American statistics
Whenever I hear a statistic about America or Americans, it's pretty much never true.  America isn't really a country, it's actually a shell company containing 50 smaller countries, each with its own economy, geography, and culture.  You can't say "America is mostly [X]" or "Americans are largely [Y]" because it's probably not true for the vast majority of the country, but because of how statistics work, it's sort of true in theory. 

I guess this sort of applies to any large heterogeneous group, and it's especially noticeable for the people who fall outside the norms of whatever statistic you're looking at. #math

Good at math
I've been pretty good at math my whole life.  As an adult I found all my old school records, and even the standardized tests from first grade said I was in the 99th percentile for math (and in the 70s for reading comprehension; still an issue to this day). 

The thing is though, math never felt easy for me.  I put just as much work and struggle and frustration into it as all my classmates, but it seemed to work out for me better than for them.  I don't know why that is. 

I do think a certain amount of it is innate, and I did nothing to deserve or earn that.  But by saying an ability is simply a product of birth, it negates the time and effort and confusion and failure I've invested in it. 

But at the same time, claiming an achievement came from time and effort also negates the lack of success experienced by people who did the same things as me. 

A recent TED Radio Hour episode was about math, and I particularly related to the part by mathematician Dan Finkel who said that math is all about being ok with being stuck.  That essentially describes my entire job and all the education that led up to it.  I don't particularly like the feeling of being stuck; I don't seek it out and relish it when I find it.  I tolerate it.  And then I make some progress.  And that's apparently why I'm good at math.  #math

Normalized numbers
I was reading something the other day that mentioned a person's IQ score being 120, and I couldn't remember if that was good or bad.  That's the problem with IQ scores and quarterback passer rating and any other numbers that aren't on a common scale:  You need two pieces of information (your score and the maximum score) to communicate anything meaningful to another person.  That's why I think we should use normalized numbers more often.  A normalized number is typically your score divided by the maximum score, which gives a value between zero and one.  Multiply that by 100 and you've calculated a percentage, which comes with its very own symbol (%) and is recognizable by pretty much every human being on earth.  We already do this for test scores in school, batting averages in baseball (normalized, not percentaged), and tons of other things.  Keeping a number non-normalized doesn't retain any additional information or add any benefit.  Just normalize it. #math

Insufficient metrics
I've written before about temperature units.  There are lots of them, and they're not based around a useful zero point.  I hope one day we can come up with a better metric to quantify temperature.  Not only because the units are dumb, but because equal temperatures don't always feel the same.  Temps in the 80s (F) in a humid area feel much hotter than temps in the 80s (F) in a dry area.  Cooking on a metal tray takes a different amount of time than cooking with stone.  That has to do with thermal conductivity and other properties of materials, whereas meteorologists have a pseudo-hack called "feels like temperature".  That's cool and all, but it would be nice if we could come up with a way to rise above these variations. 

Same with Calories in food.  A Calorie is the measure of energy in the food itself.  But I think what would be more useful to know is the nutritional value.  That's obviously a whole other can of worms, but it would still be helpful to have an established metric that showed why fast food calories are not equivalent to real food calories.  (Update:  I'm not alone.) #math

Diameter vs. mass
I was collecting firewood yesterday, and naturally I was thinking about math.  Specifically, how much more does a log with a larger diameter weigh than a log with a smaller diameter?  Assuming a log is a perfect cylinder, its mass = density*volume = density*(pi/4)*diameter2*length.  For two logs that have the same density and the same length, the change in mass is the following: 
Δm = (ρ*(π/4)*d22*ℓ - ρ*(π/4)*d12*ℓ)/(ρ*(π/4)*d12*ℓ) = (d22/d12) - 1
It's actually the same result as pizza math.  What this means in reality is that a log that's 15 inches in diameter compared to a log that's 7 inches in diameter (114% increase, or 2.1 times) is (152/72)-1 = 359% (4.6 times) heavier.  More generally, a log with x times the diameter will weigh x2 times as much.  And that's why my back hurts today. #math

Pizza math
Planet Money wrote about the economics of pizza size, but I feel like they left out the actual math.  It's not complicated, but basically since area = π*radius2 = (π/4)*diameter2, the area changes with the square of the diameter.  So for an 8-inch pizza, the area is 50 square inches, while the area of a 12-inch pizza is 113 square inches.  A 50% increase in diameter equates to a 125% increase in area.  That's the power of exponents. 

Simplifying the formula, you can write that the change in area is related to the change in diameter as follows: 
Δa = ((π/4)*d22 - (π/4)*d12)/((π/4)*d12) = (d22/d12) - 1
Helpful for the next time you want to get a wedgie in a pizza place. #math

Temperature units
As a practicing engineer and frequent user of mathematics, I do hereby proclaim:  Temperature units are stupid.  With all other units of measurement (time, distance, velocity, mass, angle, pressure, density, etc.), zero is zero, regardless of which system you use.  Zero inches is zero centimeters.  Zero mph is zero m/s.  Zero lb is zero kg.  But with temperature, zero degrees C is 32 degrees F.  And don't even get me started with Kelvin and Rankine.  Why there are four different units for one stupid measurement is beyond the scale of my angry comprehension. #math

Quart
As a child, I was forced to remember that there are four quarts in a gallon, but I never picked up on the fact that a quart is a quarter of a gallon, which is much easier for me to remember. #math

Pi song
The most recent episode of Radio Lab included this awesome three-part harmony song containing the first hundred or so digits of pi (YouTube version, "music video" YouTube version), which was part of a song written by the comedy/parody musical duo Hard 'n Phirm (consisting of Chris Hardwick and Mike Phirman -- pun!) whose own music video version of the song featured a pi-reciting robot who protected children (perhaps of the house of Gryffindor) from two men in red pointed hats whose job it appeared was to zap the children with death rays, and all made to look like a children's educational TV show from the 80s.  Ya know, pretty standard stuff. #math

Square Root Day (2)
Similar to Odd Day is Square Root Day, where the month and day are the square roots of the year.  This happens nine times each century:  01/01/01, 02/02/04, 03/03/09, 04/04/16, 05/05/25, 06/06/36, 07/07/49, 08/08/64, and 09/09/81.  No, today isn't a Square Root Day, but today was the first I heard of it.  Being the nerd that I am, I had to post this. #math

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