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Re: Cool Math Lessons
Posted:
Mar 1, 2012 1:39 PM
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On Thu, Mar 1, 2012 at 9:31 AM, Joe Niederberger
<niederberger@comcast.net> wrote:
>>What I did give as an example, consistently, and Joe you're welcome to
> quote me on this, are Ramanujan's mysterious equations, the one for
> 1/pi in particular, that I've math-blogged here:
>
>>http://worldgame.blogspot.com/2012/01/testing-math-ml.html
>
> And I countered with what in some regards an even more remarkable formulas for pi discovered in 1995 with the aid of computers and an algorithm (PSLQ):
> http://en.wikipedia.org/wiki/Bailey%E2%80%93Borwein%E2%80%93Plouffe_formula
>
> The difference as I see it is we know what processes led to the BBP discovery, but in Ramanujan's case we don't. That simply means we don't know - it doesn't imply that they must be in some sense "non-computable".
>
Using the word "process" is empty air here. We insist Ramanujan's
results be a result of "a process" as a grammatical truism.
He couldn't describe the process either, to the satisfaction those who
would generate similar expressions to his.
>
>
>>The image of a plodding machine reading punch card instructions and
> inevitably working to a solution, like a train moving along a track,
> is tempting to apply in all cases, I agree.
>
> You are agreeing with yourself -- not surprising. Its not my image at all.
>
It's an image endemic in the memes I'd say. We think of "thinking" as
"something mechanical" and picture all kinds of stuff to ourselves.
>
>>However we should distinguish appealing metaphors from known scientific principles. We actually get by fine without knowing what the limits of computation might be. By Occam's Razor, less knowing is better in this case, ...
>
> We certainly part company here - that there could even be such a thing a thing as a "non-computable function" was only discovered with the last 80 years or so. That the limiting notion of "computable function" could be so precisely rendered is a great and surprising achievement. The notion that we should perhaps stop such "meta-mathematical" investigation surrounding the admittedly broader scope of general information processes is not going to carry the day. The only thing I agree with you on is the fact that not all is known in this field. That makes it exciting, but not if the attitude is "from henceforth, any more discoveries are bad and the present state of ignorance is better."
>
>
> Joe N
You are singularly unable to represent my point of view accurately.
Discovery and new information is to be welcomed. In the meantime, I
make no assumption that my problem solving abilities are always a
result of some "process" -- I recognize the emptiness of such a claim
and would prefer clear thinking to such nonsense.
In my view, you suffer from the common misconception that to be
"scientific" means "to be able to explain everything".
Over-explainers over-play their hand and contribute little to the
conversation in my experience.
Kirby
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