> On 22 May 2019, at 12:19, 'Cosmin Visan' via Everything List > <[email protected]> wrote: > > Derive here from addition and multiplication the color red.
“Derive” here is ambiguous. If you mean literally to derive the colour red from addition and multiplication, then you ask me something impossible. Yet, what I can show is that impossibility is already derivable by the universal (Löbian, rich) machine. The first thing consists in deriving the existence of the universal machines in arithmetic, but that was entirely done in Gödel 1931. He missed the universal machine, but the followers will not miss it (and Emil Post saw it 10 years before). Just some details, to give you the idea how that is possible. The harder step is deriving first the exponentiation from addition and multiplication. Gödel used a famous idea in Number theory, sometimes called the Chinese Lemma. It is modular arithmetic, which already alone have a Babbage gear wheel universal machine. See Gödel 1931, or any textbook in mathematical logic. Once you have exponentiation, as I have explained recently, you can derive faithful (isomorphic) representation of finite sequences of numbers, in term of addition and multiplication. >From this you can imagine that we can represent simple known Turing universal >machine, and indeed all this is “well known” in this domain. Then, to please Brent, and invoking the environment, and using a physical computer , I will follow the shorter way to the colour red, by training a neural net to recognise colour, and notably the colour red. Now the difficult step: the neural net has to be largely re-entrant. It a neural in a torus, with still some entry, facing the colored objects. I need this to make the neural net Löbian, he trains itself on itself. All this has been done by the physical computers, which implement a digital universal machine, whose existence is a theorem of arithmetic. In the theory given by the Löbian machine itself, the qualia red has the property to be experientially obvious, but not belonging to the 3p describable type. The experience itself cannot be attached to any of its number theoretical implementation, but to all of them. That infinities and the unavoidable redundance, including the necessity of long and deep histories, play a role in stabilising the histories. For us “red” has many connotations, if only because it is the color of blood. Most plausibly the qualia of “red” of the simple arithmetical toroidal neural net above is quite dissimilar to our, so I don’t claim having capture the human red qualia. For this one, the numbers will be a the relative representations of yourself in arithmetic, which exists (an infinity) when we assume the digital Mechanist hypothesis. But even without the mechanist hypothesis, it is a theorem that the Löbian machine can understand that they can’t prove to anyone that they are conscious, or that they have qualia. Above the universal treshold you are confronted to the non provable, the non controllable, or insecurity, and a Lobian machine is mainly a universal machine who knows that she is universal, and she knows the price, and that price is notably that 99,9% of her accessible truth are not communicable, nor describable. But then that is why there is art, music and poets. Bruno > > On Tuesday, 21 May 2019 17:40:43 UTC+3, Bruno Marchal wrote: > >> On 21 May 2019, at 12:04, 'Cosmin Visan' via Everything List >> <[email protected] <javascript:>> wrote: >> >> What about color red ? > > As I just explained they belong to the phenomenology of numbers, which is > derivable from the addition and multiplication laws, which lead already to > Turing universality, and to the theology of the Löbian numbers (like PA) that > a weaker theory (RA) emulates integrally. > > -- > 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] > <mailto:[email protected]>. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/6abdfb87-7999-4ff5-a246-529f797b77a9%40googlegroups.com > > <https://groups.google.com/d/msgid/everything-list/6abdfb87-7999-4ff5-a246-529f797b77a9%40googlegroups.com?utm_medium=email&utm_source=footer>. -- 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 view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/A9899035-325D-4812-8175-FCB971A809D0%40ulb.ac.be.
