[HN Gopher] Ego and Math [video]
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Ego and Math [video]
Author : andersource
Score : 212 points
Date : 2023-06-21 09:51 UTC (13 hours ago)
(HTM) web link (www.youtube.com)
(TXT) w3m dump (www.youtube.com)
| photochemsyn wrote:
| Historically, mathematics that initially seemed to have little
| imaginable practical application later become core to various
| fields of physics and engineering - non-Euclidean geometry as
| developed by Gauss-Bolyai-Lobachevsky amd Riemann became the
| foundation of Einstein's general relativity, number theory became
| the basis of cryptography (to the likely dismay of GH Hardy),
| etc.
|
| So keep plowing away, mathematicians, at whatever you want to,
| and don't be surprised if some applied science type picks up the
| results and uses them for something in the so-called real world
| (but don't expect many of us to check your proofs, no thanks,
| taking it all on faith is the norm).
| k__ wrote:
| Yes, math is to physics what art is to design.
|
| It's crazy what these two fields produce, but once I a while
| something useful comes out.
| hashar wrote:
| I opened the video in the background and immediately recognized
| the person: the author behind the 3Blue1Brown YouTube channel. It
| has a long series of video regarding various mathematical topics
| which are rather accessible.
|
| My favorite by far is a "proposal" for an alternate notation
| which makes much more sense and, if adopted, would make
| mathematics way less intimidating (Triangle of Power (2016),
| 3Blue1Brown - https://www.youtube.com/watch?v=sULa9Lc4pck ).
|
| I'd give him a Fields medal (or at least an honorary mention of
| some sort) :-]
| hfkwer wrote:
| I'm a math professor with about a decade of teaching math. On
| the list of things that make math intimidating, for undergrads
| at least, the notation for powers, roots, and log, is very low.
| The "proposal" also ignores that
|
| 1. The kth root of x is often denoted x^(1/k);
|
| 2. We have convenient shortcuts for the square root and the
| natural logarithm;
|
| 3. Parentheses become a mess;
|
| 4. The notation for squares, cubes, etc. is deeply entrenched;
| does anyone really think that write "x triangle 2 above" (yup,
| it's a mess to write in ASCII) instead of x2 or x^2 would make
| mathematics less intimidating to everyday people?
|
| 5. Having symbols, subscripts, prescripts, and superscripts
| above the symbol all strewn together is much more intimidating
| to anyone.
|
| 6. How do you nest them? Try to write down log_a(log_a(x)) to
| see what I mean.
|
| I enjoy 3B1B's videos in general, but this one really only
| makes sense if you don't think too much about it.
| red_trumpet wrote:
| > On the list of things that make math intimidating, for
| undergrads at least, the notation for powers, roots, and log,
| is very low.
|
| I guess whoever reaches undergrad math courses already passed
| this hurdle. It would be interesting to know if this makes a
| difference for school children being introduced to the
| subjects, like ~8th class for roots, or ~10th class for
| logarithms.
| agumonkey wrote:
| I'm no math professional, and my struggled around some math
| topics was rarely notation, but 1) a bit of hidden
| information/culture (which can show in notation too) 2) a
| misalignment on what the topic was trying to achieve.
|
| The last bit which I can't describe clearly is 'maturity'.
| Sometimes an idea just eludes you for years, until it
| doesn't. Changing maths would probably not have fixed this.
|
| Oh, and the underlying human feelings behind the problem
| solving made by others. It seems that a lot of maths is
| lowering energy required to express or find a solution, no
| matter what subfield you work on, that seems to be the goal.
| ouid wrote:
| Composition of mathematical notation is always terrible.
| Where do I write the -1 on the square root to indicate that I
| would like the preimage? Even worse, Where do I write this on
| a trig function?
| simiones wrote:
| 1. The kth root of x being x^1/k would be written as this:
| k 1/k ^x = x^
|
| 2. I don't think these are as important. Also, ln x / log x
| is still the same or more symbols than `e^x`.
|
| 3. Not significantly more than parens in exponents. You also
| get rid of one level of parens from log.
|
| 4. Notation change is often a huge hassle, this is absolutely
| true.
|
| 5. Isn't this a problem for current notations as well?
| Especially if you ever want to put a complex expression for k
| in the k'th root notation.
|
| 6. log_a(log_a(x)) would be `a^(a^x) `.
|
| Still, I don't personally like the symbol. The biggest
| problem to me is that it requires smaller letters
| (subscripts/superscripts) all the time, which makes it more
| annoying to write than the regular notation for the base of
| an exponentiation and the argument of a log or root. Complex
| expressions in small letters are very annoying to me, and
| this notations makes it necessary to use them in all cases,
| where the normal notation at least has some cases where this
| is not needed.
| placesalt wrote:
| The answer by user 'Blue' on the same thread seems more
| practical to me. Their answer[1] uses notation that doesn't
| translate to this messageboard.
|
| Perhaps a reordering of their method, using the existing
| caret notation: b^p = r :: the result from
| base b with exponent p ^pr = b :: the base giving
| result r from exponent p br^ = p :: the exponent
| yielding r with base b
|
| [1] https://math.stackexchange.com/a/1158802
| electrondood wrote:
| For me, the intimidating bit and source of "math anxiety" is
| that there's only one right answer. You either get it or you
| don't. At the time, I had a fear of failure and this caused a
| lot of stress, especially at the chalkboard in front of the
| class.
|
| I preferred humanities, where there was wiggle room and you
| could bullshit your way around the gray areas. That all ended
| when I became a dev, where failure is nearly constant so
| there's no time for feeling bad about it.
| kandel wrote:
| mathematicians: Humanities are stressful because you don't
| know what's the right answer!
| hgsgm wrote:
| Good academics fear the difficulty of good humanities.
| Bad academics enjoy having the excuse.
|
| This is why "humanities" in general have a terrible
| reputation, but the individual people who've done great
| work are respected.
| Tainnor wrote:
| As someone who has studied both humanities and "hard"
| subjects, I'd definitely say that I respect really good
| researchers in the humanities just as much as I would a
| Fields medalist, but there's a much lower bar and there's
| a lot of shoddy research being done (as well as really
| bad students who just coast by somehow, something which
| is much harder to do in math-heavy subjects).
|
| Then there's also the problem that there's not even a
| clear consensus on what great research is in a "soft"
| field. I might find someone highly accomplished, but
| someone else might think the opposite. With maths, either
| someone proves a theorem or they don't, there's almost no
| middle ground (Mochizuki notwithstanding).
| raverbashing wrote:
| > immediately recognized the person: the author behind the
| 3Blue1Brown YouTube channel
|
| Yes, that is noted by the 3B1B in the title
|
| But yeah the asymmetry of operators in math is exhausting.
| Turneyboy wrote:
| I'm a fan of his work but that's just not what Fields medals
| are for.
| smokel wrote:
| Note that the alternate notation was suggested by someone named
| "2'5 9'2" on the Mathematics Stack Exchange [1], and not by
| 3Blue1Brown.
|
| Obviously, this should not take away from the amazing
| educational work that 3Blue1Brown has achieved, but the
| honorary mention would probably suffice :)
|
| [1]
| https://math.stackexchange.com/questions/30046/alternative-n...
| a1o wrote:
| I agree with the comment that says this removes the
| personality of each function
| hgsgm wrote:
| Why doesn't subtraction need personality?
| Tainnor wrote:
| I don't think there are many deep theorems about
| subtraction, but there are a lot of very deep theorems
| about powers (and polynomials), the exponential function
| and logarithm functions (especially in complex analysis).
| pranavjoneja wrote:
| He mentions in the video that he saw the idea in "a math
| exchange post" and he also has a link to the exact post in
| the video description. Doesn't that count?
| emiliobumachar wrote:
| It does count as properly attributing the idea, yes. It
| doesn't count as having it. Possibly the Fields Medal
| suggestion assumed it was his?
| simiones wrote:
| The point was that it's just not his invention. He
| attributes it extremely clearly, no one is accusing him of
| theft. But you don't get math prizes for presenting someone
| else's ideas.
| hgsgm wrote:
| Fortunately, you do.
|
| https://en.m.wikipedia.org/wiki/Leroy_P._Steele_Prize
| seanc wrote:
| Grant's Patreon, for anyone who feels so inclined:
| https://www.patreon.com/3blue1brown
| prvc wrote:
| On the other hand, seeking prestige at the expense of personal
| satisfaction, say, by conducting research in an "interesting" or
| "important" area, may be seen as an altruistic means of
| furthering progress in that field, and seeking personal
| fulfillment through the knowledge that one is helping others may
| be seen as a form of self-indulgence.
| zarathustreal wrote:
| That's the beauty of helping others! It's a form of self-
| indulgence which is entirely ethical. Normally "self-
| indulgence" carries with it a negative connotation. In the case
| of altruistic behaviors, it's actually a positive thing
| yantrams wrote:
| "Utility had a strange backseat for me"
|
| I kinda took that to the extreme when I was young. Used to loathe
| anything practical - experiments, programming, applied math etc
| cuz you know they weren't "pure" and engaging enough. I would
| also have a hardtime processing/registering something if I'm not
| able to derive it analytically from first principles. It felt
| like cheating if I have to use a formula without fully
| understanding how it was derived haha.
| freetinker wrote:
| Exactly my experience! Can tell you how often I was on the
| brink of failing school/college because I wanted to derive as
| much as I could from first principles - under time pressure in
| an exam! I did myself no favors.
|
| I now find I learn better by being the opposite - finding a
| problem to solve and using math as a tool.
| inimino wrote:
| That section was great. As soon as he said "interesting" I said
| "hard"! This is a real gem, there's a lot of wisdom in this
| short talk.
| agumonkey wrote:
| Wow, my thoughts word for word
|
| I'm still like that, albeit with some plasticity to avoid dying
| on my lonely rock.
| yantrams wrote:
| I've come a long way I guess in the sense that I've learned
| to adult my way through things that don't necessarily excite
| me :|
|
| Programming in particular was a gamechanger for me and helped
| me see and appreciate the beauty in practical problem solving
| using simulations etc.
| agumonkey wrote:
| Can you describe what do you mean by simulations in this
| context ? you explore various solution configurations ?
| yantrams wrote:
| Yep kinda like that. I call it Answer guided monkeying
| around :) I try and see if I can arrive at the answer
| using Monte Carlo simulations and then try to work around
| that. Often times they give valuable insights and help
| uncover symmetries etc that aren't obvious.
| agumonkey wrote:
| hmm seeking symmetries, the best kind of fun
| importantbrian wrote:
| > I would also have a hard time processing/registering
| something if I'm not able to derive it analytically from first
| principles.
|
| This really resonates with me. I always had a really hard time
| with anything where I just had to memorize formulas, but I
| didn't have any issues if I could derive it myself. For this
| reason I actually struggled a lot more with algebra in HS than
| I did with calculus in college. I don't know if it's just the
| teachers I had growing up or if it's a more broad issue with
| how the curriculum is structured, but I didn't even realize you
| could derive things from first principles until I took calculus
| in college.
| Tainnor wrote:
| > I would also have a hardtime processing/registering something
| if I'm not able to derive it analytically from first
| principles.
|
| I still find it easier to understand something if I understand
| it from the ground up instead of in an ad-hoc way. For example,
| I found it easier to reason about probability once I had seen a
| rigorous definition for what a probability distribution is. I
| guess the reason is that it gives me a way to sanity check my
| intuition.
|
| I still struggle with the fact that in software development,
| you get hundreds of technologies thrown at you and you barely
| have any time to understand them all fully. It makes me
| sometimes feel not very confident in what I do. I feel that I
| could understand e.g. Kubernetes better, if I had real in-depth
| (not just superficial) knowledge about networking. A lot of the
| time I'm just missing crucial information like "what problem
| are we trying to solve?", "why does this technology work the
| way it works?", etc. Something like Kafka is another example.
| grugagag wrote:
| I was the other way around. Only when I found utility in
| something could I finally grasp the subject properly. I
| remember how I was taught derivatives and integrals in HS, I
| knew how to do them but I was confused as hell. I asked the
| professor and once explained some uses it all clicked into
| place.
| jack_pp wrote:
| Same. There's an infinite things to learn, if you can't argue
| for the usefulness of any piece of information and if that
| use isn't related to my own goals I will stop you from
| communicating said information
| drorco wrote:
| Same. I really struggle to learn anything which I can't see a
| practical use for.
|
| Just as an example, in high school learning trigonometry was
| really difficult for me, like why would I even care about
| finding an angle in a triangle, etc.?
|
| Only once I studied physics or game dev, this has started to
| become relevant, and then studying it got SO MUCH easier.
| jerf wrote:
| I would love to have some sort of statistics on what the
| proportion of this feeling is. My suspicion is that the
| practical approach is probably about 90% of the population
| (who is willing to learn math at all). Would be helpful in
| trying to figure out how to tune learning programs. (I say
| this as one who is perfectly content to learn the theory
| directly and with little-to-no practical motivation, but my
| impression is I'm very much in the minority on that.)
|
| I was going to say that the curriculum is tuned in favor of
| those who can just learn by theory, but then I realized
| that's not even true. It's tuned in favor of those who will
| simply swallow it without _any_ idea what it is for; it is
| neither contextualized in terms of what it is practically
| good for, nor is it contextualized in terms of theory. It
| 's just... there.
| grugagag wrote:
| I'd be curious to see that as well. I loved math until it
| became too abstract for me to grasp so I lost interest in
| it. And that worked pretty well as a self selection for
| the field, well, a large part of it. I wouldn't want to
| be in the academia anyways...
| siftrics wrote:
| > I really struggle to learn anything which I can't see a
| practical use for.
|
| That's a close-minded, ignorant world view. Much of the
| world's most important advancements were made before any
| practical use could be seen. Why do you think that way?
| qorrect wrote:
| > Why do you think that way?
|
| Probably the same reason that you're such an ass (genes).
| siftrics wrote:
| Sorry man. Just asking an honest question. It's
| interesting to me that one can hold two opposing ideas
| and see no issue:
|
| - History has demonstrated clear value in discovering and
| understanding concepts that have no practical use today
|
| - One should not care to understand things that have no
| practical use today
|
| Seems bizarre to think both things. That's why I asked.
| dangerlibrary wrote:
| You are shadowboxing - fighting an argument nobody is
| making. Someone is describing their personal experience
| of the world, not arguing that this is the best way to
| think about the world. It's an opportunity to learn about
| the ways that people learn things differently, if you can
| be curious and kind about it.
| siftrics wrote:
| You're right. I could've been kinder. Apologies.
| drorco wrote:
| It's just the way my mind works and motivated. Motivation
| is a very elusive feeling that I did not find easy ways
| to manipulate. It's not as if I'm totally blocked from
| learning stuff with no clear purpose, but it will require
| much more mental capacity that is often difficult to
| muster in the day-to-day routine. Another example, is I
| did try to learn what I perceive as totally theoretical
| math such as "prove that there are infinite primary
| numbers" which was a nice idea to entertain, but it
| didn't really make me want to dig in further. On the
| other hand, learning about linear algebra in the context
| of machine learning, suddenly got Linear Algebra a lot
| more interesting and easy to learn.
| siftrics wrote:
| Makes sense. Somewhat related --- I find procrastination
| to be a very similar feeling. I know what I should do,
| but I feel compelled not to do it, for whatever reason.
|
| I think procrastination and what you are describing are
| slightly different, though, because procrastination stems
| from stress and emotions for me, whereas with what you
| describe, it doesn't sound like you have to be stressed
| to experience it.
| TeMPOraL wrote:
| > _Much of the world 's most important advancements were
| made before any practical use could be seen._
|
| In a sense, yes. But usually this was kind of accidental
| - as in, people making those breakthroughs weren't doing
| it because they loved manipulating abstract symbols, or
| believed that _someone, somewhen_ will find it useful;
| rather, they had some immediate-term reason for doing the
| work - a problem to solve, a person to impress, or just
| doing it for shits and giggles - and only later it turned
| out their work was the key to something transformative.
|
| I have a similar "mental make" as GP too. Over the years
| I realized that for me, it's not about practical use _to
| me_ - it 's about knowing why something was invented,
| what problems the inventors were trying to solve.
| Learning the historical motivation "grounds" the concept
| for me, and makes it much easier to understand.
| TeMPOraL wrote:
| Wonder how many people here have similar story.
|
| In primary and secondary school, I had troubles with math -
| mostly caused by me not doing homework exercises and
| generally avoiding work (probably an early indication of an
| issue that took 20 more years to diagnose...). It all
| changed when I got interested in gamedev - suddenly, I've
| caught up with most of the material I was bad at, quickly
| learned trigonometry beyond the secondary school program,
| and then some basic vector and matrix algebra - and I
| distinctly remember it all starting with a simple problem:
| how to make a sprite rotate and move in circles?
|
| Couple decades later, I still have a kind of
| theory+applications mindset: I always seek to generalize
| and abstract, but I feel lost when presented with a new
| abstraction without any context. Over the years, I realized
| I learn and understand things most effectively by seeking
| out answers to the question: _why?_. Not in the sense of,
| "what will I ever use this for?", but in the sense of "why
| was this invented?", "what were the problems people who
| invented it were trying to solve?". I trace the topic back
| in time until I find the point where the "why" and "how"
| are both apparent, and then go forward from there.
| Solvency wrote:
| It's mindboggling to me that every teacher doesn't just
| debut the subject with videogames as a reference.
|
| "Alright everyone, let's make a video game character out of
| triangles".
|
| "Let's make a little cannon that you can change the angle
| of. How do you calculate the angle? Funny you should ask.."
|
| "Now let's learn how you'd make the fireball move up and
| down as it travels. That's a sine wave!"
|
| Every single student understands the basic concept of a
| game visually, even if they don't play them regularly. It's
| just a perfect frame of reference and context for applying
| the concepts in 2D, and then in 3D. And it's so easy to
| help the students understand how easily those concepts get
| extrapolated to other things (engineering, sports,
| whatever).
| grugagag wrote:
| Back when I studied these videogames were much simpler. I
| was explained instead calculating areas and volumes for
| various functions and that was enough for me to get it.
| The thing is that not everyone was confused and some can
| take in theory without a practical application. They're
| different modes of thinking and I appreciate both, I just
| happen to fall in the practical group.
| drorco wrote:
| Totally! One of the first thing I did after learning
| Newton's law of gravity, was to write down a small
| simulation of planets in orbit and how they "dance"
| around each other. This little exercise totally blew my
| mind and the code was really simple to code.
|
| There's probably an untapped opportunity here, but ed-
| tech is such a difficult industry.
| chalst wrote:
| I recall encountering a simple domain-specific PL in
| school in the late 1980s that allowed physical systems to
| be easily modelled.
| poorbutdebtfree wrote:
| Ed-tech can easily make smart kids smarter but that is a
| difficult sell to the virtuous.
| TeMPOraL wrote:
| I'm sure someone actually working in ed-tech will correct
| me, or perhaps even laugh me out of the room, but I still
| believe in what I figured out around highschool: that
| edtech, particularly "educational games", have it all
| backwards.
|
| Kids aren't stupid. If you take the usual boring
| curriculum with choreful exercises, and try to "make it
| more fun" by half-heartedly sprinkling in some colors,
| characters and cheesy stories, it will backfire
| spectacularly - kids will see you're just trying to trick
| them, and not even putting much effort into it.
|
| The right way is the reverse: you need to make something
| honestly, inherently fun, but design it so that it
| educates users/players as a side effect. Take Kerbal
| Space Program: it's not designed to be an educational
| game, but it's fun, and models real-world physics well
| enough that you get 12 years old researching and
| understanding the math of orbital mechanics, all because
| they'd like to do better than "point roughly half-turn
| ahead of the Moon and go full throttle", and they'd like
| to not run out of fuel on the way. Or, look how Minecraft
| is tricking kids into learning electronics, boolean
| logic, low-level programming, etc.
|
| (I'd mention Factorio, but I think it's a wash - any
| gains society gets from the game educating kids are
| cancelled out by the amount of productivity loss the mere
| exposure to this game inflicts on software devs.)
|
| (EDIT: or, remember Colobot? A very simple third-person
| perspective game that had you find and refine resources
| to build robots, which then you used to kill some big
| bugs. The twist being, instead of controlling the robots
| like in a shooter, you had an _option_ to program them in
| a Java-like DSL, inside the game. It was a great way to
| organically learn programming. The IP owners later made a
| "fork" of the game, Ceebot, that was pretty much the
| same, except it focused on teaching you to program robots
| instead of having fun exploring and shooting stuff.
| Predictably, that simple change of focus made the game
| flop.)
|
| It doesn't even have to be a game: leave a kid in front
| of Google Earth, and they'll learn geography much faster
| and much more thoroughly than they would from a globe or
| a book. Not because the software is better at teaching,
| but because the kid is just _messing around_ with a
| virutal model of Earth, and learning stuff along the way.
|
| Etc. Etd.
|
| I think it's a tough sell to adults, particularly parents
| and educators - that if you want to motivate kids to
| learn, you need to... stop trying to motivate them to
| learn. Give them something that's honestly fun, involving
| or benefiting from real-life knowledge and skills, but
| actually trying to teach them - and then trust that
| they'll pick that knowledge up on their own.
| drorco wrote:
| They call these kind of games "chocolate covered
| broccoli" and I totally agree.
|
| I think games, have lots to teach, but that most of the
| time they are a catalyst for learning or inspiration to
| learn, but on their own, they will rarely actually teach
| you. It's hard to put the finger on it, as for example,
| I'm not a native English speaker, but I learned and
| practiced most of my English from playing video games,
| and they were the catalyst to make me WANT to learn
| English, but they didn't exactly *teach* me English.
|
| Another part of it, is I bet if you sample today's
| scientists and engineers at places like NASA, you'd
| probably find that a lot of them loved watching Star
| Trek/Star Wars as kids. So while sci-fi hasn't taught
| them how to work with Schrodinger's equation, it probably
| had a major part of what sparked their motivation to get
| started. Games probably do that too, and then some,
| thanks to interactivity.
| TeMPOraL wrote:
| Thank you! Not only I 100% agree with you, you've also
| managed to provide a few terms and phrases I've been
| missing, which could've cut my previous comment down to
| 1/4 of its size, without loss of meaning. Specifically:
|
| - "chocolate covered broccoli"
|
| - "catalyst for learning"
|
| - "inspiration to learn"
|
| > _I learned and practiced most of my English from
| playing video games, and they were the catalyst to make
| me WANT to learn English, but they didn 't exactly
| _teach* me English.*
|
| English is my second language, and I've also learned most
| of it from video games. Mostly from exposure, but
| initially through focused effort - I still vividly
| remember that time when I was maybe 10 or 12 years old,
| when I made screenshots from loading screens in Star
| Trek: Generations, and printed them out on paper, one by
| one, directly from MS Paint, to take back into my room
| and meticulously translate the story text on those
| screens, looking up every single word in an
| English->Polish dictionary. I also remember keeping that
| dictionary around when playing Fallout 1. The need to
| understand the stories and dialogues in games is what
| bootstrapped my English.
|
| > _I bet if you sample today 's scientists and engineers
| at places like NASA, you'd probably find that a lot of
| them loved watching Star Trek/Star Wars as kids. So while
| sci-fi hasn't taught them how to work with Schrodinger's
| equation, it probably had a major part of what sparked
| their motivation to get started._
|
| I agree. And Star Trek is, in fact, what got me
| interested in STEM. I owe my entire career and most of
| who I am as a person, to early exposure to captain Picard
| and the adventures of Enterprise-D.
|
| (A lot of my early STEM self-education was driven by
| trying to understand the so-called "technobabble", which
| - at least in TNG - actually made sense. Probably
| because, in those days, they had proper scientific
| advisors.)
|
| > _Games probably do that too, and then some, thanks to
| interactivity._
|
| Yup. I mentioned KSP for a reason - not only have I read
| the accounts of parents impressed by how much advanced
| math and physics their 8-12 years old kids can pick up,
| just for the sake of getting better at the game, but
| myself I also learned these things for the same reason.
| While Star Trek is what got me interested in space in the
| first place, KSP is what got me to finally grok how
| orbital mechanics and rocketry work in reality. It also
| made me no longer able to fully enjoy any space travel
| fiction, except for diamond-hard sci-fi.
| drorco wrote:
| :D
|
| I should probably give KSP a try again. I guess there's
| an initial threshold I got to power through first, as I
| got a bit exhausted after the first mission hehe.
|
| I'm actually working now on a game of my own, with themes
| of science, and it's indeed a game-first approach rather
| than an educational game, but I do hope to maybe inspire
| some ideas and motivation with at least a few players.
|
| I totally believe there's a lot of untapped potential in
| this area, and advancing towards cracking learning
| motivation + capabilities could have a huge impact.
| TeMPOraL wrote:
| > _I should probably give KSP a try again. I guess there
| 's an initial threshold I got to power through first, as
| I got a bit exhausted after the first mission hehe._
|
| What made all the difference for me was a mod (Kerbal
| Engineering ...something?) that calculated [?]v for each
| stage as you were building your rocket. Coupled with a
| [?]v "subway map" of the game's solar system, this solved
| the problem of running out of fuel half-way through the
| mission. I eventually learned how to do the math on my
| own, but I would've given up long before that happened,
| if not for this mod. It's been some time since I last
| played KSP, but I hear that this functionality is now
| built into the stock game.
|
| Good luck with your game! Give me a shout if and when you
| need someone to play-test it :).
| apomekhanes wrote:
| I think the parent comment + yours (and others off parent)
| provides a perfect encapsulation of one of the dimensions of
| teaching / learning: what's often referred to as "style"*.
| One way to summarize, specifically, might be something like
| "inductive" vs. "deductive".
|
| As my experience has ... accumulated ... through the decades,
| I've come to feel that these sorts of differences /
| preferences likely don't have much impact on ultimate
| (potential) "level"**. And, I think you see this and related
| notions of "what mathematics 'actually is'" echoed (in a very
| fractal-like way, +1 to the universe in achieving a
| consistency we'll never rival) across the development of
| individual mathematicians as well as through the history of
| mathematics [1-6].
|
| These distinctions are important in "pedagogy" - can be very
| helpful for teachers and students to be aware of and work at,
| especially at the more "basic" levels. This can make a
| massive difference in how an individual's arc unfolds - with
| extremes of "F this subject" vs. "I'm willing to accept low
| pay in exchange for torturing myself with this material for
| the rest of my life!" But, aside from trying to be mindful of
| the differences - and all involved, ideally, trying to USE
| awareness of knowledge and "EQ" and all of that in making the
| mutual learning enterprise work for everyone involved, many
| other aspects of the differences can just be outlets for
| time-wasting if focused on IMO (/ experience).
|
| * AFAIK, not really my field though and it has been ~15 years
| since I did any significant reading / study in the area - for
| the sake of 'full disclosure'
|
| ** The effects end up more in details of notes, problems and
| areas people are drawn to more or less, etc.
|
| [1] https://terrytao.wordpress.com/career-advice/theres-more-
| to-...
|
| [2] Polya's "How to Solve It", in particular, I think of
| (from the intro): "The title of the very short second part is
| 'How to Solve It.' It is written in dialogue; a somewhat
| idealized teacher answers short questions of a somewhat
| idealized student.") - many options for accessing / buying,
| but, for this text, it's in the (unfortunately images) here -
| https://math.hawaii.edu/home/pdf/putnam/PolyaHowToSolveIt.pd.
| ..
|
| [3] https://citeseerx.ist.psu.edu/document?repid=rep1&type=pd
| f&d...
|
| [4] https://www.maa.org/sites/default/files/pdf/upload_librar
| y/2...
|
| [5] https://en.wikipedia.org/wiki/Galois_theory#A_non-
| solvable_q...
|
| [6] https://en.wikipedia.org/wiki/Hilbert%27s_program
|
| ... and, so many more, of course...
| ConfusedDog wrote:
| Same here. A lot of concepts seemed didn't matter if cannot
| be reflected in real world. That has changed for me though.
| Abstract things and first principle, zero knowledge actually
| quite interesting to me now.
| grugagag wrote:
| Congrats. I've made some progress on the abstract axis but
| still with some faint endgoal to make some progress in the
| practical realm I feel more grounded in.
| tiffanyg wrote:
| _...Used to loathe anything practical - experiments,
| programming, applied math etc cuz you know they weren 't "pure"
| and engaging enough. I would also have a hardtime
| processing/registering something if I'm not able to derive it
| analytically from first principles. It felt like cheating if I
| have to use a formula without fully understanding how it was
| derived..._
|
| Hello, 'undergraduate me'.
|
| "haha" indeed. The universe is still experiencing California-
| splitting [1], planet-slapping [2] spasms of laughter at my ...
| stupidity [3] (speaking only for myself, here, of course).
|
| [1] https://www.bbc.com/news/world-us-canada-48921915
|
| [2] https://en.wikipedia.org/wiki/Tunguska_event
|
| [3] https://archive.org/details/novicetomasteron0000mori_w1f1
| minionnn wrote:
| [dead]
| 0wis wrote:
| I have an incredible feeling that this quite short commencement
| speech is quite complete in its treatment of the subject of one's
| relationship to career choices. Utility, originality and personal
| appreciation of tasks are key parameters in order to find a
| fulfilling job.
| rahimnathwani wrote:
| In case you're hesitating to click on a video link: it's only 10
| mins long.
| 93po wrote:
| Few minute read instead:
| https://youtubetranscript.com/?v=z7GVHB2wiyg&t=183
| spicyusername wrote:
| Grant Sanderson is a righteous dude.
|
| His videos on mathematics are amazing.
| jfbaro wrote:
| Can this be used in a way similar to "supercomputers" proposed
| for Haskel?
| jdeaton wrote:
| There's a small number of people I know who say in social
| contexts "I love math" but they come up blank when asked what
| fields they find beautiful. I find this correlated with
| narcissism and it makes me believe these people don't actually
| find math beautiful, but just like the idea of others thinking
| they do and want to assert that they're the smart person in the
| group.
| kandel wrote:
| Devil's advocate: they liked the little bits of math they were
| exposed to.
|
| I don't know if there's a field i like. But there's something
| intoxicating in math. Sometimes it's very strong. I listened to
| a CS lecture now and normally I find CS a bit boring but as he
| kept describing aspects of the problem he was facing (finding
| points in intersecting disks) and as the problem got more
| complicated I got the itch lol. Sitting in a logic class is
| more exciting than a roller coaster. It's a bit scary because I
| don't understand why.
| jdeaton wrote:
| Makes sense, and I think many people fall into that category.
| Saying "there's something intoxicating in math" and that you
| enjoyed the roller coaster of a logic class already excludes
| one from the situation I am describing.
|
| My comment was too judgemental. People should be allowed to
| say that they enjoy something without any follow-up and
| without being judged for it. I think that sometimes it just
| seems like a facade when people say they really like math
| because when you try start a conversation on the topic its
| like they're not actually interested in it at all. It gives
| the impression there's something disingenuous about their
| proclamation of liking math. But perhaps its just the way I
| personally have approached it.
| Tainnor wrote:
| To me the perfect example of people who claim to "love math"
| but actually don't are people who wax endlessly about something
| like Category Theory (or non-classical logic), but they can't
| even define what a group is.
|
| No disrespect towards any serious scholar of Category Theory or
| Constructivism.
| 93po wrote:
| I think you're being a bit harsh. I can barely do simple
| algebra right now but I like math. I liked my math classes in
| high school and college because it felt satisfying to both
| learn and solve problems. It felt challenging in a unique way
| that my brain had never been forced to do before. It felt good
| that I was above average at it and it felt good to understand
| something something that started off looking like gibberish.
|
| You can love paintings without knowing anything about how to
| paint.
| jdeaton wrote:
| Perhaps I'm being a bit harsh. On the other hand, I feel its
| more similar to asking someone who says "I love reading
| fiction" what is a book they liked and them not having an
| answer.
| kandel wrote:
| Yeah but it is the situation. I remember a roommate saying
| "I love math!". When I talked with her a bit I understood
| she likes doing solutions of easy integrals\derivatives
| because they are simple, relaxing, and rewarding for her -
| her math classes were easy and she could get accolades by
| just doing those simple excersizes. Ofcourse the distance
| between that and a proper field of math is vast. But that
| was math for her.
| warmcompress wrote:
| There are comments on HN I find correlate to blithe
| superciliousness. A light expression of common sentiment
| (math is beautiful!) without domain knowledge is somehow a
| marker of social superiority... yeesh. kandel's sibling
| comment being the kind of reasonable rejoinder that
| shouldn't have to exist if there was a good faith follow-up
| to this sort of conversation, instead of turning up the
| nose...
| jdeaton wrote:
| You know what, I think you're right. I should be less
| judgemental. I'm not sure why I thought that was okay. I
| think some of it comes from the disappointment when
| someone describes themselves as loving math being part of
| their personality, but then when I try to engage with
| that as a jumping-off point or common interest its like
| there's nothing there.
| munchler wrote:
| I enjoy his 3B1B videos, but this talk did not resonate with me
| at all. I was good at math as a kid, but no part of my motivation
| came from "a desire to be seen as being good at it." If anything,
| many people looked at me kind of funny for being good at math, so
| I learned to play down my ability when necessary. Maybe it's just
| because I grew up in an earlier era, but being nerdy was
| definitely not cool when I was young.
| dkarl wrote:
| I grew up in the eighties when being nerdy wasn't cool, but
| math was something that people recognized as real, not a nerdy
| invention, even if it was weird and nerdy to enjoy it. Other
| nerdy pursuits like D&D or fantasy (or, at the time, computers)
| were seen as escapes for people who couldn't face the
| difficulties of the real world and had to invent easier worlds
| to live in where they could pretend not to be lame. By
| contrast, math was real and hard. Every kid in school had
| moments when they wished they were better at math. I was a
| weirdo and an outcast, but I was a weirdo and an outcast who
| had an ability that people recognized.
|
| Being better at math to make up for being socially useless in
| every other way didn't take me very far, though. Once I got to
| a top ten PhD program and was surrounded by people who were
| just as smart, some of them much smarter, and I faced the
| likely reality of ending up at minor university cranking out
| trivial results to get tenure, permanently outed as a
| mediocrity, making minor contributions that did nothing to
| advance the real work done by brilliant people, I couldn't face
| years of hard work for that outcome. Now as a programmer I have
| zero prestige and negative social cachet, but I get to do
| useful work on educational software used in primary school
| classrooms.
| SamPatt wrote:
| Programmers don't have negative social cachet anymore.
|
| I imagine telling people "I build software to help young
| children learn" will get a nearly universal positive
| reaction.
| hgsgm wrote:
| Not from parents who've seen all the "educational software"
| and who want their kids to study and practice instead of
| more time staring at distractions on screens.
| hgsgm wrote:
| "Educational software for primary school" is a field far more
| crowded with trivial results than pure mathematics is.
|
| More videogames aren't what kids need to help learn better.
| dkarl wrote:
| That's not the kind of software I work on, but if you go to
| a classroom, you'll probably see that when students are
| practicing via a "video game," they still get all the
| elements of instruction that we did when we were kids, with
| the addition of immediate feedback and better teacher
| awareness. When I was in school, kids would work on paper
| without getting any feedback until the teacher wandered by
| their desk to look over their shoulder, which could be the
| whole class period if the teacher spent time with other
| students first. Teachers would have to be pretty sharp and
| active to notice during class time that half the class was
| struggling with a certain kind of question; they might
| catch on later when they graded assignments, or they might
| not. I saw a teacher glance over a screen of updating
| results and within minutes interrupt practice to reteach an
| idea. Again, not my software, but I wouldn't dismiss the
| value of it without seeing it in action.
|
| Teachers these days aren't that different from decades ago.
| I'm sure there are plenty of bad and lazy teachers, just
| like when I was a kid, but the ones who drive the adoption
| of software are engaged, hard-working, and interested in
| results.
| AnotherGoodName wrote:
| Being open about your motivations to yourself and others and
| identifying how that can help or hinder you is the real
| takeaway here, not the particular motivation discussed.
|
| I personally appreciate the candor and his own story of growth
| in this subject.
| jebarker wrote:
| The video resonated with me. Looking back I think that I
| studied pure math in further education because I thought that
| others perceived it as the hardest subject you could study and
| therefore would think highly of me for studying it. I think
| that motivated me much longer than Sanderson too, as I think
| it's the main reason I started my PhD in a topic that probably
| wasn't the most interesting to me. Along the way I developed an
| appreciation for the innate beauty of the subject but these
| days I find it much more rewarding to work on something that's
| useful to someone else no matter whether it's particularly easy
| or hard.
|
| The sad thing about wasting your youth trying to be seen as
| smart or successful is that later in life you'll probably have
| much less freedom of choice in what to work on.
| importantbrian wrote:
| I also grew up as a nerdy kid long before being nerdy was cool.
| All the nerdy kids I knew took a lot of pride in being smarter
| than the cool kids. Being good at math was just an extension of
| that. I actually didn't know playing down how smart you were
| was a thing until much later when some of the popular kids who
| I had just assumed weren't that bright went on to become
| engineers, or doctors, or one who went on to get a PhD in
| biochemistry. I know a few of them still and they all talk
| about playing down that side of themselves in order to blend
| in. It makes me feel pretty silly about how smug I was about my
| intelligence back then.
| dwheeler wrote:
| I think his key point applies to many other fields. I'll
| summarize it as "evaluate the work you do, at least in part, on
| its utility to others".
|
| I've heard of devs who were asked to solve simple problems, but
| went out to choose exotic and complex approaches because that
| tech is the latest new hotness (though not well tested). I'm sure
| there are other examples.
| dahart wrote:
| This comment immediately clarified a thought I was trying to
| form after watching the video, which is: math is inherently
| part _social_ activity, like almost everything else we do.
| Grant first described the ego thing in embarrassed negative
| terms like 'childish', but it's a good idea to recognize that
| this self-deprecating framing isn't the only way to look at it.
| Math is a language we learn and use to communicate, and being
| good (and being seen as being good) at speaking the language is
| usually an important step to taking part in the conversation.
| [deleted]
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