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.

-- Original Message ----- 
  From: Bruno Marchal 
  Sent: Wednesday, July 22, 2009 12:20 PM
  Subject: Re: The seven step series


  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,

(mathematically hopeless)  a.

  Let me rewrite Brent's explanation, with a tiny tiny tiny improvement:

  Take all strings of length 2
  Make two copies of each

  first copy:

  second copy

  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:

  second copy

  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}

  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, 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.


  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).



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