0687: "Dimensional Analysis"

[Ghona]

I'm sure there's a difference between the the Dutch and the Belgians, but they're pretty much the same. No-one can name 3 famous Belgians, however. Except Poirot.

Actually, it's pretty easy to name 3 famous Belgians - the problem is that many people would not recognise them as Belgian. For example Magritte, Jacques Brel, Plastic Bertrand are all famous Belgians, but many people would think they are French.

Who?

[Thesh]

This brings up an interesting question: What was there before the prius was created? I tried doing the calculation in SQL Server, but it just returns NULL.

Did the world not exist before the prius? Is our history real, or just an illusion? Was the prius created by man, Azathoth, itself, or did it just come to be? In the time before prius, did circles have a area of r^2?

[squareroot]

This brings up an interesting question: What was there before the prius was created? I tried doing the calculation in SQL Server, but it just returns NULL.

Did the world not exist before the prius? Is our history real, or just an illusion? Was the prius created by man, Azathoth, itself, or did it just come to be? In the time before prius, did circles have a area of r^2?

The solution to squaring the circle! Destroy all priuses!

[MSTK]

This is clear support for Last Thursdayism

[Zelaron]

How about:

(Planck's constant / atomic weight of carbon-14) * (Average half-life of carbon-14 / Area of the largest legally allowed coca plantation lot in Bolivia[1]) = Pi correct to within experimental error

[url]http://www.google.com/search?hl=en&source=hp&q=%28Planck%27s+constant+%2F+14.003241+u%29+*+%285730+years+%2F+1640+m^2%29&cts=1263269379564[/url]


Edit: URL BBCode won't compute.

[Monika]

England isn't an island, it's as simple as that.

Well, actually it's a bit more complicated than that. Here's a handy Venn diagram I found: http://fuckyeahbritain.tumblr.com/post/325241942/so-i-guess-a-lot-of-people-are-in-some-doubt-as-to

Apparently it is an Euler diagram and not a Venn diagram (it says so when you click on the link at the bottom and scroll down on that page). I didn't even know there was a difference.

England isn't an island, it's as simple as that.

Well, actually it's a bit more complicated than that. Here's a handy Venn diagram I found: http://fuckyeahbritain.tumblr.com/post/325241942/so-i-guess-a-lot-of-people-are-in-some-doubt-as-to

So, the bigger island of the British Isles is "Great", right? That means Irish people wouldn't mind if I called their island "Lesser Britain"?

I suppose you could try this. Once.

[Monika]

How about:

(Planck's constant / atomic weight of carbon-14) * (Average half-life of carbon-14 / Area of the largest legally allowed coca plantation lot in Bolivia[1]) = Pi correct to within experimental error

http://tiny.cc/D3rpV

Edit: URL BBCode won't compute.

Fixed that for you. And here http://tiny.cc/?act=stats&id=5512824&se ... e=gjxAk0vw you can see how many people clicked on that link.

[meat.paste]

A much more accurate result for the right side would be:

(\alpha^{2} 2 \pi e(\pi+\pi)^{\pi})^{-1}

, where "e" is the base of the natural logarithm and α is the fine structure constant.

Isn't this 3.4152 instead of 3.1416? I was using 1/137 for the fine structure constant, which I'm pulling from my memory and so could be in error.

[rcox1]

The units don't actually cancel because it's confusing a common name for different things. Specifically, "miles per gallon". The bottom unit is not units of volume! If you write it out, it becomes "miles per gallon of gasoline", where "gallon of gasoline" is a unit of energy
...
Of course, making mistakes is the point of the comic.

I disagree. From my perspective the joke is funny in two ways. From my physics background, we were often taught to use dimensional analysis a s a last resort of solving a problem and as a check in the answer. The idea is that if the dimensions were correct, we would be off, at most, by some factor. The second joke is that this is equal to pie within a experimental error. In class, anything less than 10% was experimental error, and often acceptable. The comic brings back many good time.

As far as units not canceling, they do. The assertion that one buys a certain amount of energy is false. There is an average energy stored in refined petroleum product, but we do not buy on that basis, any more than we buy milk on the basis guaranteed calories. We buy a gallon, which is volume. One might be upset if the volume of a gallon of milk were materially different from the volume of a gallon of water.

The third joke is that for most of science, there are only three units: meter for distance, kilograms for mass and seconds for time. In this way, energy over pressure is a volume, while fuel consumption(already identified as inverse area) over distance is inverse volume. Of course none of this makes sense as it true it is taken out of context, but the final joke is when teaching this stuff most students will ignore context in favor of successful manipulation.

[gmalivuk]

The assertion that one buys a certain amount of energy is false. There is an average energy stored in refined petroleum product, but we do not buy on that basis, any more than we buy milk on the basis guaranteed calories.

Right, just like you can say "I get 20 miles per gallon with my gasoline powered pickup, and 22 miles per gallon with my diesel pickup" (or something; I don't know how realistic that number is). And no one would blink an eye, nor would they question whether you were talking about actual physical gallons of diesel fuel, versus however much diesel fuel amounts to the same total energy as a gallon of gasoline.

[fiveofoh]

I looked through all four pages, and a couple people have sort of said this (qrs_iii got all the numbers, but didn't explain). I'm not sure what numbers Randall actually used, but if you go with:
Planck Energy = 1.956 × 109 J
Core pressure = 360 GPa (upper limit from Wikipedia)
Combined EPA Gas Mileage = 46MPG (for the 2009 Prius, easily found at FuelEconomy.gov)
Minimum width of the English Channel = 21 mi

You get 3.144, which is quite in range of experimental error. What this means is that since Toyota just came out with their new Prius (since the numbers seem to be based on the old one), someone had better double-check the width of the English Channel and/or the pressure in the Earth's core

Bascially, you have to use the 2009 Prius numbers and the upper core pressure, and everything works out just fine. Dimensional analysis is fun - I got a chuckle out of Joules/GPa = liters.

P.S. I just spent five minutes figuring out why my URL tag wasn't working. Evidently bbCode doesn't like ^s in URLs. The entity, for future reference, is %5E.

[Raptortech97]

Plan for world destruction:
1) Build a bridge across the English Channel
2) Give billions of dollars to whatever company makes the Prius
3) Watch the world explode
4) Be somewhere very far away from Earth. Actually, this should probably be step 2.5

EDIT: Also, for those arguing over volume vs. energy: what about checking what the people who gave the figures say?

[gmalivuk]

I got a chuckle out of Joules/GPa = liters.

Cubic meters, actually. Well, with the G there cubic millimeters is probably most correct, but J/Pa is cubic meters.

(Incidentally, the liter-atmosphere is a unit of energy which takes more explicit advantage of this relationship.)

[otac0n]

I get 3.146

Pretty close!

http://www.wolframalpha.com/input/?i=%2 ... 36.3+km%29

[battman92]

yea i did the math based off some other guys numbers of..
core:330-360gpa
planick:,5433mwh
English channel: 21mi
pirus gpa:51/48
and i got 3.617615012... and its pretty close so im thinking that we just different sources and used different numbers and all casue its close enough.

[nzelle]

Concerned Residents of the British Isles are forming a committee to lobby the Japanese car manufacturers to cease improving the Prius. Bah!

[sharyari]

Damn it, I actually created an account in the end, but I felt I had to share a similar experience (almost) at high school.

Our teacher accidentally wrote down the wrong formula for pressure of an ideal gas ( it should be p = (n*R*T)/V where V is the volume, p is the pressure and the rest is irrelevant atm), while explaining it's meaning with a metaphor involving a refrigerator. When we told him he had got it wrong, he actually insisted for maybe five minutes that the inside of the fridge would shrink when you closed the door before he gave it up

I'm glad he wasn't our original teacher.

[squareroot]

A much more accurate result for the right side would be:

(\alpha^{2} 2 \pi e(\pi+\pi)^{\pi})^{-1}

, where "e" is the base of the natural logarithm and α is the fine structure constant.

Isn't this 3.4152 instead of 3.1416? I was using 1/137 for the fine structure constant, which I'm pulling from my memory and so could be in error.

Yes, but most calculations at that point had given about 3.4/3.5. Note that I said for the right side of the equation, that is, instead of pi, one uses this expression as the result.

[Loki206]

Ok folks, this is a comic about dimensional analysis. You cannot just divide miles per gallon by kilometers and expect the result to be meaningful, or say that the units cancel. I am going to assume that we are working in the SI system here. For the first part of the equation it is Joules divided by Pascals, which is meters -- using numbers from Wikipedia anywhere from 5.93e-3 to 5.43e-3 meters (the uncertainty comes from knowing the pressure in the core). The comic specifically says combined gas mileage, not average, so that is 51 and 48 miles per gallon, equals 99 miles per gallon equals 4.2089e7 meters per cubic meter. ~5.5e-3 * ~4.2e7 does not equal pi, not even close. Yes you can massage the numbers a little, but don’t tell me that you can multiply joules over Pascals by miles per gallon over kilometers and call the result dimensionless. Add to that that pi/5.93e-3 to 5.43e-3 meters = 578 to 530 1/meters and that the width of the channel is 36.3 Km or 22.6 miles and the EPA rating is 51 and 48 gallons – no matter how you massage the last to quantities you cannot get the first. Yes by picking just the right system of units of each quantity you might get something close to pi -- at that point it is just as meaningful to define a system of units where the statement of this comic is true (which is possible) - it does not work in any generally accepted CONSISTENT system, be it Planck, SI or Imperial. What a shame to write about dimensional analysis only to thorough it out the window.

[canoemoose]

Have you not read the rest of the thread? Your arguments have been presented several times before and each time successfully refuted.

[gmalivuk]

What? Read the comic discussion before posting in it? What nonsense are you suggesting?

[crzftx]

Ok folks, this is a comic about dimensional analysis. You cannot just divide miles per gallon by kilometers and expect the result to be meaningful, or say that the units cancel. I am going to assume that we are working in the SI system here. For the first part of the equation it is Joules divided by Pascals, which is meters -- using numbers from Wikipedia anywhere from 5.93e-3 to 5.43e-3 meters (the uncertainty comes from knowing the pressure in the core). The comic specifically says combined gas mileage, not average, so that is 51 and 48 miles per gallon, equals 99 miles per gallon equals 4.2089e7 meters per cubic meter. ~5.5e-3 * ~4.2e7 does not equal pi, not even close. Yes you can massage the numbers a little, but don’t tell me that you can multiply joules over Pascals by miles per gallon over kilometers and call the result dimensionless. Add to that that pi/5.93e-3 to 5.43e-3 meters = 578 to 530 1/meters and that the width of the channel is 36.3 Km or 22.6 miles and the EPA rating is 51 and 48 gallons – no matter how you massage the last to quantities you cannot get the first. Yes by picking just the right system of units of each quantity you might get something close to pi -- at that point it is just as meaningful to define a system of units where the statement of this comic is true (which is possible) - it does not work in any generally accepted CONSISTENT system, be it Planck, SI or Imperial. What a shame to write about dimensional analysis only to thorough it out the window.

I think "The comic specifically says combined gas mileage, not average, so that is 51 and 48 miles per gallon, equals 99 miles per gallon" is a new argument. The poster clearly doesn't understand that "combined gas mileage" is an actual thing. It is neither the mean nor sum...

The calculation for combined fuel economy weights the city at 55 percent and the highway at 45 percent using the following equation:

FEcomb = 1 / (( .55 / city FE) + (.45 / hwy FE))

[The1exile]

WolframAlpha fails me yet again.

http://www.wolframalpha.com/input/?i=%2 ... nnel%29%29

Well, for starters, I too wouldn't know what the energy of the undefined plank is.

[MotorToad]

Well, for starters, I too wouldn't know what the energy of the undefined plank is.

It's the amount of energy in the plank when you burn it. Same as a gallon of gasoline! [/obviousman]

[phlip]

Evidently URLs doesn't like ^s in URLs.

FTFY

[AL_]

So, the bigger island of the British Isles is "Great", right? That means Irish people wouldn't mind if I called their island "Lesser Britain"?

The French might be a little confused, given that's Brittany (north west peninsula of France).

[verita]

Compared to some other of the strips, finding a connection like this one is not very hard which some seems to think. Just choose some measurements that end up in a commonly used unit (in this instance length) choose a constant to put on the other side. Pi is fun of course, but "1" and "e" would work as well. All you have to do now is to find a popularly known length that is easy to joke about (width of a football goal, empire state building, Chinese wall or a chewing gum) that fits the constant within your accepted error (the prius probably has a big variation in usage) and within 10% is not that hard to get.
This is not to say that the comic is not hilarious and thought provoking though, or that I would I thought of it myself

And yes, the sensible part of the world should simply block all usage of non SI units on any part or product.

[carey]

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)

You realize, I hope, that we are now confronting the dawn of a new XKCD sport (joining Geo Caching, among others): "Pi Driving". This is driving your Prius so that you average exactly 44.3 Mi/Gal and thus cause the equation to evaluate to Pi.

[Soluzar]

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.

Two way misunderstanding:

Brits: "There certainly is a big difference between English, Welsh, Scotch, ... . Why don't these non-Brits understand?!"
non-Brits: "Whatever difference between English, Welsh, Scotch, ... . Why do these Brits think we care?!"

You wouldn't find a "Brit" saying that, because "Scotch" is a drink. The term is never applied by anyone in the British isles to Scottish (or "Scots") people.

Also, while there may not be much of a relevant difference between the Scottish, Welsh and English people, there is certainly a relevant difference between the countries of Scotland, Wales and England. In order for England to drift out to sea, it would need to break off from two other countries on the same landmass. I recognise your point, but I don't see why you're referring to the separate peoples of Britain, rather than the separate countries in which they live. The two are hardly the same, unless a great many people I have met here in the midlands of England were a figment of my imagination.

[phillipsjk]

Our teacher accidentally wrote down the wrong formula for pressure of an ideal gas ( it should be p = (n*R*T)/V where V is the volume, p is the pressure and the rest is irrelevant atm), while explaining it's meaning with a metaphor involving a refrigerator. When we told him he had got it wrong, he actually insisted for maybe five minutes that the inside of the fridge would shrink when you closed the door before he gave it up

We have a relatively new freezer that pumps the warm air out when you close the door. I think the reason is to prevent the warm air from heating the contents. According to the ideal gas law, the drop in pressure should cancel the loss of air molecules, keeping T the same.

[Durin]

England isn't an island, it's as simple as that.

Well, actually it's a bit more complicated than that. Here's a handy Venn diagram I found: http://fuckyeahbritain.tumblr.com/post/325241942/so-i-guess-a-lot-of-people-are-in-some-doubt-as-to

Apparently it is an Euler diagram and not a Venn diagram (it says so when you click on the link at the bottom and scroll down on that page). I didn't even know there was a difference.

I think the most interesting thing that article shows is the link to the Wiki article on Euler diagrams which proves my old suspicions that a majority of chairs are in fact animals: http://en.wikipedia.org/wiki/File:EulerDiagram.svg

[Tony Young]

HI guys at the risk of sounding boring and killing your LOL string, Can anyone assist me with two dimensional analysis problems that I have to solve?

[hintss]

late post, but this comic came out the day before we covered dimensional analysis at school. I later posted this in my notebook.

[1055]

(not that anyone is likely to visit this discussion again but...)
My fluids professor, the awesome Gareth McKinley, used this comic in lecture yesterday. He also made a reference to the warp factor from star trek as an example of a dimensionless group.

[littlebadwolf]

If they build a better Prius, The EPA will merely adjust the test.

This gives meaningful scientific insight into the workings of the EPA.

[snowyowl]

(not that anyone is likely to visit this discussion again but...)
My fluids professor, the awesome Gareth McKinley, used this comic in lecture yesterday. He also made a reference to the warp factor from star trek as an example of a dimensionless group.

In a time-travel game I once played, changing the past caused a "ripple" to spread towards the future, changing the timeline as it went. The speed of such a ripple was measured in seconds per second. It took us a surprisingly long time to realise that that number was dimensionless. (It evaluated to 2, in case you're wondering).

[Deza]

Couldn't we rearange this equation to work out the exact pressaure at the earths core?

[McMayo]

I vote to change "Minimum width of the English Channel" to "Length of Loch Ness". It begs the question:

"Does the Loch Ness Monster have something to do with Pi?"

[Tyrannosaur]

I think the most interesting thing that article shows is the link to the Wiki article on Euler diagrams which proves my old suspicions that a majority of chairs are in fact animals: http://en.wikipedia.org/wiki/File:EulerDiagram.svg

I am never sitting in a 4-legged chair again. (Currently in my 5-legged office chair )

It begs the question

http://en.wikipedia.org/wiki/Begs_the_question
Why can't people ever use this phrase correctly?

[webdude]

I think the most interesting thing that article shows is the link to the Wiki article on Euler diagrams which proves my old suspicions that a majority of chairs are in fact animals: http://en.wikipedia.org/wiki/File:EulerDiagram.svg

I am never sitting in a 4-legged chair again. (Currently in my 5-legged office chair )

It begs the question

http://en.wikipedia.org/wiki/Begs_the_question
Why can't people ever use this phrase correctly?

I read your post after I commented on 1036 (Reviews), and realized I had just provided an example of petitio principii. Feel free to use it as an example. You can be sure it's good - and true!
Non credere omnia legere. Hoc est falsum.