On 06 Jul 2009, at 16:12, m.a. wrote (in bold):

> My answers.    m.a.
> Here we met a set of sets.
> The set of subsets of a set, can only be, of course, a set of sets.  
> The set {2, 21, 14} is a set of numbers. The set { { }, {4, 78,  
> 56} } is a set of sets. It has two elements: the empty set {}, and  
> the set of numbers {4, 78, 56}. Do not confuse a number, like 24,  
> and a set, like {24}, which is a set having a number has elements.  
> In particular it is the case that  {4, 78, 56} belongs to { { }, {4,  
> 78, 56} }. Take it easy, and meditate on the following exercise:
>
> Which of the following are true
>
> {3, 5} included-in {3, 5} True

OK.



>
> {3, 5} belongs-to {3, 5} True

Not OK. The elements of {3, 5} are 3 and 5. {3, 5} is not an *element*  
of {3, 5}.
Ask in case you are not OK with this, of course.




> {3, 5} included-in { {3, 5} } False

OK. Very good.


> {3, 5} belongs-to { {3, 5} } True

OK. {3, 5} is even the *only* element of  { {3, 5} }


No exercise today. Just a question, a suggestion, and a plan.

The question is: have you the feeling to learn something?

The suggestion: I think the best way to answer the preceding question  
consists in trying to explain what you learn to someone else. It is  
the best way to see if you remember and understand the definition. You  
could try to explain what you learn to some gentle "victim" in your  
neighborhood (wife, friend, child, parent, ...).

I give you a plan, and some more motivation. To get the seventh step  
in some proper way, there is a need to understand the mathematical  
notion of "universal machine". For this I need to explain what is a  
computable function. For this I need to explain what is a function,  
and for this I need to explain what is a set, given that functions can  
more easily be explained through sets relating sets. Once you will  
have a good grip of what is a universal machine, or what is a  
universal number, and what really means "universal", we will be able  
to tackle the notion of universal dovetailing, and especially the  
"mathematical universal dovetailing" (which is really important for  
the whole approach, and for the step eight). I am hesitating to work  
quickly on the notion of function, or to do some pieces of number  
theory and geometry to provide examples before.

As I said recently to John, the discovery of the notion universal  
machine is one of the most astonishing and gigantic discovery made by  
the humans, and what I do is just an exploitation of that discovery.  
Universes, cells, brains and computers are example of universal  
machine, and the notion of universal machine are a key to understand  
why eventually, once we say "yes to the doctor", and believe we can  
survive "qua computatio", we have to redefine physics as an invariant  
for the permutation of all possible observers, and how physics can be  
recovered from an invariant among all universal machines point-of- 
views ...

Feel free to slow me down, or to accelerate me, and to ask any  
question at whichever level of details you want. Feel free to ask any  
question that you have already asked.

Have a good day, and thanks for your effort and seriousness,

Bruno

PS. It should be obvious for everyone that if there are still  
questions, critics, objections, problems, feeling of dizziness,  
whatever, with the first six steps of the UDA, please, feel free to  
ask. And people should not hesitate to discuss other everything-like  
subject, I don't want to monopolize the list of course. But the UDA  
reasoning really changes the perspective on all possible TOEs, so I  
will feel free myself to point on UDA on each discussion where I find  
it relevant (of course also).



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




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