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To Live Your Best Life, Do Mathematics

quantamagazine.org

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Re: To Live Your Best Life, Do Mathematics

#201

Post by vanderZwan »

unixhero wrote: post #196
110011 wrote: post #63

As a counterpoint to the overly exuberant article let me chime in as a graduating theoretical computer scientist. Math is hard and despite its beauty and allure academic life doesn't take place in a vacuum- ergo there's a lot of politics and pettiness from your peers. You should expect to invest years of your life into making progress on some hard problem with little encouragement in the meantime, this takes a tremen…

Maybe I skimmed the article, but my takeaway from this article was that using our abilities to think and solve mathematical problems helps us to live a life of more intellectual resilience. In my view, this wasn't about doing mathematics as an academic career, climbing up the ivory tower, publish or perish, and all that. Edit: I tend to agree. My intellectual capacity was far improved only after doing first year Engi…

> My intellectual capacity was far improved only after doing first year Engineering Maths & Physics. I did terrible gradewise, but it has helped me visualize, juxtapose mental structures, quickly iterate on different concepts etc.

Same here, and thanks to the internet just remembering concepts is usually enough these days.

Yesterday I had to quickly guestimate for a project how much space overhead we'd have on the server if we pre-generated an image pyramid of tiles for leaflet.js[0], instead of generating a "PNG" in RAM on the fly each time and serving that. Then I realised the number of pixels shrinks by a quarter every time we zoom out, so the worst case would be the infinite sum of 1/4^n. While I vaguely remember from my first year of physics how to calculate that, it's been over a decade. But we have Wolfram Alpha these days[0], which told me it converges on 4/3. So I knew the upper boundary would be around 4/3 of our original data, plus negligible PNG header overhead, and assuming compression is about the same.

[0] http://leafletjs.com/

[1] https://www.wolframalpha.com/input/?i=sum+of+1%2F(4%5Ek)

Re: To Live Your Best Life, Do Mathematics

#202

Post by fmoralesc »

nabla9 wrote: post #54
gthtjtkt wrote: post #8

Based on all the supposed benefits of doing math, it sounds like people would be better off studying philosophy. Same benefits but a much broader appeal, and far more applicable to most people's everyday lives. When I finally "discovered" philosophy in college, I was angry that we hadn't been exposed to it at all in middle or high school. Instead, I'd been forced to waste years on things like math, biology, etc. that…

Real philosophy can't be limited to some set of tools or into some set of books and approaches that fits into curriculum. Philosophy is completely open ended pursuit. I firmly believe that philosophy without mathematically oriented thinking at the core is limiting. Teaching and studying of formal logic has been traditionally part of philosophy. In practice there is no real border between philosophy and formal science…

I think you are misunderstanding Kant.

In PTAFM 13, Kant is arguing that neither space nor time are intrinsic properties of things in themselves, and basically making the point that properties like position and congruence are relational, not intrinsic. Spatial relations fit with the intuition of space, which is the form of external experience (and one should think of this as the abstract form of any space whatsoever - people tend to think that Kant is undermined by the development of non-euclidean geometries, but I think one can push the abstraction so it fits equally well). Experience of- and reasoning about spatial objects involves both intuition that corresponds with the forms of space and time (which applies to any experience whatsoever, outer or inner), and the operation of the understanding through concepts. Now, reasoning from principles which might apply to spatial objects (in the case of algebra, geometry and topology) can go through concepts alone as long as it is logical. But those principles would be meaningless for us if we didn't have experience of any spatial objects whatsoever (if we didn't have the pure intuition of space).

"Thoughts without content are empty, intuitions without concepts are blind. The understanding can intuit nothing, the senses can think nothing. Only through their unison can knowledge arise." (KrV A51).

Re: To Live Your Best Life, Do Mathematics

#203

Post by 110011 »

spynxic wrote: post #146
110011 wrote: post #63

As a counterpoint to the overly exuberant article let me chime in as a graduating theoretical computer scientist. Math is hard and despite its beauty and allure academic life doesn't take place in a vacuum- ergo there's a lot of politics and pettiness from your peers. You should expect to invest years of your life into making progress on some hard problem with little encouragement in the meantime, this takes a tremen…

> To compensate for this horrible feedback mechanism you need to basically play the popularity game Feedback needn't be a necessity in a work. Assessments and criticism will come if the work is essential, perhaps many years in the future.

It sounds like you're not being sarcastic. So let me say that when you're working on something that almost surely has zero practical impact over the course of your lifetime, and the only possible benefit to society is the advancement of the state of our knowledge, a lack of enthusiasm from your peers can be gut wrenching no matter how mentally resilient you think you are. No one does math solely for appreciation from people they admire and respect, but the lack of it, even in the short term, can be very hard on a person.

Re: To Live Your Best Life, Do Mathematics

#204

Post by posterboy »

EternalData wrote: post #149

I took this to be a general call to learn and practice mathematics, and not as a summons to a career in academia, so perhaps I'm seeing it a bit differently. I have to say as somebody who through attrition always feared math in university that it is meaningful to think about reasons why people fear embracing certain types of knowledge. It's only after the fact that I realize how useful and even how romantic applicati…

>how romantic applications of mathematics might be.

like, in the dating market or do you mean a philosophical potential? The philosophical aspect is huge, eg. to tell once meant counting, or logic and language having a common Greek root.

Re: To Live Your Best Life, Do Mathematics

#205

Post by tremon »

sametmax wrote: post #188
nabla9 wrote: post #54

Earlier quoted context omitted.

Real philosophy can't be limited to some set of tools or into some set of books and approaches that fits into curriculum. Philosophy is completely open ended pursuit. I firmly believe that philosophy without mathematically oriented thinking at the core is limiting. Teaching and studying of formal logic has been traditionally part of philosophy. In practice there is no real border between philosophy and formal science…

It is part of the curriculum in France. The problem I got with philosophy is that it's supposed to be applied knowledge. But it's always consumed as an intellectual one. As a result, the smartest philosophy lovers that I know are incredibly unhappy. They know so many things. But knowing something doesn't mean you are able to do anything about it. Some becomes cynical. Other become depressed. Other procrastinate to he…

The problem I got with philosophy is that it's supposed to be applied knowledge.

Can you elaborate on that? On why it's supposed to be applied knowledge I mean?

To me philosophy is one of the most abstract forms of thought available, and to me abstract is the antithesis of "applied". Maybe the furthest I would go is to state that philosophy is knowledge applied recursively on itself. But that already seems an abstract formulation to me.

Re: To Live Your Best Life, Do Mathematics

#206

Post by chrisweekly »

kzisme wrote: post #129
cbsmith wrote: post #95

Earlier quoted context omitted.

Yeah, I'd argue a very un-Good Will Hunting thing: if you can be convinced you suck at math, you probably should not pursue a career in academia in math. However... being a math major is really different from a career in academia. People really should be encouraged to major in math.

I would have to agree with this, but I disagree with out math is taught by most schools. Somewhere in this thread there is a link to Francis's lectures and they are wonderful. The method/enthusiasm be has for teaching is wonderful and makes all the difference to students. Rather than going through online courses and paying for them (many university classes are mostly online math problems, and proctored during a speci…

>EDIT: The way math is currently taught really forces people to dislike math and think they suck at it. (in general)

^ THIS.^

If math education could only be more like: https://betterexplained.com

Re: To Live Your Best Life, Do Mathematics

#207

Post by tremon »

musgravepeter wrote: post #41
Stasis5001 wrote: post #22

Earlier quoted context omitted.

Math classes ramp up in a gradual way that develops critical thinking and intuition in a very small sandbox, where it's easier to appreciate the results. Thinking in, say, just the x-y plane makes it far easier to isolate relationships than philosophy, which tackles much bigger problems and gets you into controversial problems almost immediately, with no clear answers. The basic math framework is rigid and precise, w…

To me the key point is "no clear answers" in philosophy. In math you learn to follow a series of developments, building structure that leads to statements that are true. These are the foundation for more bricks in the wall and even bigger constructions. e.g. The proof of Fermat's last theorem. My sense of philosophy - after reading maybe a dozen of the classics, was there was little that was accepted as true. Yes, th…

True, but that is because philosophy doesn't deal with answers. It deals with a more fundamental question, the question of truth itself. Instead of providing a framework for finding singular answers to exact formulations like mathematics does, philosophy ultimately provides a framework for exploring and expanding the limits of certainty.

Please remember that the entire STEM field grew out of the questions of those philosophers you dismiss as "no clear answers": our entire scientific process (empirical theory-building) is based on the previous explorations of philosophers on truth and knowing. Similarly, both capitalism and Marxism grew out of the questions of philosophers about the structure of society.

You need questions before you can answer them. Philosophy deals with the questions. Our answers to those questions have become the main pillars of modern society.

Re: To Live Your Best Life, Do Mathematics

#208

Post by ihaveahadron »

EternalData wrote: post #149

I took this to be a general call to learn and practice mathematics, and not as a summons to a career in academia, so perhaps I'm seeing it a bit differently. I have to say as somebody who through attrition always feared math in university that it is meaningful to think about reasons why people fear embracing certain types of knowledge. It's only after the fact that I realize how useful and even how romantic applicati…

Get a girlfriend dude, you've been jerking it or something too long if you are calling math "romantic". I don't know how to put it, but something's wrong when people get emotional about math and science. Maybe your a homo, I don't know man figure it out, but don't call math romantic again stupidass.

Re: To Live Your Best Life, Do Mathematics

#209

Post by conjectures »

justinpombrio wrote: post #161
Balgair wrote: post #92

Earlier quoted context omitted.

Chiming in from Bio: Yep, this is true here too. I can't find the citations right now, but there was a recent study done through Elsiver's website. The group got a hold of the servers for Elsiver and took a look at page views. They wanted to know what the rates of papers being read was. It was... disheartening. They found that ~46% (again, not sure here as I can't find the source) of papers will never be looked at ou…

In CS, most authors host "preprint" copies of their papers on their own website, and most views are of those versions. So I wouldn't be surprised if Elsiver's defunct distribution system isn't getting used much (at least in this field).

Depends if they're counting abstract html views or full pdf hits. I'd expect the former to be 10x the latter at least.

Re: To Live Your Best Life, Do Mathematics

#210

Post by ihaveahadron »

posterboy wrote: post #204
EternalData wrote: post #149

I took this to be a general call to learn and practice mathematics, and not as a summons to a career in academia, so perhaps I'm seeing it a bit differently. I have to say as somebody who through attrition always feared math in university that it is meaningful to think about reasons why people fear embracing certain types of knowledge. It's only after the fact that I realize how useful and even how romantic applicati…

>how romantic applications of mathematics might be. like, in the dating market or do you mean a philosophical potential? The philosophical aspect is huge, eg. to tell once meant counting, or logic and language having a common Greek root.

He means in the dating market, he's in love with math, women just aren't doing it for him.
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