11Jan/104
Dimensional Analysis
by Jeff
Image text: Or the pressure at the Earth's core will rise slightly.
Dimensional analysis is a tool to better understand the properties of items using an equation the helps to convert between different units of measure. In this case, the comic says that the units check out.
Planck energy is a system energy made up of Planck units.
The pressure at the earth's core is over 3.5 million times atmospheric pressure.
Prius's gas mileage (as tested by the EPA) is 51 highway / 48 city.
The smallest width of the English Channel is 21 miles between Dover, England and Calais, France.
The image text is a continuation of the teacher's comments from the comic.
January 13th, 2010
The units are verified and it is evaluated here:
http://jaxwebster.wordpress.com/2010/01/13/xkcd-dimension-analysis/
The overview of it is that it does indeed work. The units cancel out and the values, when input, come to between 3 and 3.5 depending on the exact values you use. I wonder how long it took him to find that.
January 13th, 2010
one planck energy = 543.3 kWh (so sayeth wikipedia)
((543.3 kWh) / (3.5 million atm)) * ((48 mpg) / (21 miles)) = 3.33016968
(so sayeth google calculator)
January 15th, 2010
And of course the comic is making fun of the way some physicists derive the general form of a formula by looking at the units of the quantities involved. Also, the teacher’s first remark references the experimentalist’s habit to use “to within numerical precision” (depending on the numbers you use you get something between 3 and 4, which is equal to pi “up to numerical precision”) and it also makes reference to a typical crackpot argument, which tries to assign a fundamental meaning to a co-incidental combination of quantities or a co-incidental numerical result.
January 15th, 2010
The comic is a response to http://scienceblogs.com/pharyngula/2009/12/the_god_equation.php?utm_source=mostactive