Comment Furthest-most (Score 4, Funny) 94
At the furthest-most reaches
Furthest-most? When "furthest" is just not far enough?
This is the worstest made up word I've seen in a long time.
At the furthest-most reaches
Furthest-most? When "furthest" is just not far enough?
This is the worstest made up word I've seen in a long time.
Doesn't work
Yes it does.
Here is the problem. Blowing up or melting items does not work.
Here is the solution: don't do either of those things.
We have as a society been conditioned to respond to stimulae.
What else would we respond to?
According to Mr. Shatner, if the KickStarter campaign doesn't raise enough money then he will donate whatever that has been collected...
...to a politician who promise to build that water pipe.
Haha! He almost had me going there, right up until that last bit. Well played, Shatner, well played.
What?
What next? An app to remind you when to eat? Or when to take a dump and how to wipe your arse afterwards?
Wait, no, pretend you didn't hear that last one. That's my new project.
Mind you, I can't really talk. I appear to have a faulty sense of thirst. I can tell whether or not I'm thirsty, but only if I think about it, and even if I am it doesn't give me a great urge to drink. I've got into a routine of finishing off a bottle of water every day (and all without any reminders from my phone!), but before then I'd often find myself getting to chapped-lips stage almost without realising.
That these judges were required to show "loyalty" to their government by walking out, instead of asserting the independence of the judiciary
No, they showed loyalty to the judicial system by not allowing it to be railroaded into becoming part of a piece of political theatre.
A simple relic of 20th century life has taken on new meaning for archaeologists: The ring-tab beer can — first introduced 50 years ago — is now considered an historic-era artifact, a designation that bestows new significance on the old aluminum cans and their distinctive tabs that are still found across the country.
Like people, things don't suddenly become more important or interesting just because they turned 50.
The idea is that the "scale" of the observable universe is the ratio from the largest "thing" (the whole observable universe) to the smallest "thing," which is the Planck length. That ratio is 10^63 or something like that, much less than the zoom level that's achieved in the video.
Blinking (along with spinning, whirring, and clattering) was mandatory for any computer in the 60s.
You can't do it from one complex number.
I'm not quite sure what you mean. The summary says (as does Wikipedia) that the sequence goes:
0
c
c^2+c
(c^2+c)^2+c
You only need one complex input variable (the coordinate of the point) to determine whether or not the point is in the set. I think your link says as much:
The calculation of a Mandelbrot set is similar. The difference is in the values that are substituted into the equation. In the equation for f(z) the pixel coordinate (x,y) is substituted into the complex number C and (0,0) is substituted for a starting value of z.
You can instead just use skip the first iteration and use c as the starting value of z, because that's always the next result after z0=(0,0).
If what you said was true then why does every implementation - and I've written at least two[1] - use two complex variables?
Err, I dunno. You wrote them so I'm not sure why you're asking me. If you're just talking about program variables, you presumably use one to store the result of each iteration.
And why is there such a thing as a Julia set
We're not talking about Julia sets. They do use two complex variables - the coordinate of the point and a constant (for that particular set). I think that's what those Julia animations are about - altering the constant to produce different slices.
There should be no estate for Goebbels, precisely because of the person he was and the things he has done. It's that the copyright isn't valid, it's that the estate should not exist!
When I read the article it didn't seem like the normal excepts you find in a biography. The excerpts have been described as "extensive", and I think Random House could have went beyond Fair Use and into copyright violation.
Orthogonal to the copyright issue is that I don't understand why Goebbels has an estate to make a claim against Random House. It should never have been permitted to allow a convicted war criminal to pass property onto heirs or relatives and all of his property ought to have reverted to the state and have been sold at auction. So what the heck happened?
You should write it instead of cut and paste?
There is fair use, and there is lifting the work of another person. If this were an academic paper, I would be far more lenient. but this is a book written to sell a lot of books. The purpose is to make money here, and not letting publishers get a free ride is precisely why there are copyright laws.
It's not n^2 + n
Yes it is, for the second (or third, if you're starting from 0) element in the sequence. The article isn't defining the sequence, per se; it's listing elements in the sequence calculated solely from the initial complex number.
I think the confusion has arisen because n is usually used as the element number, not the complex point (which usually goes by c).
the number you multiply by itself isn't the same as the number you add.
No - well, just once - but that's not what the article says. You square the previous element, then add c.
Wikipedia says:
The Mandelbrot set is the set of complex numbers 'c' for which the sequence ( c, c^2 + c, (c^2+c)^2 + c, ((c^2+c)^2+c)^2 + c, (((c^2+c)^2+c)^2+c)^2 + c,
which is exactly what the article says, except using c instead of n.
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).
You knew the job was dangerous when you took it, Fred. -- Superchicken
