Algorithmic Information Theory...

[davidgow77]

Hi guys and girls,

I've been a bit stale for a while in terms of new ideas, but I've just read an article that I think will help me solve at least one of my problems.

Its by Gregory Chaitin, and explains the concepts of why mathematics (going on current knowledge) can never have a TOE.

Absloutely fascinating stuff, even though maths is (to put it lightly) not my strongest point.

http://www.plus.maths.org.uk/issue37...ega/index.html

Also, is there anyone out there who could explain to me how you might extract an algorithm from a sequence of numbers with a pattern. I need to set myself some exercises, and while I am starting to understand some concepts, I don't know how to go about actually doing things.

[mkirkpatrick]

Hi guys and girls,

I've been a bit stale for a while in terms of new ideas, but I've just read an article that I think will help me solve at least one of my problems.

Its by Gregory Chaitin, and explains the concepts of why mathematics (going on current knowledge) can never have a TOE.

Absloutely fascinating stuff, even though maths is (to put it lightly) not my strongest point.

http://www.plus.maths.org.uk/issue37...ega/index.html

Also, is there anyone out there who could explain to me how you might extract an algorithm from a sequence of numbers with a pattern. I need to set myself some exercises, and while I am starting to understand some concepts, I don't know how to go about actually doing things.

Nice to see you back,thanks for the link,maths is not my strong point either.

kindest regards michael.

[harmonygirl]

Hi David, thanks for the link, but what confused me (in the beginning!) was the definition of the probability for coming up with one string (101) was 1/2 x 1/2 x 1/2 (or 1/2^3), but wouldn't this be the same probability for the string 110 and 111 as well? This lack of specificity bothered me and i couldn't concentrate on the rest of the article.

[davidgow77]

Erm..... I don't understand the maths part too well, which is probably why I found the article useful as it explains the concepts behind the mathematical processes!

What I would say is that where there are 3 bits, and they can both only have the value of 1 or 0, then the probability of them taking any value would be the same for 101, 110 and 111. HOWEVER.... if my understanding of probabilities is as flawed as my understanding of calculus, then there is a high probability that I am probably wrong!



DG

PS - just looked at the article again and you (and thus me!) are definately right.

[harmonygirl]

so David (and I think this is what really threw the boomerang back) would the fact that the probability of 110 = 101 = 111 mean those strings are equal? Incidentally, I haven't done algorythms since school (although I recall I really liked them!), so I might be completely out in left field... (it's baseball season!)

[davidgow77]

yes. strings (I think) are deemed equal if they contain the same amount of information. any string with 3 bits is equal to other strings with 3 bits.



DG

[harmonygirl]

okay, I stand corrected then. I used to program in binary (back in the day!) and they certainly wouldn't have been equal! Having said that, I will reread the article and keep it in mind that it is only important how many places are occupied with a 1 at the furthest left-handed place. Everything else can be 0s and 1s with impugnity. Okay. I can do this. Thanks for your help.

[harmonygirl]

David, I'm having a difficult time with this article. The randomness equals complexity bit has released another boomerang. If you flick your pen at random, theoretically you could come up with 4 ink dots in a row separated by an inch each (or some other simple equation). Isn't this just as probable as a pattern of ink spots that are complex?

[mkirkpatrick]

In this theory,which i know little,as I have not studied it,however the little that I have gathered is that as the omega is unknowable,it is exactly the same as saying that God too is unknowable,but the distance between the
one at omegas doorway beyond the border lands of the physical universe,and
the one on the ground so to speak can be looked at and be understood,
provided of course that you further understand that there is absolute unity
in all the "apparent" diversity you think you see?


kind regards michael.

[harmonygirl]

The definition of Omega as unknowable is another boomerang for me. I don't understand how 1/2^n is defined as unknowable. It may be infinite (there are different schools of thought on that) but how do we figure it's unknowable? This is just not computing in my brain! or are you saying that the larger 2^n becomes, the smaller 1/2^n becomes and closer to zero and therefore unity? but then again, wouldn't unity be the closer it got to 1? I should get some sleep, I'm seriously confused now!