On 02 Mar 2014, at 17:34, [email protected] wrote:
On Sunday, March 2, 2014 9:39:45 AM UTC, Bruno Marchal wrote:
On 01 Mar 2014, at 21:21, John Mikes wrote:
Bruno concluded his Feb 28 post:
The "TOE" extracted from comp assumes we agree on the laws of
addition and multiplication, and on classical logic. From this you
can prove the existence of the universal numbers and or all their
computations, and even interview the Löbian numbers, on what is
possible for them, in different relative sense.
So, math comes from arithmetic, and arithmetic can explain why it
is impossible to explain arithmetic from less than arithmetic,
making arithmetic (or Turing equivalent) a good start.
God created the Integers. All the rest came when God added "Add and
Multiply".
Basically. - Bruno
Start; "TOE" extracted from comp - so we are talking about a
fraction of everything, the part as extracted.
The TOE is extracted from a reasoning, but the TOE is not the E,
like Hubble telescope is not a far away galaxy. The TOE has to be a
finite object, but the object the TOE is talking about can be
infinite, and is infinite with comp, and even more so in the inside
views.
I like to consider Everything as infinite and all, beyond what we
can know about, identify or understand.
Me too. No problem with this.
Why? Why do you both *like* to consider the world this way that
condemns the highest dreams of discovery to disappointment and
futility.
That does not follow at all. On the contrary it is the awe in front of
the infinite unknown which motivates the research and the exploration.
I could relate to assuming that for a methodological reason. And for
a sincerely believed theory reason. But I'm struggling with the
personal preference reason.
Simply because there are no choice, whatever hypotheses we choose, we
are confronted to very difficult questions, and in theology, we are
confronted with unanswerable things. That's normal.
The giganticness of the garden does not limit the butterfly, on the
contrary.
Finish: "GOD" created the integers - and the World, and the Angels,
And....(faith). He
(or She, or It) added "Add and multiply" - nothing else.
(Strictly for math, not for capitalism and/or having lots of
children).
How do fractions come out of that? Can you add, or multiply
integers, to get 0.123456?
or irrational numbers?
No problem proving the existence of 0.123456.
No problem getting all negative numbers, all rational numbers,
and ... all constructive real numbers (but the notion of all real
numbers makes no sense in the 3), but still sense for the internal
views).
In the comp TOE we cannot derive the existence of all real numbers,
but we can easily derive the existence of machines believing in all
real numbers.
For me the most significant part was Irrational Numbers...which you
seem to have overlooked in your answer.
Well, that the real numbers.
How does the comp ToE, explain, derive, and predict in nature as her
preference this cult of number? Unlike the others, this is a clear
and real oppiortunity to say something new we didn't know. Like,
what are the irrational numbers in nature we don't know about?
?
Well we know well and why, even in pure number theory, why sqrt(2),
and e and gamma plays role.
The sum of the inverse of the square numbers is PI^2 divided by 6. PA
can prove this.
I am not sure I understand your question.
What is the origin of this numbers and their function, that only
they can deliver, only because they are irrational?
I can say many thing on that, but that's math, and not so related to
the topic. Keep in mind we are on the mind-body problem, and even only
on its precise comp formulation in arithmetic.
We are not here to answer all question. But most answer here are that
all those things are consequences of RA or PA, or ZF. Those are
theories on which many can agree.
Bruno
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