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From: Bruno Marchal <marchal.domain.name.hidden>

Date: Thu, 23 Jul 2009 15:28:13 +0200

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.domain.name.hidden
*

*> 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 00 to the first and a 01 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 08 elements of B_3.
*

*>
*

*> You can do the same reasoning with the subsets. Adding an element to
*

*> a set multiplies by 02 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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Received on Thu Jul 23 2009 - 15:28:13 PDT

Date: Thu, 23 Jul 2009 15:28:13 +0200

On 23 Jul 2009, at 15:09, m.a. wrote:

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

http://iridia.ulb.ac.be/~marchal/

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To post to this group, send email to everything-list.domain.name.hidden

To unsubscribe from this group, send email to everything-list+unsubscribe.domain.name.hidden

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Received on Thu Jul 23 2009 - 15:28:13 PDT

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