[ExI] Sunday Creationist
John Clark
johnkclark at gmail.com
Wed Jul 24 00:04:41 UTC 2019
On Tue, Jul 23, 2019 at 6:55 PM Will Steinberg <steinberg.will at gmail.com>
wrote:
>> The atoms in a brain can perform calculations because they are organized
>> in the only way that can, the way Alan Turing described. The atoms in Earth
>> are not.
>>
>
> *>There are MANY atoms in the brain that do not perform calculations. *
>
No atom in the brain by itself can perform a calculation but groups of them
can if they're organized in the right way, and the right way always comes
down to Turing's way.
> * > Plus, what about the noncomputable? *
>
Yes some things can't be calculated. For example all Busy Beaver Numbers
are well defined and finite, but we only know the first 4. They are:
BB(1) =1
BB(2) =6
BB(3) =21
BB(4) =107
But those are the only values we've been able to calculate with certainty,
the problem is the Busy Beaver function grows faster than any computable
function. Some suspect that BB(5) is 47,176,870 but are far from certain of
that, and BB(6) is at least 7.4*10^36534 and BB(7) is at least
10^10^10^10^10^7 but could be much larger. Big as they are all Busy
Beaver numbers
are finite but after a certain point they are not computable and nobody
even knows exactly where that point is. It has been proven that BB(1919) is
not computable even in theory, not even if you had infinite resources. But
what is the smallest non-computable Busy Beaver integer? Nobody knows, but
I wouldn't be surprised if it were BB(5). So there are some things that a
Turing Machine can not calculate, but nothing else can either, in point of
fact nothing but a Turing Machine can calculate anything at all.
John K Clark
>
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.extropy.org/pipermail/extropy-chat/attachments/20190723/da8bb2e6/attachment-0001.htm>
More information about the extropy-chat
mailing list