On 13 Nov 2008, at 14:21, Torgny Tholerus wrote:

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> > Bruno Marchal skrev: >> I have to think. I think that to retrieve a Leibniz rule in discrete >> mathematics, you have to introduce an operator and some non >> commutativity rule. This can be already found in the book by Knuth on >> numerical mathematics. This has been exploited by Kauffman and one of >> its collaborator, and they have published a book which I have ordered >> already two times ... without success. It is a very interesting >> matter. >> Dirac quantum relativistic wave equation can almost be retrieved form >> discrete analysis on complex or quaternion. It is worth investigating >> more. Look at Kauffman page (accessible from my url), and download >> his >> paper on discrete mathematics. > > > I will look closer at the Kauffman paper on Non-commutative Calculus > and > Discrete Physics. It seems interesting, but not quite what I am > looking > for. Kauffman only gets the ordinary Leibniz rule, not the extended > rule I have found. Ah? > > > What I want to know is what result you will get if you start from the > axiom that *everything in universe is finite*. Like with comp + occam. Look I think I will concentrate on the MGA thread for a period. Meanwhile I will ask one of my student, who has a craving for discrete math, to take a look on your finite calculus, and he will contact you in case he find it interesting. Sorry but I have not so much time those days. Best, Bruno > > > For this you will need a function calculus. A function is then a > mapping from a (finite) set of values to this set of values. Because > this value set is finite, you can then map the values on the numbers > 0,1,2,3, ... , N-1. > > So a function calculus can be made starting from a set of values > consisting of the numbers 0,1,2,3, ... , N-1, where N is a very large > number, but not too large. N should be a number of the order of a > googol, ie 10^100. Because the size of our universe is 10^60 Planck > units, and our universe has existed for 10^60 Planck times. As the > arithmetic, we can count modulo N, ie (N-1) + 1 = 0. This makes it > possible for the calculus to describe our reality. > > A function can then be represented as an ordered set of N numbers, > namely: > > f = [f(0), f(1), f(2), f(3), ... , f(N-1)]. > > This means that S(f) becomes: > > S(f) = [f(1), f(2), f(3), ... , f(N-1), f(0)]. > > The sum or the product of two functions is obtained by adding or > multiplying each element, namely: > > f*g = [f(0)*g(0), f(1)*g(1), f(2)*g(2), ... , f(N-1)*g(N-1)]. > > and to apply a function f on a function g then becomes: > > f(g) = [f(g(0)), f(g(1)), f(g(2)), ... , f(g(N-1))]. > > Exercise: Show that the extended Leibniz rule in the discrete > mathematics: D(f*g) = f*D(g) + D(f)*g + D(f)*D(g), is correct! > > -- > Torgny Tholerus > > > 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 -~----------~----~----~----~------~----~------~--~---