Red Rock: Calculus equation mystery at the Red Rock
August 17th, 2012 at 7:59:47 PM
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I apologize if this has been discussed before, but this remains one of the unsolved mysteries of my life. I'm not big on unanswered questions, like who is "Mr. Sanders" as the sign says above Winnie the Pooh's door. However, let's not get into that. The question at hand refers to a hanging canopy at the LBS casino in the Red Rock. It looks like a college chemistry class blackboard. What I've been trying to get an answer to for years is the equation near the top, in the center.
The one that begins dV/dt=2πMy... There are some big brains on this site so can anybody offer any clues? Personally, I think it is just a made up equation, but am not sure.
The one that begins dV/dt=2πMy... There are some big brains on this site so can anybody offer any clues? Personally, I think it is just a made up equation, but am not sure.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
August 17th, 2012 at 8:23:08 PM
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Whats in the mug below it? It has an arrow
pointing to the equation. Its a recipe for a
mixed drink.
pointing to the equation. Its a recipe for a
mixed drink.
"It's not called gambling if the math is on your side."
August 17th, 2012 at 8:34:40 PM
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dV/dt means change in volume over time. 2piMy looks like the circumference of beer mug and the other part would be other factors like size of the mouth and the rate of gulp or some other variable like this.
The equation looks like it is measuring how fast you can drink beer.
The equation looks like it is measuring how fast you can drink beer.
Edward Snowden is not the criminal, the government is for violating the constitution!
August 17th, 2012 at 8:38:11 PM
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The expression "dv/dt" is calculus, meaning the rate of change over time.
"It's not called gambling if the math is on your side."
August 17th, 2012 at 8:40:19 PM
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Quote: AceCrAAckersdV/dt means change in volume over time. 2piMy looks like the circumference of beer mug and the other part would be other factors like size of the mouth and the rate of gulp or some other variable like this.
The equation looks like it is measuring how fast you can drink beer.
I agree, thats why the beer mug has an arrow
pointing at the equation.
"It's not called gambling if the math is on your side."
August 17th, 2012 at 8:47:54 PM
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Quote: EvenBobThe expression "dv/dt" is calculus, meaning the rate of change over time.
/dt is change over time (denominator). Numerator is dV so they are measuring change of something related to change of something else. dV is probably volume.
Example dx/dt is change of distance over change of time. This is more commonly known as velocity.
dv/dt is change of velocity over time. This is more commonly known as acceleration.
Edward Snowden is not the criminal, the government is for violating the constitution!
August 17th, 2012 at 9:09:48 PM
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Thanks, but I knew the dv/dt part. What does the rest of it mean?
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
August 17th, 2012 at 9:17:28 PM
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2 pi M y looks to be the size of the mug. L(D) can mean how full it is. Sigma (D) is how much you can drink it, or how many gulps it take.
Edward Snowden is not the criminal, the government is for violating the constitution!
August 17th, 2012 at 9:50:41 PM
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Quote: WizardThanks, but I knew the dv/dt part. What does the rest of it mean?
Just a guess here, but I imagine that the V refers to Volume, and not velocity. It looks like it some kind of an estimate of the change in volume of the head of a beer as a function of the hops that are added.
It is a guess, but if there are 6 different kinds of hops and that strange symbol which looks like (£ or ₤) without the cross hatches stands for weights.
Another photo of equation in which there seems to be some indication that the head of the beer is related to the equation.
Seriously, guys. The Wizard is a mathematician. You don't have to tell him d()/dt is calculus. I had to understand this equation in my freshman year.
<->
August 17th, 2012 at 11:31:39 PM
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Quote: pacomartinJust a guess here, but I imagine that the V refers to Volume, and not velocity. It looks like it some kind of an estimate of the change in volume of the head of a beer as a function of the hops that are added.
It is a guess, but if there are 6 different kinds of hops and that strange symbol which looks like (£ or ₤) without the cross hatches stands for weights.
There's far more than 6 types of hops. I would guess head rentention, based on the words underneath the beer glass.
"Then you can admire the real gambler, who has neither eaten, slept, thought nor lived, he has so smarted under the scourge of his martingale, so suffered on the rack of his desire for a coup at trente-et-quarante" - Honore de Balzac, 1829
August 18th, 2012 at 12:50:51 AM
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I'm damned if I can see that arrow.
Anyway, judging by some other things, like the square root symbol just thrown out there to look "brainy", I vote for this being phoney entirely. Rather than the My portion meaning m times y, it probably means My as in me, myself, and I. I'm thinking somebody wrote a phoney equation about "how much beer I can drink" given certain parameters ... Live, it was probably funny to listen to.
Anyway, judging by some other things, like the square root symbol just thrown out there to look "brainy", I vote for this being phoney entirely. Rather than the My portion meaning m times y, it probably means My as in me, myself, and I. I'm thinking somebody wrote a phoney equation about "how much beer I can drink" given certain parameters ... Live, it was probably funny to listen to.
the next time Dame Fortune toys with your heart, your soul and your wallet, raise your glass and praise her thus: “Thanks for nothing, you cold-hearted, evil, damnable, nefarious, low-life, malicious monster from Hell!” She is, after all, stone deaf. ... Arnold Snyder
August 18th, 2012 at 1:48:11 AM
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My guess woudl be: it's the time evolution of the beer head volume. L(D) would be some foam producing function (not sure what D is), and e_i(D) some more complex mechanism destroying it.
They probably picked a random scientific paper about beer foam and cited some model results. Without this context, this equation is meaningless anyway.
Edit: My guess was right:
The von Neumann relation generalized to coarsening of three-dimensional microstructures
Robert D. MacPherson1 & David J. Srolovitz, Nature 446, p. 1053 (2007)
http://www.nature.com/nature/journal/v446/n7139/full/nature05745.html
Equation (2) in the fulltext PDF.
Edit^2:
There is a minus sign missing on the board.
They probably picked a random scientific paper about beer foam and cited some model results. Without this context, this equation is meaningless anyway.
Edit: My guess was right:
The von Neumann relation generalized to coarsening of three-dimensional microstructures
Robert D. MacPherson1 & David J. Srolovitz, Nature 446, p. 1053 (2007)
http://www.nature.com/nature/journal/v446/n7139/full/nature05745.html
Equation (2) in the fulltext PDF.
Edit^2:
There is a minus sign missing on the board.
August 18th, 2012 at 2:53:37 AM
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Quote: MangoJThey probably picked a random scientific paper about beer foam and cited some model results. Without this context, this equation is meaningless anyway.
You Sir get the Googler of the Year award. While I also thought it might be some random result I had no idea how to google the equation given the unusual characters.
August 18th, 2012 at 3:32:24 AM
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I don't know how to google for equations either. I was googleing for the estimated context, i.e. articles about beer foam "theory". There were a few science journalism reports about various scientific articles - and one of them was about a Nature article in a ridiculous way ("describing why that happens takes a formula with four Greek letters, four English ones, a couple of sets of brackets (one inside the other), and numbers piled three storeys high on top of each other." - yeah and all that journalists produce are random roman letters with spaces and dots every few inch).
Well, this read as a naive description of our formula, so I gave it a try. Got the Nature article from my university account (otherwise you need to pay $30 which is -EV), and luckily found the formula right on the first page.
Skill ? Maybe. Chances are that the Red Rock people also have read Nature article (Nature has a *huge* reputation), found it funny and postet the result.
Well, this read as a naive description of our formula, so I gave it a try. Got the Nature article from my university account (otherwise you need to pay $30 which is -EV), and luckily found the formula right on the first page.
Skill ? Maybe. Chances are that the Red Rock people also have read Nature article (Nature has a *huge* reputation), found it funny and postet the result.
August 18th, 2012 at 4:29:32 AM
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This thread is total nerd alert. If it is about beer, it seems like something Sheldon and the gang would need to create to try to figure out the best way to drink to fit in with the cool kids at the party on The Big Bang Theory. Like the right volume to look like you're drinking a lot, without actually doing it.
August 18th, 2012 at 5:16:02 AM
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Quote: ewjones080This thread is total nerd alert. If it is about beer, it seems like something Sheldon and the gang would need to create to try to figure out the best way to drink to fit in with the cool kids at the party on The Big Bang Theory. Like the right volume to look like you're drinking a lot, without actually doing it.
Well of course! Nerds and fanboys are at their social peak today, thanks in part to TBBT The restaurant marketeers wrote the equation on the blackboard for a reason.
August 18th, 2012 at 5:50:50 AM
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deleted
DUHHIIIIIIIII HEARD THAT!
August 18th, 2012 at 6:34:25 AM
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Quote: MangoJThe von Neumann relation generalized to coarsening of three-dimensional microstructures
Robert D. MacPherson1 & David J. Srolovitz, Nature 446, p. 1053 (2007)
I say we all raise our pints and give three cheers to Mango for an outstanding job! I must say, I wasn't expecting that. Did you have the password to read the article? Can you share with me with me, or the whole forum, a larger screenshot to get a better idea of the background to the formula?
Sir, if you're ever in Vegas I truly owe you a big frosty mug of draft beer.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
August 18th, 2012 at 6:49:29 AM
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Quote: WizardI say we all raise our pints and give three cheers to Mango for an outstanding job! I must say, I wasn't expecting that. Did you have the password to read the article? Can you share with me with me, or the whole forum, a larger screenshot to get a better idea of the background to the formula?
A free article with the equation
I get partial credit for figuring out that V was volume and not velocity.
The growth of grains (in metals, ceramics, etc) and bubbles (in froths, foams) has been a topic of active research for many years. We hereby refer the grain cells (or bubbles) all as domains. Relatively speaking, the two-dimensional growth process is much better understood. A good example is the von Neumann-Mullins formula which states that
dA/ dt =−2π M γ( 1−1/6 n)
MacPherson and Srolovitz derived some generalizations of 2-D formula to any space dimension (including the equation on the blackboard).
dV/ dt = −2πMγ ( L(D)− 1/6*Sum from i=1 to n of ei(D) )
Here, dV/dt is the rate of change of the volume V of a closed three-dimensional domain D having piecewise smooth boundary and with any two of its faces meeting along a triple line (of the grain system) at a fixed dihedral angle of 2π/3, L(D) is the mean width of D, n is the number of triple lines (edges) of D, ei(D) is the length of i-th triple line and the summation is over all n triple lines.
August 18th, 2012 at 7:21:20 AM
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Quote: WizardDid you have the password to read the article? Can you share with me with me, or the whole forum, a larger screenshot to get a better idea of the background to the formula?
Although I have the PDF on my harddisk, unfortunately for copyright reasons I cannot share it in public. I think the screenshot above (along with the articles abstract) gives a fair deal of context. If you are very interested, you can buy the article for $30 from the website. Better way is: Get access to a university library (or university internet network), and you can most probably download/print/copy the article for free - most universities subscribe to a lot of scientific publishers, especially to the Nature group, and the online subscription is verified by IP address (no password needed).
If you search for the title in Google Scholar, you may find articles citing this paper on Open Access publishers or preprint servers (arxiv.org) (as Martin already did) - giving you more about the general context.
Sorry to be picky about this copyright issue, but as an author of similar scientific papers my perception on this topic is biased.
Living on the other end of the world, most certainly I'll probably never make it to Vegas - but if I do I'll get you some "true beer" ^^
August 18th, 2012 at 8:56:01 AM
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deleted
DUHHIIIIIIIII HEARD THAT!
August 18th, 2012 at 10:01:22 AM
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Quote: MangoJAlthough I have the PDF on my harddisk, unfortunately for copyright reasons I cannot share it in public.
For those of you not reading my post above: A free article with the equation
The original article: R. D. MacPherson and D. J. Srolovitz, The von Neumann relation generalized to coarsening of three-dimensional microstructures, Nature, 446, 1053-1055 and Supplementary Material (2007).
This article is not free!
August 18th, 2012 at 10:11:35 AM
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Quote: pacomartinRelatively speaking, the two-dimensional growth process is much better understood. A good example is the von Neumann-Mullins formula which states that
dA/ dt =−2π M γ( 1−1/6 n)
In the 2-D problem it is easy to see that formula shows that
dA/dt=0 when n=6
dA/dt>0 when n<6
dA/dt<0 when n>6
So if the cell has 6 sides it neither grows nor shrinks but it can change shape. If it has more than 6 sides it shrinks. If it has less than 6 sides it must grow.
animation
August 18th, 2012 at 11:59:12 AM
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So, in a three-dimensional beer mug, what is the equilibrium number of bordering bubbles that a bubble that is neither growing nor shrinking going to have in the foam?
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
August 18th, 2012 at 12:31:24 PM
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Quote: WizardSo, in a three-dimensional beer mug, what is the equilibrium number of bordering bubbles that a bubble that is neither growing nor shrinking going to have in the foam?
I have posted the definition of ei(D) in previous post, but I am having trouble following it myself. In the Nature paper which was partially reproduced by Mango it says see figure 2a, but Mango did not reproduce the figure. Perhaps if we had it would be easier to visualize the concept.
Even the simplest concept like slope of a line gets more complex when you go to the 3rd dimension. Slope is not enough to fully describe a plane, as an infinite number of planes have the same slope. Now it is possible to go back to basic 2D geometry and change the invariant from slope to normal vector. For instance instead of y=mx+b (where m is slope and b is y-intercept) we can change the equation of a line to <a,b>*<x,y>=rho where |<a,b>|=1 and rho is the distance from the line to the origin. Now this modified canonical form is scaleable to 3 dimensions.
In a similar manner, the constant area of the 2D problem is maintained over time when the polygon has 6 sides. In three dimensions it is not a given number of faces, but a more complex equation.
August 18th, 2012 at 1:03:12 PM
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Quote: pacomartinIn a similar manner, the constant area of the 2D problem is maintained over time when the polygon has 6 sides. In three dimensions it is not a given number of faces, but a more complex equation.
I would guess in 2D the 6-side polygon has the smallest surface for a fixed volume under the constraint of filling up the whole space.
I don't see a problem with this concept in 3 dimensions.
BTW the description of a plane by <a,b>*<x,y>=rho is called "Hesse normal form" and is taught in school in 7th or 8th grade...
October 22nd, 2012 at 6:58:19 PM
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Quote: MangoJBTW the description of a plane by <a,b>*<x,y>=rho is called "Hesse normal form" and is taught in school in 7th or 8th grade...
I think you went to an advanced school. I never saw anything like this in school curriculum at that grade.
For instance, this website instructs students on Five ways to find Distance from point to a line: Worsley School. Not one of them is the very obvious vector dot product using the normal form (although that is the easiest way to derive the general equation in method #5).
October 23rd, 2012 at 12:39:30 AM
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Maybe the 7th grade in China now. [g]
Of course all the claims that the US is behind puts US students generally up against the advanced students in China, ignoring that China is still full of peasants.
Not that we shouldn't aim high, and not that the concern shouldnt be real too.
Of course all the claims that the US is behind puts US students generally up against the advanced students in China, ignoring that China is still full of peasants.
Not that we shouldn't aim high, and not that the concern shouldnt be real too.
the next time Dame Fortune toys with your heart, your soul and your wallet, raise your glass and praise her thus: “Thanks for nothing, you cold-hearted, evil, damnable, nefarious, low-life, malicious monster from Hell!” She is, after all, stone deaf. ... Arnold Snyder
