Geometry and shit.
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Re: Geometry and shit.
this ain't geometry, but it's some math shit.
Apparently 1+2+3+4.... = - 1/12
I think you need a subscription to read this: https://medium.com/cantors-paradise/the-ramanujan-summation-1-2-3-1-12-a8cc23dea793
But some of the same (without the more mathematical proofs) are in this video:
There's some weird stuff in mathematics. The physicists in the video say they only believe this because it comes out in physical calculations. It specifically comes out in the Casimir effect which proves that there is energy in vacuum because particles just pop out of nowhere from quantum fluctuations.
Apparently 1+2+3+4.... = - 1/12
I think you need a subscription to read this: https://medium.com/cantors-paradise/the-ramanujan-summation-1-2-3-1-12-a8cc23dea793
But some of the same (without the more mathematical proofs) are in this video:
There's some weird stuff in mathematics. The physicists in the video say they only believe this because it comes out in physical calculations. It specifically comes out in the Casimir effect which proves that there is energy in vacuum because particles just pop out of nowhere from quantum fluctuations.
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Re: Geometry and shit.
nearly the same thing.
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Re: Geometry and shit.
There seems to be a whole underlying set of physics that, from my limited knowledge, we haven't quite got our head around just yet or maybe havent even thought up.
I wonder when the next really big revelation in physics will appear and unlocks a whole new field for investigation!!
I wonder when the next really big revelation in physics will appear and unlocks a whole new field for investigation!!
Re: Geometry and shit.
funny thing is, that after quantum physics, physicists pretty much recognized this was the way things worked. The mind can only be blown so many times. So they settled down and weren't surprised when particle physics and quantum electrodynamics came around, then quarks and the Standard Model. Now we are toying with string theory and dark matter/energy; both sort of going in circles but not surprising anyone. Not anymore.
We've seen the nether regions beyond our grasp since about the 1930's: quantum/particle physics doesn't mesh with Einstein's theory of gravity. Both theories work perfectly to the limits of experiment within their respective spheres. But finally something new has come along. Since Dark Matter/Energy follows gravitation but doesn't fit into particle physics, people are hopeful that it will point the way to a deeper theory. Still hammering away at it. The problem is that it doesn't fit into a laboratory setting, so all the observations are astronomical. It's almost like doing paleontology.
We've seen the nether regions beyond our grasp since about the 1930's: quantum/particle physics doesn't mesh with Einstein's theory of gravity. Both theories work perfectly to the limits of experiment within their respective spheres. But finally something new has come along. Since Dark Matter/Energy follows gravitation but doesn't fit into particle physics, people are hopeful that it will point the way to a deeper theory. Still hammering away at it. The problem is that it doesn't fit into a laboratory setting, so all the observations are astronomical. It's almost like doing paleontology.
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Re: Geometry and shit.
It is that deeper theory that I am thinking about. There must be something that governs the very basis of physics... the basic laws that thereafter split in to each specific field...?
That may be wrong and there are several end points that happen to just interact with each other to give the results that we see and no underlying starting point for all...
That may be wrong and there are several end points that happen to just interact with each other to give the results that we see and no underlying starting point for all...
Re: Geometry and shit.
The universe exists, which means our two best theories to explain it can't contradict when you reach for example the atomic scale. That's why we know there must be one theory that encompasses both but mutates them enough to fit together smoothly. Existence brooks no gray area.
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Re: Geometry and shit.
Can we know that there is only one if we dont know what it is?
Is there not a possibility that there are, to use a bad metaphor, 2 pillars that are independent in themselves but underpin everything on top?
As far as I get it classical physics works to a point then doesnt any more... quantum works to a point and then doesnt any more. And that may be because we havent joined the middle up or because they are not contingent on each other?
I, again possibly naively, assume that there are some constants in the universe that just are (maybe because they could be no other way) and may never have an explanation other than they could be no other way. They dont need to be related other than they interact with each other to produce everything we see in the universe.
Is there not a possibility that there are, to use a bad metaphor, 2 pillars that are independent in themselves but underpin everything on top?
As far as I get it classical physics works to a point then doesnt any more... quantum works to a point and then doesnt any more. And that may be because we havent joined the middle up or because they are not contingent on each other?
I, again possibly naively, assume that there are some constants in the universe that just are (maybe because they could be no other way) and may never have an explanation other than they could be no other way. They dont need to be related other than they interact with each other to produce everything we see in the universe.
Re: Geometry and shit.
There can be two separate pillars, but there shouldn't be any leaks where the roof joins them. Right now we've got leaks, or more precisely, it's like two different architects building out from each pillar and we don't see how they can possibly fit together.
There's 25 constants in the Standard Model of particle physics, with no clear relationship between them; appear to be random. The anthropic principle does place limitations: if many of them are nudged ever so little atoms above hydrogen can't form, or galaxies won't hold together, etc etc and life couldn't form. So the fact that we exist places constraints on this randomness. There may be other lifeless universes out there, we just happened to win the dice toss.
Or there could be one big over-arching theory that ties all the constants together. We don't know. But the random constants could be separate from the gravitation/quantum divide, since the standard model does not include gravity.
There's 25 constants in the Standard Model of particle physics, with no clear relationship between them; appear to be random. The anthropic principle does place limitations: if many of them are nudged ever so little atoms above hydrogen can't form, or galaxies won't hold together, etc etc and life couldn't form. So the fact that we exist places constraints on this randomness. There may be other lifeless universes out there, we just happened to win the dice toss.
Or there could be one big over-arching theory that ties all the constants together. We don't know. But the random constants could be separate from the gravitation/quantum divide, since the standard model does not include gravity.
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Re: Geometry and shit.
halfwise wrote:this ain't geometry, but it's some math shit.
Apparently 1+2+3+4.... = - 1/12
There's some weird stuff in mathematics. The physicists in the video say they only believe this because it comes out in physical calculations. It specifically comes out in the Casimir effect which proves that there is energy in vacuum because particles just pop out of nowhere from quantum fluctuations.
Remember that rule they taught you way back in 3rd grade about "you can NEVER divide by zero"?
Well sometimes you have to .... and THAT's where the magical creatures live!
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Re: Geometry and shit.
I've been frustrated many times talking to students about some physics concept, and what happens as the denominator goes to zero....expecting they'll say the fraction goes to infinity. But instead their eyes go blank and they say you can't divide by zero.
Well, it turns out we were BOTH wrong. But I still think infinity is a better answer than "you can't do that".
Well, it turns out we were BOTH wrong. But I still think infinity is a better answer than "you can't do that".
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Re: Geometry and shit.
It specifically comes out in the Casimir effect which proves that there is energy in vacuum because particles just pop out of nowhere from quantum fluctuations.- Halfy
{{Talking of infinity- what if its just turles all the way down?!
First we thought they was just nothing there, then they found out there was stuff there so it had be coming from somehwere, then we discovered this whole other wierd layer of stuff that to us looks like nothing but turns out could potentially be everything and anything butwe dont know what it is exatly or quite what its doing or how, or for that matter where it comes from, what if we find there's something else even weirder and bizzare below it that makes it and so on- like zooming into a fractal, doesn't matter how deep you go there is just more detail, more stuff. }}
{{Talking of infinity- what if its just turles all the way down?!
First we thought they was just nothing there, then they found out there was stuff there so it had be coming from somehwere, then we discovered this whole other wierd layer of stuff that to us looks like nothing but turns out could potentially be everything and anything butwe dont know what it is exatly or quite what its doing or how, or for that matter where it comes from, what if we find there's something else even weirder and bizzare below it that makes it and so on- like zooming into a fractal, doesn't matter how deep you go there is just more detail, more stuff. }}
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Pettytyrant101- Crabbitmeister
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Re: Geometry and shit.
Petty - this is one of the things I love about watching religious apologetic. One key arguement is the "something from nothing" arguement... usually put across in something like the Kalam Cosmoglical arguement (plus the random insertion of a god).
It seems we are getting closer and closer to thinking that the philosophical nothing (I.e. literally nothing... no particles, energy waves etc) is not actually possible and that we may well be looking at an infinite regress or a period before "time" that somehow managed to start time as we know it etc.
Fun stuff!
It seems we are getting closer and closer to thinking that the philosophical nothing (I.e. literally nothing... no particles, energy waves etc) is not actually possible and that we may well be looking at an infinite regress or a period before "time" that somehow managed to start time as we know it etc.
Fun stuff!
Re: Geometry and shit.
Yeah, the natural numbers are a completely artificial construct created for counting man made things and nothing more. Zero was a patch. Negative numbers were another patch. Fractions were another. Decimal notation another. Zero and fractions didn't play nice with each other so we put them in separate rooms. But it still only worked for things that stood still long enough to be counted or measured. What to do about things that were moving or changing size? What if you used letters instead of numbers, did the calculations, and only plugged the zero in after you'd done the dirty work? What if you create a thing called Infinity or Infinitesimals or limits approaching zero but never actually getting there?
It's all patches on patches on on patches on patches on patches on patches on patches .........
And it's all built on a foundation of primitive humans counting on our fingers. Of course it's all riddled with holes. That's what gives mathematicians job security!
It's all patches on patches on on patches on patches on patches on patches on patches .........
And it's all built on a foundation of primitive humans counting on our fingers. Of course it's all riddled with holes. That's what gives mathematicians job security!
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Re: Geometry and shit.
The fractal/infinite recursion supposition has been put forward before, the difference is that every time we go deeper we see something different, not just a morphed version of what we had before. It would be really helpful if nature started repeating itself on deeper levels...
But I long ago gave up on even understanding our current model. My problem is for my mind to continue to function I need to relate it to real life, and once you get a level deeper than quantum you just can't relate it to anything. You're too deep.
But I long ago gave up on even understanding our current model. My problem is for my mind to continue to function I need to relate it to real life, and once you get a level deeper than quantum you just can't relate it to anything. You're too deep.
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Re: Geometry and shit.
I LOVE this idea that negative numbers, zero, etc are all just patches. We really are constrained to grasp everything by our fingers.
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Re: Geometry and shit.
A friends wife specialised in theoretical numbers such as the square root of -1. Turns out there are loads of theorems and fancy equations that use them for proofs.
Nagual- Ringwinner
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Re: Geometry and shit.
Square root of -1 = 'i' (imaginary number) is used ALL THE TIME in real world science and engineering. Its most important use is Euler's formula:
exp(i*x) = cos(x) + i*sin(x) where exp(x) means raise e to the power of x.
It's much easier to work with exponentials than sines and cosines, and all the trig identities can be easily derived from this formula. It's spooky but magical. Any type of calculation involving waves is usually done using this formula. One cool thing you can do is the identity (using x in radians)
exp(i*pi) = -1
It's got a negative number, two irrational numbers, and the an imaginary number. You struggle to comprehend each of these these in turn in elementary school, grade school, and college. Once you understand this formula you have reached a new world of understanding.
exp(i*x) = cos(x) + i*sin(x) where exp(x) means raise e to the power of x.
It's much easier to work with exponentials than sines and cosines, and all the trig identities can be easily derived from this formula. It's spooky but magical. Any type of calculation involving waves is usually done using this formula. One cool thing you can do is the identity (using x in radians)
exp(i*pi) = -1
It's got a negative number, two irrational numbers, and the an imaginary number. You struggle to comprehend each of these these in turn in elementary school, grade school, and college. Once you understand this formula you have reached a new world of understanding.
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Re: Geometry and shit.
Start with the video, though when he gets to multiplying complex numbers I think he's no more clear then I was.
But um, yeah. The square root of negative numbers is actually related to waves and is the lifeblood of any analysis involving waves. It's a magical subworld of mathematics that most of the population doesn't even know exists but is an indispensible part of life for those who use it.
But um, yeah. The square root of negative numbers is actually related to waves and is the lifeblood of any analysis involving waves. It's a magical subworld of mathematics that most of the population doesn't even know exists but is an indispensible part of life for those who use it.
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Re: Geometry and shit.
Hmm yes, yes, it all makes sense now!
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Re: Geometry and shit.
It's one of the deeper parts of mathematics that suddenly becomes more useful rather than less as you push through the esoterica.
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Re: Geometry and shit.
Okay, this beautiful video is much simpler to follow than the above, and shows one simple example of why Newton is so revered.
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