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The Math Myth

econlog.econlib.org

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Re: The Math Myth

#131

Post by [deleted] »

jhanschoo wrote: post #111
kazinator wrote: post #62

Earlier quoted context omitted.

0.999... is equal to 1 only if we assign a particular semantics to the "..." notation. Namely if "..." means "the limit of the decimal number to the left, as the repetitions of the last digit grow ever larger", then 0.999... is an alternative notation for 1 since that limit is 1. The actual number formed by repeating 9's an infinite number of times is not constructable. Whereas 1 is constructable. So they cannot be t…

> So they cannot be the same thing. That's because, philosophically, two objects must be identical in every property to be the same object, and constructability is a property. Mathematicians have proposed several different constructions of the reals. If you were familiar with, say, constructing the rationals from the integers or constructing the reals from the rationals, you would know that this is not a problem. One…

[deleted]

Re: The Math Myth

#132

Post by Bahamut »

nostrademons wrote: post #88

This largely matches my experience - as a software engineer, I spend probably In a market economy, basically all returns come from marginal gains. The vast majority of your lifetime income will come from a dozen or fewer opportunities that you happen to be in a position to take advantage of, whether it's a new job offer or a high-profile project you volunteer for or a startup that takes off. You will qualify for thos…

There is more to math than just calculations, algebra, geometry, etc. Logic, and reasoning through choices & the effects of those choices are vital math skills as well, and for many people in math, they don't manifest until one takes a few rigorous proof-based classes, where one often sees new approaches to arriving at concepts they know, and how to properly get to a conclusion from a particular point.

I wish these skills were emphasized more earlier in people's education, they are important skills for maximizing success IMO.

Re: The Math Myth

#133

Post by tgarma1234 »

I agree that for an average american child to invest time in studying math as opposed to learning to play a musical instrument or doing sports or learning how to cook has very little utility. I think one of the main reasons people push math at civilizational/educational theory/political level is that it is basically a meaningless topic and non-controversial and fills up the school day with material that nobody on earth would find offensive... as opposed to, for example, history or political science. And I say all of that that even though I have a math degree from a legitimate university. If you need math done you can pretty much just pay someone else to do it. You almost never need math done. If there is some important math to be done, someone else is almost certainly better qualified to do it than you are, so let them do it. Life is just too short.

Re: The Math Myth

#134

Post by lisper »

kazinator wrote: post #113
yequalsx wrote: post #56

Earlier quoted context omitted.

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.

> find a decimal representation of a number 0.99999999...1 This denotes the abstract idea that we take 0.999... (infinite number of 9's) and add another digit. This is no more or less abstract than 0.999... to begin with. 0.999... is a unicorn, and 0.999...9 is a unicorn with a pink ribbon on the tip of its horn.

> add another digit

But you can't. All of the places where you might want to add a digit are already occupied by 9's.

Re: The Math Myth

#135

Post by dredmorbius »

iopq wrote: post #101
dredmorbius wrote: post #54

Earlier quoted context omitted.

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

I'm really talking about https://en.wikipedia.org/wiki/P-value Most people just look at the number of subjects in a study, but not the p-values

Thanks.

Re: The Math Myth

#136

Post by School-Cotton »

minikites wrote: post #28
NhanH wrote: post #20

Earlier quoted context omitted.

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.

Most people are happy to accept 0.33333... is the same as one third and from there it's a quick hop to 3*0.3333...

If people accept 0.33... = 1/3 but not 0.99... = 1, they are being logically inconsistent.

A "proof" that just plays a trick on people's logically inconsistent assumptions to derive a result isn't very satisfying. You're not really uncovering anything fundamental through that proof, just playing games.

Edit: what I mean to say is there are reasonable things "..." could mean such that .99... and .33... are both not equal to 1 and 1/3, respectively. But there are none for which one pair is equal and the other not, as you rightly point out. So all your proof does is show that the other person's viewpoint is inconsistent, but it doesn't give any evidence for one of the two consistent viewpoints over the other.

Re: The Math Myth

#137

Post by Ologn »

nostrademons wrote: post #88

This largely matches my experience - as a software engineer, I spend probably In a market economy, basically all returns come from marginal gains. The vast majority of your lifetime income will come from a dozen or fewer opportunities that you happen to be in a position to take advantage of, whether it's a new job offer or a high-profile project you volunteer for or a startup that takes off. You will qualify for thos…

In the spirit of what you're saying - it's possible ten people will be taught undergrad level math and only one will use it - but economically, that one person's added production value could pay for the education of all ten and then some.

The article speaks about Sputnik and one of the world's richest men, mathemetician and retired hedge fund manager Jim Simons notes that he is one of the first students to have benefited from the post-Sputnik STEM student grants. He also mentioned how many people in the US were getting doctorates in mathematics in the year Sputnik went up - I'm looking at the list of names right now and it is much less than 300. So the additional NSF funding etc. that paid for his doctorate resulted in the billions his hedge fund made.

Re: The Math Myth

#138

Post by douche »

ausjke wrote: post #87

This is not just Math. I learnt chemistry, physics, biology and all that from middle to high school. Now as a software engineer they're totally useless and I have long forgotten all those details that I spent months and years to memorize and master. Even reading a science-101 book in one day now will teach me more than what I can remember. Unless you plan to major in those fields, should we just take some introductio…

I firmly believe that one of the failings of the way we teach most subjects is that there is a very low amount of application. Grinding away and learning the theory is almost useless; for most people as soon as they move on it's out of their head and gone forever, with maybe a ghost of a memory that the topic exists.

It's a shame, because some of these things are valuable to know.

If you're felling a tree, trigonometry is pretty useful for trying to figure out whether you've got room to drop it without hitting your house. Also, when you're building that house, for how long you need to cut your rafters to get the right pitch on your roof.

You don't necessarily need to know chemistry to cook, but it doesn't hurt, and you'll understand why you need to use baking powder instead of baking edit: soda when you bake your biscuits.

There's a lot of basic physics and mechanics that can be incredibly useful if you're trying to lift heavy objects with less than adequate equipment.

Re: The Math Myth

#139

Post by linkmotif »

Every little bit of math I've learned has helped me in so many inconceivable and unexpected ways. Articles like this are sad and make me discouraged about the future of humanity.

Re: The Math Myth

#140

Post by Double_Cast »

How does an actuary get by without having learned trig? Surely, they must understand statistics at least. Is the job description the same deal as engineers, where they just look up numbers from a reference table and multiply them?
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