On 6/3/2020 3:26 AM, Lawrence Crowell wrote:
On Tuesday, June 2, 2020 at 12:34:37 PM UTC-5, Brent wrote:
On 6/2/2020 2:49 AM, Bruno Marchal wrote:
>> On 1 Jun 2020, at 22:43, 'Brent Meeker' via Everything List
<[email protected] <javascript:>> wrote:
>>
>>
>>
>> On 6/1/2020 2:08 AM, Bruno Marchal wrote:
>>> Brent suggest that we might recover completeness by
restricting N to a finite domain. That is correct, because all
finite function are computable, but then, we have incompleteness
directly with respect to the computable functions, even limited on
finite but arbitrary domain. In fact, that moves makes the
computer simply vanishing, and it makes Mechanism not even
definable or expressible.
>> That's going to come as a big shock to IBM stockholders.
>
> Why? On the contrary. IBM bets on universal machine
No, they bet only on finite machines, and they will be very
surprised to
hear that they have vanished.
Brent
For the most part computers are meant to run various algorithms that
solve some restricted set of problems, say business applications. We
use them largely as tools.
Mathematics is largely a tool. My pure mathematics friends over on
math-fun seem to have most of their fun on Mathematica.
Brent
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