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. I like to consider Everything as
infinite and all, beyond what we can know about, identify or understand.
*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? I described here already my 'story' of the Roman
numbers before the invention of zero, based on TWO hands (with fingers, '5'
one palm- two fingers)..
JM
On Fri, Feb 28, 2014 at 2:36 PM, Bruno Marchal <marc...@ulb.ac.be> wrote:
>
> On 28 Feb 2014, at 08:20, Chris de Morsella wrote:
>
> Personally the notion that all that exists is comp & information - encoded
> on what though? - Is not especially troubling for me. I understand how some
> cling to a fundamental material realism; after all it does seem so very
> real. However when you get right down to it all we have is measured values
> of things and meters by which we measure other things; we live encapsulated
> in the experience of our own being and the sensorial stream of life and in
> the end all that we can say for sure about anything is the value it has
> when we measure it.
> I am getting into the interesting part of Tegmark's book - I read a bit
> each day when I break for lunch - so this is partly influencing this train
> of thought. By the way enjoyed his description of quantum computing and how
> in a sense q-bits are leveraging the Level III multiverse to compute every
> possible outcome while in quantum superposition; a way of thinking about it
> that I had never read before.
> Naturally I have been reading some of the discussions here, and the idea
> of comp is something I also find intuitively possible. The soul is an
> emergent phenomena given enough depth of complexity and breadth of
> parallelism and vastness of scale of the information system in which it is
> self-emergent.
>
> Several questions have been re-occurring for me. One of these is: Every
> information system, at least that I have ever been aware of, requires a
> substrate medium upon which to encode itself; information seems describable
> in this sense as the meta-encoding existing on some substrate system. I
> would like to avoid the infinite regression of stopping at the point of
> describing systems as existing upon other and requiring other substrate
> systems that themselves require substrates themselves described as
> information again requiring some substrate... repeat eternally.
> It is also true that exquisitely complex information can be encoded in a
> very simple substrate system given enough replication of elements... a simple
> binary state machine could suffice, given enough bits.
> But what are the bits encoded on?
>
> At some point reductionism can no longer reduce.... And then we are back to
> where we first started.... How did that arise or come to be? If for example
> we say that math is reducible to logic or set theory then what of sets and
> the various set operations? What of enumerations? These simplest of simple
> things. Can you reduce the {} null set?
> What does it arise from?
>
> Perhaps to try to find some fundamental something upon which everything
> else is tapestried over is unanswerable; it is something that keeps coming
> back to itch my ears.
>
> Am interested in hearing what some of you may have to say about this
> universe of the most simple things: numbers, sets; and the very simple base
> operators -- {+-*/=!^()} etc. that operate on these enumerable entities and
> the logical operators {and, or, xor}
>
> What is a number? Doesn't it only have meaning in the sense that it is
> greater than the number that is less than it & less than the one greater
> than it? Does the concept of a number actually even have any meaning
> outside of being thought of as being a member of the enumerable set
> {1,2,3,4,... n}? In other words '3' by itself means nothing and is
> nothing; it only means something in terms of the set of numbers as in:
> 2<3<4... <n-1<n
>
> And what of the simple operators. When we say a + b = c we are dealing
> with two separate kinds of entities, with one {a,b,c} being quantities or
> values and {+,=} being the two operators that relate the three values in
> this simple equation.
>
> The enumerable set is not enough by itself. So even if one could explain
> the enumerable set in some manner the manner in which the simple operators
> come to be is not clear to me. How do the addition, assignment and other
> basic operators arise? This extends similarly to the basic logic operators:
> and, or, xor, not - as well.
>
> Thanks
>
>
>
> Those kind of questions are more less clarified. You cannot prove the
> existence of a universal system, or machine, or language, from anything
> less powerful, but you can prove the existence of all of them, from the
> assumption of only one. I use elementary arithmetic, because it is already
> taught in school, and people are familiar with it.
>
> 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
>
>
>
>
>
>
>
>
>
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> http://iridia.ulb.ac.be/~marchal/
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>
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