Sunday, January 8, 2017

Numerical thinking - A superpower everyone can get

There are significant advantages to being a numerical thinker. So, why isn't everyone one?

Some people can't be numerical thinkers (or won't be numerical thinkers), typically due to one of three causes:
Acalculia: the inability to do calculations; in its pure form a type of brain damage, but more commonly a consequence of bad educational system. 
Innumeracy: lack of mathematical and numerical knowledge, again generally as the result of a bad educational system. 
Numerophobia: a fear of numbers and numerical (and mathematical) thinking, possibly an attitude brought on by exposure to the educational system.
On a side note, a large part of the problem is the educational system, particularly the way logic and math are covered in it. Just in case that wasn't clear.

Numerical thinkers get a different perspective on the world. It's like a superpower, one that can be developed with practice. (Logical thinkers have a related, but different, superpower.)

Take, for example, this list of large power generating plants, from Wikipedia:

Left to themselves, the numbers on the table are just descriptors, and there's very little that can be said about these plants, other than that there's a quick drop in generation capacity from the first few to the rest.

When numerical thinkers see those numbers, they see the numbers as an invitation to compute; as a way to go beyond the data, to get information out of that data. For example, my first thought was to look at the capacity factors of these power plants: how much power do they really generate as a percentage of their nominal (or "nameplate") power.

Sidenote: Before proceeding, there's an interesting observation I should make here, about operational numerophobia (similar to this older post): in social interactions when this type of problem comes up, educated people who can do calculations in their job, or at least could during their formal education, have trouble knowing where to start to convert a yearly production of 98.8 TWh into a power rating (in MW). 
Since this is trivial (divide by the number of hours in one year, 8760, and convert TW to MW by multiplying by one million), the only explanation is yet another case of operational numerophobia. End of sidenote.

Capacity (or load) factor is like any other efficiency measure: how much of the potential is realized? Here are the results for the top 15 or so plants (depending on whether you count the off-line Japanese nuclear plant):

Once these additional numbers are computed, more interesting observations can be made; for example:

The nuclear average capacity factor is $87.7\%$, while the hydro average is just $47.2\%$. That might be partly from use of pumped hydro as storage for surplus energy on the grid (it's the only grid-scale storage available at present; explained in the video below).

That is the power of being a numerical thinker: the ability to go beyond simple numbers and have a deeper understanding of reality. It's within most people's reach to become a numerical thinker, all that's necessary is the will to do so and a little practice.

Alas, many people prefer the easier route of being numerical-poseurs...

A lot of people I interact with pepper their discussions with numbers and even charts, but they aren't numerical thinkers. The numbers and the charts are props, mostly, like the raw numbers on the Wikipedia table. It's only when those numbers are combined among themselves and with outside data (none in this example), information (the use of pumped hydro as grid-level storage), and knowledge (nameplate vs effective capacity, capacity factors) that they realize their potential for informativeness.

A numerical thinker can always spot a numerical-poseur. It's in what they don't do.

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Bonus content: Don Sadoway talking about electricity storage and liquid metal batteries: