On 25 Dec 2013, at 21:35, Edgar L. Owen wrote:

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Bruno,Correct me if I'm wrong about where you are coming from in yourbasic approach.

OK. Some other did already a good job.

Bruno seems to believe that mathematicians discover a math thatalready exists in reality (as opposed to math being a humaninvention which is the alternative view).

`Compared to most scientists, I am realist on only a tiny part of`

`arithmetic. Comp can be much less realist than most scientists, but`

`sometimes being more realist shorten the proofs, and indeed that is`

`how the observers accept new axioms from times to times.`

Thus he believes that reality itself is a mathematical structure

Not at all. You miss the main point.

`The doctor needs realism in arithmetic to just explain to the patient`

`what is meant by a digital brain, and what is Church's thesis.`

`Then I just show that IF you believe that you can survive with it (in`

`whatever reality exists making the turing emulation relatively`

`possible) THEN the TOE is given arithmetic (or any Turing equivalent`

`universal system), and physics become an arithmetical relative`

`measure problem.`

`It is a theorem. Not an idea that I propose because I would find it`

`elegant.`

which 'contains' in some sense all of the math that mathematicianshave come up with, and no doubt much more to be discovered. Thus hebelieves that ANY correct mathematical theory can be validly appliedto reality to generate true results, which he does with facility.

`On the contrary, no mathematical theory at all can exists on numbers`

`and machines. You confuse the mathematical theories, and the intended`

`reality describe by those theories. We know today that the`

`arithmetical reality cannot be described entirely by any effective`

`theories.`

However there are a number of problems with this theory.

`I don't want to look presumptuous, but it is a theorem, thus in a`

`theory, which assumes *much* less than most existing theories.`

`It seems you do favor computationalism, so you apply or not the`

`theorem. Or if you disbelieve it you can search a flaw.`

For one thing the edifice of human math is static, it just sitsthere waiting for humans to apply it to something,

`Now you are more realist than me. mathematicians evolves all the time,`

`and the human mathematics changes all the time.`

It even deepened vertiginously.

whereas the math that actually computes reality is active andcontinuously runs like software.

`Math does not compute. It is mathematicians which proves theorems.`

`They don't compute either, even if *they* are computed at some level.`

`A computer computes. Universal numbers can compute relatively to`

`universal numbers. Computations can be seen as type of arithmetical`

`relations.`

There is, in my view, no evidence at all for any math in reality atall except for what is actually running and computing reality'scurrent state.

`Hmm, Read the UDA. here you are close to digital physics, or the idea`

`that reality is a computation, but the UDA shows that this cannot`

`work. We cannot singularize first person by their computational`

`states. They are distributed in many computations.`

Therefore most of human math is NOT going to be applicable to themath of reality. One can't just apply the results of any human maththeory to reality and expect it accurately describe reality. Insteadof trying to applying Godel, Church, etc. etc. etc. to reality onehas to actually look at the actual computations reality is executingand see what they tell US, as opposed to what mathematicians try totell them. This is basic scientific method and is the correctapproach.

`GĂ¶del, Church concerns digital processes, and many of their extensions`

`on constructive ordinals. It is very general. It has nothing to do`

`with humans, I mean, no more than the Boson H, or the galaxy Andromeda.`

`Church thesis makes the notion of universal machine very general, and`

`completely arithmetical, and independent of us or any aliens.`

That is much more independent of us than Andromeda.

`Anyway, I don't defend a truth, only a theorem. What I explain is not`

`a question of agreeing or disagreeing, but of understanding or finding`

`a flaw, which can be fatal or corrigible.`

So my repeated point is that human math and reality math aredifferent.

Of course, and doubly so, as human math is plunged in "reality math".

Of course they share some fundamental logic. But human math is astructure that was first approximated from the math of reality,

The math of reality, or the real math?

`I think that you confuse mathematical structures and the theories`

`describing such mathematical structures. this will not help you to get`

`the nuance when we treat the study of mathematical theories,`

`mathematically. It is the difficulty of mathematical logic.`

but then widely generalized and extended far beyond what realitymath is actually computing in the process losing some of the actualessentials of reality math.For example all computations in reality math are finite with noinfinities nor infinitesimals since reality is granular at itselemental level and nothing actual can be infinite.

`You seem to assume a finite primitive physical universe? Frankly, it`

`is not clear what you assume.`

The human math number system is a generalized extension of reality'snumber system which is more subtle as there are no numbers that justkeep going forever (pi) to greater and greater accuracies fargreater than the scale of the universe. And there may well be nozeros in reality math, since we could expect reality math to computeonly what actually exists.

You seem to talk like if you knew what is reality.

`But if you do science, you should make clear what you assume, what is`

`your theory, what are the method allowed in your derivation, etc.`

Basically reality math is a particular program running in realitythat computes the current state of reality.

That is digital physics. It can't work.

All the other programs that don't actually run and whatever math orlogical results they may be based upon have no relevance and cannotbe blindly applied to reality math.

`Programs don't run or not run. That is a relative notion in the`

`arithmetical reality.`

`The programs can be implemented in the physical reality, in which`

`case, they run relatively to our running, relatively to our most`

`probable computations, among infinities of them.`

Therefore let me respectfully suggest that Bruno needs to examinethe actual math of reality that is actually computing reality, anduse his mathematical skills to elucidate that, rather thanautomatically trying to apply the results of human math withoutexamining whether they actually apply.

Study the theorem before making patronizing remarks.

`And then never do patronizing remarks, as they weaken your point in`

`the infinite. Always focus on the point.`

Bruno

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