bruno: God created the Integers. All the rest came when God added "Add and Multiply". richard: I trhink the multiply mat be redundant. Is that a useful property?
On Fri, Feb 28, 2014 at 2:36 PM, Bruno Marchal <[email protected]> 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 > > > > > > > > > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To post to this group, send email to [email protected]. > Visit this group at http://groups.google.com/group/everything-list. > For more options, visit https://groups.google.com/groups/opt_out. > > > http://iridia.ulb.ac.be/~marchal/ > > > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To post to this group, send email to [email protected]. > Visit this group at http://groups.google.com/group/everything-list. > For more options, visit https://groups.google.com/groups/opt_out. > -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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