On 27 Jul 2009, at 16:07, ronaldheld wrote:
>
> I am following, but have not commented, because there is nothing
> controversal.
Cool. Even the sixth first steps of UDA?
>
> When you are done, can your posts be consolidated into a paper or a
> document that can be read staright through?
I should do that.
Bruno
> On Jul 23, 9:28 am, Bruno Marchal <marc...@ulb.ac.be> wrote:
>> 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/- Hide quoted text -
>>
>> - Show quoted text -
> >
http://iridia.ulb.ac.be/~marchal/
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