explain xkcd - User contributions [en]

Talk:687: Dimensional Analysis

2013-04-01T13:10:05Z

Stamfest:

{{cot}}
Is it customary to just slap a new contributor after 5 minutes because the page was not done perfectly on the first editing? Now I will NOT research and add the actual numbers you would have to plug into the equation and I will leave this to Dave22. Genius. [[User:Stamfest|Stamfest]] ([[User talk:Stamfest|talk]]) 09:36, 1 April 2013 (UTC)
:We do put those fields there for a reason. Most editors just make a page and leave them incomplete with fields deleted or blank, oftentimes leaving admins with heaps of maintenance work to deal with. I probably *should* have waited for you to finish, but prior experience and me being busy with two simultaneous continuously updating comics led me to treat it like most other incomplete pages. Will wait in the future though, since I know how you edit now. Discussion hidden, as it covers matters outside of the comic. '''[[User:Davidy22|{{Color|#707|David}}y²²]]'''[[User talk:Davidy22|<tt>[talk]</tt>]] 10:01, 1 April 2013 (UTC)
::And I added the comment of a (very) initial explanation to the initial version. If you only want immediately perfect content, then just say so at page creation-time. This is totally against all wiki rules I have ever experienced. It is also against basic netiquette to call new contributors names upon their first submission. You might consider to change your attitude if you run or are involved with such a project. OTOH, if this is YOUR project, you are free to treat contributors all the way you want, but do not expect them to add more content if you behave like that. But the good thing is: your reaction shifted my attention back to work. Thanks for that. This won't help the page, though. Bad luck, I guess. Also, I only found out now that it is not possible to delete accounts on a wikimedia wiki... [[User:Stamfest|Stamfest]] ([[User talk:Stamfest|talk]]) 13:10, 1 April 2013 (UTC)
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Talk:687: Dimensional Analysis

2013-04-01T09:36:08Z

Stamfest: Created page with "Is it customary to just slap a new contributor after 5 minutes because the page was not done perfectly on the first editing? Now I will NOT research and add the actual numbers..."

Is it customary to just slap a new contributor after 5 minutes because the page was not done perfectly on the first editing? Now I will NOT research and add the actual numbers you would have to plug into the equation and I will leave this to Dave22. Genius. [[User:Stamfest|Stamfest]] ([[User talk:Stamfest|talk]]) 09:36, 1 April 2013 (UTC)

687: Dimensional Analysis

2013-04-01T09:32:25Z

Stamfest: David22: You are so clever, and I wasn't done with my editing. If you know better, why haven't you created it yourself. Stop whining.

{{comic
| number = 687
| date = January 11, 2010
| title = Dimensional Analysis
| image = dimensional_analysis.png
| titletext = Or the pressure at the Earth's core will rise slightly.
}}

==Explanation==
This comic makes fun of how scientists (often physicists) use dimensional analysis to quickly check if a given formular can possibly relate to a physical system or if there were some (obvious) mathematical errors in its derivation. Dimensional analysis here refers to the check if both sides of the equation arrive at the same physical unit if the units of all variables get plugged into the equation. This usually requires knowledge of the system of units and the relation between different physical units.

The comic uses the following equation to make fun of it:

(Planck energy) / (Pressure at the core of the earth) * (Prius combined EPA gas milage) / (minimum width of the english channel) = pi

The right hand side is dimensionless (The constant pi = 3.14... by definition is the relation of two lengths, the circumference and the diameter of a circle). The left hand side requires to plug in the dimensions of the named physical quantities:

*Plank energy: given in Joules [J]
*Pressure at the core of the earth: Given in Pascals [Pa]
*Prius combined EPA gas milage: miles/gallon, SI units: meters/litres [m/l]
*minimum width of the english channel: meters [m]

When plugged into the left hand side this amounts to:

[J / Pa * (m/l) / m] = [Nm / (N/m²) * (m/m³) / m] = 1

Using the following unit relations (this does not reduce units to the seven SI units, but does use some derived units):

*1 Joule = 1 Newton-meter [J] = [Nm]
*1 Pascal = 1 Newton per square-meter [Pa] = [N/m²]
*1 cubic-metre = 1000 litres [m³] = 1000 [l]

Note that for dimensional analysis constant factors are not taken into account. Here square brackets are used to denote dimensional analysis. Here square brackets are used to denote dimensional analysis. In the above equation the unit of force (newton) as well as all the units of length (meter) cancel out each other.

Another aspect of the comic is, that sometimes dimension analysis of equations that were not derived but rather "made up" can provide insight. However, in reality such an equations would have to be somehow "motivated", which is more of an art than science and requires great experience in the field the equation should relate to. The presented equation combines values that have no immediate causal relation with each other, so it does not make sense.

For such relations it is also true that many of them can be made up by searching for matching values for variables to derive at the wanted number finally. Eg. if it is desired to arrive at e instead of pi on the comic-equation, this could be done by using a different car model and/or a different length measurement and/or a different pressure (eg. by choosing a different planet) and/or some other arbitrary energy.

This is another comic in the infrequent [[My Hobby]] series.

==Transcript==
:[On a blackboard.]
:(Plank energy/Pressure at the Earth's core) x (Prius combined EPA gas mileage/Minimum width of the English Channel) = pi

:[A teacher indicates this equation with a pointer in front of a class.]
:Teacher: It's correct to within experimental error, and the units check out. It must be a fundamental law.
:Student: But what if they build a better Prius?
:Teacher: ''Then England will drift out to sea.''

{{comic discussion}}
[[Category:My Hobby]]
[[Category:Comics featuring Cueball]]
[[Category:Comics featuring Ponytail]]

687: Dimensional Analysis

2013-04-01T09:30:05Z

Stamfest:

687: Dimensional Analysis

2013-04-01T09:19:53Z

Stamfest: Created (very) initial explanation

{{comic
| number = 687
| title = Dimensional Analysis
| image = dimensional_analysis.png
| titletext = Or the pressure at the Earth's core will rise slightly.
| imagesize =
}}

==Explanation==

This comic makes fun of how scientists (often physicists) use dimensional analysis to quickly check if a given formular can possibly relate to a physical system or if there were some (obvious) mathematicals errors in its derivation. Dimensional analysis here refers to the check if both sides of the equation arrive at the same physical unit if the units of all variables get plugged into the equation. This usually requires knowledge of the system of units and the relation between different physical units.

The comic uses the following equation to make fun of it:

(Planck energy) / (Pressure at the core of the earth) * (Prius combined EPA gas milage) / (minimum width of the english channel) = pi

The right hand side is dimensionless (The constant pi = 3.14... by definition is the relation of two lengths, the circumference and the diameter of a circle). The left hand side requires to plug in the dimensions of the named physical quantities:

* Plank energy: given in Joule [J]
* Pressure at the core of the earth: Given in Pascal [Pa]
* Prius combined EPA gas milage: miles/gallon, SI units: meters/litres [m/l]
* minimum width of the english channel: meters [m]

When plugged into the left hand side this amounts to:

[J / Pa * (m/l) / m] = [Nm / (N/m²) * (m/m³) / m] = 1

Using the following unit relations (this does not reduce units to the seven SI units, but does use some derived units):

* 1 Joule = 1 Newton-meter [J] = [Nm]
* 1 Pascal = 1 Newton per square-meter [Pa] = [N/m²]
* 1 cubic-metre = 1000 litres [m³] = 1000 [l]

Note that for dimensional analysis constant factors are not taken into account. Here square brackets are used to denote dimensional analysis.

This is another comic in the infrequent [[My Hobby]] series.
==Transcript==
:[[My Hobby]]: Dimensional Analysis

{{comic discussion}}
[[Category:My Hobby]]