Comments on: Digital Philosophy – I: The Real is Unreal

By: Shubhendu Trivedi

Shubhendu Trivedi — Sat, 21 Jan 2012 18:03:15 +0000

Nice article! I had been planning to write on something similar but from an inference perspective.

I only wanted to point out one thing in your articles about Digital Philosophy and Kolmogorov Complexity. It might just be a minor point.
But Ray Solomonoff’s contributions to Kolmogorov Complexity are as fundamental as are Kolmogorov’s and Chaitin’s. He approached the idea from Inductive Inference, Chaitin and Kolmogorv approached it from randomness. Infact Solomonoff wrote the first set of papers on the area.

By: DavidC

DavidC — Sun, 07 Aug 2011 02:37:28 +0000

“… so why is our subjective perception capable of a continuity illusion?”

Is there really a case that we subjectively perceive a continuum (complete, hence uncountable, hence almost all un-nameable, etc.) of space rather than just something dense (i.e., not discrete)?

How would you even know the difference?

Since my training is in mathematics, I think I tend to consider the continuum (like most mathematics?) a useful and pretty fiction. Completeness is nice for lots of theorems. (As you note, there’s also a certain ugliness to it, but that’s fine.)

By: What are good laymen physics books to read after A Brief History of Time? - Quora

Sat, 11 Dec 2010 17:24:53 +0000

[...] alternative approach to physics. Here's an incomplete 3-part series I started to write.http://www.ribbonfarm.com/2007/0…http://www.ribbonfarm.com/2007/0…The unwritten part iii would have been about Seth Lloyd's [...]

By: jld

jld — Tue, 27 Jul 2010 05:04:17 +0000

Stumbling upon this thread while checking some material about a more recent post I want to add a very relevant reference against the appropriateness of the continuum idea (as we know it, i.e. the real line) for describing reality: Does matter differ from vacuum? by Christoph Schiller. But is not digital either, the real coordinates just "melt away" below some very small scale, hé, hé...

By: Venkat

Venkat — Sat, 18 Aug 2007 12:51:10 +0000

I think you can't argue for the line of marbles becoming a line. It would become a point. If r is the radius, both 2r and 2nr converge to 0 in the limit. But yes, you can map the integers to an arbitrarily small part of the real line. Take for instance the sequence 1, 1/2, 1/3....1/n,..., which maps to (0,1]. I think the only good reason to keep the continuum around is this. Let's agree with the problems highlighted by thought experiments and conclude that physical reality has no continuum aspect. Let's go further and take as an article of faith what some physicists are claiming (namely that you can rewrite fundamental physics in discrete terms). So our sense that space is continuous (or time) is an illusion. But then, why is our fundamentally digital brain even capable of generating this particular illusion? Our retinal cells for a discrete (CCD like) array. Our visual cortex does a series of discrete image processing passes (segmentation, edge detection etc.), so why is our subjective perception capable of a continuity illusion? One way to resolve this is to say that subjective consciousness forms a continuous background to thought. Even though the Cartesian theater is a flawed way of looking at mental perception, the idea that all consciousness has a "background" is not implausible.

By: kapsio

kapsio — Fri, 17 Aug 2007 21:01:15 +0000

Here is one thought experiment with the concept of “adjecent” points.
Imagine an infinite collection of marbles, touching each other and arranged along a straight line. Now imagine the marbles shrinking…. shrinking and crowding together, such that the marbles always keep touching the adjecent ones. Let them shrink away to size zero. So what does this entire setup shrink to? A point? A line? I guess you could argue either ways.
THe starting point was really the set of integers. If it shrinks to a point, then is that what the set of integers is equivalent to? A point? If it shrinks to a line, how and when did the transcendentals creep in ? cause they cant really be any of the marbles themselves (marbles being countable). If you imagine that the marbles started shrinking at t=0 and shrunk to size 0 at t=1, then all the transcendentals appeared out of nowhere at exactly t=1.
Even though we may have all these problems with the continuum, why give up on it? why go digital? You could build models and play around…but the continuum will always haunt.

By: kapsio

kapsio — Fri, 17 Aug 2007 19:04:49 +0000

Since rationals are countable (i.e. I can assign an integer to any rational and say it is the nth rational), and can “appear” to be “as continuous as the continuum”, it follows — integers can also “appear” to be “as continous as the continuum”.

In my case, I think early on (6th – 10th grade) I struggled with the idea of the continuum, cause the concept of a point “adjecent” or “next” to another point doesnt make sense. It took me some time (11th – 12th grade) to get used to the fact that between any two points there are infinitely more points (and that too in an uncountable way). Then I stopped thinking after that, and now you want to swing me back to thinking that the concept of the “adjecent” point makes sense. Thats a bit too much I say !

As usual, thanks for all the pointers. Your articles are becoming increasingly link-rich. Keep ‘em coming.