On 05 Jul 2009, at 14:37, John Mikes wrote:

> We also believed 'in school' that God created the world as it is,  
> yet in later studies we scrutinize the details and try to look  into  
> more than just the final phrases 'learned' in school.

In some school the motto is that God is a human product. It is crazy  
what you can make children believe!

> Once you identified 3 and 4 I need more knowledge to get to the  
> abbreviation of 34. You can say: 34 is a set with the value of '34',  
> but then you involved characteristics of the set -
> as "known" stuff, - which is just what I am scrutinizing.
> "Find it natural" stands for lack of scrutinizing.

It is your right to scrutinize, even for billions years. But you can  
miss some trains.

> ------
> I think you referred to my sentence:
> > Nothing is excluded
> > from the a/effects (relations)  of the rest of the world.<
> when you remarked:
> BM: "...This sentence seems to me far more subtle than anything I am  
> trying to explain."
> It reflects my 'totality' based worldview: an interrelated  world,  
> ALL elements in relation with ALL elements - securing the image of  
> 'order' upon which we can base a science. No part can be excluded or  
> isolated, (not even elements within a set) it would 'create' havock  
> in theories we try to learn/formulate.

I build on what 99% of people know or remember of arithmetic. It is  
not really the time to re-evaluate them, it is on the contrary the  
time to remember them, and use them.

There is no magic, it asks for works. But here just ask question when  
you don't understand a solution to an exercise, for example.  
Mathematical intuitions about some object comes from playing with  
those objects. It needs a minimum amount of exercise and practice, for  
not being fool by the superficial choice of the words.

> ---------
> BM: "...Be careful with the term "uncountable" which will have a  
> precise technical meaning.
> I call 'uncountable' what we cannot count (in toto)

Good try.
But what do you mean by "we" ? I asked you that question before. We  
the humans? We the mammals? We the animals? We the live being? We the  
universal numbers? We use the universal numbers with oracle, ...
And then there is the problem to define "count", which is a very  
interesting unsolved problem. But there are progress: we can explain  
why universal machine have difficulties when they try to define  
concept like "0, 1, 2, 3 ...".

> - the effects exercised on items within a set (as well as on  
> anything in the world) by "the rest of the world" to which we have  
> only a limited access - eo ipso we CANNOT count the unknown part.  
> Infinite IMO is uncountable, because you can always add 'another' to  
> it (common sense argument). I try to evade the word 'infinite'  
> because of too many 'technical' connotations attached to it, use  
> rather unlimited, which may refer to a finite item of which we don't  
> know (yet?) the total.

We, and by we I mean the readers of the posts of this thread, will be  
invited, I'm afraid there is no escape, of a bit Cantor theory of the  
Infinites, note the s.
Cantor discovered the Diagonalization technic, which works in set  
theory, mathematical logic and computer science.

> ---------
> BM: "We will axiomatized some mathematical notions, but only when we  
> are sure that we get the intuition right. The reason will NOT be a  
> search of explicit rigor, but will be related in helping universal  
> machine to get the "understanding".
> I appreciate the 'axiomatize' what I understand as retrospect  
> formulations to make our theories workable. Not vice versa.

Yes, yes, yes. Important to always keep this in mind. Theories/ 
machines/numbers are tools, they just push light on something, but  
they can introduce shapes and shadows themselves.
Be careful now of not confusing a theory and the "betted things" the  
theory is supposed to talk about. In the case of numbers and machine  
they can be both the studying thing and the studied things, and this  
makes some hard to predict surprises if I can say.

> *
> I feel the paragraph as 'reverse thinking': our intuition is the  
> working of our human mindset, I would not apply it as proof for  
> getting the basics right, of which our mindset is a product.
> Similarly the 'universal machine' is a product of the human mind so  
> it cannot be invoked as evidencing the total which includes the  
> human mind. (Circularity).

I think that the idea that  ''universal machine' is a product of the  
human mind"  is a  product of your mind.
And as such I respect that idea as an opinion.

My opinion is that the universal numbers are indeed the product of  
universal numbers, and they have only partial controls on the relations.

But there can be notable historical events like when amoeba invented  
the cable to develop into what we call brain, which are universal  
machine/number ...  But this happened before, and after ...
A more human-biased account could be that the universal machine has  
been discovered by Babbage, and then by Post, Turing, Suze, Markov,  
Kleene, Church, and some others.

Accepting Church thesis, for a theoretical computer scientist it is a  
theorem, which can be proved  for all enumerable class of computable  
function known up to now (hundreds of universal numbers are appearing  
each day, you are using one indirectly), or an axiom, in attempt to  
The universal machine has many names, you know: fortran, lisp, prolog,  
c, peano, zf, 3-body problem, quantum vacuum topology,...

But please, I am explaining this right now, or read the literature or  
try to keep a later train, but it is on the type reasoning, and we  
have to get some amount of familiarity with computer science.

You think the Mandelbrot Set is a product of the mind?

Remember that the definition of the Mandelbrot set M is not much  
longer than the definition of the circle. It is has been discovered by  
Fatou and Julia, and Mandelbrot. An important discovery, and I am  
about sure that, well not really M, but the rational part of C \minus  
M, is among the
fortran, lisp, prolog, c, peano, zf, 3-body problem, quantum vacuum  
topology,... , company.

> BM: "...What is the "occamisation of a set"?
> The application of Occam's razor to cut off all that makes "it"  
> harder to understand and concentrate on the easy part. It includes  
> the (limited?) understanding of a problem by the person doing such  
> 'occamization' - whatever he finds just complicating the issues he  
> emphasizes. Such issues, however, may reach into the roots of our  
> poor (mis?)understanding. I find 'Occam' the ultimate reductionism.

Hmm.... Here you talk like someone who is a set realist. I am agnostic  
there. Hmm... I can understand that "set" is an occamization of  
"concept", but set is supposed to be as occamized as possible, for  
practical purposes. So that we can easily figure out the meaning of  
the most elementary relations and operations on them. Sets are  
building block to talk about other things, like functions, computable  
functions, etc.

> (I wonder if Russell will excommunicate me for that?)

He could as well if he comes to suspect that you try to occamize what  
I am trying to say.

The beauty of it, John, is that, with comp, the universal machine,  
despite its infinity of names, is such that it is able to demolish all  
attempts, by machines and even many gods, to be occamized.  (By 'gods'  
I mean entities non emulable by universal machines).

If the Supreme Secretary or any Ayatollah really knew what is a  
universal machine, they would send it immediately to a Gulag, both the  
machine and its universal user, I'm afraid.

The universal machine or number or whatever finite thing is *the*  
major discovery. The real heroin of all I try to say. To understand  
the mathematical root of that discovery is what is needed to get the  
seventh step, and to understand why a computation is different from a  
description of computation. This helps for the last step. The eighth  
step, where you can add "QED", and, in the least, understand a  
different conception of "realities" than the current naturalist one.  
In the most, you understand why it is necessary, when assuming "we"  
are no more than turing universal, whatever "we" are.


> Original message:
> On 04 Jul 2009, at 22:42, John Mikes wrote:
> > Dear Bruno, thanks for the prompt reply, I wait for your further
> > explanations.
> > You inserted a remark after quoting from my post:
> > *
> > > If you advance in our epistemic cognitive inventory to a bit  
> better
> > > level (say: to where we are now?) you will add (consider)  
> relations
> > > (unlimited) to the names of 'things' and the increased notion will
> > > exactly match the 'total' (what A was missing from the 'sum'). It
> > > will also introduce some uncertainty into the concept (values?)  
> of a
> > > set.
> >
> > I am not sure that I understand.
> > *
> > Let me try to elaborate on that: What I had in mind was my
> > 'interrelated totality' view.
> > As you find it natural that 3 (!!!) and 4 (!!!!) make 34 - if
> > written without a space in between - representing a quite different
> > meaning - (not 7 as would be plainly decipherable: 3+4),
> I am not sure What you mean by finding "natural". I have just learn in
> school to abbreviate IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII by 3*10 +4,
> itself abbreviated by 34.
> >  so all elements of a set carry relations to uncountable items in
> > the unlimited totality (even if you try to restrict the
> > applicability into the identified  {  }  set. Nothing is excluded
> > from the a/effects (relations)  of the rest of the world.
> This sentence seems to me far more subtele than anything I am trying
> to explain. Be careful with the term "uncountable" which will have a  
> precise technical meaning.
> > No singularity or nivana IN OUR WORLD
> >
> > Your 2+2=4 includes a library of conditions, axioms, relations,
> > clarifiers, just as e.g. the equation 4-2=2 includes the notion "NOT
> > in ancient Rome" (where it would have been '3')
> We will axiomatized some mathematical notions, but only when we are
> sure that we get the intuition right. The reason will NOT be a search
> of explicit rigor, but will be related in helping universal machine to
> get the "understanding".
> Concerning the natural numbers, the more we will be familiar with
> them, the more we will be aware we don't really know what they capable
> of, and why they are fundamentally mysterious. But there is no need to
> add more mystery than the very subtle one which will grow up. This is
> not obvious, and has begun with the work of Dedekind, and Gödel, ...
> > So I referred to the tacitly included 'relations' (I use this word
> > for all kinds of knowables in connection with potential effects of
> > other items) implied in your technical stenography.
> > Since the relationally interesting items are unlimited, there is no
> > way WE (in our present, limited mind) could exclude uncertainty FOR
> > 'ANY' THING. Sets included. Occamisation of a set does not make it
> > rigorous, just neglects additional uncertainty.
> I still have no clues why and how you relate "infinity" with
> uncertainty. What is the "occamisation of a set"?
> >
> > Have a good weekend
> I wish you the same,
> Bruno
> http://iridia.ulb.ac.be/~marchal/
> >


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