>> Scientific facts have been found to be incorrect. There are far fewer
>> examples of mathematical truths which have needed to be adjusted. And
>> there are vanishingly few examples of widely accepted *proofs* that turn
>> out to be wrong - it tends to be things lots of mathematicians "think"
>> are true that eventually turn out to be disproven.
> 
> Exactly my point, but with a narrower focus.  Things lots of *people* 
> "think" are true sometimes/frequently/often turn out to be disproven.

Show me one single mathematical result which was *proven* to be true, 
and verified independently by a large number of mathematicians, and 
subsequently turned out to actually be false.

I can think of any number of results in *science* that were widely 
believed to be true but turned out not to be. But mathematics is different.

>> You're missing my point: It doesn't *matter* that we can't know the
>> future. Simple logical deduction demonstrates that ANY machine we can
>> construct will have the same problem, REGARDLESS of how it works.
> 
> It's simple logical deduction that unless I have a screwdriver, I can't 
> drive a screw.
> 
> Until you realise that the screw has a hex head and an allen wrench will 
> do the job just as nicely.
> 
> *Sometimes* all you need is a new tool.  Sometimes the new tool hasn't 
> been invented yet.

And I suppose next you'll be telling me that some day, some future 
technology might enable us to find a sequence of chess moves whereby a 
bishop can get from a black square to a white square, despite it being 
trivially easy to mathematically prove the impossibility of this...

> I think it's a mistake to say "we know all there is to ever know about 
> 'x'".  There have been many points in history where humankind has made 
> such declarations about many things - including mathematics - and it has 
> turned out that we'd only scratched the surface.  It's the height of 
> hubris to assume we can't learn anything new.

I'm not claiming that nothing new can be learned - I am saying that, at 
least in mathematics, learning new things doesn't invalidate what we 
already know.

>> Making transistors out of paper is a question of physics - a branch of
>> science. Infinite compression ratios is a question of mathematics.
>> Therein lies the critical difference.
> 
> And yet you agreed with another post in this thread that said that 
> something was possible.  Look at the refocusing capabilities of some of 
> the tools for that to reconstruct detail in blurred images.  Blurring is 
> lossy compression, yet being able to recover that data isn't impossible; 
> that's been proven.

Hey, guess what? Blurring isn't compression. It might *look* like it is, 
but it isn't.

>> If your point is that science is sometimes wrong, or at least needs to
>> be amended, then I agree. If your point is that widely held beliefs are
>> sometimes wrong, then I also agree. If your point is that every proven
>> mathematical result could actually be wrong, then I completely disagree.
> 
> I believe that's just a limitation of our understanding of things as they 
> are now.

Sure. And no doubt some day we'll discover that 2+2 isn't actually 4. I 
won't hold by breath for that though. :-P

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

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