# Re: Do we live within a Diophantine equation?

```> On 9 Jul 2018, at 19:23, John Clark <johnkcl...@gmail.com> wrote:
>
> On Mon, Jul 9, 2018 at 7:03 AM, Bruno Marchal <marc...@ulb.ac.be
> <mailto:marc...@ulb.ac.be>> wrote:
>
> ​>>​By using p-adic numbers mathematicians found more than a century ago
> there are a infinity of ways the numbers could be arranged because there are
> a infinity of ways distance between numbers could be defined and all of them
> are logically consistent. If you want to use Euclidean geometry or even the
> sort of non-Euclidean geometry Einstein used you've got to use standard
> arithmetic, but there are other ways. For example, in the 7-adic system the
> distance between 56666 and 66666 is smaller than the distance between 66665
> and 66666; and 28814 is closer to 2 than 2 is to 3.
>
> ​>​All Turing universal system would do. p-adic numbers presupposes
> elementary arithmetic.
>
> It would be equally true to say elementary arithmetic presupposes p-adic
> numbers, although humans were not smart enough to figure that out until 1897.```
```

I doubt this. I am not sure you can define p-adic number without assuming
natural number.s If you can, show me.

> Out of all the ways numbers could be manipulated there is only one thing that
> is unique about arithmetic, its not unique because its the only one that is
> self consistent, its unique because its the only one that is consistent with
> physical reality and the laws of physics.

Non standard model of arithmetic are also consistent with the laws of physics.

>
> ​> ​The notion of computations do not rely not on heaven either. Robinson
> arithmetic is Turing universal, and that can be proved in Peano Arithmetic.
>
> ​And there are only 2 instances when Robinson arithmetic or Peano Arithmetic
> exists:
> 1) In heaven.
> 2) When they are implemented in matter that obeys the laws of physics.
>
> ​>​If a computation is physical, it has to admit a physical definition. But
> apparently you cannot find it.
> Apparently you can't find a definition of “definition”. But never mind, I
> have something vastly superior to a definition of a physical computation, I
> can point to an actual example of a physical computation
>

That is a version of the knowing table argument. You can do this in my dreams
too.

> and all you can do is point to a book full of ASCII characters.
>

I was pointing on the content of the book.

> You can not point to one single example of a non-physical computation. Not
> one.
>
>

Here is one:

s(0) +s(0)
s(s(0) + 0)
s(s(0))

Here is another one:

SB(S(K(SM))K)AB
Bx((S(K(SM)K)A)B
A(S(K(SM))KAB)
A(K(SM)A(KA)B)
A(SM(KA)B)
A(MB)(KAB)
A(BBA)

> Examples are far more important and vastly more fundamental than definitions
> because examples always come first, it is only later that somebody dreams up
> a definition that fits all the examples in a class. And sometimes a
> definition never comes at all, most people live their entire lives and manage
> to communicate just fine in this ultra complex physical world and yet have
> never seen a dictionary in their lives. That was the error early AI
> researchers made, they tried to give their machines definitions of everything
> in the physical world and that didn’t work out very well, today they use
> examples.
>
> ​> ​something is primary if we have to assume it
>
> It's so ubiquitous there is no choice but to assume matter, otherwise you
> couldn't read a book because that is made of matter, you couldn't even think

Nobody doubt Matter. But that does not make it primary, which is the debated
point.

> Heaven is not made of matter and neither is the Luminiferous Aether but our
> physical world is indifferent to the existence or non-existence of them, in
> other words physics can't prove they don't exist but it can prove the idea is
> silly.

Physics is not concerned with fundamental existence. Metaphysics is. Confusing
physics and metaphysics is the “error" of Aristotle, which is debunked in the
frame of computationalism. This why we have to backtrack to the greeks, we have
adopted that mistaken view since long.

>
> ​> ​He is uncertain about where he will find itself after the duplication.
>
> That would be true if the man were like you and didn't understand what the
> words "YOU WILL BE DUPLICATED"   mean.

But the guy has bet on comp, and so he knows that once duplicated, the two
copies will feel to be unique, and see only once city, and understand that it
was impossible to write that unique city name in his diary in Helsinki.

>
> ​​>>​Bruno, you're always talking about definitions but this is one of those
> rare occasions where one is desperately needed, so if you want me to answer
> that question you must first give me a PRECISE definition of exactly what you
> mean by "the Helsinki man". ​
>
> ​>​It is guy who will survive in both Moscow and Washington,
>
> ​If that's what "the guy" means then obviously "the guy" will see 2 cities.

At no moment at all this could occur for all persons concerned, unless you add
telepathy or wires, which are not in this protocol.

> And before you start with the from the peepee not the poopoo stuff remember
> it was you who said "the guy" means "the guy who will survive in both Moscow
> and Washington", if that definition is too simple then give me a better one.

No, it is good, but you have to remember that the question is not about where
the guy will be, but where the guy will feel to be. In that case, it certain
that he will feel to be in only one city, as this is lived  by the two copies
in both cities.

> I don't have a fetish about definitions as you do but in this case I have a
> precise unambiguous logically self consistent definition of "The Helsinki
> Man". Do you?

Of course. This works for any guy undergoing that duplication experience in
Helsinki.

>
> ​>​and before I can say we agree about the H-guy I need to know exactly
> precisely what you mean by "the H-guy”.​
>
> ​>​The guy before the duplication.
>
>
> OK, now with this new definition of yours about what "the H-guy" means  "the
> H-guy" will never see any city *after* the duplication or see anything else
> for that matter because the defining characteristic of "the H-guy" that you
> just mentioned is existing *before* the duplication.

Not at all. By definition of Computationalism, the H-guy survives in the two
cities. You talk like if the H-guy died in the process, but we have both agreed
that he survives the duplication.

> Try again, maybe the third time is the charm. As for me I think a more useful
> definition is "the H-guy is anybody who remembers being in Helsinki before
> the duplication”.

Of course he remembers, that is why we can say he survived. But he still feel
unique in each city after the duplication, and understand that in Helsinki, he
would not have been able to predict which one.

Bruno

>
> ​John K Clark​
>
>>
>
>
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