are shapes finite?
- Thread starter stat
- Start date
It's flawed, take four line sof equal length and you can have an infinite number of shapes. A shape with four equal sides is a rhombus, taking two adjacent lines for each angle bewteen them in the interval (0,pi], there is a unique rhombus. The interval (0,pi] is an infinite set.
Shippou-Sensei
4:1:2.5
stat said:
even if it's just changing the angle between the lines, there are actully a infinite amount of angles between 0 and 90
90 and 90.00000000000000000000000000000000000000000000000000000000000001 are diffrent angles even if you cannot see any diffrence on a small scale
shapes only match other shapes if you mesure them imperfectly there are an infinet amount of tiny chages you can make
angry bob said:
Theorists are only just coming to terms with it.
angry bob said:
None in anything remotely resembling English, I'm afraid. No-one - that know of, and I've been looking quite hard - knows how to say it in English
Google up "Loop Quantum Gravity" and report back, please
angry bob said:
That's a very, very interesting question
bluestreak
HomosexualityIsStalin’sAtomBombtoDestroyAmerica
i love geeks. i'm just not maths enough to do this properly. i operate based on guesswork and bouncing ideas off the bits i understand 
Shippou-Sensei
4:1:2.5
prusmamablt this is mathmatical shapes not realworld shapes as real world constrains will mean the shap is imperfect and non identical anyhow
Leaving aside the fact that the "If the universe is infinite, it contains every possible arrangement of X" argument is fallacious, there is no limit to the number of edges a three-dimensional object can have, so theoretically, there is an infinite number of possible shapes.stat said:
acidifiedaussie
Active Member
Take a look at the planes of existence these shapes are on. are you taking iinto account super dimensions, disected dimensions, if so then the number of shapes is infinte. Put it on a plane of x,y,z,ie 3 dimensions and the number of shapes that can be created is immense to say the least
In Bloom said:
That's about the only point I've been able to understand on this thread
I thought that my initial argument was flawed because even if shapes were finite, and space infinite, all the shapes didn't *have* to re-occur.
I can see now that the number of possible shapes must be infinite, as the number of edges can always be increased. But, just supposing that Ben Nevis had 100 million edges, I still can't see how the number of variations of 100 million edges can be infinite. Which means that in an infinite universe, the probability of a similarily-shaped 100 million edged shape must be quite real, right?
bluestreak
HomosexualityIsStalin’sAtomBombtoDestroyAmerica
stat said:
real, but statistically also so small as to be infinitely unlikely!
bluestreak
HomosexualityIsStalin’sAtomBombtoDestroyAmerica
laptop said:Ooooh... let's not leave it aside.
John Barrow must be told
who?
bluestreak said:
"Professor Infinity" John Barrow
Author of The Infinite Book: a short guide to the boundless, timeless and endless
Jonti said:
I meant the arrow paradox ... and I realise that there are resolutions to that too ... its just that I find them rather unsatisfactory.
I like this guys solution the best:
http://www.eurekalert.org/pub_releases/2003-07/icc-gwi072703.php
i.e. that there is no such thing as an instant in time ... there is no now
(but of course, if space isnt continuous, then Zeno's paradox is no longer a paradox!)
bluestreak
HomosexualityIsStalin’sAtomBombtoDestroyAmerica
laptop said:
sounds complicated but i'll stick it on my reading list. ta,.
In Bloom said:
I'm not sure that I follow this.
Given that there is a finite probability of a particular event occuring in any given finite region of space-time (i.e. the formation of the Ben Nevis mountain), then infinite space implies infinite Ben Nevis's ... indeed in every possible (finite probability) arrangement.
The product of a finite number and infinity is infinity ... I think
fudgefactorfive
New Member
angry bob said:I'm not sure that I follow this.
Given that there is a finite probability of a particular event occuring in any given finite region of space-time (i.e. the formation of the Ben Nevis mountain), then infinite space implies infinite Ben Nevis's ... indeed in every possible (finite probability) arrangement.
The product of a finite number and infinity is infinity ... I think
No, not necessarily. Just because you have an infinite space to work with, doesn't mean that things can't be unique. There is an infinite number of numbers, for example, but only one seven.
bluestreak
HomosexualityIsStalin’sAtomBombtoDestroyAmerica
fudgefactorfive said:
yeah, but i don't think it works like that, as seven is only a way of keeping count. there may only be one seven but things that have a value of seven will occur within the range 0-infinity within an infinite universe. IYSWIM. i think.
fudgefactorfive
New Member
bluestreak said:
No I don't SWYM, sorry
But yeah, it's a crap example. A better one was the Mandelbrot set example I posted earlier. There's infinite space there, and infinite complexity: but every configuration of patterns within it is unique, and there are possible patterns that will never come up. Having infinite space doesn't mean that anything can happen. (It might - but just being infinite doesn't guarantee it.)
bluestreak
HomosexualityIsStalin’sAtomBombtoDestroyAmerica
i dunno, if you've got infinite space to work within then the possibilities of any event happening surely has to take into account that infinite space. it might only end up being a 0.000000000000000000000000000*insert lots of zeroes*00000001 chances in infinity. it doesn't say it HAS to exist, but the possibility is there. it may be extremely unlikely given our current understanding of the laws of physics, but who knows what will be discovered tomorrow!
So what you are saying (perhaps ) is that there are infinitely small probabilities?
i.e. given infinite numbers, the probability of one chosen at random being 7 is infinitely small?
So the number of 7s are infinity/infinity = 1
I realise that infinity/infinity is meaningless ... you'll have to throw in the appropriate limits
) is that there are infinitely small probabilities?i.e. given infinite numbers, the probability of one chosen at random being 7 is infinitely small?
So the number of 7s are infinity/infinity = 1
I realise that infinity/infinity is meaningless ... you'll have to throw in the appropriate limits
bluestreak said:
I think it's overrated, actually. And there's some very wierd speculation in the final chapter. It's just that Barrow does have a rep as "Prof. Infinity" and is IIRC very keen on the idea that in an infinite universe everything will happen, er, infinitely many times.
fudgefactorfive
New Member
angry bob said:
Within that fractal pattern, yes. But they're possible in the sense that I could draw a grid with something looking a bit like the Mona Lisa on it, or imagine the Mona Lisa in my head. But just because the Mandelbrot set is infinitely complicated, doesn't mean that the Mona Lisa is going to crop up somewhere inside it. It never will, even if you looked forever.
I'm not saying the universe is a giant fractal. I'm just pointing out that just because something is infinite doesn't mean it can contain anything/everything.
fudgefactorfive said:
Ah, I see.
So the infinitude of the Mandelbrot set is of a different kind to the infinitude of the Universe.
Or so most people have presumed... the results of it not being so would be quite interesting.
Let's see (tho' very tired):
The infinity of the Mandelbrot set would seem to be a countable infinity, wouldn't it?
Most considerations of the infinitude of the Universe have assumed each dimension to be continuous. So there's no way it's a countable infinity.
But if we take the quantisation of space seriously - see above reference to Loop Quantum Gravity - then the Universe, too, would seem to be countable.
But^2, there's no reason why a countable infinity shouldn't contain infinite Mona Lisas, considering that each Mona Lisa has a finite amount of detail (a very large Hamiltonian matrix describing its quantum wavefunction
)So either the infinitude of the Mandelbrot set is constrained in some other way, or you're wrong and there are Mona Lisas in there somewhere...
fudgefactorfive
New Member
laptop said:
I'm very very very rusty on this terminology and can only follow about 3/4 of your post but dredging it all back up, I'm assuming no, it's not countable, because the set is plotted on an Argand diagram, with real numbers on one axis and imaginary numbers on the other. These two axes are continuous.
fudgefactorfive said:
That's worrying me, too.
But does the fact that it's drawn on a continuous background necesarily mean that the detail (or "quantity of detail") of the set is uncountable?. After all, large parts of it are "flat".
The continuity of the background (the Argand diagram) means that there is an uncountable infinity of points in the set.
But when we look at it at any particular scale, what we seem to see are connected areas - usually with eminently countable numbers of swirly bits hanging off them. That's what makes me intuit there's something countable about the level of detail.
But if you zoom in on one swirly bit you see it as a connected area with more countable swirly bits off it - bearing a very strong resemblance to those at radically different scales.
If it can be proved that there's no Mona Lisa in there, I suspect the proof has something to do with this self-similarity, Or to put it another way the sheer bloody repetitiveness of that bloody hippy graphic
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