Universal Computation using 4 instructions

[SteveA]

Here's an interesting article showing a manner in which a single thread/space/memory of computation can perform universal computation using only 4 forms of instructions (I think there's actually a way to reduce it to 3 using swaps instead of load/store, but that's a side note):

Load
Store
Increment
Goto

http://www.jucs.org/jucs_2_11/condit...anching_is_not

There would be ways we could analogize these to fundamental particles/operations in physics.

I think there's actually an even better one though - we only need 3 operations on 2 complimentary spaces - each "moves" through the other and the load/store instructions are replaced with a merge/union/duplicate operation instead. The dimensionality of each is only half the number of the space through they appear to move as a composite relative to each other (so, for example, in a 3 dimensional space, each object exists with an equivalent of 1 1/2 dimensions of complexity and this can easily creates a very complex, fractal and chaotic "landscape" to this space).

Another way to look at it is that any point along this string/space/memory lies at the intersection of two identical dimensionality of spaces on either side - the swaps/merges/unions of these two pieces of information as seen at that point can appear to make the space appear to be double the dimensionality of either half alone. The increment instruction would be similar to sliding along the thread a unit and the goto instruction would be similar to constructing a finite object by looping the thread over some distance or combining adjacent elements into a single higher dimensional object (like a spacial compression or attraction).

Anyway, this the general "flavor" of theory I'm working on, though the elements of this thread are infinitely diverse forms of conscious experience and they require an ordering along this thread as well, otherwise we'd just be working with indistinguishable elements that could be arbitrarily swapped - though these could be swapped, there would still need to be a fundamental ordering to them (and possibly a manner to untangle merged elements according to some fundamental property or value of the experience?)

Anyway, I'm just tossing this out to see if stimulates any thoughts for anyone else.

[AntonioLao]

Using symmetric Hadamard matrices I could reduce it to 2 instructions or operations: matrix addition and matrix multiplication. I get the ratio of the mass of a proton to the mass of an electron as 1832. The experimental value is 1836.

[SteveA]

Very nice Antonio Congratulations!

Now consider one more thing - two operations over time constructs the equivalent "instruction space" of a zigzagging line over time through a two dimensional space - and that's one dimension too many to compute

Now consider, similar to the predetermined execution of a subroutine in a larger computation, a timeline of experience that counts a predetermined number of iterations of such an operation but compressed down to one dimension and one operation (though the specific operation can likely not be known).

There's still one more cool step - slowing that motion in that linear timeline and reexpanding in the second dimension - of course to do that most effectively, you need to figure out what the best spots of the terrain were that you covered - head back, grab them all and then party time!

To put it better, I think life is similar to learning new orthogonal forms of motion - these are similar to "primes" in their characteristics - unique and irreducible operations.

Not much control during exploration (or none) can occur or you have the problem of a closed loop attractor - can't fall into an unseen gravity well and the moth figuratively needs to be blind to candle flames, but once the samples along that trajectory are taken, then a new pathway can be constructed that runs past all these highlights and effectively reorders a timeline.

Now that's heaven, but short lived ... why not stretch things out a bit and turn time into a recycling superconductor?

Let's say we have a sequence of events, A, B, C and D ordered in a preferential manner. If we simply repeat these, we gain nothing, if we simply truncate things it might be "heaven" but short lived and then back to the fields.

Now here's something interesting to consider. If we keep all the elements but rearrange them in various contexts, we can extend the number of unique sequences. In order to go backwards though, we'd need a set of physical laws that were symmetrical in time ... whew, how lucky could we get, they are

So now we have both forward and backward motions available but we can also rearrange or "rotate" segments and this creates a factorial growth in the space (now how's that for an efficient recycling program - greater than exponential efficiency relative to the exposure to unknowns or external time)

Though there's a catch - time is growing faster than perceptions can distinguish between these - the senses need upgrades as well and we figuratively need more "colors of the rainbow", or depth of experience (it takes an exponential growth in precision for a linear increase in information content, though that's just for perceptions that exist in terms of a linear intensity, combining these sums the information content, so orthogonal components create higher dimensional spaces and transform a logarithmic growth in information content to a linear growth instead at only a logarithmic cost - and I think Hadamard matrices, being binary could be optimal in that respect, though that could require quite a complex diversity of perceptions) to work with and each of those needs to be present in a manner similar to an irreducible component of experience - and that's where the primes and asymmetries come in.

...

And I think that's as far out as I'm interested in - found at least one good spot, though that would be a rinse and repeat process, but then again, infinity always seems to have new pathways open up along the way, so who knows.

Plenty of time to explore the terrain but I'm happy

[AntonioLao]

Hadamard matrices, being binary could be optimal

Exactly a year ago, I discovered that symmetric 2 by 2 Hadamard matrices could be derived from the matrix inverses found anywhere within a sieve of Diophantus. In the other respect I created the sieve simply to position all the infinite number of prime numbers. Fortunately, the sieve is a transfinite order matrix.

[SteveA]

Exactly a year ago, I discovered that symmetric 2 by 2 Hadamard matrices could be derived from the matrix inverses found anywhere within a sieve of Diophantus. In the other respect I created the sieve simply to position all the infinite number of prime numbers. Fortunately, the sieve is a transfinite order matrix.

About everything you said 'clicks' for me and you hit a lot of my favorite keywords though

I had done some simulations of objects similar to quaternions and had searched through spiralling pathways in 3 dimensions (just matrix exponentiation equivalent to inertial rotations, accumulating unit motions) and then constructing a map the trajectories that ultimately returned and remained oscillating near the origin. Basically it's just a 2 dimensional space and it closely resembled the map of stability of atomic isotopes (though it actually 3 islands of stability - one trivial and similar to fundamental particles and one similar to some predictions but there was even a small area beyond that that appears very unstable but still something possibly significant).

Also the trajectory by which they pass through the origin can be rotated and so this sort of embeds a second rotation, after each spacial cycle into it as well and this could be interpreted similar to a continued fraction or irrational number in that we have cycles within cycles etc.

But I'm trying to think of what all these things are in abstract sense - all of the properties of these "classes" of systems and they appear to arise along the edges of logic and determinism as we move toward spaces with precisions beyond complete determinism and begin to see something similar to an ever increasing and detailed level of complexity, I picture it almost like the edge of a beautifully intricate dance that appears to have no boundaries to its possible complexity - like a fragmentation of determinism into fractal forms and beyond into chaos and from there into the ultracomplexities of nothing specific at all ... effectively randomness in appearance, yet potentially deterministic on scales we can't see.

I've been stunned to think that there may actually be a truly infinite thing in existence and the existence of time appears to imply it, and that opens up endless possibilities. I think the uniformity of space is deceptive ... it seems so easy to count 1,2,3,... but it's amazing how much detail and diversity can be created with just a small number of unique properties and infinity has changed from being a straight line (which in one respect it still is) to something incredibly complex that we're only seeing the first few "letters" of and I think that any form of deterministic computation we could describe can always be mapped to the passing a single line of computation in time through spaces of different properties - you always have to maintain a count of the iterations of a process in order to be able to determine, relative to an origin, where that computation is and everything needs to fit into a single process or timeline otherwise we're working with separate spaces and there are no relationships between them (this is a common mistake with calculus and real numbers).

But I do a lot of programming and the general trend appears to be that basically, if it can be imagined, it can be done - it just a matter of paying attention to every detail and recognizing when some assumption creates a paradox and working around that etc., but to me it already seems like there are plenty of "tools" we have to explore some quite interesting landscapes ... now how do we up the "bandwidth" of the mind?

(My forte is in digital logic and designing computations all the way up from discrete logic but ultimately none of these things "move" or grow on their own - they all need external power cords or time etc. and many areas of mathematics try to contain infinity in their descriptions but I don't think they really do it successfully either and instead it's just a belief that we've successfully used an infinite quantity for a computation. The reality appears to be that we can only determine things within our abilities and these are always finite - they only "do" something when we expose them to unknown changes - and that even agrees with observations in physics in that we're always detecting energies which actually reflect a change in a form - and that's similar to the idea of a wave/particle dual - the creation of determinism or the creation of logic).

Yes, I've rambled (and I need to head out) but your ideas are always stimulating Antonio. I wish I could present my thoughts in a more concrete manner ... actually there's a program I posted here before that you might enjoy - it shows structures embedded in the Logistic function as real time controllable parameters in up to 4 dimensions (3-D projection plus color coding).

I could find it but here's an example of a 4-D structure embedded within a 1-D computation of the Logistic function (this is basically an example of what an object in my "Theory of The String" looks like):

[AntonioLao]

none of these things "move" or grow on their own

Have you tried John Conway's game of life? See http://en.wikipedia.org/wiki/Conway's_Game_of_Life
In the early 80's I did a simple program using the BASIC computer language based on pseudo random numbers generator. The results exceeded my expectations. I was the only student of my class who succeeded coding, developing, and implementing the program and got an "A" for the course.

[SteveA]

Have you tried John Conway's game of life? See http://en.wikipedia.org/wiki/Conway's_Game_of_Life
In the early 80's I did a simple program using the BASIC computer language based on pseudo random numbers generator. The results exceeded my expectations. I was the only student of my class who succeeded coding, developing, and implementing the program and got an "A" for the course.

Yes, I've had some fun with that before and have experimented with ideas in 1 dimension as well (I even did some simulations interpreting segments of the line similar to fundamental particles and then from a random "seed", like a Big Bang constructed trees of probabilities of interactions between them depending upon their neighbors etc.

I High School I received the Computer Science award (I'd finish most the assignments without even testing them on a computer - he'd give us something to write over the next two days. I'd sit down and write up the code in 10 minutes and give it to him and then go write games and fake operating systems for the next couple days. I came in second place in one software competition in California and tied for 5th place out of 100 school in Southern California in Mathematics also, but electronics was really my forte.

I tried to do college twice but it just felt like wasting time.

As you know a lot of my interested are with regard to prime numbers (and I like some of the ideas Paradigm has put up) and I've found the equivalent of discrete spectrums in terms of probabilities. If the probability of an event is 1/n, then we can rewrite this in terms of parallel or series probabilities (AND or OR).

If we have a uniform and unknown binary space then every element gives us a 1/2 probability of being in either state. If we were to sample information though in a 3 dimension space with 3 way symmetries, then it would take an infinite number of 1/3 probabilities to approach even a single 1/2 probability.

Every piece of information placed in terms of a uniform 1 of 3 possible states, gives us log(3)/log(2)~=1.585 bits of binary information.

Now consider that some "volumes" of these 3-way and 2-way symmetrical spaces have volumes very close to each other and a mapping very close to 1 to 1 can be made (never precise though).

For example, listing powers of 2 and 5 and 11 (yes, I intentionally selected these because of one area that's close), we have:

2,4,8,16,32,64,128,256,512,1024,2048,4096,...
5,25,125,625,3125,...
11,121,1331,14641,...

2^7=128
5^3=125
11^2=121

Now let's say we have information in terms of 5 uniformly distributed physical senses and we wanted to "map" these to similar representations in other "dimensions", well if we group 3 such 5 way symmetries we can closely map them to 7 binary or 2 of the 11-way (11 dimensional?) symmetries.

But it's still not perfect and we have an irrational ratio involved.

log(125)/log(128 )~=1-(1/204.584)
log(121)/log(125)~=1-(1/148.458 )

So we have the equivalent of a shift in synchronization between these channels that can appear to "bend" the spaces between them, and similar to there not being precisely 365 days in a year, we need to occasionally insert new offsets and this is like a decomposition of an irrational number into "orbitals" in higher and higher dimensions, but over larger and larger times.

We can optimize things some by pairing two of these 125 way symmetries into a single 128 way symmetry and another 121 way symmetry.

log(121*128 )/log(125*125)~=1-1/137.064

two of these 3, 5 way clusters to have a 6 dimensional 5 way symmetric object and then describe is both a pairing of 7 units of a binary symmetry and 2 units of an 11 way symmetry and we get closer to a synchronization:

log(128*121)/log(125*125)~=1-8/137.064

Yes, I intentionally scaled it by 8 to show a possible correlation with the fine structure constant.

But I guess the main comment was just that discrete information in terms of 1/n probabilities can be made to approach uniform mappings of spaces of 1/m probabilities, even with n and m being relatively prime, but this appears to give irrational "curvatures" and orbits that could potentially be considered to occur in unlimited numbers of dimensions and the periods of time over which such an orbit occurs in each dimension could be closely related to the construction of a continuous fraction describing the ratios of the logarithms of these (so we're just basically "folding" information along a string of information in terms of 1/n symbols into a similar representation of information but in terms of some other probability/symmetry "spectrum").

It also gives a manner to convert between discrete spaces to something closer to irrationally orbiting continuous spaces and a way to tie together the possible existence of infinite numbers of spaces all orbiting relative to each other in many dimensions (they're all translating things into an infinite number of languages over infinite quantities of time and it looks like a giant solar system).

Anyway, that's just another idea that's been sitting on the "back burner" (Trying to tie as much together as possible).

[AntonioLao]

My question is the reality of a random multivariate generator that can equalize all the infinite number of degrees of freedom of the quantum vacuum fluctuations of zero-point energy. If I can control this generator then I can possibly extract limitless amount of energy from the vacuum.