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Mandelbrot Zooms Now Surpass the Scale of the Observable Universe
StartsWithABang writes You're used to real numbers: that is, numbers that can be expressed as a decimal, even if it's an arbitrarily long, non-repeating decimal. There are also complex numbers, which are numbers that have a real part and also an imaginary part. The imaginary part is just like the real part, but is also multiplied by i, or the square root of -1. It's a simple definition: the Mandelbrot set consists of every possible complex number, n, where the sequence n, n^2 + n, (n^2 + n)^2 + n, etc.—where each new term is the prior term, squared, plus n—does not go to either positive or negative infinity. The scale of zoom visualizations now goes well past the limits of the observable Universe, with no signs of loss of complexity at all.
Mandelbrot Zooms Now Surpass the Scale of the Observable Universe
First off, does that even mean anything? What units is the "scale" of a universe expressed in?
Okay, let's take it to mean the ratio of the size of observable universe to the size of the Planck length, for lack of any better definition. In that case, Mandelzooms surpassed that years ago.
with no signs of loss of complexity at all.
You make it sound like we're expecting a loss of complexity, and we just haven't found it yet. But isn't it mathematically proven that the Mandelbrot set has the same "complexity" at all scales? Kind of inherent in the whole "fractal" thing, I thought...
I'd have thought it would be more interesting to talk about, for example, how all the pretty colours that everyone gawps at aren't even points in the set. They're just colour-coded as to how long the sequence takes to reach a certain value (all of the coloured points ultimately diverge to infinity, which is what makes them not part of the set).
systemd is Roko's Basilisk.
In the 60s we didn't need no blinkin computer
Indeed. Ed Lorenz was able in 1963 to visualize the attractor behind deterministic nonperiodic flow with only rudimentary manual graph plotting done on basis of numeric printouts. And Mandelbrot wrote his pioneering papers on fractals (such as 'How long is the coast of Britain') in the middle Sixties, and although he was at IBM's Thomas J. Watson, the computing resources were those available at that time.
When stuff falls into a black hole, it gets measurably heavier. If a charged particle falls into one, the black hole retains a measurable electric field. If a black hole picks up angular momentum from gas circling in sideways, the hole spins faster, and the gas fired from the jets comes out at a higher speed.
Your argument that mass or energy exists that isn't measurable since it isn't observable sounds a little illogical... how would you even know there was such a thing if nobody had measured it for you in the first place?
Actually Stephen Hawking would have agreed with you in 1997, but by 2004 he decided he had lost the bet with John Preskill of Caltech.
I read the book "Fun With Numbers" by Mir publications, Moscow in 10th grade. It talked about simple things like immensity of a number like pow(2,64) explained in a simple language a 10th grader could get. (pow(2,64) rice grains would need a barn 3 meter wide, 3 meters tall and several times the distance of Earth to Moon or something like that).
So Mandelbrot set could exceed the resolution of the known universe, by some version of the definition of these terms, in as little as 64 iterations.
sed -e 's/Chuck Norris/Rajnikant/g' joke > fact
Sure they are. The set of concepts that humans can conceive are those which human brains, either directly or through tools like computers, can handle. Human brains evolved in the context usually called "the observable universe", so all concepts - including but not limited to abstract mathematical objects - we can think about are encoded within it, just in a real roundabout way. In other words, you can not know anything that isn't encoded in your causal past; even the very notion of abstraction only exists because it's inherent in the physical universe to such a degree that evolution encoded the principle into your brain.
And besides, the notion that math is supernatural - something that exists above physical reality, independent of it - is an unproven and probably unprovable assertion.
Forget magic. Any technology distinguishable from divine power is insufficiently advanced.