On Sun, Apr 23, 2017 at 7:30 AM, Bruno Marchal <[email protected]> wrote:

​
>> ​>> ​
>> Suppose just for ​
>> ​t​
>> he sake ​of argument that non-physical computations did not exist, how
>> would our physical world be different?
>
>
> ​> ​
> It would like if the number 2 does not exist.
>

​No it would not because if non-physical computations did not exist then
one physical rock and another physical rock would STILL have the same
effect on the physical universe as 2 physical rocks do..​



> ​> ​
> Computation and "universal machine" are non physical notions,
>

​Notions require intelligence and
​intelligence requires matter that obeys the laws of physics.​


> ​> ​
> discovered independently by mathematicians
>

​And ​
mathematicians
​,​
​ just like everybody else, are made of matter that obeys the laws of
physics.​

​> t​
> he fact that the physical reality can implement computations might suggest
> already that the physical reality might emerge from computations.
>

If the non-physical number manipulation 1+1=2 exists then the non-physical
number manipulation 1+1=3 exists too. Physics can tell one from
​of ​
manipulation from the other because in the physical world one rock and
another rock will never behave like 3 rocks. How can pure mathematics do
the same thing? You can talk about Robinson arithmetic all you want but
there are a infinite number of ways numbers can be manipulated in pure
mathematics and Robinson arithmetic is just one of those ways. But there is
​one and ​
only one way numbers can be manipulated that is consistent with the
physical world, and we call that one way of manipulation a
​"​
calculation
​"​
.

 ​John K Clark​

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