannot prove their own self consistency.

In other words, sufficiently powerful axiomatic formulations of number theory cannot be both consistent and complete. (This gives us yet another dualism.) How could he do this? The beauty of Gödel's Incompleteness Theorems, as they are known, lies not just in the theorems, but rather the method used in the proof.

Gödel's proof consists of encoding a Gödel statement (G) of the form "G cannot be proved in formulation F" using the mapping of symbols (which have a semantic meaning associated with them) to integers (the Gödel mapping or numbering) in a number theoretic formulation F. By performing arithmetic operations on these integers, a given statement can be proved. Thus the Incompleteness Theorem is proven by contradiction. What proof indicates is that if you have a powerful enough symbolic representation of a system, an inconsistent statement within that system can be arrived at by an appropriate mapping of the symbols. This mapping can be thought of as existing in a higher (or meta) level.

Physics

Research into theories of quantum gravity considering spacetime as a fluid and an emergent property of fundamental particles is more along the lines I'm thinking of. Thus Quantum information theory is very relevant to what is talked about here. In general the bits I'm talking about may be thought of as qubits, but these qubits themselves represent an information theoretic bitstring, and no-cloning and no-teleportation (no complete measurement) would apply; perhaps interactions with the universal bitstring which is inescapable is what causes this phenomenon.

Chaos/complexity

Perhaps chaos/complexity theory offers the best visual representations of the kind of evolution I'm talking about, that links what Hofstadter talks about, to chaos theory, to quantum chaos, to quantum consciousness, to poised realm. This image of a strange attractor is what I see a bitstring initially evolving to, before and after the Big Bang (or as part of the Big Evolution). This also indicates a higher dimensional space that we are embedded in to create this strange attractor that is our universe. The description of the strange attractor feedback loops are related to the higher dimensional mappings used to prove Göodel's Incompleteness Theorem.

Biology

If all of nature (physics) is scale free then it follows that the results of nature (evolution) are also scale free. See the mapping to medicine for actual research we're doing in this area.

Medicine

Our CANDO drug discovery project as well a lot of the research we do exploits this bitstring universe model.

Music

The songs Particle Man and My Evil Twin by They Might be Giants, and the albums Dark Side of the Moon and The Wall by Pink Floyd are related metaphors.

A lot of the music by my solo project, TWISTED HELICES, including songs like Renaissance: Art, Philosophy, and Science which has extensive mappings and a recursive structure and the Proteomusic which converts protein structure to music are artistic examples of the same recursive bitstring themes being proposed here.

Movies

The movies The Matrix, The One, and Dark City to name just a few, are related metaphors.


History

I have been using the bitstring model to recursively enumerate problem spaces in biology and then using knowledge based scoring functions to pick the most promising solutions. I came up with generalising this completely to quantum mechanics and relativity using nothing but binary digits and progression of strings via a step function that represents time. This happened while I driving down to the local grocery store with my daughters and my neighbour's daughter. It just struck me that I could just recurse on the most basic quantities using a binary representation and obtain everything we know about quantum mechanics and general relativity. Indeed, I realised that this model covers everything we know about physics and mathematics.

I spent the next few days discussing this with my group who provide a great intellectual foil and working out minor kinks. Every time I ended up seemingly stuck, staying true to the model ultimately resolves it. And why wouldn't it? The universal recursive function is the definition of a digital computing device.


Caveats

The above model presented is just that, a speculative theory that makes no new testable predictions at this time. I assert that I've followed this bitstring model throughout my entire life and scientific career and it is the reason why the tools developed by us work to the extent that they do. So the only shred of evidence that they eventually may end up being correct is the value our research has on this world. If the research we do improves human health and quality of life, then I'd say following the model has paid off.

Also, the above model is a bit of a cop out, since anything we talk about can be thought of using concepts from information theory, so there could be something further underlying the bits (and this might go on infinitely or even recurse back to everything, i.e., 0 and 1 are intimately connected). Again, I refer to auantum information theory and potential mappings to physics.


Final words

If I had to write a story about how everything came about (and this is probably the best way to describe what I am thinking of), it would be go like this:

"Nothing created the universe. Nothing was bored and wanted something to happen, and then lo behold, to nothing's surprise, there was something..."

We could rephrase it in whatever way that makes one comfortable (for example, replace "no one" instead of "nothing") but read what I'm writing carefully. Am I or am I not attributing conscious action to nothing? What does it mean when I do the above?

I think and feel that the answer to what happened with the universe lies with what happens with any conscious object or entity (primarily humans for us, since we can't really evaluate what dolphins and elephants think and feel). When you are conceived, are you conscious? How about when you are born? When you are two years old? Three? Is it the same for all humans? Do YOU remember when you gained consciousness? How far is your earliest memory?

When/if we achieve the singularity, we'll know whether the above is possible or not. Even then, we can also speculate as to what actually happened short of going back in time to when our universe was created.


Pseudointellectual ramblings || Ram Samudrala || me@ram.org