[extropy-chat] mathematical induction

[Mike Dougherty]

On 4/24/07, Damien Broderick <thespike at satx.rr.com> wrote:
> At 09:35 AM 4/24/2007 -0400, Mike Dougherty wrote:
> What is the relevance of this "mathematical induction" of which you
> speak? Sure you're not getting it confused with "empirical
> induction," when actually (as far as I know) it's a form of deduction
> applicable only to a restricted formal mathematical realm?

Hopefully for the sake of the discrete math final I have next week I
am clear enough on methematical induction.  However, I will admit that
what applies to numbers does not apply to words or concepts because
the ambiguity precludes the rigid formalism of eg. Real Numbers.  In
that vein, the reference to induction was the nearest concept to what
I was thinking and that I failed to express myself clearly enough.

> "Inductive hypothesis"? Would that be like saying: "String theory
> uses 11 dimensions, so there must be 12, and if there are 12 there
> must be 13... there must be an infinite number of actual physical
> dimensions"? This looks like another category mistake to me.

I was thinking more of the idea:  If we agree to the exponential curve
leading to the Singularity, (i'll entertain either side of that
argument, but whatever)  then given two starting positions with one
slightly farther up that curve - how can the lower level surpass the
higher level?  In the measure required to reach the higher level
civilization (for example) the civilization that started at that point
has risen exponentially farther away from the lower.  Perhaps this is
in the identitity class with Zeno's paradox.  (or for an interesting
diversion off Zeno paradox, check out Thompson's Lamp)  Anyway, it
might still be a category mistake.  I have no strong attachment to
defend this idea.