John Urschel tackles his lifelong balance of math and football in new memoir
news.mit.edu
news.mit.edu
About the football, I think CTE issue is going to balloon in the coming years. In the UK there's a Rugby World Cup winner who can't remember winning it. Parents are wise to observe the decisions of a guy who would have been paid millions a year but chose not to, in order to preserve his mind. It's unfortunate because gridiron is a fascinating sport.
As a mathematician, I read that headline and say "what are your axioms?" And that's a quantitative response to that qualitative headline, so no apologies.
Pointing out that someone else is aimlessly pointing out "errors" gets downvotes, apparently. That would be a hypothesis.
It's probably not fair to indict too strongly on this phrase; people use exaggerated language all the time ("X is the best" to mean "X is very very good"), and so reading it as "thinking quantitatively is very very important" seems appropriate.
Nonetheless, as valuable as quantitative thinking is, it has (immeasurable) diminishing returns. It can never be more than a tool to realize our qualitative human values. Somewhere we have to "cash out" the numbers into things we care about, which don't have numbers attached: human dignity; individual autonomy; the look of joy in a child's eyes; the emotional security of family and friends; etc.
> It's probably not fair to indict too strongly on this phrase; people use exaggerated language all the time ("X is the best" to mean "X is very very good"), and so reading it as "thinking quantitatively is very very important" seems appropriate.
To me, the point isn't about pedantic enforcement of grammar and linguistics, but more so about to underlying thinking that this use of language suggests. To what extent does lazy/imprecise/presumptive/forgiving communication and thinking permeate the systems that implement our incredibly technically advanced advanced societies, where it is simultaneously common to find people who smell like pee sleeping on the sidewalk, and hardly anyone bats an eye, or finds the situation even remotely curious?
This comment isn't directed at you, it's just more of an esoteric observation.
That’s not really fair. Someone who doesn’t like to dance? Entire world missing. Only speaks a single language? Doesn’t really appreciate or enjoy food? Worlds missing.
Doesn’t know a lot about music or art? Has poor emotional intelligence? Enjoys history but not literature?
Worlds missing.
Only socialized in a real way with people like them? World missing.
I can go on. But yeah, quantitative skills are important, and yeah the world is big. It’s even bigger than math.
I like that, even if his politics are problematic.
Just saying there's a lot of things in the math world that if you didn't put down a stake early on, you won't know that you don't know them.
But this is true of many (all?) fields, not just quantitative. For example, recently I've been learning ancient Hebrew and one of the things I learned early on was that it (like Arabic) has a "dual number" which is in a similar grammatical category to English singular and plural, but implies the things usually come in pairs, like hands and eyes. It uses this construct to refer to "the heavens" in Genesis, which immediately raises the question of why ancient Hebrew cosmology identified "the heavens" as dual in number.
There's something I didn't even know I didn't know until I started into the field.
English and Germanic have vestiges of dual number, it's pretty interesting. Like the word "both", it seems like a weird thing to have in a language that normally is single/plural. I came across it because I was reading about languages at one point, but all I used to get there was just ordinary reading. Yes, I didn't hear about it until I heard about it, but I also wasn't prevented from learning this little tidbit from a lack of supporting knowledge. By contrast, there are areas of math that would take me years to even understand what the research questions are.
Hahahaha you clearly don’t know how much you don’t know about art, music, philosophy, ummm psychology.
Sorry to be a bit mean but come on man .... :).
I’m not denying that math isn’t special in certain ways. It is.
And you could even make arguments about the mathematical nature of music.
But man, to be a serious classical musician or serious jazz musician you have to study and practice your entire life since childhood. Just to have a running.
You wanna get good? Achieve mastery and knowledge? Compose work in dialogue with the great work of the past? Would take you years just to get started.
Or Picasso. His father? A painter. He was literally born into it.
I encourage you to read some good biographies of some artists.
Or even a biography on say, Winston Churchill. Or Lincoln. True political / leadership skill takes a lifetime of study and acquiring experience.
To pick more examples of obviously challenging and cavernous non-math stuff, have you read any Thomas Pynchon, Don deLilo, or David Foster Wallace? Or James Joyce or Samuel Beckett?
Or Homer, for gods sakes. Or the Bible, the Koran, the Old Testament, the Tao Te Ching?
Allow for creative, rational thought which is less precise but more complex than pure logic or math (ie allow for human fucking language), and you get what is maybe the deepest cavern there is.
You underestimate both the time and effort needed to gain a real understanding of literature and art, and, to create it on a high level. And all the fields of human experience which we are unable to completely describe our understanding of via mathematics.
As someone else said, math is hard because it is easy. Humanities are easy because they are hard.
You're not wrong, but it's hard not to feel bad for people who bucket others into such confining batches. You'll miss out on so many friendships if you think that way.
There's no special insight needed for being able to appreciate good company, or to play guitar together. And I think a good guitarist can explore as many interesting facets of the world as the best mathematician. Complex numbers to a guitarist may as well be frets on a fretboard to a quant who doesn't play.
IMHO, you have it backwards: the best guitarists explore as many interesting facets of the world as a good mathematician.
You could also use a physics-based model. That has lots of math, including calculus. https://en.wikipedia.org/wiki/String_vibration
I'm not sure what it takes to appreciate good company, but graph theory and statistics seem likely. You'd have to model the social network somehow. Facebook and Twitter would know more.
>Being capable of thinking quantitatively — it’s the single most important thing
https://www.washingtonpost.com/news/early-lead/wp/2017/02/03...
There is also qualitative thinking which is criminally underrated. I reckon that one needs to combine qualitative and quantitative thinking. Qualitative thinking can drive quantitative thinking. Some research on qualitative factors was done on Olympic swimmers. This link below shows its application for excellence for anyone interested.
1. https://www.amazon.com/Problem-Solving-Decision-Professional...
-- 1. Take an interest in data. Be interested in the details of how statistics and numbers make things more complicated than black or white. Take a look each day at some of the more popular plots on https://www.reddit.com/r/dataisbeautiful/ . Go to wikipedia and read about the demographic distribution of the USA, or the federal tax brackets, and how you would visualize those in data. And think about what data, numbers, information you would need to plot such things. Write down the example data you would need and think about how to plot it, or make some conclusion about it. Think about where in your cases you would bring in data (and of what kind) to support the point.
-- 2. Be interested in why small differences in data can change the "takeaway" point of what you're seeing. What would it take in numbers to reach the conclusion you're reaching? How reliable are those numbers, and how do they interact that some error in one would change your whole conclusion? Learning to like the detail behind a "principle" is important. When Justice xyz questioned the petitioner on the distance radius of doctors who were able to be affiliated with an abortion-performing hospital and the effect on the number of women with access to medical procedures, why did that matter?
-- 3. Don't be satisfied with the summary numbers that someone tells you. Learn to ask the next level question about the numbers and think about what it means. When some article or person on the news says, "xyz went up by 30%", ask for more -- what number did it go from to? When was it measured, and by what metric? What was the error? If it went from 3 to 4, well, is that meaningful to say it went up by 30%? When they say a vaccine has 90% efficacy, what does that mean? What numbers are they looking at to say such a thing? What number would you look at?
You will know you've reached a level of quantitative thinking when you can call bullshit on other people's claimed statistics, or ask "did they really measure that in a meaningful way?".
If you don't take an interest in numbers and how people present them, and what they mean, you can just be led around by other people who are in control of them. It will be in your interest and increase your future success against adversaries to feel comfortable with numbers.
Lacking emotional skills is, when profound, a disease called Autism. Which makes a lot of things really hard. I don't believe there to be anything comparable for lacking quantitative skills while being of normal intelligence otherwise.
There's a thing called dyscalculia, I believe. Have you ever heard of it? Have you heard of dyslexia? Is the latter one more widespread, or is it more profound? The answer doesn't actually matter for the conclusion not to worry too much about the phenomenon.
The best advice is to be excellent at what you're good at, while trying to foster high regard for other disciplines, an to find people and involve them where appropriate, and to try to track how useful their advice is and, if it is, to seriously consider it.
Incidentally, all those are emotional skills and, in my experience, lawyers are far better at respecting statistics or math than STEM graduates are at not sneering at any intellectual endeavour that doesn't glorify Richard Feynman.
(who, by the way, was the rare exemption. And not only because it would have been awkward for him to sneer at any discipline that doesn't glorify him)
Though written a fairly long time ago, the subject fares better over time than many more qualitative ones.
I was thinking of the following argument and cut it far too short: "Don't believe a mathematician that quantitative skills are the most important, don't believe a psychologist that interpersonal skills are most important, and don't believe a programmer that python is more important than English".
Instead in trying to learn what formula to use, look up how to derive that formula. Deriving your own formulas is a skill you can develop that will change how you think, while collecting formulas to plug things into might be useful but won’t grow you new angles and frames of mind.
Most of all, just practice turning intuitive things into their mathematically precise equivalents, a level of precision and unambiguity you’re probably already nurturing as a law student.
I played 7 years of rugby growing up and I hope I haven't done long term damage. I've been concussed a few times, etc.
What, are they all bad mathematicians now? What a bizarre perspective.
I'm guessing he's being highlighted as an unusual and inspirational role model case for an American kid (if he were American). Football, Baltimore, black. That example growing-up environment does not exactly favor a kid to be encouraged to pursue intellectual strengths unless you have an incredible teacher or parents for example. At worst, you are even harrassed for trying to escape your environment, and called a class traitor for thinking you're better than everyone else. This is a big problem.
Wikipedia says "Urschel was born in Winnipeg, Manitoba, Canada. His parents, John Urschel and Venita Parker, were a surgeon and attorney, respectively. He grew up in Buffalo, New York, where he attended Canisius High School." With no other information, that "growing-up" environment (notably including a private school) sounds great for an academically precocious kid.
Baltimore inner city. No amount of well-intentioned BLM protest is going to change the day to day lived experience of someone in that environment. It has to be change in the community itself.