Actor (Terrence Howard) Claims His New Theory of Everything Improves Physics

[tadmjones]

Stephen 

Is it that the question about the Babylonians is based on archaeology only, or is there an argument based on math theory, so to speak , that given the rigor of their computational output suggests a lack of the concept of ‘infinite numbers’?

It reminded me of Wolfram’s computational irreducibility. That idea would imply that prior to electronic computation making the calculations humanly feasible , no one can know prior to the completion of the operation the ‘places’ or ‘amount of digits’ of the ‘answer’. But it may be I am misapplying the concept to this particular operation. The thought struck me as interesting anyway. 

[Boydstun]

@tadmjones – (i) Every irrational in its decimal representation has an infinite train of digits, which does not terminate nor have repeating patterns. (ii) Euclid, for early example, proved that the square root of 2 is irrational. I’m pretty sure that (i) is proven classically and does not require reliance on electronic computing machines. 

I think the deal with the Babylonians is simply that, unlike Euclid, the clay tablets have not revealed whether they understood irrational numbers and that a decimal representation of them would have digits going on endlessly. I’ll try to check further on that tomorrow.

[Boydstun]

8 hours ago, Boydstun said:

@tadmjones . . .

I think the deal with the Babylonians is simply that, unlike Euclid, the clay tablets have not revealed whether they understood irrational numbers and that a decimal representation of them would have digits going on endlessly. I’ll try to check further on that tomorrow.

Although they had an algorithm yielding a good approximation, there is as yet no evidence they knew it would not yield exactitude in a finite number of iterations, according to this report.

[StrictlyLogical]

12 hours ago, Boydstun said:

@tadmjones – (i) Every irrational in its decimal representation has an infinite train of digits, which does not terminate nor have repeating patterns. (ii) Euclid, for early example, proved that the square root of 2 is irrational. I’m pretty sure that (i) is proven classically and does not require reliance on electronic computing machines. 

I think the deal with the Babylonians is simply that, unlike Euclid, the clay tablets have not revealed whether they understood irrational numbers and that a decimal representation of them would have digits going on endlessly. I’ll try to check further on that tomorrow.

@Boydstun

I was trying to think of a thought experiment to concretize the “incommensurate” nature of various mathematical quantities as demonstrated by irrational numbers, to better help visualize this sort of thing.  I have a concretized example… but as to whether it is intuitive… is another question.

So far I have this.

Imagine a mathematical circle with a diameter of 1, rolling inside a second mathematical circle with a circumference of 10.  Now imagine a moment when the smaller circle is at the very bottom of the larger circle, touching/intersecting at a single point at the bottom of both circles.  Imagine “marking” those points on the smaller circle’s circumference and the larger circle’s circumference (even though the larger circle never moves).

Now imagine rolling the smaller circle within the larger one and waiting to see when that smaller circle’s dot coincides again with the larger circle’s dot…

Once you have proven to yourself the answer… ask what this might say about the old (Roman?) idea of infinite loops of time  repeating giving rise to every possibility including living again…

[Boydstun]

SL, I am curious if the Roman idea of infinite loops of time explicitly stated that such gives rise to the possibility of living again. Do they? Much later the possibility of living again being within possibilities in an infinite time was stressed by Nietzsche in the 1880’s. He called that the eternal return. He claimed it solved a hefty philosophical conundrum or two, but the solving power was only by contemplation of his construct of eternal return said to be quite a mystery. I put it in the can where metaphysical crystals should be sent along out the house.

The idea of the eternal return occurred to me on my own when I was a youth, having never heard of the idea from anyone before. It seemed so simple: if your life did not occur again in a billion years, then consider the possibilities becoming actuals in the 100 billion years beyond that first billion, and so forth. Because there is assumed to be infinite future time, there is time for the infinity of possibilities to become actual. “Every possibility has its day” one might say, and the possibility of same life again and again . . . has its days of actuality. 

That is all false. For truth on the matter, in moving fiction, I recommend the novel One Hundred Years of Solitude, read entirely to its end.

The infinity of time would be only the lowest sort of infinity and that is trite in comparison to the larger sort of infinite possibilities attaching to the unfolding of five minutes of the earth today. The supposed infinity of time does not show that the possibility I shall again live and be typing this note to you will be fulfilled. Indeed, from the nature of the different orders of infinity, we know this will never happen again.

I was disappointed in Nietzsche the atheist to be embracing and putting about the idea of the eternal return of the same in the years of his mature, original philosophy. Listening to his own common sense should have prevailed against such a view of the world being correct, even if he was not apprised of the new explorations of infinity by the mathematicians of his day. On the personal psychology side of him, it seemed to me that he, an atheist, had failed to fully own up to the very plain fact that at the end of his life he personally would cease to exist through all future time of the things continuing to exist (just as in the infinity of time before his mind was launched. Now there is something of a circle).  

[StrictlyLogical]

1 hour ago, Boydstun said:

SL, I am curious if the Roman idea of infinite loops of time explicitly stated that such gives rise to the possibility of living again. Do they? Much later the possibility of living again being within possibilities in an infinite time was stressed by Nietzsche in the 1880’s. He called that the eternal return. He claimed it solved a hefty philosophical conundrum or two, but the solving power was only by contemplation of his construct of eternal return said to be quite a mystery. I put it in the can where metaphysical crystals should be sent along out the house.

The idea of the eternal return occurred to me on my own when I was a youth, having never heard of the idea from anyone before. It seemed so simple: if your life did not occur again in a billion years, then consider the possibilities becoming actuals in the 100 billion years beyond that first billion, and so forth. Because there is assumed to be infinite future time, there is time for the infinity of possibilities to become actual. “Every possibility has its day” one might say, and the possibility of same life again and again . . . has its days of actuality. 

That is all false. For truth on the matter, in moving fiction, I recommend the novel One Hundred Years of Solitude, read entirely to its end.

The infinity of time would be only the lowest sort of infinity and that is trite in comparison to the larger sort of infinite possibilities attaching to the unfolding of five minutes of the earth today. The supposed infinity of time does not show that the possibility I shall again live and be typing this note to you will be fulfilled. Indeed, from the nature of the different orders of infinity, we know this will never happen again.

I was disappointed in Nietzsche the atheist to be embracing and putting about the idea of the eternal return of the same in the years of his mature, original philosophy. Listening to his own common sense should have prevailed against such a view of the world being correct, even if he was not apprised of the new explorations of infinity by the mathematicians of his day. On the personal psychology side of him, it seemed to me that he, an atheist, had failed to fully own up to the very plain fact that at the end of his life he personally would cease to exist through all future time of the things continuing to exist (just as in the infinity of time before his mind was launched. Now there is something of a circle).  

I could be completely wrong about the origin of that idea… and how it got into my head… for some reason I associate it with some thinker who I think was Roman.

 

As for the circle demonstration, it strikes me as mysterious that the circle could, not only be progressed forward infinitely, it could also be reversed infinitely… and all across the number of rotations the coincidence would only occur at one point.  

Of course one could write down a function, distance between the points as a function of the “number” of circumferential surfaces the inner circle has engaged contact with the outer circle, while rolling, and it would have precisely one zero… but it’s still somewhat counterintuitive… 

I had set out to find an example where the incommensurate-ness seemed to make sense intuitively, but it seems that I have achieved the opposite.