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Advice to mathematicians Advice to mathematicians
by Joseph Gatt
2020-02-10 07:22:27
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Math is simple and should stay simple. I know it's in the DNA of people to make their jobs sound less accessible than they actually are, and I know mathematicians like to make it sound like they have brains three times the size of a non-mathematician. If they had brains three times the size of a non-mathematician, perhaps they would start by not imitating Einstein's haircut that would be a good start.

mat01_400Of course the vast majority of mathematicians I meet are the lovely, humble, simple kind. Albeit that in the world of math, mathematicians often have to take jobs hundreds of miles away from their family and friends, simply because there aren't that many math research labs in the world. There's a shortage of mathematicians, and there's also a shortage of math departments, and math is often not frequently taught at universities, or taught by Teaching Assistants or high school math teachers at universities.

But what is math? It's the science of quantifying things. You either quantify space (that's called geometry) or you quantify objects. In geometry, measures are an abstract notion, just like words in language are an abstract notion. Why is a meter a meter long? Why is it called a meter in the first place? Why didn't we name it an exclavatator or something. So a meter is a meter and is a meter long.

So in geometry you quantify space, either by measuring area, circumference, surface or other more obscure things like spheres, globes, gases, liquid masses and the like.

In calculus, you count objects or any countable item. A liked page on Facebook is a countable item, the number of pictures you upload on Facebook is a countable item, the number of friends you have on Facebook is a countable item. And Facebook wants to stop counting those items because apparently people go manic depressive when they find out someone has way more friends than they do.

Then there are philosophical questions in calculus. Let's say you have ten pencils. If I break the ten pencils and sharpen them, do I get 20 pencils? What about the notes vs. value of the notes. If I have 10 one dollar bills and 10 one hundred dollar bills, we have the same number of notes, but their values are different.

OK then in math we can do this thing where we can guess missing information from quantitative information that we have. If I ever have children and they grow up and ask me what I did for a living, I will tell them that I guessed missing information by using and analyzing the available information that I had. Let's take an example. We know mommy baked five cookies, and we only have three cookies on the plate. How many cookies disappeared? 2 cookies. What happened to the cookies? Now this is no longer math but social science.

Now at school we teach kids how to find missing information by only looking at one or two, perhaps three variables: cookies. But in the real world, adults tend to search for missing information by using increasingly gigantic sets of data that is numerical values. Let's say there are two billion Facebook accounts. Let's say Facebook users click an average of 150 times a day on the site. Let's say the average Facebook user inputs 15 actions a day (could be a post, a “like” or a comment or “liking a page” or visiting someone else's page).

So now that we have that available information on Facebook, how do we figure out the missing information? One variable we have on Facebook is the time of the day the person entered and browsed Facebook. So what Facebook tries to figure out, among other things, is what you do when you're not on Facebook.

Now here's where math gets complicated. In school, they teach you that there's a correct answer for every question. If that were true, and if there really was a correct answer for every question, I'd be unemployed, and insane, because my job involves a lot of guessing.

And that's what most of math really does: guess. With the Facebook example, we can guess with 95% accuracy how much money someone makes, by looking at “liked” pages, interactions, time of entry and exit of their Facebook profile and so on. Let's take it to Twitter. We can guess with around 75% accuracy whether Twitter users will vote, and who they will vote for. 25% is the swing vote, and we know with 70% accuracy that the 25% is undecided, that is there's a 30% chance the undecided voter is actually decided.

Then there's the annoying kind of math, what I like to call “salesman's math.” That is, like in every trade and business, some mathematicians will try to sell you their algorithm or formula by claiming that it's a miracle formula, just like Molasses was said to cure everything in the 1930s (and Molasses cures nothing). Then it was Castor oil, and castor oil cures nothing.

Same goes for math. Some mathematicians like to claim that there are formulas that can test the accuracy of so and such, or that can enable you to measure such and such with exact precision. Then you have Trump being elected president, and just like people did end up realizing castor oil is a scam, people realized all those “precision” formulas and algorithms were a complete scam.

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