On 23 Jul 2009, at 15:09, m.a. wrote: > Bruno, > Yes, yours and Brent's explanations seem very clear. I > hate to ask you to spell things out step by step all the way, but I > can tell you that when I'm confronted by a dense hedge or clump of > math symbols, my mind refuses to even try to disentangle them and > reels back in terror. So I beg you to always advance in baby steps > with lots of space between statements. I want to assure you that I'm > printing out all of your 7-step lessons and using them for study and > reference. Thanks for your patience, m.a.

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Don't worry, I understand that very well. And this illustrates also that your "despair" is more psychological than anything else. I have also abandoned the study of a mathematical book until I realize that the difficulty was more my bad eyesight than any conceptual difficulties. With good spectacles I realize the subject was not too difficult, but agglomeration of little symbols can give a bad impression, even for a mathematician. I will make some effort, tell me if my last post, on the relation (a^n) * (a^m) = a^(n + m) did help you. You are lucky to have an infinitely patient teacher. You can ask any question, like "Bruno, is (a^n) * (a^m) the same as a^n times a^m?" Answer: yes, I use often "*", "x", as shorthand for "times", and I use "(" and ")" as delimiters in case I fear some ambiguity. Bruno > > > > > -- Original Message ----- > From: Bruno Marchal > To: everything-list@googlegroups.com > Sent: Wednesday, July 22, 2009 12:20 PM > Subject: Re: The seven step series > > Marty, > > Brent wrote: > > On 21 Jul 2009, at 23:24, Brent Meeker wrote: > >> >> Take all strings of length 2 >> 00 01 10 11 >> Make two copies of each >> 00 00 01 01 10 10 11 11 >> Add a 0 to the first and a 1 to the second >> 000 001 010 011 100 101 110 111 >> and you have all strings of length 3. > > > Then you wrote > >> I can see where adding 0 to the first and 1 to the second gives 000 >> and 001 and I think I see how you get 010 but the rest of the >> permutations don't seem obvious to me. P-l-e-a-s-e explain, Best, >> >> >> >> m >> . (mathematically hopeless) a. >> >> > > > Let me rewrite Brent's explanation, with a tiny tiny tiny improvement: > > > Take all strings of length 2 > 00 > 01 > 10 > 11 > Make two copies of each > > first copy: > 00 > 01 > 10 > 11 > > second copy > 00 > 01 > 10 > 11 > > add a 0 to the end of the strings in the first copy, and then add a > 1 to the end of the strings in the second copy: > > first copy: > 000 > 010 > 100 > 110 > > second copy > 001 > 011 > 101 > 111 > > You get all 8 elements of B_3. > > You can do the same reasoning with the subsets. Adding an element to > a set multiplies by 2 the number of elements of the powerset: > > Exemple. take a set with two elements {a, b}. Its powerset is {{ } > {a} {b} {a, b}}. How to get all the subset of {a, b, c} that is the > set coming from adding c to {a, b}. > > Write two copies of the powerset of {a, b} > > { } > {a} > {b} > {a, b} > > { } > {a} > {b} > {a, b} > > Don't add c to the set in the first copy, and add c to the sets in > the second copies. This gives > > { } > {a} > {b} > {a, b} > > {c} > {a, c} > {b, c} > {a, b, c} > > and that gives all subsets of {a, b, c}. > > This is coherent with interpreting a subset {a, b} of a set {a, b, > c}, by a string like 110, which can be conceived as a shortand for > > Is a in the subset? YES, thus 1 > Is b in the subset? YES thus 1 > Is c in the subset? NO thus 0. > > OK? > > You say also: > >> The example of Mister X only confuses me more. > > Once you understand well the present post, I suggest you reread the > Mister X examples, because it is a key in the UDA reasoning. If you > still have problem with it, I suggest you quote it, line by line, > and ask question. I will answer (or perhaps someone else). > > Don't be afraid to ask any question. You are not mathematically > hopeless. You are just not familiarized with reasoning in math. It > is normal to go slowly. As far as you can say "I don't understand", > there is hope you will understand. > > Indeed, concerning the UDA I suspect many in the list cannot say "I > don't understand", they believe it is philosophy, so they feel like > they could object on philosophical ground, when the whole point is > to present a deductive argument in a theory. So it is false, or you > have to accept the theorem in the theory. It is a bit complex, > because it is an "applied theory". The mystery are in the axioms of > the theory, as always. > > So please ask *any* question. I ask this to everyone. I am intrigued > by the difficulty some people can have with such reasoning (I mean > the whole UDA here). (I can understand the shock when you get the > point, but that is always the case with new results: I completely > share Tegmark's idea that our brain have not been prepared to > have any intuition when our mind try to figure out what is behind > our local neighborhood). > > Bruno > > > > http://iridia.ulb.ac.be/~marchal/ > > > > > > > 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 everything-list@googlegroups.com To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~----------~----~----~----~------~----~------~--~---