"Yes but then what, does physics reduce to mathematics or does mathematics reduce to physics?"
...that's the $64000 question that quite a few people on this list are decided on in different ways. For example, if physics reduces to maths, then it isn't legitimate to say that a theory of quantum gravity precludes the existence of real numbers. But if maths reduces to physics then there is no *a priori* reason to assume that "infinity" is anything more than a string of meaningless letters. On 30 September 2014 06:44, John Clark <[email protected]> wrote: > On Sun, Sep 28, 2014 at 12:33 PM, Bruno Marchal <[email protected]> wrote: > > > Bit the *way* you are stuck in step 3 makes me think that you have your >> religion about all this >> > > Wow, calling a guy known for disliking religion religious, never heard > that one before, at least I never heard it before I was 12. > > >> Not all analog machine can be computable, some things are not >>> computable. Turing proved that not all numbers are computable, >> >> >> > I guess you mean "real number". >> > > No I do not. I don't just mean numbers that can't be expressed as > fractions, and I don't mean transcendental numbers life PI or e that are > not the solution to any polynomial equation, I mean non computable numbers, > that is numbers for which there is not a infinite sequence or a algorithm > of any sort that can even approximate them. Turing proved that all non > computable numbers are real but not all real numbers are non computable, > although nearly all of them are. > > >> except for random number generators every analog machine human beings >>> have ever made is computable. >>> >> >> > > Not sure about that. I read that soap bubbles in some lattice can >> generate non computable surface "theoretically" at least. OK, >> >> No natural phenomenon has ever been found where nature has solved a >> NP-hard problem in polynomial time. As for the soap bubble thing the key >> word is "theoretically", Scott Aaronson actually tried it and this is what >> he reports: >> >> " taking two glass plates with pegs between them, and dipping the >> resulting contraption into a tub of soapy water. The idea is that the soap >> bubbles that form between the pegs should trace out the minimum Steiner >> tree — that is, the minimum total length of line segments connecting the >> pegs, where the segments can meet at points other than the pegs themselves. >> Now, this is known to be an NP-hard optimization problem. So, it looks like >> Nature is solving NP-hard problems in polynomial time! >> >> Long story short, I went to the hardware store, bought some glass plates, >> liquid soap, etc., and found that, while Nature does often find a minimum >> Steiner tree with 4 or 5 pegs, it tends to get stuck at local optima with >> larger numbers of pegs. Indeed, often the soap bubbles settle down to a >> configuration which is not even a tree (i.e. contains “cycles of soap”), >> and thus provably can’t be optimal. >> >> The situation is similar for protein folding. Again, people have said >> that Nature seems to be solving an NP-hard optimization problem in every >> cell of your body, by letting the proteins fold into their minimum-energy >> configurations. But there are two problems with this claim. The first >> problem is that proteins, just like soap bubbles, sometimes get stuck in >> suboptimal configurations — indeed, it’s believed that’s exactly what >> happens with Mad Cow Disease. The second problem is that, to the extent >> that proteins *do* usually fold into their optimal configurations, >> there’s an obvious reason why they would: natural selection! If there were >> a protein that could only be folded by proving the Riemann Hypothesis, the >> gene that coded for it would quickly get weeded out of the gene pool." >> >> By the way I just finished reading Scott Aaronson's book "Quantum >> Computing since Democritus" and it's excellent. >> > > And not only that but the fundamental laws of physics tell us that every >>> machine we or anybody or anything else will ever build will also be >>> computable. >>> >> >> > > Again, that is not so easy, because nature might exploits real numbers >> > > Nobody has ever seen nature due this and if a quantum theory of gravity > actually exists then nobody ever well because that would mean that > spacetime is quantized and nature wouldn't even recognize real numbers. > > > We have evidence that we can reduce biology to chemistry, and chemistry >> to physics >> > > Yes but then what, does physics reduce to mathematics or does mathematics > reduce to physics? For example, if nature never uses real numbers to decide > what to do next can it even be said that real numbers exist? I don't think > anybody knows enough to answer that question, I know that you don't. > > >> If it goes both ways then it's more than a correlation and that's what >>> we've got in this case. Change the brain and the mind always changes. >>> Change the mind and the brain always changes. And that is why nobody needs >>> to assume computationalism (not to be confused with "comp") because we >>> already know for a fact that it's true. >> >> >> > > At which substitution level? >> > > I don't understand the question. > > >The problem with computationalism, is that it needs to assume some level >> of description, to encapsulate the finiteness of information content of the >> teleportation beam. So comp truncates the person >> > > I don't know about "comp" but if nature never has to deal with a infinite > number of anything then in computationalism that beam hasn't truncated > anything. > > > you do very bad science and/or bad religion >> > > Wow, calling a guy known for disliking religion religious, never heard > that one before, at least I never heard it before I was 12. > > John K Clark > > > > -- > 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/d/optout. > -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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