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The Math Myth

econlog.econlib.org

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Re: The Math Myth

#51

Post by rntz »

NhanH wrote: post #20
iopq wrote: post #18

I think society would be a lot better if BASIC math and statistics would be better understood. How many times do you see a study posted here with N=23 and people say "the sample size is too small" when it's clearly not? How many people ask for a card deck change to change their luck? How many times do people read a poll like 49% +/- 3% vs. 43% +/- 3% and conclude the two candidates are statistically tied? I could pro…

To be fair, 0.9999... = 1 is not quite basic. You need to know things like infinitesimals, the distinction between value and representation of numbers etc.

You don't need to understand anything about infinitesimals to understand 0.999... = 1. Perhaps you meant limits? The "standard" approach would be to point out that Σ_{i=1}^∞ 9/(10^i) = 1 (that is, the sum from i = 1 to infinity of 9/(10^i) is 1), and understanding an infinite summation requires the concept of a limit. (Of course, there are simpler proofs that use only basic algebra and intuition about decimals; a limit is just the most direct approach.)

You're spot-on about needing to understand there's a distinction between a number and its decimal representation, though.

Re: The Math Myth

#52

Post by th0ma5 »

I saw someone joke on Twitter that their anxiety level lately is the first derivative of the graph on the 538 2016 election forecast. So to get that I guess I needed to be able to see that in my head briefly. I think I didn't pick up that skill until calculus which for me at least was 11th grade.

Re: The Math Myth

#53

Post by majos »

I think one non-obvious benefit of a good mathematics education is that you have little choice but to develop a tolerance for and understanding of being wrong. See Jeremy Kun's blog post [1] for more, but my own experience has been that in e.g. discussing different ways to solve a problem or prove something almost every person eventually has an "oh, no, I see, I'm wrong and you're right" moment. Not that every mathematician is necessarily a font of humility and grace, but I think math offers more regular and irrefutable demonstrations of your own fallibility than many other fields, and this is good.

[1] https://medium.com/@jeremyjkun/habits-of-highly-mathematical...

Re: The Math Myth

#54

Post by dredmorbius »

iopq wrote: post #42
rrtwo wrote: post #23

Earlier quoted context omitted.

What is the generalised rule/case where small sample sizes are sufficient?

If the difference between samples is VERY large, you don't need a very large sample size. In other words, we're trying to find the chance that the result we got was due to chance. Let's say you have numbers like these: A: 11, 11, 12, 12, 13, 13, 13, 13, 13, 13, 14, 15 B: 90, 92, 93, 94, 94, 95, 95, 96, 97, 99, 99, 101, 101 What is the chance that those two samples come from the same distribution? On the other hand, i…

That sounds intuitively reasonable. Is there a cononical reference argument that you're aware of?

Re: The Math Myth

#55

Post by MichaelBurge »

iopq wrote: post #45
MichaelBurge wrote: post #32

Earlier quoted context omitted.

> I mean I wonder how many people even understand that 0.999... = 1? To be honest, I think it's unreasonable to expect anybody - even with a Ph.D in a field other than mathematics - to be able to even define the real numbers: My definition is probably very different from yours(I tend to say there's countably many real numbers).

https://en.wikipedia.org/wiki/Cantor%27s_diagonal_argument

https://en.wikipedia.org/wiki/L%C3%B6wenheim%E2%80%93Skolem_...

Re: The Math Myth

#56

Post by yequalsx »

NhanH wrote: post #20
iopq wrote: post #18

I think society would be a lot better if BASIC math and statistics would be better understood. How many times do you see a study posted here with N=23 and people say "the sample size is too small" when it's clearly not? How many people ask for a card deck change to change their luck? How many times do people read a poll like 49% +/- 3% vs. 43% +/- 3% and conclude the two candidates are statistically tied? I could pro…

To be fair, 0.9999... = 1 is not quite basic. You need to know things like infinitesimals, the distinction between value and representation of numbers etc.

Property of real numbers: between distinct real numbers is at least one other number. Now try to find a decimal representation of a number bigger than 0.9999999... but less than 1.0. You clearly can't. They must be equal. No need for infinitesimals.

Re: The Math Myth

#57

Post by Nursie »

analog31 wrote: post #25

At my workplace, we have about 60 scientists and engineers. The author's observation is accurate, that most people never use math beyond Excel and 8th grade math. They also never use most of the theory that they learned in their science (including CS) and engineering educations. The typical career arc is to get through college, then sit down at a CAD workstation, or programming terminal, and forget all of your math a…

I do complex mathematics for fun sometimes, it always surprises me when I start talking about the fractal images I generate and a large percentage of other engineers are wowed at how, well, complex it must all be. Then start to glaze over a bit...

I loved studying all that stuff at school, pretty pictures or no. But as a coder the opportunities to use much of it in anger are really quite restricted.

Re: The Math Myth

#58

Post by [deleted] »

analog31 wrote: post #25

At my workplace, we have about 60 scientists and engineers. The author's observation is accurate, that most people never use math beyond Excel and 8th grade math. They also never use most of the theory that they learned in their science (including CS) and engineering educations. The typical career arc is to get through college, then sit down at a CAD workstation, or programming terminal, and forget all of your math a…

[deleted]

Re: The Math Myth

#59

Post by sramsay »

merpnderp wrote: post #24

How would this same conjecture apply to History, Literature, Biology, Physics, etc etc? How much of any advanced learning do most people use in their day to day lives? All of it in the periphery would be my counter-conjecture. I was always taught trade schools were for learning a particular skill. College was to equip you with the knowledge and ability to think logically required to have a better life.

I had the same thought. Follow the author's conclusions, and you'll end up rejecting college as such on the basis of its apparent lack of "utility."

But why should everything be tied to the demands of the workforce? At some level, saying "Don't bother learning calculus because you'll never need it" seems akin to saying, "Don't bother looking at the Mona Lisa, because you'll only ever have to read road signs."

Is there no intrinsic value to learning? No need to be connected to the cultures of the past (or the present)? Nothing to be gained by studying all those ideas that underlie those CAD programs?

The author traces the myth back to Sputnik. It sounds to me much more like every kid who's ever wept over their algebra homework and asked "When am I ever going to use this?"

Re: The Math Myth

#60

Post by dredmorbius »

Biologist Edward O. Wilson makes a case for a similar, though not identical view, in his Letters to a Young Scientist. 2nd essay is "Mathematics". Distilled:

* A strong mathematical background does not guarantee success in science.

* There's a large amount of foundational theory and work which involves thinking in images and facts, not mathematics.

* Maths phobia deprives science of an immeasurable amount of talent.

* True maths talent is probably at least partially hereditary.

* Maths and conceptual work are complements, not replacements.

http://www.worldcat.org/title/letters-to-a-young-scientist/o...

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