Humans : Pattern finding machines

[DevilSolution]

Going of the basis that axioms are sets of laws or rules which explain or dictate the core relationship of mathematical concepts, it's got me curious as the whether there is any way of finding patterns in axioms or numerological systems that could create new axiomatic laws;

 

Now from what i know of numbers this would seem rather impossible due to the actual reality in which the numbers are being used, so for example i'd have no way of finding euclidean axiom based on pure numbers per say because euclidic axioms are based firstly on the concept of the cortesian plane and secondly based on the concept of shapes (vectors, vertices, angles, Pythagorean laws etc ) which both are concepts separated from pure number, they have a direct relation and use in the physical world and i think numbers just hypothetically exist to explain some phenomena.

 

However i would argue that although we are hypothetically using numbers to explain a law of physics or chemical reaction, that law would already exist in a purely mathematical world. For example if we take 5 + 7 = 12 as our proof of a simple axiom then we can assert some rule to axioms here on out. Firstly i think we must look at numbers as a single irreducible unit of measurement (the smallest number calculable), so we'd have 5 units of 1 and secondly that there's only 2 functions used in the whole of mathematics, these being addition (of which multiplication is a function and division a function of multiplication etc) and the inverse function (subtraction). If we take these 3 concepts as a base axiom then its conceivable that all axioms already exist within these 3 concepts. This is true because every mathematical formula and variable could be said to already exist in the form of a single irreducible number in combination with the 2 base functions that make all other functions possible. This makes sense if you think of a very complex formula explaining some astronomical phenomena and then break the formula down into base components such as having "A" AIU (amount of irreducible units) divided by "B" AIU multiplied by "C" AIU multiplied by "A" AIU, now this actual axiom is actually just

 

X = A * ( C * ( A / B ) )

 

The actual equation is quite simple, and within the infinite set mathematical possibilities it would actually be conceived quite early, in so much as if you were to write out every possible type of equation such as a+a,a+b, a-a, a-b. b-a, a/a, a/b, b/a, a*a, a+a+b, a+a-b, a-a+b, a-a-a etc etc etc..................... a * (c * (a / b)), then you'd reach this axiom quite quickly. When speaking of the infinite set mathematical possibilities i'm referring to the infinite amount of different equations you could create.

 

To elaborate a little further; I think we've established that within the infinite set of mathematical possibilities every possible axiom already exists. However the troublesome activity for us humans is finding which axioms are to be used and where. So lets say i handed you 10 double sided a4 pages of these axioms from the simplest upwards and then handed you 3 variables; time, distance and speed, how long would it take you to find the correct 2 formulas that defined this axiom? what would the process be of figuring it out? how could it proven? and quintessentially would it be possible for us to recognise an axiomatic pattern that is capable of giving us the relationship between certain things??

 

Another thing i would like to offer is that from a computational point of view, iv'e always believed that mathematical and physical laws are only true if they can be simulated and proven by a computer; This works for all mathematics to the extent that we can work in 3d dimensional space, we do things with waves and circles work with primes and probabilities and even prove patterns and relationships between numbers etc. However i'm not quite sure how full of a picture we have from physics, though alot of the laws we currently use for engineering, chemistry and physics are very accurate and do exactly what they're designed to do, which is why planes can fly, speakers can create sound and a microwave oven can heat food in less time time than it takes to eat it).

I don't believe every possible law has been found (which means unknown variables still exist) or that we have the full picture of how all the laws relate to one another. Also almost everything in physics is linked at some basic level, if you were to find the axiomatic relationship between what i presume are a few basic laws, then it could be that the other laws are actually an effect of and calculable to these base laws and hence could probably discovered by some axiom that finds relational patterns.

 

One final thing to consider is that for a pattern finding machine to actually discover relative axioms it would need some partial perception of the concept in which its being used, so if you programmed a 2 dimensional cortesian plane into a computer with the core axioms for shapes such as euclidean geometry then it would probably be able to find higher level relationships in things like symmetrical shapes, shapes that are proportional (like 2 right angled triangles and a square), multiple vectored shapes like polygons and perhaps with enough time it would start working in 3 dimensional space after its exerted all possible 2 dimensional axioms (although it wouldnt because quite by accident it would have already be calculating these by using vectors inverse to the tangent)

 

haha thinking about it, it would get stuck number crunching on circles when it starts looking at axioms inside of it, such as how its diameter is proportional to its circumference........

 

One final final note is that of all the possible knowledge that can be known, its probable that finding even the base axioms for all the different aspects of physics is nigh on impossible, as intelligent as we are and good finding patterns, some concepts are outside the reach of human understand.

 

Cheers for reading it all if you managed to stay with me this far.

[ydoaPs]

!

Moderator Note

Moved to Speculations.

[Arnaud Antoine ANDRIEU]

From my point of view, the distance have two dimensions : direction (straight) and curvature.

e mc ² includes only a linear development of its radius mass energy. We are going to add one more variable. E=mc ²(4D) until it returns to its point of origin. (value converted into linear to circle, .. Smith chart by example)

[Popcorn Sutton]

Pattern Recognition- the ability to determine the impracticality of randomness. (often thought to be statistical).

 

The problem is computational efficiency. There is a proposed solution to this problem. I think it's very plausible, it's just that the physical process needs to be accessible to consciousness, which is no easy task. However, if you suit in front of your computer screen for a while with the python gui up, you'll figure out what the problems are real quick.

[DevilSolution]

Pattern Recognition- the ability to determine the impracticality of randomness. (often thought to be statistical).

 

The problem is computational efficiency. There is a proposed solution to this problem. I think it's very plausible, it's just that the physical process needs to be accessible to consciousness, which is no easy task. However, if you suit in front of your computer screen for a while with the python gui up, you'll figure out what the problems are real quick.

 

This reply is interesting but ambiguous at best. Are you talking about AI? HCI? Processing capability? Higher level thinking?

 

The perplexity of AI is overbearing, the rest i can deal with.

 

Do computers only work in 2-d mathematics? Do our minds work in 3-d mathematics? Does reality work in 4-d?

 

By python gui are you referring to the shell interpreter or an actual gui?

[Popcorn Sutton]

I'm taking about AI with language capabilities. That is where my research has focussed mostly and that is where I've seen the most success.

 

I meant the interpreter for python (IDLE). I use 2.7 and I'd like to work with others. Soon I'll have an open source program on the internet in hopes that it will lead to a TOE. The ultimate goal is something different.

 

In my experience, in this area of study at least, and this could be generalized to all behavior (even that of the universe), the simplest assumption is to assume that everything is 2 dimensional (not that any clear distinctions can actually be drawn between dimensions). 1d = a point on 2d, 2d = a surface, 3d = y(2d), 4d = penetration of 2d.

 

I think thats how things work.

 

I think its a matter of amplitude and frequency. But subjective time is different, its well known that we have access to the past.

[DevilSolution]

I'd be interested in helping, however AI is a very large discipline, i actually start a module on it soon (mainly pathfinding though). I dont have a great deal of experience in python but its an intuitive language so i should pick it up quick enough to help i think. (we use c, java and scala)

 

I once wrote a detailed account of what i thought AI required, i think i came up with 7 or so key aspects such as self learning, emotions, memory, language, purpose etc but never put any of it into code (at the time i couldnt code).

 

I still dont understand what you meant when you said it would become evident when i get the python interpreter up?

[Przemyslaw.Gruchala]

Do computers only work in 2-d mathematics?

 

Computer work on one integer or two integer arguments and outputs 1 result. 1 dimension operation in single instruction.

 

Everything else is simulated.

 

SSE extension to CPU introduced built-in operation on vectors 2d (2x 64 bit) and 4d (4x 32 bit) at the same time.

 

 

By python gui are you referring to the shell interpreter or an actual gui?

Python is joke. Anybody serious is using C/C++ which is thousands times faster...

 

DevilSolution, I like your approach.

Calculate the all possibilities, and then judge them picking up the best one and output.

That's how chess game AI works.

 

But you need to be really advanced programmer (or have $10k+ per month to hire such)..

Edited March 11, 2013 by Przemyslaw.Gruchala

[Popcorn Sutton]

I'd be interested in helping, however AI is a very large discipline, i actually start a module on it soon (mainly pathfinding though). I dont have a great deal of experience in python but its an intuitive language so i should pick it up quick enough to help i think. (we use c, java and scala)

 

I once wrote a detailed account of what i thought AI required, i think i came up with 7 or so key aspects such as self learning, emotions, memory, language, purpose etc but never put any of it into code (at the time i couldnt code).

 

I still dont understand what you meant when you said it would become evident when i get the python interpreter up?

What do you mean pathfinding? I can extend the metaphor somewhat to what my program currently does. And who is we?

 

I agree with self-learning, I think emotions will emerge on their own (it's pragmatics), memory is a given, lets leave language out of this (the concept isn't properly defined), and purpose is reducible to an initial occurrence.

 

If you want to work together, I know a lot of code, and I do know of a way that we can literally work on the same file at the same time so if you're open to that, then I'm going to have to teach you the vocabulary I use.

 

I said that the problems will become evident when you have the interpreter up because even if you have a complete, unified theory worked out for how it should work, Python is another language in itself. You have to learn it. And doing code is a lot of trial and error. A lot of the time, you'll know that you have the right line of code, or a line that works well for your purposes, but you need to figure out where it goes (and it needs to be exactly in the right place or else the whole system will fail). If you don't have it in the right place, and you don't make it explicitly state exactly what it is doing, then you could accidentally change something thats perfectly fine. And often, to have it print out everything that it's doing is just unreasonable.

 

I've taken about a decade to work out a theory of how to get a program to acquire language, and luckily I've had the opportunity to work with some serious geniuses and highly intellectual people to help flesh out the details. It wasn't until a year ago that I started learning Python, and I've overcame a lot of problems since then, but now, after having solved the language problem (whatever, I'll ambitiously say that the problem has been solved in my eyes. I got some great functional code and vocabulary to help me with the process, vocabulary that you simply cannot find in a dictionary), I need to move on to the next part (getting it up on the internet). This part makes me sigh. It doesn't have to do with language, it has to do with building an interface and all the other jargon associated with it that I am not equipped with.

 

The reason I use Python is because it's simple. I've heard too many stories of people facerolling using C and C++, but I've never tried using them, I just know that Pythons syntax is A THOUSAND times easier to understand. Also, you don't have to define every variable (and this is absolutely crucial for my method).

 

As for the post above this, I think he's wrong. I don't think he is an expert on this topic for multiple reasons. But, the main reason is that he says "calculate all the possibilities and then judge them picking the best one". Chomsky has expressed enthusiastically for a very long time that language is infinite (I don't agree, but for all intensive purposes, sure). Conceptually, it is infinite, and to calculate all the possibilities is like calculating EVERY SINGLE NUMBER THAT CAN POSSIBLY EXIST. You can't do that, it's far too inefficient. This is why I make the distinction between possibility and probability. The input can almost be anything possible, but the output is always probable. Introspect about this and ask yourself, is the behavior I just did probable? I cannot accept no for an answer, because if you say no, then you acknowledge the existence of chaos, and there is absolutely, positively, no evidence for chaos. There is no such thing as random. DNE (does not exist). You can't compute random. Even the people who have made these so called "random number generators" know that they're not random.

 

If you want to work with me, you need to understand and accept these things.

Edited March 11, 2013 by Popcorn Sutton

[DevilSolution]

Pathfinding is one of the most basic concepts in AI, just google A* algorithm or pathfinding for more info.

 

We is my university.

 

Yeh python is higher level than c / c++, i have worked with python (learn python the hard way) a few years ago so can pick the syntax up quickly.

I presume your talking about github or subversion? we use subversion for graphics this semester and used it for high performance computing last semester, ive done multi-threaded scala, c and java applications and distributed scala and c (code runs on multiple machines + threads over a network). The actual application i used openMPI for was a graphical line finding algorithm used in ray tracing.

 

I understand the basics of random number generation (not being random), its briefly explained in K&R C book.

 

My current modules are Advanced software engineering (fixing broken code / making a compiler) & Computer graphics and AI (working with trig / polygons & computational decision making algorithms)

 

Whats the actual purpose for this AI, to be self conscious? to do tasks for you? etc etc

 

check this out: http://en.wikipedia.org/wiki/Recursion_(novel) (this is an interesting book, its related to computational recursion and AI)

 

As for numbers, im currently trying to link 3 dimensional space to a polarized circle graph and show how time exists as the last 1/4. Also how the existence and relationship between integers create 3-d space and circles relation to our 2-d irrational representation of it, but this will take some time.

 

I'll work with you, i can atleast make you a GUI, if your using github then link me and ill branch your trunk. Also what's the vocab i need?

[Popcorn Sutton]

I haven't started using github yet, the short term goal is a TOE, long term, if we give it the right tools, it will be able to do whatever we teach it. But, the program I have only does whatever unit had the strongest capacity, which seems to produce grammatical output.

 

Theres alot more to say about this but I'll have to reread your post.

[DevilSolution]

What do you mean by TOE?

 

http://en.wikipedia.org/wiki/TCP_offload_engine?

[Popcorn Sutton]

*looks left... looks right... checks the walls for cameras... leans in and whispers* deryuhevrytin

 

*does the dance from dumb and dumber*