# BIG, little.

April 2, 2007 1:27 PM Subscribe

A Mandelbrot zoom that is much larger than our known universe.

Previously mentioned here, but it deserves its own mention. Via.

Previously mentioned here, but it deserves its own mention. Via.

whoa. dude.

posted by Mach5 at 1:41 PM on April 2, 2007 [1 favorite]

posted by Mach5 at 1:41 PM on April 2, 2007 [1 favorite]

woah, at 38 seconds in the whole shape apears again. Is that normal?

posted by delmoi at 1:46 PM on April 2, 2007

posted by delmoi at 1:46 PM on April 2, 2007

Anyone have any source information on this? I'm curious what point is the focus of the zoom.

posted by grimmelm at 1:47 PM on April 2, 2007

posted by grimmelm at 1:47 PM on April 2, 2007

Mandelbrot has a new book coming out, I was working on putting together a post for tomorrow morning.

While visual representations of fractals are interesting, I always found fractal dimensions (Hausdorf dimensions) with more application outside the world of pure mathematics. In at least I think it has some application in describing such things as stock charts, but I've yet to see a useful application of such. In his last book, Mandelbrot does go to some length to talk about cotton prices and using fractals to find patterns. It was interesting in so much that one can find much different patterns occurring at different time intervals, the seemingly non-repeating nature would seem to indicate that it is as much like a fractal than anything else. Of course how one can use this to predict the market isn't really the point of his book, but he does apparently (and I use that loosely) show that it can be used to predict when things are not going like they should, which would indicate a time to get out of whatever position you're in.

Of course that's a very loose interpretation of what he was working on, but if anyone is really interested in him they should check out where he started: analyzing the cotton market.

posted by geoff. at 1:49 PM on April 2, 2007

While visual representations of fractals are interesting, I always found fractal dimensions (Hausdorf dimensions) with more application outside the world of pure mathematics. In at least I think it has some application in describing such things as stock charts, but I've yet to see a useful application of such. In his last book, Mandelbrot does go to some length to talk about cotton prices and using fractals to find patterns. It was interesting in so much that one can find much different patterns occurring at different time intervals, the seemingly non-repeating nature would seem to indicate that it is as much like a fractal than anything else. Of course how one can use this to predict the market isn't really the point of his book, but he does apparently (and I use that loosely) show that it can be used to predict when things are not going like they should, which would indicate a time to get out of whatever position you're in.

Of course that's a very loose interpretation of what he was working on, but if anyone is really interested in him they should check out where he started: analyzing the cotton market.

posted by geoff. at 1:49 PM on April 2, 2007

A note about arbitrary precision and deep zooming in fractals, via Fractint, the original homebrew fractal exploration tool:

So how far can you zoom? How does 10^1600 sound--roughly 1600 decimal digits of precision. To put *this* magnification in perspective, the "tiny" ratio of 10^61 is the ratio of the entire visible universe to the smallest quantum effects. With 1600 digits to work with, you can expand an electron-sized image up to the size of the visible universe, not once but more than twenty times. So you can examine screen-sized portions of a Mandelbrot set so large all but a tiny part of it would be vastly farther away than the billion or so light year limit of our best telescopes.posted by loquacious at 1:51 PM on April 2, 2007

You can explore the Mandelbrot set (and other fractals) in real time, even on slow computers, with the free and open source XaoS. I don't think you can zoom in that far with it though, but you get much higher resolution and loads of interactive features.

posted by drew3d at 1:54 PM on April 2, 2007

posted by drew3d at 1:54 PM on April 2, 2007

I don't know how I am going to get any work done for the rest of the day. I feel like I just experienced the transformation scene in Altered States.

posted by rubyeyo at 2:01 PM on April 2, 2007

posted by rubyeyo at 2:01 PM on April 2, 2007

*woah, at 38 seconds in the whole shape apears again. Is that normal?*

Yes, that's common to all fractals. Self-similarity is one of the attributes of fractals.

posted by empath at 2:02 PM on April 2, 2007

My God. It's full of stars.

posted by Dave Faris at 2:03 PM on April 2, 2007 [5 favorites]

posted by Dave Faris at 2:03 PM on April 2, 2007 [5 favorites]

loquacious: I found myself asking, "What are the units?" when considering whether the fractal was, indeed, "larger than our known universe". After reading your blockquote, I'd have to answer my own question with "Pick a unit. Any unit. It's still larger than the known universe."

I feel so insignificant now.

(Alright, then. You talked me into it.)

posted by LordSludge at 2:07 PM on April 2, 2007

I feel so insignificant now.

(Alright, then. You talked me into it.)

posted by LordSludge at 2:07 PM on April 2, 2007

Bah, it is not larger than my laptop screen.

posted by dov3 at 2:10 PM on April 2, 2007 [1 favorite]

posted by dov3 at 2:10 PM on April 2, 2007 [1 favorite]

It seems like so many things are "larger than the known Universe" these days that I'm starting to think it's actually our Universe which is pretty small - at least as far as Universes go.

posted by vacapinta at 2:13 PM on April 2, 2007 [2 favorites]

posted by vacapinta at 2:13 PM on April 2, 2007 [2 favorites]

Ah, good ol' Fractint. I remember downloading that off of Compuserve forums using WinCIM! I wonder how long it'd take my schmancy 1.5 ghz lappy to chug through one of the several hour ones I generated back then.

I guess everyone's moved on to Xaos by now?

posted by JHarris at 2:18 PM on April 2, 2007

I guess everyone's moved on to Xaos by now?

posted by JHarris at 2:18 PM on April 2, 2007

Burhanistan, let me try to explain this:

...

Ok I tried.

posted by Mister_A at 2:21 PM on April 2, 2007 [4 favorites]

...

Ok I tried.

posted by Mister_A at 2:21 PM on April 2, 2007 [4 favorites]

*How can anything be "larger then the known Universe"?*

women ask me that all the time

posted by pyramid termite at 2:23 PM on April 2, 2007 [12 favorites]

*How can anything be "larger then the known Universe"? Pardon my simple, backwards way of looking at things, but uni means one. As in Universe contains everything, known or unknown. So, nothing is bigger.*

posted by Burhanistan at 2:14 PM on April 2 [+]

[!]

posted by Burhanistan at 2:14 PM on April 2 [+]

[!]

Notice the use of the compound phrase "known Universe." To quote from Wikipedia's entry on Universe:

A majority of cosmologists believe that the observable universe is an extremely tiny part of the "whole" (theoretical) Universe and that it is impossible to observe the whole of comoving space. It is presently unknown whether or not this is correct, since according to studies of the shape of the Universe, it is possible that the observable universe is of nearly the same size as the whole of space, but the question remains under debate.[2][3] If a version of the cosmic inflation scenario is correct, then there is no known way to determine whether the (theoretical) universe is finite or infinite, in which case the observable Universe is just a tiny speck of the (theoretical) universe.

A majority of cosmologists believe that the observable universe is an extremely tiny part of the "whole" (theoretical) Universe and that it is impossible to observe the whole of comoving space. It is presently unknown whether or not this is correct, since according to studies of the shape of the Universe, it is possible that the observable universe is of nearly the same size as the whole of space, but the question remains under debate.[2][3] If a version of the cosmic inflation scenario is correct, then there is no known way to determine whether the (theoretical) universe is finite or infinite, in which case the observable Universe is just a tiny speck of the (theoretical) universe.

Is that clearer?

posted by vacapinta at 2:23 PM on April 2, 2007

If people knew how big the observable universe was, *then* I'd be impressed- hey, but what are a few factors here or there?

Still, let's play with this. The fractal zoom took 220 of your earth seconds, and the universe is, let's say, around 90 billion of your earth light years across. So the diameter of the fractal set was expanding at roughly five hundred million light years per second.

Where's your Einstein now, Terran?

Seriously, I lack the maths to even begin to work this out, but if you could accurately simulate a universe in approximately real time and could simultaneously observe two points more than their light distance (in the non-simulated universe that you're simulating) apart, would that contravene the c limit? I know (roughly) that there are limits to how much computation you can do per unit mass, but, um, if c limits the speed at which information can move and you can ascertain the information at greater than c through other means...

I think I'm going to go and have a little lie down,close my eyes and... oh god, the fractals!

posted by Devonian at 2:27 PM on April 2, 2007 [3 favorites]

Still, let's play with this. The fractal zoom took 220 of your earth seconds, and the universe is, let's say, around 90 billion of your earth light years across. So the diameter of the fractal set was expanding at roughly five hundred million light years per second.

Where's your Einstein now, Terran?

Seriously, I lack the maths to even begin to work this out, but if you could accurately simulate a universe in approximately real time and could simultaneously observe two points more than their light distance (in the non-simulated universe that you're simulating) apart, would that contravene the c limit? I know (roughly) that there are limits to how much computation you can do per unit mass, but, um, if c limits the speed at which information can move and you can ascertain the information at greater than c through other means...

I think I'm going to go and have a little lie down,close my eyes and... oh god, the fractals!

posted by Devonian at 2:27 PM on April 2, 2007 [3 favorites]

It's simpler to explain than that. If you play Doom 3, the environment is larger than your house. How can that be when the computer is INSIDE your house?

posted by empath at 2:28 PM on April 2, 2007 [5 favorites]

posted by empath at 2:28 PM on April 2, 2007 [5 favorites]

*How can anything be "larger then the known Universe"? Pardon my simple, backwards way of looking at things, but uni means one. As in Universe contains everything, known or unknown. So, nothing is bigger.*

Put it simply, the scale from the stopping point in the fractal to the beginning point is larger than the scale of an electron to the actual universe. So if you were to watch a video that started with the universe and zoomed in to an electron, it would take less time. Or, that's what I think they're talking about.

Of course, this fractal is an imaginary thing, so it isn't

*really*bigger than the universe. Unless our imaginations are.

posted by Citizen Premier at 2:30 PM on April 2, 2007 [1 favorite]

I think "larger than the known Universe" in this case means at mathematical scales greater than any scale difference that is meaningful. Of course the Mandelbrot set doesn't occupy any physical space as a pure mathematical concept.

The observable universe is around 10

posted by demiurge at 2:31 PM on April 2, 2007

The observable universe is around 10

^{27}meters in diameter. The Planck length is around 10^{-35}meters. So the biggest difference in scales for our physics is going to be around 10^{62}.posted by demiurge at 2:31 PM on April 2, 2007

There's a universe beyond my laptop screen?

posted by yeti at 2:35 PM on April 2, 2007 [1 favorite]

posted by yeti at 2:35 PM on April 2, 2007 [1 favorite]

I personally still use Fractint. It has way, way more fractal types, more parameters, more features and it's the original. 3D raytraced plots, 3D stereographic outputs, color cycling, and more. Plus it has a built in scripting language and all kinds of stuff.

But Xaos' "near realtime" zooming when I boot into KDE is pretty fucking awesome on a stick.

It's still not Fractint. Every time I'm in Ultrafract or Xaos I just feel my fingers twitching for that awesome oldschool DOS-hotkey menu that Fractint uses. I can run a damn good light show just in Fractint. Ultrafract and Xaos, not so much. I still love fractint so much I'm strongly considering making a bootable DOS 6.22 disc just so I can run Fractint natively in SVGA/XGA modes without the Windows overhead.

posted by loquacious at 2:35 PM on April 2, 2007 [2 favorites]

But Xaos' "near realtime" zooming when I boot into KDE is pretty fucking awesome on a stick.

It's still not Fractint. Every time I'm in Ultrafract or Xaos I just feel my fingers twitching for that awesome oldschool DOS-hotkey menu that Fractint uses. I can run a damn good light show just in Fractint. Ultrafract and Xaos, not so much. I still love fractint so much I'm strongly considering making a bootable DOS 6.22 disc just so I can run Fractint natively in SVGA/XGA modes without the Windows overhead.

posted by loquacious at 2:35 PM on April 2, 2007 [2 favorites]

*How can anything be "larger then the known Universe"? Pardon my simple, backwards way of looking at things, but uni means one. As in Universe contains everything, known or unknown. So, nothing is bigger.*

We can create algorithms for generating things larger than the known universe; we're intimately familiar with such things, even if we don't think about it in those terms.

Suppose a universe composed of a (very large) finite number of base particles. Quarks or subquarks or whatever you like.

Now give each one a number.

Did you run out of numbers? No? Then the set of counting numbers is bigger than the whole universe, in that sense. Even if you found a good way to represent each number in the set with a single particle, you'd run out of particles. Hell, fit a thousand numbers on each particle, or a million—you'll still run out.

You want to build a computer that will simulate the whole universe? What will you build it out of? How will you represent every speck of anything in the whole system? The tricky part is making a computer that's not bigger than the universe itself.

</semicoherent armchair philosophication>

posted by cortex at 2:35 PM on April 2, 2007

"Oh dear," says God, "I hadn’t thought of that," and promptly disappears in a puff of logic.

posted by isopraxis at 2:41 PM on April 2, 2007 [7 favorites]

posted by isopraxis at 2:41 PM on April 2, 2007 [7 favorites]

*Then chew on this: if you make a fractal set or other algorithm that could superficially said to be "larger than the known universe", then wouldn't that fractal set or algorithm in fact then increase the size of the "known universe" by creating a new concept or knowledge point?*

Not if I presume that all mathematical algorithms exists

*a priori*and that my invention is merely identification. That the universe contains the instructions for building things larger than itself is, I guess, the key idea.

posted by cortex at 2:51 PM on April 2, 2007

*How can anything be "larger then the known Universe"?*

First it's larger, and then there's the known Universe. First this, then that. Simple!

posted by jiawen at 3:00 PM on April 2, 2007 [2 favorites]

Cortex, obviously you'd use data compression. I mean, look at how much of the universe is empty vacuum! That'd zip right up into a handful of bits. Mind, the actual planets and stars would be a bit tricky without some fairly hard-core compression heuristics....

posted by JHarris at 3:05 PM on April 2, 2007 [1 favorite]

posted by JHarris at 3:05 PM on April 2, 2007 [1 favorite]

Oh, some sort of RLE would be implied, to be sure.

posted by cortex at 3:07 PM on April 2, 2007 [1 favorite]

posted by cortex at 3:07 PM on April 2, 2007 [1 favorite]

Do the colors in fractals mean anything or are they purely aesthetic additions? I've never really understood that aspect of fractal illustrations.

posted by aladfar at 3:10 PM on April 2, 2007

posted by aladfar at 3:10 PM on April 2, 2007

Burhanistan, I think the problem here is a confusion between the idea of size, as of space, and size, as of the realm of possibilities.

The full expansion of a graphical output of the Mandelbrot set, visible at once, would be larger than the visible universe. Yet, to borrow from the joke I made before, it can be data-compressed quite easily, into the Mandelbrot formula, and that can be written on a simple piece of paper.

Thus logically that idea is contained within the universe, yet its full implications is not.

posted by JHarris at 3:19 PM on April 2, 2007

The full expansion of a graphical output of the Mandelbrot set, visible at once, would be larger than the visible universe. Yet, to borrow from the joke I made before, it can be data-compressed quite easily, into the Mandelbrot formula, and that can be written on a simple piece of paper.

Thus logically that idea is contained within the universe, yet its full implications is not.

posted by JHarris at 3:19 PM on April 2, 2007

Strictly speaking, there are no colors in the mandlebrot set. Each point is easier in the set or not.

Colors on most graphic representations of fractals have to do with how many iterations it takes to determine that a point is not part of the set.

posted by empath at 3:19 PM on April 2, 2007

Colors on most graphic representations of fractals have to do with how many iterations it takes to determine that a point is not part of the set.

posted by empath at 3:19 PM on April 2, 2007

In case anyone doesn't know, that entire sequence is from this formula:

z -> z^2 + c

posted by empath at 3:20 PM on April 2, 2007 [2 favorites]

z -> z^2 + c

posted by empath at 3:20 PM on April 2, 2007 [2 favorites]

jharris-- there's no such thing as a full expansion of the mandlebrot set. It's infininitely complex.

posted by empath at 3:22 PM on April 2, 2007 [1 favorite]

posted by empath at 3:22 PM on April 2, 2007 [1 favorite]

"...but if you could accurately simulate a universe in approximately real time..."

Heh heh heh. No seriously, let's do this. We'll just do an easy small one. What could possibly go wrong?

Aladfar, I'm pretty sure you can think of the colors like another dimension. Like height or temperature. Someone else probably has a better explanation.

posted by Area Control at 3:23 PM on April 2, 2007

Heh heh heh. No seriously, let's do this. We'll just do an easy small one. What could possibly go wrong?

Aladfar, I'm pretty sure you can think of the colors like another dimension. Like height or temperature. Someone else probably has a better explanation.

posted by Area Control at 3:23 PM on April 2, 2007

Er, did anyone read the gloss on the right of the video which is the origin of the "bigger than the universe" quote? It says

posted by Bugbread at 3:24 PM on April 2, 2007 [2 favorites]

*"If the final frame were the size of your screen, the full set would be larger than the known universe."*That's all. If the final frame were the size of a quark, it might be, I dunno, half the size of the universe. If the final frame were the size of the universe, the whole thing would be*considerably bigger*than the universe. The fractal itself isn't any*size*, it's a mathematical formula that's been illustrated. Saying "it is X big" is like saying "3 x 9 = 27 is bigger than my car".posted by Bugbread at 3:24 PM on April 2, 2007 [2 favorites]

The Nerd is strong in this thread.

posted by loquacious at 3:27 PM on April 2, 2007 [3 favorites]

posted by loquacious at 3:27 PM on April 2, 2007 [3 favorites]

Sorry to interupt the 'how big is the universe' thing, and I've read that Chaos theory book from the 90s, but what am I looking at exactly in that video?

posted by serazin at 3:31 PM on April 2, 2007

posted by serazin at 3:31 PM on April 2, 2007

Of course, this fractal is an imaginary thing...

Of course, this fractal is an imaginary thing...

There's nothing imaginary here, except the imaginary number

**i**, which, if I may say so, we don't want to think of as

*too*imaginary.

posted by Wolfdog at 3:33 PM on April 2, 2007

*If the final frame were the size of a quark, it might be, I dunno, half the size of the universe.*

Actually, that's the point. If the final frame were the size of a quark, the full set would

*still*be larger than the known universe.

posted by monju_bosatsu at 3:37 PM on April 2, 2007

*Actually, that's the point. If the final frame were the size of a quark, the full set would still be larger than the known universe.*

monju: Unless you have more info than I do, we don't really know what level of zoom is being used. Certainly, we know it is possible to make such a video with the zoom greater than the ratio in size between the smallest thing physicists have yet found and the universe itself (see loquacious above), but we don't know about this particular video, which might not have that much zoom (the info that comes with it only deals with the screen:universe ratio).

posted by ssg at 3:47 PM on April 2, 2007

Yah bugbread, there is an aspect of arbitrariness to it. If they had zoomed in deeper they'd have found still more detail, and then that would be bigger than the universe, but if the screen resolution were better it'd then be smaller, etc.

But still, despite that, somehow, yow.

posted by JHarris at 3:49 PM on April 2, 2007

But still, despite that, somehow, yow.

posted by JHarris at 3:49 PM on April 2, 2007

I waited for three minutes for Spock to mind-meld with V'ger, and nothing.

posted by solistrato at 3:49 PM on April 2, 2007 [2 favorites]

posted by solistrato at 3:49 PM on April 2, 2007 [2 favorites]

*It's simpler to explain than that. If you play Doom 3, the environment is larger than your house. How can that be when the computer is INSIDE your house?*

Fractals, of course!

*There's nothing imaginary here, except the imaginary number i, which, if I may say so, we don't want to think of as too imaginary.*

Otherwise, it becomes complex.

posted by eriko at 3:51 PM on April 2, 2007 [1 favorite]

Here's a little exposition on deep zooming, focused on a region far to the left on the real axis (very, very near -2). There are bulbs of the M set associated to different periodicities - the period 3 bulb is large and clearly visible at the top of the standard "unzoomed" view of the set. The bulbs associated to powers of two lie on the negative real axis, and for higher powers of two they are very, very, tiny and hard to find by zooming. The pictures of the 2^12 bulb show an apparent regularity (deceptive, though) that qualitatively looks quite different from the paisleys and seahorses we're used to seeing.

The wikipedia article has a wealth of interesting stuff in it. Fun facts beyond the "ooh pretty" stuff: the Hausdorff dimension of the

posted by Wolfdog at 3:53 PM on April 2, 2007 [1 favorite]

The wikipedia article has a wealth of interesting stuff in it. Fun facts beyond the "ooh pretty" stuff: the Hausdorff dimension of the

*boundary*of the set is exactly 2, but it's still not known whether it has positive Lebesgue measure in the plane; the Mandelbrot set is connected, but it's still not known whether it is*locally connected*, which is a rather strange state of affairs (and seems paradoxical, but the technicalities of the definitions make it possible for a set to be connected but not locally connected.)posted by Wolfdog at 3:53 PM on April 2, 2007 [1 favorite]

*monju: Unless you have more info than I do, we don't really know what level of zoom is being used.*

You're right. I was working on the assumption that the creator of the video used the maximum level of zoom available in fractint.

posted by monju_bosatsu at 3:53 PM on April 2, 2007

I'm looking at this and I think I know what a house dog feels like. Just looking at the TV and hearing a dog howling from inside of the box.

posted by nola at 3:54 PM on April 2, 2007

posted by nola at 3:54 PM on April 2, 2007

Actually, you wouldn't need to use anywhere near the maximum level of zoom; you would only need to zoom to a ration of about 10^45, only a fraction of fractint's 10^1600 capability.

posted by monju_bosatsu at 3:55 PM on April 2, 2007

posted by monju_bosatsu at 3:55 PM on April 2, 2007

"Pathological monsters!" cried the terrified mathematician...That's one bad-ass fucking fractal.

posted by unregistered_animagus at 4:09 PM on April 2, 2007 [1 favorite]

posted by unregistered_animagus at 4:09 PM on April 2, 2007 [1 favorite]

I still think that Period 3 Implies Chaos is one of the weirdest and most wonderful theorems lurking around out there.

posted by Wolfdog at 4:17 PM on April 2, 2007

posted by Wolfdog at 4:17 PM on April 2, 2007

The zoom scale is 10**89, mentioned by the source here.

There is much sharper and larger WMV version there also.

demiurge has the sense of what I meant when I said larger

than the known universe.

This video zoom makes me feel a little weird and bothered.

posted by the Real Dan at 4:18 PM on April 2, 2007 [1 favorite]

There is much sharper and larger WMV version there also.

demiurge has the sense of what I meant when I said larger

than the known universe.

This video zoom makes me feel a little weird and bothered.

posted by the Real Dan at 4:18 PM on April 2, 2007 [1 favorite]

That's all well and good, except that the universe

posted by It's Raining Florence Henderson at 4:21 PM on April 2, 2007 [1 favorite]

*itself*is a lossless compression of statistical models of infinite numbers of algorithms, within which these particular algorithms*and their expansions*are little more than whispers in a bugs ear. Well, that's what my fortune cookie said, anyway.posted by It's Raining Florence Henderson at 4:21 PM on April 2, 2007 [1 favorite]

**monju_bosatsu**writes

*"Actually, that's the point. If the final frame were the size of a quark, the full set would*still

*be larger than the known universe."*

Based on what?

I'm not saying you're wrong; maybe there's a page that provides the actual numbers, but without them, I don't see anywhere where there are numbers that show how much

*that particular*fractal was zoomed in.

- The only actual numbers I've seen are that Fractint
*can*zoom to 10^1600, and that at that magnification, a fractal 20 times the size of the universe would end up zoomed in to the span of an electron. - However, if this video were zoomed in to, say, 10^1598, you'd have moved from "10 universes to 1 electron" down to a more manageable "0.5 universes to 1 electron" (or, easier stated, "Initial size of 1 universe zoomed to span of 2 electrons".
- If the max zoom were, say, 10^1590, you'd now be talking "Initial size of 1 universe, zoomed to span of 512 electrons".
- How about a max zoom of 10^1572? If my math is right, we're now talking "initial size of 1 universe, zoomed to span of 1 cm".
- 10^1570? Now we're talking "initial size of 1 universe, zoomed to span of 100 cm, which is quite a bit bigger than a YouTube screen".

*isn't*, but there isn't really anything saying it

*is*, either. So if the last frame were the size of a quark, it might be half the size of the universe, or a 50th the size, or 20 times the size. It's impossible to say.

Hence the important thing here isn't "Is this animation IN ITSELF a depiction of something bigger than the universe" (which is impossible to say, because it's just a formula, damnit, not a "thing"), but "If the final frame were the size of your screen, the initial set would be bigger than the universe".

Going back to numbers, it's like saying "100 is bigger than my car". That makes no sense. Now, if we say "If 1 is the size of a large pig, then 100 is bigger than my car", well, that makes sense. But saying "the Mandelbrot set is bigger than the universe", without defining any units, is dumb.

posted by Bugbread at 4:23 PM on April 2, 2007

Ah, mandelbrot. How I've missed you.

posted by jeffamaphone at 4:25 PM on April 2, 2007

posted by jeffamaphone at 4:25 PM on April 2, 2007

Also, and I don't think I mentioned this before, looking at the Mandelbrot set is for a small but viscerally-hooked-up part of my brain a genuinely terrifying experience. It's just pretty much screaming the whole time, and I've had to look away on occasion. Fuckin' mindbending fractals.

posted by cortex at 4:35 PM on April 2, 2007 [1 favorite]

posted by cortex at 4:35 PM on April 2, 2007 [1 favorite]

D00d - yer just an equation, expanding at the speed of life.

posted by It's Raining Florence Henderson at 4:38 PM on April 2, 2007

posted by It's Raining Florence Henderson at 4:38 PM on April 2, 2007

**It's Raining Florence Henderson**said:

*That's all well and good, except that the universe itself is a lossless compression of statistical models of infinite numbers of algorithms...*

What makes you so sure it's lossless?

posted by atbash at 4:40 PM on April 2, 2007

*What makes you so sure it's lossless?*

Black holes apparently have hair.

posted by eriko at 4:43 PM on April 2, 2007

The first law of thermodynamics. And cause fortune cookies never lie.

posted by It's Raining Florence Henderson at 4:45 PM on April 2, 2007

posted by It's Raining Florence Henderson at 4:45 PM on April 2, 2007

Burhanistan, the answer is simple: the Universe is really big, but math is

posted by Malor at 4:46 PM on April 2, 2007 [2 favorites]

*even bigger*.posted by Malor at 4:46 PM on April 2, 2007 [2 favorites]

This should have been what Christopher Walken saw at the end of

posted by localroger at 4:47 PM on April 2, 2007

*Brainstorm*.posted by localroger at 4:47 PM on April 2, 2007

*Black holes apparently have hair.*

A little trim, a little bleach... Your event horizon will be sweet as a peach.

posted by It's Raining Florence Henderson at 4:47 PM on April 2, 2007 [3 favorites]

bugbread: I think you got confused - you were saying that fractint's limit is the size of an electron to the size of the known universe times twenty. The fractint quote states you can do that resizing twenty times, which means it's exponentiation, not multiplication.

posted by aubilenon at 4:49 PM on April 2, 2007

posted by aubilenon at 4:49 PM on April 2, 2007

Here. Puff on this; it'll blowww your mind:

What if the whole universe is, like, one huge atom?posted by LordSludge at 4:51 PM on April 2, 2007 [2 favorites]

There's some good fractal learning to be had in this Mandelbrot lecture I posted.

posted by MetaMonkey at 4:55 PM on April 2, 2007 [1 favorite]

posted by MetaMonkey at 4:55 PM on April 2, 2007 [1 favorite]

Ok, someone help me with my remedial math.

If I remember my multiplication of powers, you add them, right? 1,000 x 1,000 is 1,000,000. That is, 10^3*10^3=10^(3+3)=10^6.

posted by Bugbread at 4:57 PM on April 2, 2007

If I remember my multiplication of powers, you add them, right? 1,000 x 1,000 is 1,000,000. That is, 10^3*10^3=10^(3+3)=10^6.

- An electron, as far as I knew, was sizeless, but since the Fractint explanation talks about the zoom in relation to the size of an electron, I googled, and came up with 10^-14 cm.
- So a cm is 10^14 as big as an electron.
- There are 100 cm in a meter, so a meter is 10^16 the size of an electron.
- There are 1000 cm in a km, so a km is 10^19 the size of an electron.
- There are approx 10^13 km in a light year, so a light year is 10^32 the size of an electron.
- The universe is estimated at 93 billion light years wide in diameter. Let's say 100 billion, or 10^9 light years. So the universe would be 10^41 electrons wide.

posted by Bugbread at 4:57 PM on April 2, 2007

*WTF Stupidly Gigantor*

I loved that movie!

posted by It's Raining Florence Henderson at 5:00 PM on April 2, 2007 [2 favorites]

If you keep on zooming for three more hours and add vomiting and dizziness, this video is pretty much what I experienced one night last winter after a bong hit gone tragically wrong.

posted by The Card Cheat at 5:05 PM on April 2, 2007

posted by The Card Cheat at 5:05 PM on April 2, 2007

**aubilenon**writes

*"I think you got confused - you were saying that fractint's limit is the size of an electron to the size of the known universe times twenty. The fractint quote states you can do that resizing twenty times, which means it's exponentiation, not multiplication."*

Ah, once again, the answer was posted while I was writing a comment (d'oh!!).

Now I'm confused the other way:

- Iteration 1 = 10^41 * 10^41 = 10^81
- Iteration 2 = 10^82 x 10^82 = 10^164
- Iteration 3 = 10^164 x 10^164 = 10^328
- Iteration 4 = 10^328 x 10^328 = 10^656
- Iteration 5 = 10^656 x 10^656 = 10^1312
- Iteration 6 = 10^1312 x 10^1312 = 10^2624
- Iteration 7 = 10^2624 x 10^2624 = 10^5248
- Iteration 8 = 10^5248 x 10^5248 = 10^10496
- Iteration 9 = 10^10496 x 10^10496 = 10^20992
- Iteration 10 = 10^20992 x 10^20992 = 10^41984
- Iteration 11 = 10^41984 x 10^41984 = 10^83968
- Iteration 12 = 10^83968 x 10^83968 = 10^167936
- Iteration 13 = 10^167936 x 10^167936 = 10^335872
- Iteration 14 = 10^335872 x 10^335872 = 10^671744
- Iteration 15 = 10^671744 x 10^671744 = 10^1343488
- Iteration 16 = 10^1343488 x 10^1343488 = 10^2686976
- Iteration 17 = 10^2686976 x 10^2686976 = 10^5373952
- Iteration 18 = 10^5373952 x 10^5373952 = 10^10747904
- Iteration 19 = 10^10747904 x 10^10747904 = 10^21495808
- Iteration 20 = 10^21495808 x 10^21495808 = 10^42991616

(Note to self: discovering the trick in Excel where you can combine formulas and regular text in results has proved useful far earlier than expected)

posted by Bugbread at 5:07 PM on April 2, 2007

Wait, 1600, not 16000. So that would be somewhere between iteration 5 and 6.

posted by Bugbread at 5:09 PM on April 2, 2007

posted by Bugbread at 5:09 PM on April 2, 2007

Your favorite universe sux.

“If the final frame were the size of your screen, the full set would be larger than the known universe.”

But wouldn’t my screen and thus the final frame still be in the universe? or at least the new universe created by this? And if I’m looking at it, wouldn’t it then be ‘known’? Even if virtually?

(Always wondered where the sticklers championing empirical knowlege go in arguments like these. I guess the no ‘God’ thing is a one trick pony.)

I suspect that the ‘If’ there is bigger than the Mandelbrot zoom

posted by Smedleyman at 5:21 PM on April 2, 2007

“If the final frame were the size of your screen, the full set would be larger than the known universe.”

But wouldn’t my screen and thus the final frame still be in the universe? or at least the new universe created by this? And if I’m looking at it, wouldn’t it then be ‘known’? Even if virtually?

(Always wondered where the sticklers championing empirical knowlege go in arguments like these. I guess the no ‘God’ thing is a one trick pony.)

I suspect that the ‘If’ there is bigger than the Mandelbrot zoom

posted by Smedleyman at 5:21 PM on April 2, 2007

*But wouldn’t my screen and thus the final frame still be in the universe? or at least the new universe created by this? And if I’m looking at it, wouldn’t it then be ‘known’? Even if virtually?*

Why would an attempt to make a screen big enough to display the proposed final rendering require the universe to grow to accommodate it? Why wouldn't it just, you know, not fit?

posted by cortex at 5:25 PM on April 2, 2007

(although it is nifty, and damn big)

posted by Smedleyman at 5:26 PM on April 2, 2007

posted by Smedleyman at 5:26 PM on April 2, 2007

I'm a hopeless nerd. But, a pop nerd. You know, the useless kind. What that means is, I kept expecting Homer or Cartman to show up at the end of this.

Spoiler alert!

posted by furiousthought at 5:32 PM on April 2, 2007

Spoiler alert!

posted by furiousthought at 5:32 PM on April 2, 2007

bugbread: Iteration two should be 10^82 * 10^41. Each time you do an electron -> universe zoom you're multiplying by 10^41, not squaring the whole thing.

so (10^41) ^ 20 = 10^800. Hmm. Still not the stated figure, but at least we're only off by SQUARED instead of by a hojillion.

posted by aubilenon at 5:42 PM on April 2, 2007

so (10^41) ^ 20 = 10^800. Hmm. Still not the stated figure, but at least we're only off by SQUARED instead of by a hojillion.

posted by aubilenon at 5:42 PM on April 2, 2007

Looks like I picked a great week to start sniffing glue.

posted by robocop is bleeding at 6:07 PM on April 2, 2007

posted by robocop is bleeding at 6:07 PM on April 2, 2007

Of course, this fractal is an imaginary thing...

There's nothing imaginary here, except the imaginary number i, which, if I may say so, we don't want to think of as too imaginary.

posted by Wolfdog at 3:33 PM on April 2 [+]

[!]

Of course, this fractal is an imaginary thing...

There's nothing imaginary here, except the imaginary number i, which, if I may say so, we don't want to think of as too imaginary.

posted by Wolfdog at 3:33 PM on April 2 [+]

[!]

Well, numbers are a concept, and all concepts are imaginary. Which is to say they exist inside the brains of human beings and nowhere else.

But I think maybe some scientists or mathematicians would beat me up if they heard me say that.

posted by Citizen Premier at 6:08 PM on April 2, 2007

*Ah, good ol' Fractint. I remember downloading that off of Compuserve forums using WinCIM! I wonder how long it'd take my schmancy 1.5 ghz lappy to chug through one of the several hour ones I generated back then.*

I used to write them in PostScript for high resolution and leave them running and hogging the office printer over the weekend.

Weekend workers must have wondered why the printer never worked.

posted by HTuttle at 6:09 PM on April 2, 2007 [1 favorite]

Here's a more concrete example, starts with the Milky Way galaxy, zooms to quarks by powers of 10: http://micro.magnet.fsu.edu/primer/java/scienceopticsu/powersof10/ (java req.)

(Pretty sure I've seen it here before, but Google Fu fails...)

posted by LordSludge at 6:14 PM on April 2, 2007 [1 favorite]

(Pretty sure I've seen it here before, but Google Fu fails...)

posted by LordSludge at 6:14 PM on April 2, 2007 [1 favorite]

*a fractal 20 times the size of the universe would end up zoomed in to the span of an electron.*

wha?

what is the diameter of an electron?

posted by sergeant sandwich at 6:17 PM on April 2, 2007

aladfar: "

The Mandelbrot set is actually an either or thing, when graphing it, things that belong to the set are colored one color and things outside the set are colored another.

The fancy colors are then derived by coloring everything not in the Mandelbrot set a different color, based on how quickly it approaches infinity (when being run through the polynomials that determine the set)

posted by mulligan at 6:27 PM on April 2, 2007

*Do the colors in fractals mean anything or are they purely aesthetic additions? I've never really understood that aspect of fractal illustrations.*"The Mandelbrot set is actually an either or thing, when graphing it, things that belong to the set are colored one color and things outside the set are colored another.

The fancy colors are then derived by coloring everything not in the Mandelbrot set a different color, based on how quickly it approaches infinity (when being run through the polynomials that determine the set)

posted by mulligan at 6:27 PM on April 2, 2007

Lots of

posted by Ethereal Bligh at 6:30 PM on April 2, 2007 [1 favorite]

*a little knowledge is a dangerous thing*in this thread.posted by Ethereal Bligh at 6:30 PM on April 2, 2007 [1 favorite]

Man, I’d like to be bigger than the known universe, that’d be sweet. Who’s the big man now, huh? I am buddy. Even if you had a gun, it’d be like, no way. I’m bigger than the known universe buddy. Eat it.

posted by Smedleyman at 6:31 PM on April 2, 2007

posted by Smedleyman at 6:31 PM on April 2, 2007

They should have sent a poet.

posted by poweredbybeard at 6:49 PM on April 2, 2007

posted by poweredbybeard at 6:49 PM on April 2, 2007

The set of all natural numbers evenly divisible by my big toe is also larger than the known universe, but it's not as pretty to look at. The known universe is nothing compared to the unknown universe.

posted by sfenders at 6:51 PM on April 2, 2007

posted by sfenders at 6:51 PM on April 2, 2007

I'm surprised no one has brought up the (to my knowledge) original zooming film - Charles and Ray Eames Powers of 10. The video can be found on Google Video.

There's also a Simpsons version.

posted by pombe at 6:56 PM on April 2, 2007

There's also a Simpsons version.

posted by pombe at 6:56 PM on April 2, 2007

Of course, this fractal is an imaginary thing, so it isn't really bigger than the universe. Unless our imaginations are.

posted by Citizen Premier at 5:30 PM on April 2

Of course, this fractal is an imaginary thing, so it isn't really bigger than the universe. Unless our imaginations are.

posted by Citizen Premier at 5:30 PM on April 2

What's the difference?

posted by krash2fast at 7:09 PM on April 2, 2007

Well I picked a great day to quit dropping acid, apparently.

posted by Benny Andajetz at 7:11 PM on April 2, 2007

posted by Benny Andajetz at 7:11 PM on April 2, 2007

It really seems to me that this discussion is a lot like "the biggest number" problem. Who can imagine two universes? Can something in the universe describe something bigger than the universe? Of course it can! Case closed!

posted by Area Control at 7:11 PM on April 2, 2007 [1 favorite]

posted by Area Control at 7:11 PM on April 2, 2007 [1 favorite]

Sorry Doug Adams did it the best :

Space is big. You just won't believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it's a long way down the road to the chemist's, but that's just peanuts to space.

posted by MrLint at 7:25 PM on April 2, 2007

Space is big. You just won't believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it's a long way down the road to the chemist's, but that's just peanuts to space.

posted by MrLint at 7:25 PM on April 2, 2007

Every once in a while I recognized one of those famous spiky pig shapes and wished they would veer off the center into one of them. To me, that's an even bigger mind-blower -- zooming into one of those horns and seeing that it's made up of similar but not identical versions of the same thing.

posted by ken_zoan at 8:02 PM on April 2, 2007

posted by ken_zoan at 8:02 PM on April 2, 2007

probably the shaders and audio, but regardless, i think quaternions are a bit scarier

posted by sponge at 8:17 PM on April 2, 2007 [1 favorite]

posted by sponge at 8:17 PM on April 2, 2007 [1 favorite]

If your mind is as yet insufficiently blown, allow me to introduce to the other side of the Mandelbrot set: the Buddhabrot.

The best way to see it is Albert Lobo's staggering Buddhabrot video on youtube or high-res avi, and here's his Buddhabrot zooming applet.

posted by MetaMonkey at 8:26 PM on April 2, 2007

The best way to see it is Albert Lobo's staggering Buddhabrot video on youtube or high-res avi, and here's his Buddhabrot zooming applet.

posted by MetaMonkey at 8:26 PM on April 2, 2007

**mulligan**Well put. The colors are generally derived from the amount of iterations it takes to escape the unit circle in the complex plane. Anything within the Mandelbrot set (black) is assumed to never escape the unit circle since it doesn't after n iterations. (n varies by the program). In theory the Mandelbrot set could be empty.

Note that even though you see a similar set when you've zoomed all the way in, it's not exactly the same set, just similar... at least no one has found an exact mini Mandelbrot within this set. Let me know when you find one...

posted by jeblis at 8:28 PM on April 2, 2007 [1 favorite]

**Sponge**:

*i think quaternions are a bit scarier*

The quaternions aren 't so scary if you turn down the music. They remind me of time elapsed photography of organic growth or decay, which if you think about it would make sense in that just as nature has congruent shapes that appear all through it in the inner workings of life from the microscopic level to the naked eye level, so would "time" as one of the primary forces of the universe, also have similar iterating basic shapes fashioned by some certain forces or laws that hold the fabric of reality together. It would be interesting if you could add gravity as another element to quarternions. Maybe that would be approaching something like a visualization of String Theory.

As for that Mandlebrot zoom, I may be completely wrong, but I think the shapes and colors are about as real or meaningful, as the shadows playing on the wall in Socrates's cave in

*Plato's Republic*. And like that, it's not so much about what you see but the movement produced in your imagination by seeing, just as Mandlebrots set is not about the numbers, but the interaction of the numbers. To sum up, it is an opening and an opportunity for the mind to go to a different place.

posted by Skygazer at 8:53 PM on April 2, 2007

That's one hell of a non-standard

1. In non-technical language, "wrong".

posted by Ethereal Bligh at 9:07 PM on April 2, 2007

^{1}reading of the cave analogy in*Republic*.1. In non-technical language, "wrong".

posted by Ethereal Bligh at 9:07 PM on April 2, 2007

*Well, numbers are a concept, and all concepts are imaginary. Which is to say they exist inside the brains of human beings and nowhere else.*

But I think maybe some scientists or mathematicians would beat me up if they heard me say that.

But I think maybe some scientists or mathematicians would beat me up if they heard me say that.

Citizen Premier: I doubt that the scientists or mathematicians are all too worried about it. I'd imagine, though, that there are a bunch of philosophers sharpening knives and lighting torches. Watch out for zombie Plato!

posted by ssg at 9:11 PM on April 2, 2007

Turn left dammit! Left! I said LEFT!!!

MetaFilter:

posted by CG at 9:34 PM on April 2, 2007 [1 favorite]

MetaFilter:

*WTF Stupidly Gigantor*posted by CG at 9:34 PM on April 2, 2007 [1 favorite]

I have this on my itunes.

posted by Wonderwoman at 9:41 PM on April 2, 2007

posted by Wonderwoman at 9:41 PM on April 2, 2007

*"But I think maybe some scientists or mathematicians would beat me up if they heard me say that."*

Most mathematicians today are, by training, formalists. So they would agree with you, not beat you up. However, I've read one mathematician who claims that most of them are "secretly" platonists. This seems right to me as many people who are drawn to math think in terms of "discovery", not "invention". Nevertheless, unlike the case with the sciences, math is pure abstraction and thus the argument of formalism vs platonism is not irrelevant or esoteric to the discipline. There are good reasons why math has largely adopted formalism in the last hundred years.

On the other hand, many or most (but certainly not all) the physicists I've known have been what I call naive materialists or possibly a sort of platonist. With regard to math, though, they may well be formalists, seeing math as a formalist tool used to describe platonic principles (if they're inclined to that sort of platonism) or, alternatively, they may see math as a formalist tool used to describe their materialist universe. Only a certain kind of physicist involved in stuff like information theory would, as ssg says, find this interesting. But it is an important matter, though largely settled, in math.

posted by Ethereal Bligh at 9:51 PM on April 2, 2007 [1 favorite]

Ethereal: I don't think it is fair to paint mathematicians as "secretly" platonist. Of course mathematicians think in terms of discovery: they "discover" facts that follow from their chosen axioms. I don't see how that is incompatible with a formalist position. Sure, mathematicians tend to immerse themselves within the formalist framework, but I don't see why this leads them to ontological conclusions about mathematical objects.

Physicists, though, I'd say you've portrayed fairly: math is just a useful tool to most of them. I think most of them would just stare at you if you questioned the ontological status of material vs. mathematical objects. So Citizen Premier is safe from them at least.

posted by ssg at 10:22 PM on April 2, 2007

Physicists, though, I'd say you've portrayed fairly: math is just a useful tool to most of them. I think most of them would just stare at you if you questioned the ontological status of material vs. mathematical objects. So Citizen Premier is safe from them at least.

posted by ssg at 10:22 PM on April 2, 2007

A fractal bigger than the known universe? But what if the known universe IS a fractal?

An astrophysicist by the name of Laurent Nottale has proposed a theory called scale relativity, in which the geometry of space-time itself is fractal. Some people seem to think scale relativity is nonsense, not even deserving to be called a theory, but Nottale has published many papers on the subject, and continues to do so.

I find the idea pretty appealing, but I'm not a physicist, so I have no idea how valid it is.

Also: Does anyone remember CHAOS: The Software?

posted by benign at 10:47 PM on April 2, 2007

An astrophysicist by the name of Laurent Nottale has proposed a theory called scale relativity, in which the geometry of space-time itself is fractal. Some people seem to think scale relativity is nonsense, not even deserving to be called a theory, but Nottale has published many papers on the subject, and continues to do so.

I find the idea pretty appealing, but I'm not a physicist, so I have no idea how valid it is.

Also: Does anyone remember CHAOS: The Software?

posted by benign at 10:47 PM on April 2, 2007

Didn't see any Basilisks.

Unless that weird little thing expanding at the top left is ...

posted by thatwhichfalls at 11:03 PM on April 2, 2007

Unless that weird little thing expanding at the top left is ...

posted by thatwhichfalls at 11:03 PM on April 2, 2007

I think I was prejudiced by a book I started reading about Fermat's Last Theorem. The author explained how mathematics was immutable and contained the secrets of the universe. That didn't put me off as much as when he said it was superior to science because scientific theories change.

Still, I don't have a good reason to assume other mathematicians are like that. But I still think so.

posted by Citizen Premier at 11:22 PM on April 2, 2007

Still, I don't have a good reason to assume other mathematicians are like that. But I still think so.

posted by Citizen Premier at 11:22 PM on April 2, 2007

whoa...

The posted video seemed a bit jittery at points, and what I really missed was some color cycling.

Then someone posted quaternion videos, & I remembered that, years ago, I wanted to paint my walls with a slice of a quaternion fractal.

And that buddhabrot's awesome. I see the nebula comparison.

posted by Pronoiac at 1:04 AM on April 3, 2007

The posted video seemed a bit jittery at points, and what I really missed was some color cycling.

Then someone posted quaternion videos, & I remembered that, years ago, I wanted to paint my walls with a slice of a quaternion fractal.

And that buddhabrot's awesome. I see the nebula comparison.

posted by Pronoiac at 1:04 AM on April 3, 2007

"That's one hell of a non-standard reading of the cave analogy in Republic."

Okay, well it's been a while since we went over it in philosophy, but although it's an unusual application of it I think he follows the theme pretty well.

Some people are saying that the "scale" and the set itself is arbitrary, but the apparent arbitrariness of the set, and it's scale, is only as arbitrary as mathematics.. which is arguably *LESS* arbitrary than the universe itself - as it is derived phenomenologically (from our senses) rather than logically. That is, the universe is subject to bias of perception, wheras mathematics, and therefore the mandelbrot *isn't*

In a round about way, the mandelbrot is more real than you are :)

But I think the reason people are having an issue with this is when a set with no scale or units whatsoever is apparently bigger than the universe. A few people have already explained it better than I could, but if you want something nice and simple:

The mandelbrot set, like all fractals, extends infinitely in scale in both directions. Although this set doesn't have numbers (or at least show them) if you were to take a frame of the video, any frame, and give it any size you want, the set would still be bigger than the universe, because it extends infinitely. That's why there are no shown units - they are largely irrelevant, as the only point of reference is the start of the calculation.

In reference to mathmaticians, I would say that it depends on the field but I think you can safely generalise that the more abstract the field the more philosophical and inclined to platonist the mathmatician is likely to be.

I know a few phD math students, I think I might pose the question to them, could be interesting to see if my intuition is correct.

posted by Dillonlikescookies at 4:16 AM on April 3, 2007

Okay, well it's been a while since we went over it in philosophy, but although it's an unusual application of it I think he follows the theme pretty well.

Some people are saying that the "scale" and the set itself is arbitrary, but the apparent arbitrariness of the set, and it's scale, is only as arbitrary as mathematics.. which is arguably *LESS* arbitrary than the universe itself - as it is derived phenomenologically (from our senses) rather than logically. That is, the universe is subject to bias of perception, wheras mathematics, and therefore the mandelbrot *isn't*

In a round about way, the mandelbrot is more real than you are :)

But I think the reason people are having an issue with this is when a set with no scale or units whatsoever is apparently bigger than the universe. A few people have already explained it better than I could, but if you want something nice and simple:

The mandelbrot set, like all fractals, extends infinitely in scale in both directions. Although this set doesn't have numbers (or at least show them) if you were to take a frame of the video, any frame, and give it any size you want, the set would still be bigger than the universe, because it extends infinitely. That's why there are no shown units - they are largely irrelevant, as the only point of reference is the start of the calculation.

In reference to mathmaticians, I would say that it depends on the field but I think you can safely generalise that the more abstract the field the more philosophical and inclined to platonist the mathmatician is likely to be.

I know a few phD math students, I think I might pose the question to them, could be interesting to see if my intuition is correct.

posted by Dillonlikescookies at 4:16 AM on April 3, 2007

My universe can beat up your universe.

posted by Mr.Encyclopedia at 4:22 AM on April 3, 2007

posted by Mr.Encyclopedia at 4:22 AM on April 3, 2007

**Dillonlikescookies**writes

*"Some people are saying that the 'scale' and the set itself is arbitrary, but the apparent arbitrariness of the set, and it's scale, is only as arbitrary as mathematics."*

Er, no, because the scale is completely and totally arbitrary. It is based on a guy saying "Ok, imagine that the last image is screen sized. If that is the case, then blah blah blah". Mathematics, as you point out, is less arbitrary than the universe. If we accept that the universe, in a worst case scenario, is absolutely and completely arbitrary, then mathematics must be less than completely and absolutely arbitrary. Since the scale of this is absolutely and completely arbitrary, it isn't "only as arbitrary as mathematics", it's "more arbitrary than mathematics".

Or, perhaps rephrased: The scale of this isn't really "arbitrary". It's based on the writer of that blurb's way of imagining things, it's based on the size of modern computer monitors, it's based on the way people make analogies. These are all phenomenologically determined things. Mathematics, as you point out, is not. Mathematics is less arbitrary than that. Hence, the scale of this is more arbitrary than mathematics.

**Dillonlikescookies**writes

*"if you were to take a frame of the video, any frame, and give it any size you want, the set would still be bigger than the universe"*

Yes, but the issue here isn't whether the Mandelbrot set

*itself*is bigger than the universe, but if the

*section of it that was shown in the video*is bigger than the universe. These two arguments are not equivalent.

Doing the math here, it appears that if the final image were screen sized, the first image would indeed be bigger than the universe. However, that's not true for all zooms. Let's say I create a video where I zoom in from an image of a fractal, sized 1 cm x 1 cm, to 2x zoom. If I say "imagine that the last frame is the size it appears on screen (1 cm x 1 cm). The first image, then, would be bigger than the universe!" No, it would be 2 cm x 2 cm. The Mandelbrot set

*itself*might be infinite, but the particular zoom I did would not be infinite.

posted by Bugbread at 5:58 AM on April 3, 2007

Gee, I have a stupid question: how can they say that it's "larger than the known universe" if no scale is given?

posted by zorro astor at 6:38 AM on April 3, 2007

posted by zorro astor at 6:38 AM on April 3, 2007

"Er, no, because the scale is completely and totally arbitrary"

You could say so, but what I meant is that the scale is defined mathematically, ie, by the calculations of the mandelbrot equation. Point taken though.

"how can they say that it's "larger than the known universe" if no scale is given?"

To give the creator a bit of artistic license, if you will, i think they imagined full screen viewing when they made the statement, which puts it well within the realm of fact i believe. Take any *natural* scale (ie, Planck's length) and apply it to the last image and it should still work.

Pretty wacky claim to make, really, I would have put a little scale on the last frame to avoid this silly debate :P

posted by Dillonlikescookies at 7:26 AM on April 3, 2007

You could say so, but what I meant is that the scale is defined mathematically, ie, by the calculations of the mandelbrot equation. Point taken though.

"how can they say that it's "larger than the known universe" if no scale is given?"

To give the creator a bit of artistic license, if you will, i think they imagined full screen viewing when they made the statement, which puts it well within the realm of fact i believe. Take any *natural* scale (ie, Planck's length) and apply it to the last image and it should still work.

Pretty wacky claim to make, really, I would have put a little scale on the last frame to avoid this silly debate :P

posted by Dillonlikescookies at 7:26 AM on April 3, 2007

**zorro astor**writes

*"Gee, I have a stupid question: how can they say that it's 'larger than the known universe' if no scale is given?"*

They don't say "it's larger than the known universe", they say "

**If the final frame were the size of your screen**, the full set would be larger than the known universe."

**Dillonlikescookies**writes

*"Take any *natural* scale (ie, Planck's length) and apply it to the last image and it should still work."*

Someone mentioned that the zoom scale is 10^89. The ratio of the Planck length to the diameter of the universe is, according to Wikipedia, 2.7 × 10^61. So, yeah, it'll work with pretty much any natural scale.

posted by Bugbread at 9:13 AM on April 3, 2007

*"Okay, well it's been a while since we went over it in philosophy, but although it's an unusual application of it I think he follows the theme pretty well."*

No, because you said something like "the shadows are what's happening in our heads". But Plato's Forms are intimately related to his theory of Recollection. The

*physical world*and our direct experience of it

*are the shadows on the wall*and

*our comprehension of them is our ability to recollect the Forms*. So you've got it backward in your analogy.

*"In reference to mathmaticians, I would say that it depends on the field but I think you can safely generalise that the more abstract the field the more philosophical and inclined to platonist the mathmatician is likely to be."*

No, you've got that backward, too. In short, R&W's

*Principia*and Godel's response are some of the most "philosophical" and "abstract" mathematics there is and that was the time that mathematicians reluctantly began to embrace formalism. The disciplines within math that are the most "philosophical" are those which are most attuned to, and educated in, the reasoning that leads to formalism.

As for my relating the claim by a mathematician that most of them are ostensibly formalists but secretly platonists, this was in Davis and Hersh's

*The Mathematical Experience*, which I recommend. Their argument was that

*by temperament*, mathematicians are something like romantics and are emotionally inclined to mathematical platonism,

*feeling*that they are discovering the "truest" universe and that it exists independently of the minds thinking about it. By training, though, because of what I said in the previous paragraph, they

*know*better and are formalists.

posted by Ethereal Bligh at 11:41 AM on April 3, 2007

**delmoi**writes

*"Are you guys having an argument about this? Sheesh."*

On behalf of all people who enjoy discussing things that you personally don't, I apologize.

posted by Bugbread at 12:38 PM on April 3, 2007 [2 favorites]

I personally think its smaller than the known universe by a few inches.

Great zoom though, reminds me of a large part of my childhood rendering Mandelbrot and Julia zooms with fractint on an old 386. For a good VESA result it would take close to five minutes just for one frame, which makes this video even more impressive to me.

posted by samsara at 1:11 PM on April 3, 2007

Great zoom though, reminds me of a large part of my childhood rendering Mandelbrot and Julia zooms with fractint on an old 386. For a good VESA result it would take close to five minutes just for one frame, which makes this video even more impressive to me.

posted by samsara at 1:11 PM on April 3, 2007

OK, here's something that I was thinking about recently, but didn't find any reference to in my comprehensive searching of the internet (read: quick glance at the wikipedia article on fractals): we pretty much always see fractals as 2-d representations on a plane. The self-similarity thing is two dimensional, and that's groovy.

But what about when we bump it up a dimension? It still makes sense, doesn't it, to use (I guess) the platonic solids to build something that's fractally self-similar in three dimensions?

And then what happens when we go to higher dimensions even?

I don't know, it makes my brain shiver. And I probably had a course in all this stuff back in my math days, but thanks to repeated head trauma and too much, I've forgotten more than I ever learned. Or something.

posted by stavrosthewonderchicken at 5:07 PM on April 3, 2007

But what about when we bump it up a dimension? It still makes sense, doesn't it, to use (I guess) the platonic solids to build something that's fractally self-similar in three dimensions?

And then what happens when we go to higher dimensions even?

I don't know, it makes my brain shiver. And I probably had a course in all this stuff back in my math days, but thanks to repeated head trauma and too much, I've forgotten more than I ever learned. Or something.

posted by stavrosthewonderchicken at 5:07 PM on April 3, 2007

Duh. I googled 'platonic solids fractals' and whambam. So, yeah, snazzy.

posted by stavrosthewonderchicken at 5:09 PM on April 3, 2007

posted by stavrosthewonderchicken at 5:09 PM on April 3, 2007

IRFH: Did your fortune cookie also mention the part about the origin of consciousness in the time-traveling heat sink? (Bicameral mind, schmicameral mind. I'm tellin' ya, it's all about

posted by eritain at 9:47 PM on April 3, 2007

*cooling the monkeys.*)posted by eritain at 9:47 PM on April 3, 2007

A while back, I was really stoned, and I realized that we all can see in N-number of dimensions.

(Bear with me here.)

We've all seen 2D graphs, say pressure vs. time; it's a simple XY chart with a line and two axes. We've all seen 3D graphs, say pressure vs. time vs. volume. What do you do when you want to include a 4th axis (i.e., a 4th dimension), say pressure vs. time vs. volume vs. temperature? Add color to the chart -- red = hot, blue = cold, etc. What if you want to include another, say pressure vs. time vs. volume vs. temperature vs. cost? Add a texture -- light dots mean cheap, heavy dots mean expensive. Etc. Etc... It starts getting crowded after 6 or 7 dimensions, but you can represent an arbitrary number of variables on a graph this way.

Now, look around and consider what you see -- say, a coffee table. It has length, width, and height. Three dimensions that could map to any three variables, pressure vs. time vs. volume if you like. It also has the fourth dimension of color. Map that to "temperature". It has texture -- five dimensions. Map it to "cost". It has a material type, wood vs. aluminum, vs. whatever. It has density. It has opacity. Etc., etc...

Voila, now you can see in N dimensions too! (And you can abstract those N dimensions to N variables, as a sort of "physical chart", ack!)

Use your new superpowers wisely.

And then I started wondering whether my cat is "hawt" -- to other cats, I mean. What really

Or is it more about attitude...?

posted by LordSludge at 8:01 AM on April 4, 2007 [1 favorite]

(Bear with me here.)

We've all seen 2D graphs, say pressure vs. time; it's a simple XY chart with a line and two axes. We've all seen 3D graphs, say pressure vs. time vs. volume. What do you do when you want to include a 4th axis (i.e., a 4th dimension), say pressure vs. time vs. volume vs. temperature? Add color to the chart -- red = hot, blue = cold, etc. What if you want to include another, say pressure vs. time vs. volume vs. temperature vs. cost? Add a texture -- light dots mean cheap, heavy dots mean expensive. Etc. Etc... It starts getting crowded after 6 or 7 dimensions, but you can represent an arbitrary number of variables on a graph this way.

Now, look around and consider what you see -- say, a coffee table. It has length, width, and height. Three dimensions that could map to any three variables, pressure vs. time vs. volume if you like. It also has the fourth dimension of color. Map that to "temperature". It has texture -- five dimensions. Map it to "cost". It has a material type, wood vs. aluminum, vs. whatever. It has density. It has opacity. Etc., etc...

Voila, now you can see in N dimensions too! (And you can abstract those N dimensions to N variables, as a sort of "physical chart", ack!)

Use your new superpowers wisely.

And then I started wondering whether my cat is "hawt" -- to other cats, I mean. What really

__does it__for cats, anyhow? Shiny coat? Bushy tail? Pink nose? What??Or is it more about attitude...?

posted by LordSludge at 8:01 AM on April 4, 2007 [1 favorite]

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