103. Dimensional Analysis | THUNK

Dimensional analysis is awesome, but human brains are depressingly easy to distract with number-crunching.

-Links for the Curious-

[thiagomartins]

I really don't understand why this channel doesn't have more than 1 million subscriber. So awesome!! Love your work! ;)

[paulk]

When I was in high school, we had a guest speaker talking about the wind farm nearby our school. Someone asked him how many birds they killed, and I was amazed that he actually had an answer for her. If I remember right, he gave his answer in units of "dead birds per kilowatt hour", which I thought was the funniest sounding unit.

[SamVidovich]

You've definitely made a major point here. The theory is far more important than the calculation!

[mulimotola]

I learned it just in the recent year through Khan Academy as I'm improving my math skills. It is quite amazing, because I really had a lot of trouble with word problems involving fractions and different units. Dimensional Analysis really helps solving these problems, and I find myself using it in everyday life. Just yesterday I used it to figure out how many cups of water I need to add to the rice, since I used a cup and a half of rice. I can also do it intuitively, but it's nice seeing the solution clearly and precisely using DA

[Orpheus]

I don't remember the first thing I used it on. But I DO remember teaching it to someone who was having a lot of trouble with the concept in chemistry back in high school. I illustrated the concept using money-conversion calculations. Dollars to quarters, that sort of thing.

[morrman]

I used to always have trouble in Physics trying to figure out the units of concepts that I wasn't completely familiar with (latent heat, wavelength, forces etc.) until one day I realized this. Like some others in the comments, Khan Academy was the instigator of this realization. I haven't struggled with units of anything since!

[itisdevonly]

Fascinating video. Deserves so many more views! But that's probably the math nerd in me thinking that this would be widely appealing. Haha. I'm one of those weird people who always liked word problems in math, since they were so much more interested, and "practical" (even though the scenarios depicted might have been incredibly impractical).

I remember learning and using dimensional analysis in high school advanced chemistry. I didn't know the term for it, though, or that it was a revolutionary and modern bit of "magic." But it has been useful. For exactly the example you gave--calculating miles per gallon. I live in Europe where they consider fuel consumption in liters per kilometer, but, being an American, my "intuitive" (learned) comprehension of fuel efficiency is in mpg, so I have to mentally invert and convert to get it into a number that makes intuitive sense to me.

[Huststyler]

I actually have to explicitly think about this whenever dealing with maths and I'm a 3rd year economics undergrad with a very good understanding of maths! Even after all these years I have to make myself remember and think about mathematical expressions and models else I'd be stumped, then when I calculate something there's a good 5-10 second delay for what I'd like to call a "correctness of correctness check" (and almost every time the first number that pops into my mind is right)-just wish I could remove that mental check because I deal with numbers A LOT both as a to-be-economist and as a game programmer....

EDIT: first time I used dimensional analysis was with percentages something along the lines of "this product is 30% off and it's $40, so what is its full price?", the thought process went something like this:
(1-0.3)x = 40
so 0.7x = 40 (70% of the full price, x, is $40)
then x = 40/0.7 (ah that's the full price)

This was back in 9th grade where I realised I was better at visualising expressions than rote learning expressions (which are almost the same anyways).

The second time I used it (probably not an example of dimensional analysis) was when I wanted to convert arbitrary numbers (anywhere from -70k to +15k) into a 0.0-1.0 range so I could graph them onto a virtual plane of different width and heights by multiplying them by a factor which led me to this: (x-min)/(max-min) and only after I learnt a bit about statistics 2 years back did I realise that this was a very well known(the standard) way to normalise values.. I was slightly impressed that I could come up with this back in 11th grade but now that I think about it, it's nothing to be impressed at considering the complex formulas other people are capable of inferring with just a simple thought and a goal..

[proto]

Dimensional analysis, the practice of multiplying by 1

[rhythmandacoustics]

This reminded of Richard Feynman's Philosophical Question or Story about the Ancient Aztecs calculating the movement of the stars and another person asking maybe that the Earth is round and the no only that the heavenly bodies but we are moving as well. Then imagining the Aztecs to ignore the theory and focus on the calculations. Oh well reminds me of Philosophy of Science. Oh ya this video reminded me also of the History of Chemistry and the philosophical debate whether it was Lavoisier or Black who discovered Oxygen. Did Lavoisier use dimensional analysis though in his measurements?

[simpfally]

I just remember thinking "why the hell didn't we start by this" instead of learning stupid formulas.

[JasonOlshefsky]

I continue to be perfectly ambivalent about a calculator that includes units of measure (as well as error ranges or statistical range) and ones just as dumb as we have today (in common use.)

Off hand I don't remember the _first_ time I used dimensional analysis, but I have recently become enamored with the "R-value" unit of insulation, (square feet)*(delta Farenheit)/(British thermal unit) and how that all relates to the heat power being transferred through a wall and how that relates to the insulation, area, and temperature difference.

[Tobbence]

May sound like an odd question but does that mean there are no professional mathematicians that are mute? Feels wrong just saying it...