Re: Theory of Everything based on E8 by Garrett Lisi
[EMAIL PROTECTED] skrev: When I talk about pure mathematics I mean that kind of mathematics you have in GameOfLife. There you have gliders that move in the GameOfLife-universe, and these gliders interact with eachother when they meet. These gliders you can see as physical objects. These physical objects are reducible to pure mathematics, they are the consequences of the rules behind GameOfLife. -- Torgny That kind of mathematics - models of cellular automata - is the domain of the theory of computation. These are just that - models. But there is no reason for thinking that the models or mathematical rules are identical to the physical entities themselves just because these rules/models can precisely predict/explain the behaviour of the physical objects. You only need models of cellular automata. If you have a model and rules for that model, then one event will follow after another event, according to the rules. And after that event will follow another more event, and so on unlimited. The events will follow after eachother even if you will not have any implementation of this model. Any physics is not needed. You don't need any geometric properties. In this model you may have a person called Torgny writing a message on a google group, and that event may be followed by a person called Marc writing a reply to this message. And you don't need any implementation of that model. -- Torgny --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Theory of Everything based on E8 by Garrett Lisi
Hi, Le Wednesday 28 November 2007 09:56:17 Torgny Tholerus, vous avez écrit : [EMAIL PROTECTED] skrev: When I talk about pure mathematics I mean that kind of mathematics you have in GameOfLife. There you have gliders that move in the GameOfLife-universe, and these gliders interact with eachother when they meet. These gliders you can see as physical objects. These physical objects are reducible to pure mathematics, they are the consequences of the rules behind GameOfLife. -- Torgny That kind of mathematics - models of cellular automata - is the domain of the theory of computation. These are just that - models. But there is no reason for thinking that the models or mathematical rules are identical to the physical entities themselves just because these rules/models can precisely predict/explain the behaviour of the physical objects. You only need models of cellular automata. If you have a model and rules for that model, then one event will follow after another event, according to the rules. And after that event will follow another more event, and so on unlimited. The events will follow after eachother even if you will not have any implementation of this model. Any physics is not needed. You don't need any geometric properties. In this model you may have a person called Torgny writing a message on a google group, and that event may be followed by a person called Marc writing a reply to this message. And you don't need any implementation of that model. Sure, but you can't be ultrafinitist and saying things like And after that event will follow another more event, and so on unlimited. Also why do you limit yourself to one computational model ? Turing Machine, Lambda calcul, cellular automata are all equivalents. Regards, Quentin Anciaux -- All those moments will be lost in time, like tears in the rain. --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Theory of Everything based on E8 by Garrett Lisi
Le 28-nov.-07, à 05:48, [EMAIL PROTECTED] a écrit : On Nov 28, 3:16 am, Bruno Marchal [EMAIL PROTECTED] wrote: Le 27-nov.-07, à 05:47, [EMAIL PROTECTED] a écrit : Geometric properties cannot be derived from informational properties. I don't see why. Above all, this would make the computationalist wrong, or at least some step in the UDA wrong (but then which one?). I'll find the flaw in UDA in due course ;) Thanks. I recall that there is an argument (UDA) showing that if comp is true, then not only geometry, but physics, has to be derived exclusively from numbers and from what numbers can prove (and know, and observe, and bet, ...) about themselves, that is from both extensional and intensional number theory. The UDA shows *why* physics *has to* be derived from numbers (assuming CT + yes doctor). The Lobian interview explains (or should explain, if you have not yet grasp the point) *how* to do that. Bruno If the UDA is sound that would certainly refute what I'm claiming yes. I want to see how physics (which as far I'm concerned *is* geometry - at least I think pure physics=geometry) emerges *purely* from theories of sets/numbers/categories. OK. Note that UDA says only why, not how. how is given by the lobian interview, and gives only the propositional physics (as part of the propositional theology). I base my claims on ontological considerations (5 years of deep thought about ontology), which lead me to strongly suspect the irreducible property dualism between physical and mathematical properties. Thus I'm highly skeptical of UDA but have yet to property study it. Lacking resources to do proper study here at the moment :-( We are in the same boat ... Bruno http://iridia.ulb.ac.be/~marchal/ --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Theory of Everything based on E8 by Garrett Lisi
Le 28-nov.-07, à 09:56, Torgny Tholerus a écrit : [EMAIL PROTECTED] skrev: When I talk about pure mathematics I mean that kind of mathematics you have in GameOfLife. There you have gliders that move in the GameOfLife-universe, and these gliders interact with eachother when they meet. These gliders you can see as physical objects. These physical objects are reducible to pure mathematics, they are the consequences of the rules behind GameOfLife. -- Torgny That kind of mathematics - models of cellular automata - is the domain of the theory of computation. These are just that - models. But there is no reason for thinking that the models or mathematical rules are identical to the physical entities themselves just because these rules/models can precisely predict/explain the behaviour of the physical objects. You only need models of cellular automata. If you have a model and rules for that model, then one event will follow after another event, according to the rules. And after that event will follow another more event, and so on unlimited. The events will follow after eachother even if you will not have any implementation of this model. Any physics is not needed. You don't need any geometric properties. In this model you may have a person called Torgny writing a message on a google group, and that event may be followed by a person called Marc writing a reply to this message. And you don't need any implementation of that model. OK. Do you agree now that the real Torgny, by which I mean you from your first person point of view, cannot known if it belongs to a state generated by automata 345 or automata 6756, or automata 6756690003121, or automata 65656700234676611084899 , and so one ... Do you agree we have to take into account this first person indeterminacy when making a first person prediction? Bruno http://iridia.ulb.ac.be/~marchal/ --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Theory of Everything based on E8 by Garrett Lisi
Bruno Marchal skrev: Le 28-nov.-07, à 09:56, Torgny Tholerus a écrit : You only need models of cellular automata. If you have a model and rules for that model, then one event will follow after another event, according to the rules. And after that event will follow another more event, and so on unlimited. The events will follow after eachother even if you will not have any implementation of this model. Any physics is not needed. You don't need any geometric properties. In this model you may have a person called Torgny writing a message on a google group, and that event may be followed by a person called Marc writing a reply to this message. And you don't need any implementation of that model. OK. Do you agree now that the real Torgny, by which I mean you from your first person point of view, cannot known if it belongs to a state generated by automata 345 or automata 6756, or automata 6756690003121, or automata 65656700234676611084899 , and so one ... Do you agree we have to take into account this first person indeterminacy when making a first person prediction? I agree that the real Torgny belongs to exactly one of those automata, but I don't know which one. So I can not tell what will happen to the real Torgny in the future. I can not do any prediction. If we call the automata that the real Torgny belongs to, for automata X, then I can look at automata X from the outside, and I will then see that all that the real Torgny will do in the future is completely determined. There is no indeterminacy in automata X. -- Torgny --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Last post before the key post (was OM = SIGMA_1) 1
Le 27-nov.-07, à 17:27, Günther Greindl a écrit :
Dear Bruno,
thanks for your posts! I like them very much!
Looking forward to further stuff,
Thanks for telling.
In this post I recall Cantor's proof of the non enumerability of the
set of infinite binary sequences. First with a drawing, and then with
mathematical notation. The goal is to train you with the notations.
Then I do the same with the almost exactly identical proof that the set
of functions from N to N is also non enumerable.
I hope you have no more problem with the identification of the set of
functions from N to 2 (where 2 = {0, 1}), with the set of infinite
binary sequences. Please ask in case of any trouble with that. A
function from N to any set A always gives rise to an infinite sequence
of elements of A.
Note that I will never use Cantor's result. I explain it just to
illustrate the use of diagonalization, and to contrast it with the use
in the next post which will illustrate a capital feature of all
universal machine.
***
1) 2^N is not enumerable (proof by drawing)
Cantor argument goes like this. It is a reductio ad absurdo:
Suppose that the set of infinite binary sequence is enumerable.
That means that there is a bijection between N and that set. Such
a bijection will have a shape like:
0 00010110010100111...
1 001010011...
2100011001001000100110...
3101010101001010100100...
4100100010...
5000110010...
...
But then I can find an infinite binary sequence which *cannot* be in
the image of that bijection. Indeed here is one:
1 0 1 1 1 0 ...
It is the complementary sequence build from the diagonal sequence. QED.
***
1bis) 2^N is not enumerable (proof without drawing).
Suppose that the set of binary infinite sequences is enumerable.
That means there is a bijection between N and that set. It means that
for each natural number i, there is a corresponding sequence s_i, and
that all infinite binary sequences belongs somewhere in the enumeration
s_0 s_1 s_2 s_3 s_4 s_5 ...
Each s_i is a function from N to 2. For example, if s_0 denote the
first sequence in the drawing above, it means that s_0(0) = 0, s_0(1)
= 0, s_0(2) = 0, s_0(3) = 1, s_0(4) = 0, s_0(5) = 1, s_0(6) =1, etc.
That is, s_i(j) the jth number (0 or 1) in the sequence s_i.
s_i(j) gives the matrix drawn above, for i and j natural numbers.
Then the number s_i(i), for i natural numbers gives the diagonal
sequence, and the sequence 1- s_i(i) gives the complementary of the
diagonal, and that sequence cannot belongs to the list of the s_i.
We can make explicit the contradiction. If the sequence 1- s_i(i) was
in the list s_i, there would exist a number k such that s_k(x) = 1 -
s_x(x). But then for x = k, s_k(k) = 1 - s_k(k). But s_k(k) has to be
one or zero, and in the first case you get 1 = 1 - 1 = 0, and in the
other case you get 0 = 1 - 0 = 1. Contradiction.
Damn... I must already go. I suggest you work by yourself the very
similar proof that N^N is not enumerable. Of course you can derive this
immediately from what we have just seen, given that a function from N
to 2, is a particular case of a function from N to N. But it is a good
training in *diagonalisation* to find the direct proof.
I hope you can see that the set of all functions from N to N can be
identify with the set NXNXNX... of sequences of natural numbers.
I do quickly the drawing proof, and let you write the more explicit
proof (without drawing).
Suppose there is such a bijection. It will look like:
0 23 456 7667 ...
1 08 235 ...
2 67 10 10123 ...
3 900 4 ...
...
But then the sequence of numbers:
24 9 11 5
cannot be in that list. All right?
See you tomorrow,
Bruno
Bruno Marchal wrote:
Hi Mirek, Brent, Barry, David, ... and all those who could be
interested
in the INTRO to Church thesis,
I have to go, actually. Just to prepare yourself to what will follow,
below are recent links in the list . It could be helpful to revise a
bit, or to ask last questions.
I will ASAP come back on Cantor's Diagonal, (one more post), and then
I
will send the key fundamental post where I will present a version of
Church thesis, and explain how from just CT you can already derive
what
I will call the first fundamental theorem. This one says that ALL
universal machine (if that exists) are insecure.
It is needed to explain why Lobian machine, which are mainly just
Universal machine knowing that they are universal, cannot not be above
all theological machine. As you can guess, knowing that they are
universal, will make them know that they are insecure.
All the term here will be defined precisely. In case you find this
theorem depressing, I suggest you read The
Re: Last post before the key post (was OM = SIGMA_1) 1
Hi Bruno, I'm ready. Luckily, it is not long time ago, I've received my university degree in CS, so it was rather easy to follow :-) Sincerely, Mirek Bruno Marchal wrote: Le 27-nov.-07, à 17:27, Günther Greindl a écrit : Dear Bruno, thanks for your posts! I like them very much! Looking forward to further stuff, Thanks for telling. In this post I recall Cantor's proof of the non enumerability of the set of infinite binary sequences. First with a drawing, and then with mathematical notation. The goal is to train you with the notations. Then I do the same with the almost exactly identical proof that the set of functions from N to N is also non enumerable. --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Theory of Everything based on E8 by Garrett Lisi
On Nov 28, 9:56 pm, Torgny Tholerus [EMAIL PROTECTED] wrote: You only need models of cellular automata. If you have a model and rules for that model, then one event will follow after another event, according to the rules. And after that event will follow another more event, and so on unlimited. The events will follow after eachother even if you will not have any implementation of this model. Any physics is not needed. You don't need any geometric properties. In this model you may have a person called Torgny writing a message on a google group, and that event may be followed by a person called Marc writing a reply to this message. And you don't need any implementation of that model. -- Torgny A whole lot of unproven assumptions in there. For starters, we don't even know that the physical world can be modelled solely in terms of cellular automata at all. Digital physics just seems to be the latest 'trendy' thing, but actual evidence is thin on the ground. Mathematics is much richer than just discrete math. Discrete math deals only with finite collections, and as such is just a special case of algebra. Algebraic relations extend beyond computational models. Finally, the introduction of complex analysis, infinite sets and category theory extends mathematics even further, beyond even algebraic relations. So you see that cellular automata are only a small part of mathematics as a whole. There is no reason for thinking for that space is discrete and in fact physics as it stands deals in continuous differential equations, not cellular automata. Further, the essential point I was making is that an informational model of something is not neccesserily the same as the thing itself. An informational model of a person called Marc would capture only my mind, not my body. The information has to be super-imposed upon the physical, or embodied in the physical world. --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
