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0687: "Dimensional Analysis"

Posted: Mon Jan 11, 2010 5:05 am UTC

Alt-text: Or the pressure at the Earth's core will rise slightly.

England drifted out to sea...

And nothing of value was lost.

Re: "Dimensional Analysis" discussion

Posted: Mon Jan 11, 2010 5:06 am UTC
lolwut?! I think I need to perform some calculations.

Re: "Dimensional Analysis" discussion

Posted: Mon Jan 11, 2010 5:06 am UTC
I'm interested in knowing if the math actually works out.

Re: "Dimensional Analysis" discussion

Posted: Mon Jan 11, 2010 5:07 am UTC
I thought it was California that would drift out to sea first. No fair, England...

Re: "Dimensional Analysis" discussion

Posted: Mon Jan 11, 2010 5:07 am UTC
Someone post the math!

Re: "Dimensional Analysis" discussion

Posted: Mon Jan 11, 2010 5:09 am UTC
Wow, Randall certainly has a lot of time on his hands...

I'm curious if this not only works out numerically, but whether or not the units actually cancel.

Re: "Dimensional Analysis" discussion

Posted: Mon Jan 11, 2010 5:10 am UTC
Pressure at core: 330 to 360 GPa
Planck Energy: 0.5433 MWh
English channel: 34 km (21 mi)
Pirus MPG: 51/48

I'll let you guys work it out.

Re: "Dimensional Analysis" discussion

Posted: Mon Jan 11, 2010 5:13 am UTC
England drifted out to sea...

And nothing of value was lost.

ouch, that's cold man

Re: "Dimensional Analysis" discussion

Posted: Mon Jan 11, 2010 5:13 am UTC
i think its just that it works out to be unitless like pi? i dunno. this guy has too many hobbies.

Re: "Dimensional Analysis" discussion

Posted: Mon Jan 11, 2010 5:13 am UTC
Draco18s wrote:Pressure at core: 330 to 360 GPa
Planck Energy: 0.5433 MWh
English channel: 34 km (21 mi)
Pirus MPG: 51/48

I'll let you guys work it out.

I used slightly different numbers, but yes, it's close...
http://www.wolframalpha.com/input/?i=(1.956+*+10^9+Joules+%2F+345+GPa)+*+(50+mpg+%2F+34+km)
= 3.545 (unitless)

Re: "Dimensional Analysis" discussion

Posted: Mon Jan 11, 2010 5:14 am UTC
Wonder if it is at all related to: http://www.scientificblogging.com/hammo ... se_gravity

Derivation of Newtonian Gravity from information theory assuming a holographic universe.

Re: "Dimensional Analysis" discussion

Posted: Mon Jan 11, 2010 5:14 am UTC
Hasn't England already drifted out to sea technically?

Re: "Dimensional Analysis" discussion

Posted: Mon Jan 11, 2010 5:14 am UTC
Yeah, the units cancel (according to Google Calculator), but it's not as close to pi and he wants you to think.

Re: "Dimensional Analysis" discussion

Posted: Mon Jan 11, 2010 5:15 am UTC
I'm not sure about the numbers but the units cancel

Re: "Dimensional Analysis" discussion

Posted: Mon Jan 11, 2010 5:16 am UTC
bulbmusic5 wrote:Yeah, the units cancel (according to Google Calculator), but it's not as close to pi and he wants you to think.

"It's correct to within experimental error..."

Re: "Dimensional Analysis" discussion

Posted: Mon Jan 11, 2010 5:17 am UTC
Values I found from quick Googling:

Planck energy = 1.956 GJ
Pressure at core = 360 GPa
Prius combined MPG* = 49.5 MPG
English Channel minimum width = 34 km

Total = 3.36301177...

*calculated by me as the average of the highway and city ratings of the 2010 model

Not quite as close as I expected, but I still snickered.

Re: "Dimensional Analysis" discussion

Posted: Mon Jan 11, 2010 5:18 am UTC
Units work

1 (J / kPa) * ((m / L) / m) = 1
J=(kg*m^2)/s^2
kPa=(kg/(m*s^2))*1000
L=dm^3

Re: "Dimensional Analysis" discussion

Posted: Mon Jan 11, 2010 5:19 am UTC
Google doesn't have anything nice to say about the units as given by draco18

oops, g is not gallon! it works with gal.

Re: "Dimensional Analysis" discussion

Posted: Mon Jan 11, 2010 5:19 am UTC
Zorlin wrote:England drifted out to sea...

And nothing of value was lost.

Technically correct. Because, hey, it was already an island. It'll just be an island in a slightly different place now.

Re: "Dimensional Analysis" discussion

Posted: Mon Jan 11, 2010 5:19 am UTC
How does he know the Planck energy won't change?

Re: "Dimensional Analysis" discussion

Posted: Mon Jan 11, 2010 5:20 am UTC
ELProphet wrote:
Draco18s wrote:Pressure at core: 330 to 360 GPa
Planck Energy: 0.5433 MWh
English channel: 34 km (21 mi)
Pirus MPG: 51/48

I'll let you guys work it out.

I used slightly different numbers, but yes, it's close...
http://www.wolframalpha.com/input/?i=(1.956+*+10^9+Joules+%2F+345+GPa)+*+(50+mpg+%2F+34+km)
= 3.545 (unitless)

For the units exactly (In SI Base):
Joules = kg m^2 s^-2
Pascal = kg m s^-2
J/P = m

mpg (G) = m m^-3 = m^-2
E Chan = m
G/E = m^-1

So, yes, it is dimensionless. My question: How much time did Randall spend on this one?

Re: "Dimensional Analysis" discussion

Posted: Mon Jan 11, 2010 5:21 am UTC
Omegaton wrote:I'm curious if this not only works out numerically, but whether or not the units actually cancel.

Well it depends on what you use as units, really. Dimensions do properly cancel, as already discussed:
$\frac{force\times length}{force/length^2}\times \frac{length/length^3}{length}$
(I left force as-is because it immediately cancels in the first term, anyway.)

Re: "Dimensional Analysis" discussion

Posted: Mon Jan 11, 2010 5:21 am UTC
I'm surprised no one has posted yet that they have a problem with the spacing between the words "and" and "the".

Re: "Dimensional Analysis" discussion

Posted: Mon Jan 11, 2010 5:22 am UTC
dude we might be like six models of prius away from the earth exploding

Re: "Dimensional Analysis" discussion

Posted: Mon Jan 11, 2010 5:22 am UTC
lordlicorice wrote:Google doesn't have anything nice to say about the units as given by draco18

Google thought (51 mi/g) was "Miles / Gram". It's little things like that that've made me switch to Wolfram Alpha in the past semester.

Re: "Dimensional Analysis" discussion

Posted: Mon Jan 11, 2010 5:23 am UTC

Re: "Dimensional Analysis" discussion

Posted: Mon Jan 11, 2010 5:23 am UTC
torontoraptor wrote:Hasn't England already drifted out to sea technically?

More the sea rose up and surrounded England, with the cliffs of Dover as battlements.

Also, in before The Day After Tomorrow, the Isle of Britain as of a few days ago:

So now the water is going for aerial bombardment.

Re: "Dimensional Analysis" discussion

Posted: Mon Jan 11, 2010 5:24 am UTC
Tom wrote:I'm surprised no one has posted yet that they have a problem with the spacing between the words "and" and "the".

He still has better handwriting than me , I'm fine with it

Re: "Dimensional Analysis" discussion

Posted: Mon Jan 11, 2010 5:26 am UTC
Holy balls, i love this comic

Re: "Dimensional Analysis" discussion

Posted: Mon Jan 11, 2010 5:26 am UTC
The first thing I thought of when I saw the title-text was the movie 2012. Just imagine the disaster movie that would result from this strip: "Sir, we've designed a Prius that gets unprecedented efficiency, but our calculations show that if we put it into production, the extra pressure on the Earth's core could destroy the world!" Obligatory Hollywood badguy: "Do it anyway, it'll at least stop global warming."

Re: "Dimensional Analysis" discussion

Posted: Mon Jan 11, 2010 5:27 am UTC
Man, we had a lot of fun when we got our engineering calculators in EDDT that came pre-programmed with nearly every unit imaginable, seeing what we could equate into other things (especially when I showed people that watts and gallons could be expressed in totally different figured). This comic tops our best ones, though, I think.

Re: "Dimensional Analysis" discussion

Posted: Mon Jan 11, 2010 5:28 am UTC
Another excellent "My Hobby" comic. Oh, it doesn't equal exactly pi? You measured wrong.

Re: "Dimensional Analysis" discussion

Posted: Mon Jan 11, 2010 5:31 am UTC
I bet this is related to the "God Equation" nonsense.

Re: "Dimensional Analysis" discussion

Posted: Mon Jan 11, 2010 5:32 am UTC
He says that the numbers are within "experimental error."

I'd be willing to bet that the experimental error of the earth's inner core pressure is going to be large enough to justify having a misplaced decimal or two in the final answer...

Re: "Dimensional Analysis" discussion

Posted: Mon Jan 11, 2010 5:38 am UTC
yeah the error in the earth's core is big, but I think the joke here is how bad epa numbers are.

Re: "Dimensional Analysis" discussion

Posted: Mon Jan 11, 2010 5:41 am UTC
Planck Energy * Prius combined EPA mileage / Pressure at the earth's core * Minimum width of the english channel =
1.956 * 10^9 J * 19.68 km/l / (345 +/- 15 GPa) * 34 km =
1.956 * 10^9 Pa*m^3 * 1.968*10^7 m/m^3 / 345 *10^9 Pa * 34000 m (+/- 4.3%) =
3.282 +/- 4.3% =
3.282 +/- 0.141.

So pi actually does fall within the experimental error, since 3.282 - .141 = 3.141. It's not "close", it is within the range, as the comic says.

Re: "Dimensional Analysis" discussion

Posted: Mon Jan 11, 2010 5:49 am UTC
++mmaluff;

Re: "Dimensional Analysis" discussion

Posted: Mon Jan 11, 2010 5:50 am UTC
Nice to see another "My Hobby" comic.

Re: "Dimensional Analysis" discussion

Posted: Mon Jan 11, 2010 5:51 am UTC
The Pi on the right side of the equation isn't lowercase pi (a particular constant that equals 3.14159... and is most notably used in a variety of geometric and trigonometric formulas, but also has strange applications elsewhere), it's uppercase Pi as used in the Buckingham Pi Theorem http://en.wikipedia.org/wiki/Buckingham_Pi . The actual value of this Pi depends completely on the units used, but if you're consistent with the units then the constant will be valid (if the systems truly are similar, which obviously these aren't - but that's part of what makes it a joke).

And yes, the dimensional analysis appears to be correct.

Re: "Dimensional Analysis" discussion

Posted: Mon Jan 11, 2010 5:51 am UTC
Either Randall (via his stick man avatar) means Britain will drift further out to sea, or Scotland and Wales are about to get very squished.

Or he means the United Kingdom and what's left of the dispute over Northern Ireland is about to get a lot more interesting.