On 27.03.2011 23:18, Patricia Shanahan wrote:

> On 3/27/2011 2:03 PM, Screamin Lord Byron wrote:

>> On 27.03.2011 22:30, Patricia Shanahan wrote:

>>> On 3/27/2011 1:19 PM, Screamin Lord Byron wrote:

>>>> On 27.03.2011 21:18, Patricia Shanahan wrote:

>>>>> On 3/27/2011 9:10 AM, Screamin Lord Byron wrote:

>>>>>> On 26.03.2011 21:56, Dirk Bruere at NeoPax wrote:

>>>>>>> The Human brain is also subject to the Turing

>>>>>>> limitation (as far as is known)

>>>>>>

>>>>>> If what you're saying is true, then how can the human brain prove

>>>>>> things

>>>>>> like, say, Fermat's last theorem?

>>>>>

>>>>> How would you deduce inability to prove Fermat's last theorem from the

>>>>> Turing limitation?

>>>>

>>>> There can not be an algorithmic proof of Fermat's last theorem because

>>>> of the halting problem....

>>>

>>> Why does the halting problem imply anything at all about the existence

>>> or otherwise of a proof for Fermat's last theorem?

>>> Can you give a proof, or point to one I can read?

>>

>> Yes. Sir Roger Penrose's book "Emperor's New Mind". I have a copy which

>> is translated to my language, so I can't give you exact page numbers

>> where he talks about that specifically (should be within first 100

>> pages), but the book is absolutely worth a read in its entirety.

>>

>

> I don't have a copy, so that is not currently one I can read. Perhaps

> you can restate the proof in your own words, or give an on-line reference?
In fact I have. I didn't have much hope to find it online, but I got

lucky I guess.

http://bit.ly/gCPoot
Long link:

<http://books.google.hr/books?id=oI0grArWHUMC&pg=PA75&lpg=PA75&dq=emperor' s+new+mind+hilbert+problem&source=bl&ots=04Ljj-YNVy&sig=GNJwD-YkfZ1R5u2oFHD2vjrEqns&hl=hr&ei=T6yPTYnyHIrysgbi7Y2 NCg&sa=X&oi=book_result&ct=result&resnum=1&ved=0CB gQ6AEwAA#v=onepage&q&f=false>