The Math Myth • Hacker News Board

Re: The Math Myth

#71

Post by kazinator » Sat, Sep 03, 2016, 2:00 PM UTC

soVeryTired wrote: post #65

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…

They're coming out of the woodwork... Edit: sorry, didn't mean to ad hominem, but I'm going to leave my original comment there all the same. To make my post a bit more constructive, OP, what exactly is your definition of "constructible"? Because it doesn't relate to any mathematical concept I'm familiar with. Other than maybe "finitary".

https://en.wikipedia.org/wiki/Constructivism_(mathematics)

Do you have remarks not regarding the semantics of "constructable"?

Re: The Math Myth

#72

Post by jupiter90000 » Sat, Sep 03, 2016, 2:02 PM UTC

Seems kind of ironic that the math professor writing this article uses conjecture as evidence for recommendations to what people should be learning instead of actual statistics. He didn't even need 8th grade math to make his argument for fewer people needing to learn higher mathematics (though perhaps he's correct).

Re: The Math Myth

#73

Post by recursive » Sat, Sep 03, 2016, 2:05 PM UTC

kazinator wrote: post #62

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…

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…

Correction: Induction is how we can understand that a property holds for all finite values.

It seems that you object to the commonly accepted meaning of "...".

Re: The Math Myth

#74

Post by elliott34 » Sat, Sep 03, 2016, 2:05 PM UTC

sp527 wrote: post #19

This has so much more to do with the lack of easily monetizable applications of complex mathematics. I'm sure a significant number of engineers and STEM professionals feel (as I do) that they're deliberately eschewing those subjects not for a lack of interest, but rather as a response to market demand. The market of people who are genuinely passionate about complex subjects in math and science is saturated relative t…

I wish everyone on r/MachineLearning and those preparing for data science careers would read this comment and heed the advice of those of us who have actually spent time on data science teams and have experienced all of this first hand.

Re: The Math Myth

#75

Post by nabla9 » Sat, Sep 03, 2016, 2:05 PM UTC

sp527 wrote: post #19

This has so much more to do with the lack of easily monetizable applications of complex mathematics. I'm sure a significant number of engineers and STEM professionals feel (as I do) that they're deliberately eschewing those subjects not for a lack of interest, but rather as a response to market demand. The market of people who are genuinely passionate about complex subjects in math and science is saturated relative t…

The market for STEM professionals is superstar economy similar to the market of comedians, athletes, musicians and artists. The payout in the profession follows Zipf's distribution.

btw. 12% of US millionaires are educators. http://www.barrons.com/articles/SB50001424053111904370004577...?

The Economics of Superstars Sherwin Rosen The American Economic Review Vol. 71, No. 5 (Dec., 1981), pp. 845-858 https://www.jstor.org/stable/1803469?

Re: The Math Myth

#76

Post by p333347 » Sat, Sep 03, 2016, 2:07 PM UTC

Its quite well known that engineers need maths only to pass exams and for work all they need is an appropriate handbook. :-]

Re: The Math Myth

#77

Post by heydenberk » Sat, Sep 03, 2016, 2:08 PM UTC

I have relatively little mathematical education and have been seeking to correct that by self-educating over the last year, so I have a certain bias. Nonetheless, I disagree with the key points of this article.

The article asserts that most modern professional jobs requires only "Excel" and 8th grade programming. In my experience, over-reliance on software like Excel rather than a basic competency in numerical programming is a hindrance to economic growth. Spreadsheet-based numerical programming is opaque and ill-suited to interoperation. This leads to subtle errors, duplication of work, difficulty of replication and silo-ing of meaningful results in the private sector, the public sector and academia.

I take the second point that the transferability of critical thinking skills developed by learning mathematics is unproven. Nonetheless, history is flush with anecdotal evidence of this hypothesis, and in the absence of empirical evidence, it seems unwise to reject that hypothesis out of hand.

EDIT: removed an assertion that the article was poorly argued.

Re: The Math Myth

#78

Post by setra » Sat, Sep 03, 2016, 2:08 PM UTC

soVeryTired wrote: post #65

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…

They're coming out of the woodwork... Edit: sorry, didn't mean to ad hominem, but I'm going to leave my original comment there all the same. To make my post a bit more constructive, OP, what exactly is your definition of "constructible"? Because it doesn't relate to any mathematical concept I'm familiar with. Other than maybe "finitary".

https://en.wikipedia.org/wiki/Finitism

Re: The Math Myth

#79

Post by kazinator » Sat, Sep 03, 2016, 2:09 PM UTC

recursive wrote: post #73

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…

Correction: Induction is how we can understand that a property holds for all finite values. It seems that you object to the commonly accepted meaning of "...".

So you're saying that "for all positive integers n : property(n)" means that property(k) might not hold for some k that is not a "finite value"?

The only problem is that this not-finite value does not occur among the integers; thus the inductive procession doesn't actually have that value k as its target. It does not lie in its path, so to speak.

> It seems that you object to the commonly accepted meaning of "...".

I formulated it as a limit and stated that it denotes 1 in the case of 0.999...

How do I object?

Re: The Math Myth

#80

Post by jdietrich » Sat, Sep 03, 2016, 2:11 PM UTC

majos wrote: post #53

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 mathem…

In my experience, a surprising number of people with a humanities education simply don't believe in "wrongness", but merely differences of opinion. They regard truth as peculiar abstraction used by mathematicians and hard scientists, not a phenomenon that actually exists. It's hard for someone to admit to being wrong if they don't even believe in the concept.