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Plausible nonsense...

Post Icon Posted: Submitted by Newtonswig on 4 March 2008 - 6:10pm.

Joined: 2006-10-01
Posts: 427

Inspired by Cosmin's notation for level 2 procrastination (here ), I hereby announce the innaugural bullsh*t equation writing contest.

Entries should look plausible to a first or (slightly slow witted) second year but must have no mathematical meaning whatsoever. Bonus points go to anyone with a derivation/justification good enough to fool the above.

Winner gets a hat.

‹ PBIG's Conjecture Monday's talk ›
Post Icon Posted: 4 March 2008 - 6:48pm

Joined: 2007-10-03
Posts: 382
$$ \oint_{\partial\Sigma} \nabla\cdot(\nabla\mathbf{F}+\nabla\times\mathbf{F}) \, \mathbf{\omega} = \int_{\omega} \Delta\mathbf{F} \,d \mathbf{\Sigma} $$

Proof :
Obviously $ \int_{\omega} \Delta\mathbf{F} \,d \mathbf{\Sigma} = \oint_{\partial\Sigma} \Delta\mathbf{F} \,\mathbf{\omega} $ by the interchange lemma, where the $ \oint $ is necessary as we are integrating along a closed curve.

Recall that $ \nabla \cdot (\nabla\mathbf{F}+\nabla\times\mathbf{F}) = \underbrace{\nabla\times\nabla\mathbf{F}}_{=0}+\underbrace{\nabla\cdot\nabla\times\mathbf{F}}_{=\nabla\cdot\nabla\mathbf{F}}=\nabla\cdot\nabla\mathbf{F} $ by the cross distributivity property.
But $ \Delta \mathbf{F}=\nabla \cdot \nabla \mathbf{F} $, therefore $ \oint_{\partial\Sigma} \nabla\cdot(\nabla\mathbf{F}+\nabla\times\mathbf{F}) \, \mathbf{\partial\Sigma} = \oint_{\partial\Sigma} \Delta\mathbf{F} \, \mathbf{\omega}=\int_{\omega} \Delta\mathbf{F} \,d \mathbf{\Sigma} \qquad \Box $

(I'll try a more nonsensical one later :p)
Post Icon Posted: 4 March 2008 - 6:53pm

Joined: 2006-11-02
Posts: 1017

So much for plausibility. Writing bullshit equations with a friend was a bit of a hobby of mine in boring (read "all") lectures back in France. :P

I'll make a serious attempt later on, shouldn't be too hard. In fact it's fairly easy to find valid equations in number theory that look totally ridiculous:

$$\limsup_{n\to \infty} \frac{(p_{n+1}-p_n)(\log\log\log p_n)^2}{(\log p_n)(\log\log p_n)(\log\log\log\log p_n)}\geqslant 4 e \gamma \alpha^{-1},$$

where $ p_n $ is the nth prime number and $ \alpha $ is the solution to $ x = 3+e^x $.
Post Icon Posted: 4 March 2008 - 9:57pm

Joined: 2006-10-09
Posts: 327

/me copypasta's the original PBIG conjecture in here.

/me realises that unfortunately this doesn't satisfy the "plausible" part, only the "nonsense."

/me leaves.
Post Icon Posted: 5 March 2008 - 12:41am

Joined: 2006-11-02
Posts: 1017

Damn it, I was about to make a PBiG joke myself.
Post Icon Posted: 5 March 2008 - 1:16am

Joined: 2007-10-04
Posts: 190

I think that's true most of the time :p
Post Icon Posted: 5 March 2008 - 6:19pm

Joined: 2006-10-10
Posts: 519

I'll go one level further and give you an entire subject with no mathematical content:

http://en.wikipedia.org/wiki/Combinatorics
Post Icon Posted: 5 March 2008 - 6:20pm

Joined: 2006-10-10
Posts: 519

Also, check this image for a sublime piece of mathematical nonsense:

http://www.encyclopediadramatica.com/Image:MATH.JPG
Post Icon Posted: 5 March 2008 - 6:25pm

Joined: 2006-11-02
Posts: 1017

That first one is actually true (the $ H_n $ one) assuming the epsilon is short for $ O(n^5) $.
Post Icon Posted: 5 March 2008 - 6:29pm

Joined: 2006-10-10
Posts: 519

It's internally true, from the point of view of number theory, but remember that number theory is just that: just a theory. So, like evolution, it's false and non-noteworthy

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