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0687: "Dimensional Analysis"

Posted: Mon Jan 11, 2010 5:05 am UTC
by Zorlin
Image

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
by chocolate.razorblades
lolwut?! I think I need to perform some calculations.

Re: "Dimensional Analysis" discussion

Posted: Mon Jan 11, 2010 5:06 am UTC
by Draco18s
I'm interested in knowing if the math actually works out.

Re: "Dimensional Analysis" discussion

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

Re: "Dimensional Analysis" discussion

Posted: Mon Jan 11, 2010 5:09 am UTC
by Omegaton
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
by Draco18s
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
by Salamnzer
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
by mwn3d
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
by ELProphet
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
by PiAndWhippedCream
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
by torontoraptor
Hasn't England already drifted out to sea technically?

Re: "Dimensional Analysis" discussion

Posted: Mon Jan 11, 2010 5:14 am UTC
by bulbmusic5
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
by Veritro
I'm not sure about the numbers but the units cancel :)

Re: "Dimensional Analysis" discussion

Posted: Mon Jan 11, 2010 5:16 am UTC
by chocolate.razorblades
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..." :P

Re: "Dimensional Analysis" discussion

Posted: Mon Jan 11, 2010 5:17 am UTC
by Kimble
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
by twild1990
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
by lordlicorice
Google doesn't have anything nice to say about the units as given by draco18

http://www.google.com/search?q=0.5433+MWh+%2F+360+GPa+*+((51+mi%2Fg)+%2F+34km)

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

Re: "Dimensional Analysis" discussion

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

Re: "Dimensional Analysis" discussion

Posted: Mon Jan 11, 2010 5:20 am UTC
by ELProphet
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
by gmalivuk
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:
[math]\frac{force\times length}{force/length^2}\times \frac{length/length^3}{length}[/math]
(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
by Tom
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
by a386
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
by ELProphet
lordlicorice wrote:Google doesn't have anything nice to say about the units as given by draco18

http://www.google.com/search?q=0.5433+MWh+%2F+360+GPa+*+((51+mi%2Fg)+%2F+34km)


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
by knight427

Re: "Dimensional Analysis" discussion

Posted: Mon Jan 11, 2010 5:23 am UTC
by westrim
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:
Satellite_image_of_snow-covered_Great_Britain_on_7_January_2010.jpg


So now the water is going for aerial bombardment.

Re: "Dimensional Analysis" discussion

Posted: Mon Jan 11, 2010 5:24 am UTC
by ELProphet
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 :oops: , I'm fine with it

Re: "Dimensional Analysis" discussion

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

Re: "Dimensional Analysis" discussion

Posted: Mon Jan 11, 2010 5:26 am UTC
by The Origamist
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
by Mighty Jalapeno
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
by BlazeOrangeDeer
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
by squelart
I bet this is related to the "God Equation" nonsense.

Re: "Dimensional Analysis" discussion

Posted: Mon Jan 11, 2010 5:32 am UTC
by point and laugh
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
by billedluh
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
by mmaluff
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
by Ph0X
++mmaluff;

Re: "Dimensional Analysis" discussion

Posted: Mon Jan 11, 2010 5:50 am UTC
by '; DROP DATABASE;--
Nice to see another "My Hobby" comic.

Re: "Dimensional Analysis" discussion

Posted: Mon Jan 11, 2010 5:51 am UTC
by petiejoe
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
by sab39
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.