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.
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/
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