Eureqa's Unification Theory

[ori milstein]

I'm sure pretty much everyone thought about it, but wouldn't it be
neat to feed Eureqa with data about how the small world acts and how
the macro world acts, and see what unification theory it comes up
with?
I'm a layman so I have no clue how to do this, but I'm sure a lot of
people are as anxious for some curious physicist to take this on. (:

[Damir Olejar]

Here is an idea for a beginning:

1. Define "world"

2. Define "acts" and the metrics to measure it.

What you can do instead is to generate three columns of totally random numbers.

Try to find a for a third column.  Whatever formula you get after 1 day, save it, subtract it from a third column and let the new values represent a third column.  Try to find a formula for a new third column but this time define it as 

10*f = 10*f(x) ...  then repeat the same after one day except that every next day you are looking for a 10^n  = 10^n*f(x) where n is a number of elapsed days. This is how you "zoom-in" the smaller world.

Let us know whether you get a final formula, or whether you get to a point where you can't get any formula any further.  

If you get a final formula, then your data is not random. If you get to a point where you can't get any formula any further, then Eureqa is not complete and you may suggest a new method for upgrading Eureqa. If you can go on to infinity finding the unification formula, then you got very nice random data and Eureqa is just the right tool.

Explanation, and reasoning behind:

"...showing that Hilbert's program to find a complete and consistent set of axioms for all mathematics is impossible, giving a negative answer to Hilbert's second problem."

http://en.wikipedia.org/wiki/G%C3%B6del's_incompleteness_theorems

PS In my humble opinion only.

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[Tilmann Zäschke]

Well I'm not a mathematician or physicist, but reading the sentence:

> "...showing that Hilbert's program to find a complete and consistent set of axioms for all mathematics is impossible, giving a negative answer to Hilbert's second problem."

... it seems to me that the problem is only that certain things can not be proven to be true. Even if that would mean that there is no unified theory of everything, it doesn't mean that the there are theories/formulas that are much better than what we have currently. I guess it could even mean that there can be a universal formula, it just can not be proven to be universal. Who knows, maybe the formula/system is even trivial enough to not be affected by Goedels theorem? I guess simplt assuming that the univere is deterministic means that there needs to be some universal formula. How could it be deterministic otherwise? But maybe it isn't deterministic at all ...

Furthermore some other systems also don't fall under Goedels theorem, as I understand, if you check further down in Wikipedia under "Limitations of Gödel's theorems".

Anyway, I would guess that searching for such a formula in Eureqa is impractical, but I'm not gonna stop anyone from trying it :-)

Cheers,
Tilmann

[Damir Olejar]

You are right, some things are simply to be taken for granted instead of proven, for being too obvious or according to practical experiences.

I think that determinism can be easily refuted with the causation, begging a question what causes the caused (ad infinitum), assuming that some things do not need a cause (such as initial state in deterministic automata)... classical philosophy. Therefore since some things do not have a cause, it could mean that some things do not have (or cannot be expressed with) a deterministic formula.  

Anyway, I don't want to ignite any deep philosophical debates, but thank you for a reply.

Damir

2012/2/9 Tilmann Zäschke <zaes...@gmx.de>

[L]

 

Searching for the unified theory of everything using Eureqa might only yield a good approximation, and that only if you had a good sample of everything.

 

Now, as it just so happens, every dataset is a sample of everything.  Not, mind you, necessarily a particularly representative sample, but that's a different question.  It's something, and every something is some of everything. 

 

So there you go.  We're all getting there together.

 

From: Tilmann Zäschke <zaes...@gmx.de>
To: eureqa...@googlegroups.com
Sent: Thursday, February 9, 2012 2:38 PM
Subject: Re: Eureqa - Eureqa's Unification Theory

Well I'm not a mathematician or physicist, but reading the sentence:

> "...showing that Hilbert's program to find a complete and consistent set of axioms for all mathematics is impossible, giving a negative answer to Hilbert's second problem."

... it seems to me that the problem is only that certain things can not be proven to be true. Even if that would mean that there is no unified theory of everything, it doesn't mean that the there are theories/formulas that are much better than what we have currently. I guess it could even mean that there can be a universal formula, it just can not be proven to be universal. Who knows, maybe the formula/system is even trivial enough to not be affected by Goedels theorem? I guess simplt assuming that the univere is deterministic means that there needs to be some universal formula. How could it be deterministic otherwise? But maybe it isn't deterministic at all ...

Furthermore some other systems also don't fall under Goedels theorem, as I understand, if you check further down in Wikipedia under "Limitations of Gödel's theorems".

Anyway, I would guess that searching for such a formula in Eureqa is impractical, but I'm not gonna stop anyone from trying it :-)

Cheers,
Tilmann


On 09.02.2012 20:05, Damir Olejar wrote:

Here is an idea for a beginning:

1. Define "world"

2. Define "acts" and the metrics to measure it.

What you can do instead is to generate three columns of totally random numbers.

Try to find a for a third column.  Whatever formula you get after 1 day, save it, subtract it from a third column and let the new values represent a third column.  Try to find a formula for a new third column but this time define it as 

10*f = 10*f(x) ...  then repeat the same after one day except that every next day you are looking for a 10^n  = 10^n*f(x) where n is a number of elapsed days. This is how you "zoom-in" the smaller world.

Let us know whether you get a final formula, or whether you get to a point where you can't get any formula any further.  

If you get a final formula, then your data is not random. If you get to a point where you can't get any formula any further, then Eureqa is not complete and you may suggest a new method for upgrading Eureqa. If you can go on to infinity finding the unification formula, then you got very nice random data and Eureqa is just the right tool.

Explanation, and reasoning behind:

"...showing that Hilbert's program to find a complete and consistent set of axioms for all mathematics is impossible, giving a negative answer to Hilbert's second problem."

http://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems

[Damir Olejar]

(my last on this topic)

Integral of everything = -1

the end

[ori milstein]

It is late at night here in Israel, and I'm a little tipsy, so for now
most of your replies went over my head; I'll try and read it deeply
tomorrow. But I was referring more to the unification of theory of
relativity with quantum theory. Not some ethereal thing... We have
good data on how the world works on the scale of an atom and on the
scale of large masses and high speed. On the scale of the atom data
looks like *this*- yet on a larger scale data looks like *that*. We
can work first within the framework that we know, that is, using the
paradigms and variables of relativity and quantum theory and feed the
matching data to the matching scale.. They are good theories and there
is very good reason to believe that the data describes the world with
pretty high accuracy. Scientists have been and are constantly trying
to unify these two theories that work well yet contradict each other-
why not give Eureqa a shot?

On a side note, and more far-fetched, it is interesting to see whether
Eureqa could be designed to use some methods such as that which
Einstein used, like take data that describes only Newton's theory and
by fiddling with the some axioms (for example- time and space don't
have to be absolute- speed of light does) suggest a formula that
explains the given "middle world" data but goes deeper.

[Tilmann Zäschke]

I was also talking about physics. But I think using Eureqa for that
might be hard.
If the result is simple, such as E=mc^2, then it might indeed work.
But it has been suggested that the formula in question may by much more
complex such as a E8 Lie algebra, as proposed by Antony Lisi, see
https://en.wikipedia.org/wiki/An_Exceptionally_Simple_Theory_of_Everything
Again, I'm really out of my depth here, but I understand that this is
more a whole set of formulae, which Eureqa can probably not deliver.

Also, again, I really would not want to stop anyone from trying :-)

As an aside, are there been plans to integrate Eureqa/Formulize with
services such as BOINC for access to volunteered computing power?
https://boinc.berkeley.edu/index.php
I guess this is best known for SETI@home and LHC@home

Cheers,
Tilmann

[Damir Olejar]

Ori, I do not wish to troll. The point of my babble was to discuss the possibility of finding the unification formula and problems you may encounter.

Just for you, lets put it this way, very bluntly and in a plain English... 

For analogy's sake, lets say that Image-viewer for JPG files represents a quantum-model. Then, lets say that Movie-player for AVI files represents a relativity-model. Let the computer represent the universe where everything happens. What you are trying to do is to find some middle-ground that would connect the Image-viewer and the Movie-player. You can extract images from a movie and view it in a image-viewer. You can play the images one by one to animate them in an image-viewer.  Yes, you can have very nice, squeaky clean, and incredible data. However, you are still missing the sound, and without completely changing the Image-viewer software, or starting a third program, you cannot bridge the gap between the two programs (it is missing the sound-player).

Why is this so? because quantum approach and the relativity are axiomatic models of the universe (just like the Image-viewer and the Movie-player analogy). So, the third solution-model will be neither the quantum nor the relativity, as such, it will not be the bridge for a gap, but a model to explain what the other two cannot. Again, there will be no bridge between the models, and gaps will exist.

Furthermore, the science of such modeling, is the science of algorithms... as such, it states that there is no universal language for an universal modeling. Bluntly put, not everything can be modeled.

What we said is that some things are to be taken for granted, if they cannot be modeled...as the limit of our methods and knowledge, or as a starting-point to some other approach/method/knowledge. 

I hope my intentions to explain what I previously said are more clear, and that I am not trolling this group.

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[L]

I also do not wish to troll.  (I don't mind joking a little bit though.)  And I am certainly no physicist.

 

But it was not just for Ori, as I too appreciate the plain English - although I admit to understanding it only on the metaphoric level.

 

If you are correct in saying that this problem can never be modelled, then I think you are saying that no such unification is ever possible, at least not for such as us who live within the universe.  I think you are even saying that it cannot even be approximated.

 

It is certainly no disparagment of a program, to suggest that it can't do the impossible!!

 

Now, I freely admit that I may even misunderstand the metaphoric level.  However I grasp just barely enough of Goedel and just barely enough of Turing to appreciate that "that there is no universal language for an universal modeling."  [Note to developers: Please implement a future release ported to an infinite Turing machine.  Thanks. ;-) ]

 

In order to resolve two systems by any tool, the two systems need to have some common language elements.  Even an incomplete set might allow for some approximate mapping, always with the awareness that some unknowns must always remain unknowable.

Are you saying that even this is impossible?

 

We are very far afield from Eureqa, as such.  Out of respect for this fact, I promise not to extend this thread on this forum beyond your reply (should you be kind enough to provide one).

 

From: Damir Olejar <olejar...@gmail.com>
To: eureqa...@googlegroups.com
Sent: Friday, February 10, 2012 6:13 AM
Subject: Re: Eureqa - Eureqa's Unification Theory

[Damir Olejar]

Sorry L, this is how far I will go, because of the Ad Hominem regarding what I might have said but really did not.

[L]

 

I hope it was not from me, such was not my intent.  Sometimes between the impersonal nature of text, and language barriers, statements come through other than intended.

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From: Damir Olejar <olejar...@gmail.com>
To: eureqa...@googlegroups.com

Sent: Friday, February 10, 2012 5:53 PM

Subject: Re: Eureqa - Eureqa's Unification Theory

Sorry L, this is how far I will go, because of the Ad Hominem regarding what I might have said but really did not.

[Damir Olejar]

Perception window. GOT IT!  :)))  No hard feelings mr. L.

Alright, to make the story short (or to cut my own crap), there might be a way to see if there exists a common ground to quantum physics and the relativity... I am currently trying to EQ something which might take a bit of time to complete. It gave very nice results with the fast approximations that I did on my cheap laptop. If we could respect the property of each-other, I would love to collaborate with anyone from here since I am trying to make this approach a patent (considering that nobody did it before, yatta yatta yatta). Nevertheless, I would also love to have my name written somewhere if there is a common ground to these two theories since it would make the breaking news.

My knowledge about the quantum physics and the relativity is limited, but here is the type of data I need to make this thing work:

Consider entities A and B (rocks, stones, atoms, light-waves, neutrinos... anything!) such that A and B both contain the same elements (by elements I mean: a subset of entities by which A and B are composed), and there are also elements that A contains but B does not (and vice-versa... vice-versa is a very important condition). The entities A and B can be approximations of the real physical entities, computer models, or theoretical entities. 

-on a quantum level, an "amount" of elements that A contains and the "amount" of elements that B contains, and what those elements are

-same with the relativity

-it does NOT matter what those elements are, as long as we can say with a certainty that we did not miss anything that is in the same rank of elements.

What is needed is the big list of such entities, about 10000 of those data rows.

if such data can be obtained, send me a personal e-mail message stating that you'd like to collaborate, that you won't misuse my approach without giving me a proper credit, and I will help you with this kick-start and elaborate everything in nice details...

Lets rock'n'roll !  ;-)

[Douglas Eadline]

Damir

Some comments on your proposal. First, it is not possible to patent
physical laws or mathematics. Second, your proposal is at best
naive. I have been following this thread and you may find it useful
to further study some of the topics you mention. I would suggest
that you are trying to square a circle and your final product will
be warmer room.

--
Doug

[Damir Olejar]

Doug, I am talking about a method for classifying the data. 

But alright, do as you wish... 

[L]

OK, I lied.  I'm extending this thread after all....

There is a possible approach, although it's very different and it's at best far-fetched.  Anybody who wants to publish, patent, copyright, or otherwise profit from this, knock yourself out.  Just list me in a footnote and give me one share of stock when you issue your IPO.  If you're feeling generous, list me as the most minor co-author, lol.  

It is possible to encode any equation as a vector of numeric values.  Basically, everything that goes through a computer, including this email, is so-encoded.  If the various equations share variables, these encodings could be entered into Eq, and it could be cut loose to curve fit.  Perhaps this is the downfall: perhaps the common terms don't exist.  But for the moment, let us assume they do, in order to elaborate the concept.

In order to interpret any result, it would be necessary to reverse the encoding at the end.  Probably, the best way to do this would be to build out a wrapper routine which encodes a set of symbolic expressions into spreadsheet form, calls Eq, and decodes the result.

 

Bear in mind that if a variable is, say, velocity - then the output is not (in part - and if it fits) a function of velocity directly, but rather of the encoding of velocity.  Interpreting the output is not quite direct.

What this would do, is use Eq - a numeric solver - as the engine for a symbolic manipulator.

Which is kinda silly, in that I expect that Eq embeds its own symbolic manipulator already....

Now don't you go forgetting my footnote, ya hear?

---

From: Douglas Eadline <ead...@gmail.com>
To: eureqa...@googlegroups.com
Sent: Saturday, February 11, 2012 10:21 AM

Subject: Re: Eureqa - Eureqa's Unification Theory

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[Damir Olejar]

Hehehe... well, I was about to do something that is like the Vector-Space analysis of the data (if that has anything in common with the "equation as vector numeric values" you mentioned?) . It is exactly what you said. If it can go trough a machine, like this e-mail, it can be processed and compared in some way or another. So yes, we can compare the circles, rectangles, squirrels, potatoes and temperature of the room. It does not mean that they have anything in common however.

And yes, I was about to suggest using Eureqa as the engine to "connect" the classifications together. If the R^2 and correlation coefficient are good, then we can say that there is a common-ground to circles, rectangles... So far for the method part, I got Correlation Coefficient r = 0.99830144 and R² Goodness of Fit R²=0.77322235 but that is only the 1/2 trough.  Doing it all-over again on a better computer, trying to get a better fit.

The only reason I am investigating the patent option is not to make the money, but to pave the way for the future studies, references, job opportunities and so on... I have no intentions to sound naive, and I do take myself seriously. And, footnote goes to mr. L  :)

I don't know everything, and it is true that I might want to research this before making bold statements, but there is too much on a plate I have to do.  This is written in my spare-time which I got almost NONE!

So... elaboration of this might be posted within a few days on the Internet, if I can go from the creative commons onto a patent... explaining how to find out whether the quantum physics can have a connection with the relativity... and then how to find what connects them, and how to see whether squirrels have anything in common with the potatoes and the room temperature.

Take care y'all good folks!

[L]

> Hehehe... well, I was about to do something that is like the Vector-Space analysis of the data (if that has anything in common with the "equation as vector

> numeric values" you mentioned?) . 

Not really.  

But let it go.  I called it silly, and that time, I wasn't joking.

---

From: Damir Olejar <olejar...@gmail.com>

To: eureqa...@googlegroups.com
Sent: Saturday, February 11, 2012 1:37 PM

Subject: Re: Eureqa - Eureqa's Unification Theory

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-------------------------------------------------

[Damir Olejar]

There is absolutely no need to be a jerk L. or to get from Ad hominem from Ad personam, but no problem. 

I'll take care of my stuff in a most civil manner, and you people take care of yours. 

You deserved nothing from me and I can't expect better from a public forum anyway.

So long!

[L]

I meant that MY suggestion was silly, this is why I placed such a low "price" on it in the first place.

But whatever.

 

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<sig>&SIGFILE; NOT FOUND ERR 000121</sig>

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From: Damir Olejar <olejar...@gmail.com>
To: eureqa...@googlegroups.com

Sent: Sunday, February 12, 2012 4:44 AM

Subject: Re: Eureqa - Eureqa's Unification Theory