[ExI] The "Unreasonable" Effectiveness of Mathematics in the Natural Sciences

[Jef Allbright]

On Fri, Sep 26, 2008 at 9:36 AM, Damien Broderick <thespike at satx.rr.com> wrote:
> At 07:17 AM 9/26/2008 -0700, Jef wrote:
>
>> > How much of the universe would have to go in order to eliminate 17?
>> > For example, would there be a 17 if there were only 16 electrons and
>> > nothing else? One electron? Empty space?
>>
>> ...The question presumes the ontological status of "17."  A valid
>> question would be one that can be modeled as a system providing a
>> defined output.  Otherwise, what can it ***mean***?
>
> I'm inclined to think that "17" is the name of an operation, not of a thing.
> That interpretation might map onto Jef's and, I suspect, Lee's. This view
> has implications for incalculably large numbers and infinities, no doubt,
> but only if they really are incalculable. (But I am not a mathematician.)

Yes, when the discussion tends toward scenarios outside our common
experience, then our thinking must become more rigorous.  Ultimately,
an object is  never known in terms of "what it is", but always only in
terms of its observed interactions.

It may helpful here to consider why people struggle with concepts such
as 0.999... == 1.0.

- Jef