Re: A curious puzzle - teaching a computer to understand infinity

2015-08-13 Thread Bruno Marchal
On 13 Aug 2015, at 14:33, Pierz wrote: On Saturday, July 18, 2015 at 4:35:06 AM UTC+10, Bruno Marchal wrote: On 17 Jul 2015, at 06:21, Pierz wrote: On Thursday, July 16, 2015 at 7:07:50 PM UTC+10, Bruno Marchal wrote: On 15 Jul 2015, at 20:54, John Mikes wrote: I think JC resoinded to

Re: A curious puzzle - teaching a computer to understand infinity

2015-08-13 Thread Pierz
On Saturday, July 18, 2015 at 4:35:06 AM UTC+10, Bruno Marchal wrote: > > > On 17 Jul 2015, at 06:21, Pierz wrote: > > > > On Thursday, July 16, 2015 at 7:07:50 PM UTC+10, Bruno Marchal wrote: >> >> >> On 15 Jul 2015, at 20:54, John Mikes wrote: >> >> I think JC resoinded to Brent: >> >> *"​I don

Re: A curious puzzle - teaching a computer to understand infinity

2015-07-20 Thread John Clark
On Mon, Jul 20, 2015 at 3:10 AM, Bruno Marchal wrote: ​> ​ > The quantization of space time has no need to extend to the mathematical > space used to evaluate the amplitude of probability. > ​That probability is obtained by taking the square of the absolute value of Schrodinger's Wave Function,

Re: A curious puzzle - teaching a computer to understand infinity

2015-07-20 Thread Bruno Marchal
On 20 Jul 2015, at 00:38, John Clark wrote: On Sun, Jul 19, 2015 at 1:17 PM, Bruno Marchal wrote: ​>>​But the truth is if space-time IS quantized then the​ Real Numbers are a mathematical fiction​. ​> ​That does not follow. You might still need the real in the amplitudes. The irratio

Re: A curious puzzle - teaching a computer to understand infinity

2015-07-19 Thread John Clark
On Sun, Jul 19, 2015 at 1:17 PM, Bruno Marchal wrote: ​>>​ >> But the truth is if space-time* IS* quantized then the >> ​ >> Real >> Numbers are a mathematical fiction >> ​. >> > > ​> ​ > That does not follow. You might still need the real in the amplitudes. The > irrational sqrt(2) will not go

Re: A curious puzzle - teaching a computer to understand infinity

2015-07-19 Thread Bruno Marchal
On 18 Jul 2015, at 23:33, John Clark wrote: ​Some bozo by the name of John K Clark wrote:​ ​"​it all depends on if space-time is quantized or ​not; if it's not then the Real Numbers are a mathematical fiction​" But the truth is if space-time IS quantized then the Real Numbers are a mathe

Re: A curious puzzle - teaching a computer to understand infinity

2015-07-18 Thread John Clark
​Some bozo by the name of John K Clark wrote:​ ​"​ it all depends on if space-time is quantized or ​not; if it's not then the Real Numbers are a mathematical fiction ​" But the truth is if space-time* IS* quantized then the Real Numbers are a mathematical fiction ​. John K Clark​ ​ -- You re

Re: A curious puzzle - teaching a computer to understand infinity

2015-07-18 Thread John Clark
On Fri, Jul 17, 2015 at 12:42 AM, Pierz wrote: > ​> ​ > Don't you think there's a difference between "not thinking" and "thinking > of nothing"? > ​No, I don't think there is a difference and you gave the reason why thinking of nothing is equivalent to not thinking when you said: ​ ​"​ "Nothing

Re: A curious puzzle - teaching a computer to understand infinity

2015-07-17 Thread Bruno Marchal
On 17 Jul 2015, at 06:21, Pierz wrote: On Thursday, July 16, 2015 at 7:07:50 PM UTC+10, Bruno Marchal wrote: On 15 Jul 2015, at 20:54, John Mikes wrote: I think JC resoinded to Brent: "​I don't have a visceral grasp of the true immensity of infinity. Do you?" ​ I wonder if 'immensity'

Re: A curious puzzle - teaching a computer to understand infinity

2015-07-16 Thread Pierz
On Friday, July 17, 2015 at 3:32:06 AM UTC+10, John Clark wrote: > > On Wed, 2:54 PM, John Mikes > wrote: > > ​> ​ >> I think JC resoinded to Brent: >> *"​I don't have a visceral grasp of the true immensity of infinity. Do >> you?" ​*​ >> I wonder if 'immensity' means - B I G - ? in which case

Re: A curious puzzle - teaching a computer to understand infinity

2015-07-16 Thread Pierz
On Thursday, July 16, 2015 at 7:07:50 PM UTC+10, Bruno Marchal wrote: > > > On 15 Jul 2015, at 20:54, John Mikes wrote: > > I think JC resoinded to Brent: > > *"​I don't have a visceral grasp of the true immensity of infinity. Do > you?" ​* > > I wonder if 'immensity' means - B I G - ? in which

Re: A curious puzzle - teaching a computer to understand infinity

2015-07-16 Thread John Clark
On Wed, 2:54 PM, John Mikes wrote: ​> ​ > I think JC resoinded to Brent: > *"​I don't have a visceral grasp of the true immensity of infinity. Do > you?" ​*​ > I wonder if 'immensity' means - B I G - ? in which case I cannot refrain > from thinking about the* infinite SMALL* as well. > ​It's t

Re: A curious puzzle - teaching a computer to understand infinity

2015-07-16 Thread Bruno Marchal
On 15 Jul 2015, at 20:54, John Mikes wrote: I think JC resoinded to Brent: "​I don't have a visceral grasp of the true immensity of infinity. Do you?" ​ I wonder if 'immensity' means - B I G - ? in which case I cannot refrain from thinking about the infinite SMALL as well. The infinit

Re: A curious puzzle - teaching a computer to understand infinity

2015-07-15 Thread John Mikes
I think JC resoinded to Brent: *"​I don't have a visceral grasp of the true immensity of infinity. Do you?" ​* I wonder if 'immensity' means - B I G - ? in which case I cannot refrain from thinking about the* infinite SMALL* as well. Just like I may think for 'eternal' as being momentary and tim

Re: A curious puzzle - teaching a computer to understand infinity

2015-07-15 Thread Bruno Marchal
On 14 Jul 2015, at 20:25, meeke...@verizon.net wrote: On 07/14/15, John Clark wrote: On Tuesday, July 14, 2015 , Brent wrote: ​> ​Just ask yourself how you grasp the notion of infinity. ​I don't have a visceral grasp of the true immensity of infinity. Do you? ​ No, I don't, whi

Re: Re: A curious puzzle - teaching a computer to understand infinity

2015-07-14 Thread meekerdb
On 07/14/15, John Clark wrote: On Tuesday, July 14, 2015 , Brent wrote: ​> ​Just ask yourself how you grasp the notion of infinity. ​I don't have a visceral grasp of the true immensity of infinity. Do you? ​ No, I don't, which was more or less my point. What we think of as our "

Re: A curious puzzle - teaching a computer to understand infinity

2015-07-14 Thread John Clark
On Tuesday, July 14, 2015 , Brent wrote: > > ​> ​ > Just ask yourself how you grasp the notion of infinity. ​I don't have a visceral grasp of the true immensity of infinity. Do you? ​ On Mon, Jul 13, 2015 at 9:26 PM, Pierz wrote: ​ ​> ​ > Sure. It's a concept even very young children ca

Re: A curious puzzle - teaching a computer to understand infinity

2015-07-14 Thread Bruno Marchal
On 14 Jul 2015, at 03:26, Pierz wrote: On Tuesday, July 14, 2015 at 2:08:35 AM UTC+10, Brent wrote: Just ask yourself how you grasp the notion of infinity. It's not by dividing by zero. It's by using "and then..." Sure. It's a concept even very young children can understand - probably

Re: A curious puzzle - teaching a computer to understand infinity

2015-07-13 Thread John Clark
On Mon, Jul 13, 2015 Pierz wrote: ​> ​ > Here's something that bothers me when I try to think of the brain too much > as a computer. How would I teach a computer the notion of infinity? > ​A computer already knows about some integers, and it knows how to find the successor to some integers; it'

Re: A curious puzzle - teaching a computer to understand infinity

2015-07-13 Thread Pierz
On Tuesday, July 14, 2015 at 2:08:35 AM UTC+10, Brent wrote: > > Just ask yourself how you grasp the notion of infinity. It's not by > dividing by zero. It's by using "and then..." Sure. It's a concept even very young children can understand - probably almost as easily as zero. "There are

Re: A curious puzzle - teaching a computer to understand infinity

2015-07-13 Thread Bruno Marchal
On 13 Jul 2015, at 18:08, meeke...@verizon.net wrote: Just ask yourself how you grasp the notion of infinity. It's not by dividing by zero. It's by using "and then..." There's no obstacle in principle to having a computer reason about the consequences of having an axiom of succession.

Re: A curious puzzle - teaching a computer to understand infinity

2015-07-13 Thread meekerdb
Just ask yourself how you grasp the notion of infinity. It's not by dividing by zero. It's by using "and then..." There's no obstacle in principle to having a computer reason about the consequences of having an axiom of succession. It doesn't need to have an infinite memory capacity to do s

Re: A curious puzzle - teaching a computer to understand infinity

2015-07-13 Thread Bruno Marchal
On 13 Jul 2015, at 15:29, Pierz wrote: Here's something that bothers me when I try to think of the brain too much as a computer. How would I teach a computer the notion of infinity? That's an excellent question. Logic put some light on this, by showing that the notion of "finite" (and t

A curious puzzle - teaching a computer to understand infinity

2015-07-13 Thread Pierz
Here's something that bothers me when I try to think of the brain too much as a computer. How would I teach a computer the notion of infinity? In simple terms, how can I represent infinity in a computer program? All a computer knows about infinity is 'stack overflow' (or simply integer overflow