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The Thinker
Join Date: Mar 2005 Posts: 3,278
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11-03-2005, 03:46 PM
| Quote: |
Originally Posted by AntonioLao Given the antiderivative or probability distribution function F(t), and the probability density function f(t) then F(t)=∫f(t)dt, which says that F(t) is the integral of f(t) running along differential time dt. | oh thanks.
One think, what is the differenc between octonions and quaternions? | | | | Raider of the lost time
Join Date: Nov 2003 Posts: 6,036
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11-03-2005, 04:04 PM
| | no idea
Quote: |
Originally Posted by GUILLE what is the differenc between octonions and quaternions? | I have no idea. As long as they are not useful in describing the centers of physics, I am not that much interested.
__________________
Time independence: [∂E(g)]²=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: ¶a(t)·¶r(t)=c²
| | | | The Thinker
Join Date: Mar 2005 Posts: 3,278
48 | |
11-03-2005, 05:39 PM
| Quote: |
Originally Posted by AntonioLao I have no idea. As long as they are not useful in describing the centers of physics, I am not that much interested. | But they are, because quaternions are describen in "the road to reality" so they must be important. | | | | Moderator
Join Date: Aug 2005 Posts: 7,749
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11-03-2005, 11:47 PM
|  What about less analysis and more utilization.
My grandfather used to say before they shot him! that too much analysis
leads to paralysis.and that the elementary and the simple seem to be completly
overlooked,it seems that these great minds of science and maths seem to want to out-complacate each other,invent more and more hyper-complex theories.
reminds me of when I was at school in the toilet all the lads tring to pee higher
than his chum!The last thing anybody wants or Needs is a complex Analysis
please in the name of simplicity,keep it simple?
kind regards michael. | | | | The Thinker
Join Date: Mar 2005 Posts: 3,278
48 | |
11-04-2005, 09:32 AM
| | Analysis leads to paralisis, good one!
I had never heard it before, it's great. But there is in contrast another saying: "too much action leads to destruction". Because if you jsut do things without thinking, then you will end up having no sense.
But I do agree complex analysis is a bit too complex. But we cannot simplyfy it now, definatelly not. because, as Russell said, when you get an idea you can't simplify it, because if you simplify it, it will not mean the same as it did when i was complex. | | | | Raider of the lost time
Join Date: Nov 2003 Posts: 6,036
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11-04-2005, 01:17 PM
| | usefulness of quaternions
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Originally Posted by GUILLE because quaternions are describen in "the road to reality" so they must be important. | Heaviside and Gibbs derived the widely used effective vector analysis from quaternions. Maxwell and Tait did used quaternions in the original formulations of electrogmagnetism but the modern days vector formulations are more effective and practical.
On the other hand, Roger Penrose had been using twistors since 1967 and still he could not unify quantum mechanics and general relativity. Einstein used tensors to unify general relativity and electromagnetism and he was not successful. Twistors and tensors (spinors) all have deep similarities with quaternions.
__________________
Time independence: [∂E(g)]²=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: ¶a(t)·¶r(t)=c²
| | | | The Thinker
Join Date: Mar 2005 Posts: 3,278
48 | |
11-05-2005, 08:29 AM
| Quote: |
Originally Posted by AntonioLao Heaviside and Gibbs derived the widely used effective vector analysis from quaternions. Maxwell and Tait did used quaternions in the original formulations of electrogmagnetism but the modern days vector formulations are more effective and practical.
On the other hand, Roger Penrose had been using twistors since 1967 and still he could not unify quantum mechanics and general relativity. Einstein used tensors to unify general relativity and electromagnetism and he was not successful. Twistors and tensors (spinors) all have deep similarities with quaternions. | So spinors is the set of twistors and tensors? If so, then is there any kind of spinors apart from twinstors and tensors? And if there is, has it been used to try and make the TOE? | | | | Raider of the lost time
Join Date: Nov 2003 Posts: 6,036
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11-05-2005, 03:28 PM
| | twistor to spinor
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Originally Posted by GUILLE So spinors is the set of twistors and tensors? | In my opinion, twistors are extensions of spinors. Both use complex numbers.
__________________
Time independence: [∂E(g)]²=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: ¶a(t)·¶r(t)=c²
| | | | The Thinker
Join Date: Mar 2005 Posts: 3,278
48 | |
11-05-2005, 05:23 PM
| Quote: |
Originally Posted by AntonioLao In my opinion, twistors are extensions of spinors. Both use complex numbers. | And do twistors themselves have extensions? Or are they the ultimate part of complex analysis? | | | | Raider of the lost time
Join Date: Nov 2003 Posts: 6,036
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11-05-2005, 05:29 PM
| | Spinors are two elements matrices. The twistors are 16 elements matrices.
__________________
Time independence: [∂E(g)]²=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: ¶a(t)·¶r(t)=c²
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