4 ms·

As an aside, I feel like the whole notion of Kolmogorov complexity seems to just be moving the goal posts. With the classic example of the Mandelbrot fractal, i

As an aside, I feel like the whole notion of Kolmogorov complexity seems to just be moving the goal posts. With the classic example of the Mandelbrot fractal, is the representation of the fractal as an iterated formula really any more compact when you include the complexity of the computer that has to execute the program to produce a meaningful result?

eru 3y ago
If you want to generate lots of pictures of your Mandelbrot fractal zoomed into different spots, then yes, shipping the program is much smaller. I remember spending countless hours with Fractint (https://en.wikipedia.org/wiki/Fractint https://en.wikipedia.org/wiki/Fractint) in the 1990s. Back then the programme fit on a floppy disk (or so). Today the latest version from https://fractint.org/ https://fractint.org/ is about 9 MiB in size. If you want to transmit n pictures of the Mandelbrot set, you can either send me n PNGs, or you can transmit Fractint once and n tuples of (top, left, bottom, right) coordinates. You can do the math what size n you need before the former becomes much, much bigger than the latter. But, I like the spirit of your comment. So perhaps the thought-provoking thing might be the following observation: Most of the bytes and complexity in the fractint binary are not at all necessary for displaying the fractals. You could generate them with much simpler software. No, most of the bytes are there to generate the fractals _quickly_. Kolmogorov complexity doesn't care about runtimes as long as they are finite. Humans do.
malf 3y ago
The choice of computer is just an additive constant.
- srcreigh 3y ago
  Assuming the Church-Turing thesis is correct, that is.
- intalentive 3y ago
  Solomonoff's invariance theorem
FartyMcFarter 3y ago
Any Turing complete computer can generate the Mandelbrot fractal. You don't need a complex computer to get Turing completeness. In fact, Turing completeness is notable for showing up even in extremely simple systems.
m3047 3y ago
I once encountered a postscript file which computed and printed a Mandelbrot fractal (as you call it). It came over the transom as DOS / possible malware. We let it run over the weekend on an HPLJ4 and by Monday it had spit a piece of paper out. Yup.

eru 3y ago

If you want to generate lots of pictures of your Mandelbrot fractal zoomed into different spots, then yes, shipping the program is much smaller. I remember spending countless hours with Fractint (https://en.wikipedia.org/wiki/Fractint https://en.wikipedia.org/wiki/Fractint) in the 1990s. Back then the programme fit on a floppy disk (or so). Today the latest version from https://fractint.org/ https://fractint.org/ is about 9 MiB in size. If you want to transmit n pictures of the Mandelbrot set, you can either send me n PNGs, or you can transmit Fractint once and n tuples of (top, left, bottom, right) coordinates. You can do the math what size n you need before the former becomes much, much bigger than the latter. But, I like the spirit of your comment. So perhaps the thought-provoking thing might be the following observation: Most of the bytes and complexity in the fractint binary are not at all necessary for displaying the fractals. You could generate them with much simpler software. No, most of the bytes are there to generate the fractals _quickly_. Kolmogorov complexity doesn't care about runtimes as long as they are finite. Humans do.

malf 3y ago

The choice of computer is just an additive constant.

srcreigh 3y ago
Assuming the Church-Turing thesis is correct, that is.
intalentive 3y ago
Solomonoff's invariance theorem

FartyMcFarter 3y ago

Any Turing complete computer can generate the Mandelbrot fractal. You don't need a complex computer to get Turing completeness. In fact, Turing completeness is notable for showing up even in extremely simple systems.

m3047 3y ago

I once encountered a postscript file which computed and printed a Mandelbrot fractal (as you call it). It came over the transom as DOS / possible malware. We let it run over the weekend on an HPLJ4 and by Monday it had spit a piece of paper out. Yup.