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Topic: all of math is just addition and multiplication
Replies: 36   Last Post: Jun 17, 2013 6:04 PM

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kirby urner

Posts: 1,638
Registered: 11/29/05
Re: all of math is just addition and multiplication
Posted: Jun 6, 2013 2:23 PM
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On Thu, Jun 6, 2013 at 10:02 AM, Joe Niederberger
<niederberger@comcast.net>wrote:

<< SNIP >>


> The only question that remains difficult, is whether humans do things
> mathematical things with their minds that are non-computational in fact or
> principle. Kirby has mentioned more than once a formula for pi from
> Ramanujan that he says is evidence that the mind can do non-computable
> tings. Others have pointed to Gödelian Incompleteness as serving the same
> purpose. Roger Penrose wrote on book on it, "The Emporer's New Mind".
>
> So, those are a couple of people "taking issue". I find neither of them
> conclusive. Do you have any issues to raise?
>
>
> Cheers,
> Joe N
>


Having heard Penrose (Sir Roger) live on a few occasions, I will add a
little more here on what I take to be his claim: that humans are sometimes
a source of intelligence which no computational theory or practice
currently has a way to explain much less duplicate.

However it's important to add that a formal proof may later be constructed
that substantiates a human contribution i.e. proves that it's true. In the
case of Ramanujan's formulas, I think there may be proofs here and there
for some, whereas others have only been empirically verified.

However, be that as it may, he did not arrive at these formulas by a
proving process. This was considered one of his weaknesses, which is
another way of saying a cause of frustration to other mathematicians who
were unable to gain any insight into how he achieved his results.

I believe this is quite a common phenomenon in mathematics: that a flash
of insight puts a dot on the map, which is then incorporated only later (if
ever) into a structure of proved theorems.

In terms of just practice, I don't find the claim controversial i.e. humans
routinely do things which no algorithm can do given our current state of
computational ability.

In terms of theory, the claim that humans *in principle* have access to a
Platonic Realm that machines never will: that's harder to argue, but is
what I take to be Penrose's position, push come to shove.

Kirby


Date Subject Author
6/3/13
Read all of math is just addition and multiplication
Donald Sauter
6/4/13
Read Re: all of math is just addition and multiplication
Dave L. Renfro
6/5/13
Read Re: all of math is just addition and multiplication
Robert Hansen
6/4/13
Read Re: all of math is just addition and multiplication
kirby urner
6/5/13
Read Re: all of math is just addition and multiplication
Joe Niederberger
6/5/13
Read Re: all of math is just addition and multiplication
Joe Niederberger
6/6/13
Read Re: all of math is just addition and multiplication
Michael de Villiers
6/6/13
Read Re: all of math is just addition and multiplication
Joe Niederberger
6/6/13
Read Re: all of math is just addition and multiplication
kirby urner
6/7/13
Read Re: all of math is just addition and multiplication
Joe Niederberger
6/7/13
Read Re: all of math is just addition and multiplication
Joe Niederberger
6/7/13
Read Re: all of math is just addition and multiplication
Louis Talman
6/8/13
Read Re: all of math is just addition and multiplication
Robert Hansen
6/7/13
Read Re: all of math is just addition and multiplication
Joe Niederberger
6/8/13
Read Re: all of math is just addition and multiplication
Joe Niederberger
6/8/13
Read Re: all of math is just addition and multiplication
GS Chandy
6/8/13
Read Re: all of math is just addition and multiplication
GS Chandy
6/8/13
Read Re: all of math is just addition and multiplication
GS Chandy
6/8/13
Read Re: all of math is just addition and multiplication
Joe Niederberger
6/8/13
Read Re: all of math is just addition and multiplication
GS Chandy
6/9/13
Read Re: all of math is just addition and multiplication
Joe Niederberger
6/14/13
Read Re: all of math is just addition and multiplication
kirby urner
6/9/13
Read Re: all of math is just addition and multiplication
Joe Niederberger
6/10/13
Read Re: all of math is just addition and multiplication
GS Chandy
6/10/13
Read Re: all of math is just addition and multiplication
Joe Niederberger
6/11/13
Read Re: all of math is just addition and multiplication
GS Chandy
6/11/13
Read Re: all of math is just addition and multiplication
Joe Niederberger
6/11/13
Read Re: all of math is just addition and multiplication
Robert Hansen
6/12/13
Read Re: all of math is just addition and multiplication
GS Chandy
6/12/13
Read Re: all of math is just addition and multiplication
GS Chandy
6/12/13
Read Re: all of math is just addition and multiplication
Robert Hansen
6/12/13
Read Re: all of math is just addition and multiplication
Joe Niederberger
6/13/13
Read Re: all of math is just addition and multiplication
GS Chandy
6/13/13
Read Re: all of math is just addition and multiplication
Joe Niederberger
6/13/13
Read Re: all of math is just addition and multiplication
GS Chandy
6/17/13
Read Re: all of math is just addition and multiplication
Donald Sauter
6/17/13
Read Re: all of math is just addition and multiplication
Donald Sauter

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