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The Math Myth

econlog.econlib.org

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Re: The Math Myth

#41

Post by analog31 »

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…

Speaking of BASIC, I took a high school course in BASIC, in 1981, and it changed my life. For one thing, it changed my approach to math.

I think that computation should be part of elementary math, not to produce the next generation of career programmers, but because computation is actually how a lot of math is done. And it might change the curriculum -- having students think about more complex problems that they have the tools to solve, rather than learning algorithms by rote.

I speculate that people might have a better grasp of statistics if they could just play around with artificial distributions generated by a computer -- even just in a spreadsheet.

Re: The Math Myth

#42

Post by iopq »

rrtwo wrote: post #23
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…

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, if A averaged something like 12.5 and B averaged something like 12.4 it would require a huge sample size to prove that those two samples come from two different distributions.

Re: The Math Myth

#43

Post by ar0 »

I don't buy the sports analogy with which he argues that it is "self-serving nonsense" if people state that mathematics education trains your general problem solving skills. His argument that soccer players should only play soccer seems not to be anchored in reality: Of course professional soccer players spend a lot of time in the weights room or go running to enhance their general strength and stamina [1]! They do not only train their bodies by playing soccer...

I do think that learning math does help you to think more clearly and to analyze problems in a more systematic matter.

Now, he does not define well what he means by "higher mathematics": I agree that (as with almost all learning) there is diminishing marginal utility in mathematics education. While I would argue that learning how to work with percentages and also basic calculus (to get a feeling for the difference between a change in position and a change in velocity, for example) increase your general problem solving skills by a lot, if you have been through all this then learning about Ricci flow will probably not do that much to your general problem solving anymore.

[1]: http://well.blogs.nytimes.com/2014/07/16/train-like-a-german...

Re: The Math Myth

#44

Post by sp527 »

moron4hire wrote: post #30
sp527 wrote: post #27

Earlier quoted context omitted.

It's also not strictly, theoretically true. More an 'for all intents and purposes' kind of thing.

No, it is true in the strictest sense of the word.

Hardly. We use this reduction because it's essential from a mathematical and axiomatic perspective and because limits are a fundamental construct. But more philosophically, a natural and nonterminating simulation of 0.999... (were it possible) would never strictly equal 1. You would wait an infinite amount of time for it to do so. This comes down to how you view the problem. I would never argue with this through the lens of abstract higher mathematics. I think about it from a computability perspective, which is one way in which you can discount the observation.

Re: The Math Myth

#45

Post by iopq »

MichaelBurge wrote: post #32
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…

> 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

Re: The Math Myth

#46

Post by mathattack »

Perhaps the arc of my career is different but I've seen the opposite. I've been in Finance jobs where people who don't understand more advanced probability can't figure out how to price things. And even people with advanced knowledge make mistakes.

I've also been in analytics jobs where college educated people mistake correlation for causality. (It seemed so profound when I learned the concept only in how often it's abused)

I've seen people in customer support management make enormous judgment errors because they think don't comprehend the difference between a 500K account and a 1K account.

Requiring calculus of everyone may not solve this, but requiring a couple years of hard (beyond 8th grade) stats could help.

As for the CS/engineering/Math requirement for jobs - I think that's just a reaction to the weak rigor (on average) of so many other majors.

Re: The Math Myth

#47

Post by keithgabryelski »

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…

I just wish they would teach the common curtesy of putting (page#/totalPages) on each slide of their power point presentation so I can decide whether I can make it through the deck or cut my wrists now.

Re: The Math Myth

#48

Post by iopq »

sp527 wrote: post #44
moron4hire wrote: post #30

Earlier quoted context omitted.

No, it is true in the strictest sense of the word.

Hardly. We use this reduction because it's essential from a mathematical and axiomatic perspective and because limits are a fundamental construct. But more philosophically, a natural and nonterminating simulation of 0.999... (were it possible) would never strictly equal 1. You would wait an infinite amount of time for it to do so. This comes down to how you view the problem. I would never argue with this through the…

It's not a reduction. If you try to find where to put 0.999... on the number line, it has to go exactly where 1 is.

For one thing, 1 - 0.999... = 0.000... because you never get to have any remainder since 0.999... is infinite.

Or here's another proof:

x = 0.999...

10x = 9.999...

10x - x = 9.999... - 0.999...

9x = 9.000... = 9

9x = 9

x = 1

Re: The Math Myth

#49

Post by moron4hire »

sp527 wrote: post #44
moron4hire wrote: post #30

Earlier quoted context omitted.

No, it is true in the strictest sense of the word.

Hardly. We use this reduction because it's essential from a mathematical and axiomatic perspective and because limits are a fundamental construct. But more philosophically, a natural and nonterminating simulation of 0.999... (were it possible) would never strictly equal 1. You would wait an infinite amount of time for it to do so. This comes down to how you view the problem. I would never argue with this through the…

You are discarding an essential part of the representation. You are moving the goal post to make yourself right. Just because people don't always understand infinitesimals doesn't make them right. It's the reason they are wrong. There just plain don't know what they are talking about.

You can't represent 0.2 exactly using IEEE floats, either, but that doesn't mean the representation 0.2 is not exactly equal to 1/5th.

Re: The Math Myth

#50

Post by [deleted] »

sp527 wrote: post #44
moron4hire wrote: post #30

Earlier quoted context omitted.

No, it is true in the strictest sense of the word.

Hardly. We use this reduction because it's essential from a mathematical and axiomatic perspective and because limits are a fundamental construct. But more philosophically, a natural and nonterminating simulation of 0.999... (were it possible) would never strictly equal 1. You would wait an infinite amount of time for it to do so. This comes down to how you view the problem. I would never argue with this through the…

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