[HN Gopher] Lessons I Wish I Had Been Taught (1996) [pdf]
       ___________________________________________________________________
        
       Lessons I Wish I Had Been Taught (1996) [pdf]
        
       Author : zerojames
       Score  : 234 points
       Date   : 2024-06-27 10:06 UTC (12 hours ago)
        
 (HTM) web link (www.ams.org)
 (TXT) w3m dump (www.ams.org)
        
       | sebg wrote:
       | Love these reflections from Gian-Carlo Rota
       | 
       | In the past, similar discussions have occured:
       | https://hn.algolia.com/?q=Gian-Carlo+Rota
        
       | mkl wrote:
       | (1997)
       | 
       | The last time it was discussed, four years ago:
       | https://news.ycombinator.com/item?id=23722803
        
         | bambax wrote:
         | Yes it does come back on HN frequently; it's worth a re-read
         | every time though! ;-)
        
         | dang wrote:
         | Yup! Related:
         | 
         |  _Gian Carlo Rota 's Ten Lessons_ -
         | https://news.ycombinator.com/item?id=40113970 - April 2024 (2
         | comments)
         | 
         |  _Lessons I wish I had been taught (1996)_ -
         | https://news.ycombinator.com/item?id=32081288 - July 2022 (62
         | comments)
         | 
         |  _Ten Lessons I Wish I Had Been Taught (1997) [pdf]_ -
         | https://news.ycombinator.com/item?id=23722803 - July 2020 (52
         | comments)
         | 
         |  _Lessons I Wish I Had Been Taught (1996) [pdf]_ -
         | https://news.ycombinator.com/item?id=15989599 - Dec 2017 (28
         | comments)
         | 
         |  _Lessons I wish I had been taught (1996)_ -
         | https://news.ycombinator.com/item?id=11747598 - May 2016 (20
         | comments)
         | 
         |  _Lessons I wish I had been Taught_ -
         | https://news.ycombinator.com/item?id=3220746 - Nov 2011 (20
         | comments)
         | 
         |  _Ten Lessons I Wish I Had Been Taught_ -
         | https://news.ycombinator.com/item?id=110091 - Feb 2008 (1
         | comment)
         | 
         |  _" Ten Lessons I wish I Had Been Taught", by Gian-Carlo Rota_
         | - https://news.ycombinator.com/item?id=85611 - Dec 2007 (1
         | comment)
         | 
         | Also related:
         | 
         |  _Gian-Carlo Rota on Alonzo Church (2008)_ -
         | https://news.ycombinator.com/item?id=9073466 - Feb 2015 (1
         | comment but it's so good I put it in
         | https://news.ycombinator.com/highlights)
         | 
         | and
         | 
         |  _Lessons I wish I had learned before teaching differential
         | equations [pdf] (1997)_ -
         | https://news.ycombinator.com/item?id=38248532 - Nov 2023 (248
         | comments)
         | 
         |  _Lessons I wish I had learned before I started teaching
         | differential equations [pdf] (1997)_ -
         | https://news.ycombinator.com/item?id=32530035 - Aug 2022 (177
         | comments)
         | 
         |  _10 lessons I wish I had learned before I started teaching
         | differential equations_ -
         | https://news.ycombinator.com/item?id=19005798 - Jan 2019 (2
         | comments)
         | 
         |  _Lessons I Wish I Had Learned Before Teaching Differential
         | Equations (1997) [pdf]_ -
         | https://news.ycombinator.com/item?id=15163979 - Sept 2017 (108
         | comments)
         | 
         |  _Ten lessons I wish I had learned before teaching differential
         | equations (1997) [pdf]_ -
         | https://news.ycombinator.com/item?id=11207183 - March 2016 (118
         | comments)
         | 
         | and
         | 
         |  _10 Lessons of an MIT Education_ -
         | https://news.ycombinator.com/item?id=32115290 - July 2022 (17
         | comments)
         | 
         |  _Lessons of an MIT Education_ -
         | https://news.ycombinator.com/item?id=31775074 - June 2022 (1
         | comment)
         | 
         |  _Lessons of an MIT Education_ -
         | https://news.ycombinator.com/item?id=15628869 - Nov 2017 (247
         | comments)
         | 
         |  _" 10 Lessons of an MIT Education" by Gian-Carlo Rota_ -
         | https://news.ycombinator.com/item?id=53322 - Sept 2007 (14
         | comments)
        
       | Frummy wrote:
       | That's pretty good. Feynman keeping problems in his mind
       | constantly, like a monk, is easy said but difficult to do.
       | Attention and the harmony required to maintain it, in this day
       | and age, is a few new theorems the reward for that? I guess you
       | have to enjoy the process of working on problems like that as
       | well, to dedicate your attention to it all day long even
       | passively.
        
         | mightybyte wrote:
         | I really like an expansion of this idea that I heard somewhere
         | awhile back:
         | 
         | Keep a few significant problems in your mind...and also keep a
         | few significant solutions / problem solving techniques in your
         | mind. Then when you encounter new problems, check them against
         | your set of solutions and see if any of them apply. Also, when
         | you encounter new problem solving techniques, check them
         | against your set of problems to see if they're applicable.
         | Whenever you encounter a new problem or solution that seems
         | unusually significant, add it to the list that you keep track
         | of
        
           | almostgotcaught wrote:
           | > heard somewhere awhile back:
           | 
           | This is verbatim how Feynman describes it in "surely you're
           | joking" (the chapter with spinning plate and QED iirc).
        
             | mightybyte wrote:
             | Ahh ok. I think my source was someone else, but it sounds
             | like they were probably citing Feynman. Good to know.
        
           | pm215 wrote:
           | Hamming's _You and Your Research_ (another HN perennial) has
           | a variant on the theme too:
           | 
           | "Most great scientists know many important problems. They
           | have something between 10 and 20 important problems for which
           | they are looking for an attack. And when they see a new idea
           | come up, one hears them say ``Well that bears on this
           | problem.'' They drop all the other things and get after it. "
        
         | almostgotcaught wrote:
         | > problems in his mind constantly, like a monk, is easy said
         | but difficult to do.
         | 
         | You're misunderstanding what's being described - there's
         | nothing monk like about it.
         | 
         | Using myself as an example, you have a couple techniques you're
         | good at (linear programming) and a couple of problems you've
         | tried to solve before but failed (fixed parameter tractable
         | problems). Every time someone tells you about a problem (or you
         | run into one) you try apply the thing you're good at ("will an
         | LP work here"). Every time someone tells you about an approach
         | they took with their problem you try it out on your thing.
         | 
         | It all happens completely automatically/naturally/fluently if
         | you're good at the technique and have actually tried to solve
         | said pet problem. Like I don't need to write code or calculate
         | anything because I know by now exactly where/what my blockers.
         | Conversely I know very quickly when an LP is appropriate
         | because I know the assumptions/requirements very well.
        
           | lupire wrote:
           | On a lay level, people think I'm a genius because I can
           | finish their unfinished crossword puzzles. But they never see
           | me when I fail to do a crossword puzzle from scratch myself.
        
             | Suppafly wrote:
             | I used to be amazed that my dad could finish crosswords
             | when I was a kid until one time as an adult I was sitting
             | across from him at the table and realized that I knew
             | several of the answers that he hadn't figured out yet. I
             | suspect a lot of it is generational too, where the
             | questions get updated for more current events and that
             | makes them more approachable for working aged adults vs the
             | children or the retired class.
        
         | BizarroLand wrote:
         | A simple way to do that is to write your problems down
         | somewhere where they are seen often, with a simple command at
         | the top like:
         | 
         | Solve these:
         | 
         | or a question to kick start this like:
         | 
         | What is the solution to these problems:
         | 
         | You'll quickly reach the point where you are ignoring what is
         | written, but the subtle visual reminder will keep a small
         | portion of your mind churning away at them.
        
       | robinhouston wrote:
       | If you enjoyed this, I am sure you will enjoy Rota's funny and
       | charming book _Indiscrete Thoughts_. It includes this essay,
       | together with many others.
        
         | great_wubwub wrote:
         | It may be funny and charming but Amazon wants $105 for it (or
         | $35 to rent the ebook) and it's nowhere to be found in my
         | statewide library system.
         | 
         | wow.
        
           | achenet wrote:
           | if you're the type of ruthless criminal who would commit
           | horrific crimes like downloading a car, your diseased
           | conscience may enable you to use pirate websites like library
           | genesis to get it for free.
        
             | AnimalMuppet wrote:
             | Um... am I missing something? Legalities aside, how does
             | one download a car? Is that actually a thing?
        
               | madcaptenor wrote:
               | It's a reference to this old PSA:
               | https://www.youtube.com/watch?v=P-pYiWGSN8w
        
               | blipvert wrote:
               | Related IT Crowd bit
               | 
               | https://youtu.be/ALZZx1xmAzg
        
             | almostgotcaught wrote:
             | no one will ever be able to convince me that i should feel
             | bad for using https://libgen.is/
        
           | robinhouston wrote:
           | I said you would enjoy it, not that you would be able to
           | afford to buy it. :-)
           | 
           | I would guess that quite a few HN readers are in the happy
           | position of being able to spend $105 on an interesting book
           | without suffering financial hardship as a result.
        
             | dylan604 wrote:
             | That's just how much Amazon thinks you will enjoy it. I
             | mean, if something is that enjoyable, surely it's worth a
             | higher monetary price tag? It's a luxury read.
        
           | vgk7 wrote:
           | Open library has it. https://openlibrary.org/books/OL22471553
           | M/Indiscrete_thought...
        
         | eleveriven wrote:
         | Thank you for suggesting it!
        
       | xanderlewis wrote:
       | > After fifty minutes (one microcentury as von Neumann used to
       | say)
       | 
       | I like this. I also had to check: 100 years * 10^-6 = 52.56
       | minutes.
        
         | jeffwass wrote:
         | And on a similar note :
         | 
         | Pi seconds is a nanocentury!
        
         | gniv wrote:
         | It's a cute remark, but why is 50 minutes the right cutoff? For
         | a technical talk it seems long. For an entertaining keynote it
         | seems short. Movies are 90+ minutes.
        
           | xanderlewis wrote:
           | At both the universities I've attended, lectures lasted 50
           | minutes. The odd few we had that were 100 had a short break
           | in the middle supposedly inspired by research on how
           | attention levels decay and recover over time. Conference
           | talks seem to usually hover around the 60 minute mark.
           | 
           | I find movies have become too long -- especially in recent
           | years.
        
             | meristohm wrote:
             | Same here, regarding movies- we preferentially watch films
             | under two hours, ideally 90-100 minutes, because that both
             | fits between our child's bedtime and ours, and it's a
             | better economy of time for a story in that format, rather
             | than an indulgent marathon.
             | 
             | I doubt I will ever watch Heat again, unless over a couple
             | days, and unless my child wants to I won't watch the Lord
             | of the Rings again (and especially not The Hobbit movies;
             | that was largely a waste of time, though I will gladly read
             | The Hobbit at least once more before I die).
             | 
             | Mad Max: Fury Road (Black & Chrome version) I watched for
             | the third time recently, but over two days.
             | 
             | Engaging conversation, though? I recently had the luxury of
             | time and privilege of talking for three hours straight with
             | a well-read college student. Not being a high school
             | teacher anymore I'm out of touch with young-adult
             | perspectives, and I have so many follow-up questions now.
        
             | 082349872349872 wrote:
             | Have movies really become longer again?
             | 
             | I consider 3+ hours indulgent (we get ice cream and beer,
             | once or twice, during what used to be the reel changes
             | here), but two and half hours is about right.
             | 
             | Two hours would be my bare minimum for "feature length",
             | and when I see one and half hour "films" I wonder "why was
             | this not made-for-TV"?
        
               | xanderlewis wrote:
               | The Matrix (which was being shown in cinemas recently,
               | remastered, for the 25th anniversary), is 2 hours and 16
               | minutes. It feels like the perfect length to me.
        
               | endofreach wrote:
               | Still haven't seen some of recent movies that got
               | recommended to me & that probably would like a lot.
               | Because i know i just cant stop mid-movie and finish
               | another day like some people can. And i can't justify
               | watching a 3h movie... what a commitment... while i have
               | no issue watching just one episode(... after another...
               | before the sunlight screams that i am an irresponsible
               | moron for binge-watching 6h during the week...)
        
             | eleveriven wrote:
             | It seems like movies have been getting longer. Streaming
             | platforms has influenced movie lengths I think in some
             | ways.
        
           | tialaramex wrote:
           | Humans don't do well concentrating on something for more than
           | about an hour. So fifty minutes seems like a reasonable rule
           | of thumb.
           | 
           | You can improve this if you make it more varied, adding
           | interactions, changing media, multiple speakers taking turns,
           | that sort of thing, but having a rule of thumb helps.
           | 
           | And it fits calendars nicely, fifty minutes per talk, ten
           | minutes break between, one talk per hour.
        
             | gniv wrote:
             | > fifty minutes per talk, ten minutes break between
             | 
             | Yes, I suspect that's the real reason.
        
               | dylan604 wrote:
               | But that break was typically how long it took to get to
               | the next class. So it might have been a break from active
               | brain activity (as evidenced by the brain dead decisions
               | of navigating hallways/lockers), it's not a break per se.
               | Maybe one was determined by the other, but I remember
               | having to hustle to get from one end of campus to the
               | other in those 10 minutes in a very un-break like use of
               | energy
        
               | LodeOfCode wrote:
               | > I remember having to hustle to get from one end of
               | campus to the other in those 10 minutes
               | 
               | Yeah, personally I read it less as 50 minutes being some
               | biological limit of human attention and more as once you
               | go over people start thinking about how much longer
               | you're going to be, how long it'll take to get to their
               | class, weighing missing the end of this talk vs the start
               | of the next one vs skipping their bathroom
               | break/sprinting. Plus the added the distraction of people
               | who have reached their limit getting up and squeezing
               | their way past to leave.
        
             | eleveriven wrote:
             | That's why Pomodoro Technique works great..
        
           | WalterBright wrote:
           | In lectures in college, I always looked at my watch 35
           | minutes in, and it was downhill from there.
        
         | velcrovan wrote:
         | Some of my favorites:
         | 
         | nanoacre = about 4 square millimeters
         | 
         | microfortnight = about 1.2 seconds
         | 
         | beard-second = 5-10 nanometers (depending on who you ask), or
         | the length an average beard grows in one second
        
           | schubart wrote:
           | And a light foot is a nanosecond. Think about it...
        
             | daynthelife wrote:
             | Beat me to it!
        
               | __rito__ wrote:
               | You will like this:
               | https://www.youtube.com/watch?v=9eyFDBPk4Yw
        
             | tutipop wrote:
             | a light nanosecond is a foot :)
        
           | anal_reactor wrote:
           | I think the beauty of "microcentury" is that things that take
           | 50 minutes indeed feel like a "microcentury"
        
             | eleveriven wrote:
             | The feeling of how long certain tasks can feel!
        
             | dingnuts wrote:
             | my mind immediately went to college classes, which were
             | almost always exactly 1 microcentury
             | 
             | perfect
        
           | daynthelife wrote:
           | Working in HFT, my favorite is 1 nanosecond [?] 1 foot
        
             | harrison_clarke wrote:
             | grace hopper would carry around nanosecond-long wires, for
             | demonstrations
             | 
             | https://youtu.be/ZR0ujwlvbkQ?si=aAj2OkbS8cj_MeGo&t=2707
        
             | cubefox wrote:
             | My favorite from What if? (xkcd):
             | 
             | 20 miles per gallon [?] 0.1 mm2
             | 
             | https://www.wolframalpha.com/input/?i=1%2F%2820+mile%2Fgall
             | o...
        
           | volemo wrote:
           | Also attoparsec [1] [?] 3 cm.
           | 
           | [1]: https://youtube.com/@attoparsec
        
           | myself248 wrote:
           | Saturating 100Mbps will move about 1TB/day.
        
         | jihadjihad wrote:
         | I love GNU Units for stuff like this, it's just such a fun
         | utility:                 You have: microcentury       You want:
         | minutes        * 52.594877        / 0.019013259
        
         | eleveriven wrote:
         | Love that! One nanocentury - about 3.16 seconds
        
       | kkfx wrote:
       | Hum... Mine personal ones would be:
       | 
       | - teach enough IT at the right time, a teenager MUST know enough
       | to produce nicely formatted docs with graphs, tables etc, LaTeX
       | level, at least with some pre-made templates, how to take notes,
       | do simple computations etc on a desktop, it's the writing ability
       | of today, people MUST know enough or they will suffer for the
       | entire life struggling with bad tech and allowing bad tech to
       | spread;
       | 
       | - teach like universities from the start, I do no know how does
       | primary schools works in the USA, here in EU they teach with
       | regular assignments and continuous checks instead of pushing
       | children to take notes ALONE, study in their own notes and form
       | their own knowledge valuating more their memory and conformism
       | than the knowledge they really have acquired;
       | 
       | - teach without frills, I do not need slides and co, I need
       | lectio magistralis who INTEREST people and makes them feel the
       | passion in any subject, than test the acquired knowledge making
       | your students teach a lesson on what they have learnt, that's the
       | way to prove themselves what they have understood instead of
       | blindly remembered;
       | 
       | - be clear, giving real life examples you audience should have
       | lived sometimes.
        
         | thfuran wrote:
         | >teach like universities from the start
         | 
         | Do you know of any research suggesting that would be an
         | effective way of teaching first graders?
        
           | Miraltar wrote:
           | I'm wondering as well, because it seems to me that it would
           | just cause most children to drop school very early
        
           | JackFr wrote:
           | "Sticking Crayons Up Noses: A longitudinal study"
        
           | screye wrote:
           | Most advice for creating high achieving people is meant for
           | high achieving kids of high achieving parents.
           | 
           | Independent study is perfect when the student has a strong
           | base for subject navigation and requisite enterprisingness to
           | investigate by themselves.
           | 
           | A beginners needs to be hand held, because they often don't
           | know what they don't know. Keeping the cognitive load low
           | helps keep the student from developing aversion foe the
           | subject.
           | 
           | I only fully grasped this when I tried to learn drums as an
           | adult. Training wheels and strictly guided practice is
           | essential to reach the first level of competence. You can own
           | your development journey after that.
           | 
           | Exceptions exist, and those are the geniuses. To me, a genius
           | is someone who can demonstrate competence in a field, despite
           | bad pedagogy. They should never be used to guide teaching
           | methods for the other 99%.
        
             | kkfx wrote:
             | I suggest an old book, the Carl von Clausewitz short
             | summary of his treaty on war, where he say "even an
             | imbecile who understand few basic rules and apply them
             | slavishly could drive an army and being seen as a war
             | master", that's to say that even very modest child can
             | learn if they are taught by a Teacher, while even very
             | smart child without a good teacher are easily frustrated
             | and dispersed by schools.
             | 
             | A teacher who know, know how to communicate, how to
             | interest his/her audience will be able to makes good
             | students out of any kind of students, certainly not all
             | will became luminaries, but they'll keep going anyway
             | without frustration and finding their way in the society.
             | 
             | So yes, I'm advocate to teach ALL with the teaching
             | technique that works for the most skillful students in top
             | schools. Some will dig, in a direction or another, some
             | others not, but all learn something, while the classic
             | "standard school only indoctrinate mediocrity frustrating
             | the smartest and the dumbest as well, dispersing knowledge
             | and only forming useful idiots
             | https://www.theatlantic.com/ideas/archive/2020/08/i-was-
             | usef...
        
         | jimhefferon wrote:
         | I wonder if you have any experience in teaching at the primary
         | level?
        
           | kkfx wrote:
           | No, I have not. But I help some son friends and "my" teaching
           | have "made miracles" for them, switching from "under-
           | performing, unable to understand" to "brilliant". Just
           | interesting them, just showing them practical reasoning and
           | examples and pushing them going further alone.
           | 
           | You might like as well a book from a real teacher
           | https://en.wikipedia.org/wiki/A_Mathematician%27s_Lament as a
           | good example of the same concept.
        
       | dotancohen wrote:
       | > Be Prepared for Old Age
       | 
       | This sums up the last two years of my life exactly. Somehow I've
       | become a fixture - and I've had a hard time identifying exactly
       | what happened until I read this. Spot on.
        
         | noso wrote:
         | I can relate to this experience as well. The transition catched
         | me off guard. My advice would be to embrace the change while
         | staying true to yourself. Live without regrets and, as Arnold
         | Schwarzenegger would say, don't listen to the naysayers.
         | 
         | I also love the fact the paper has the word "miffed", you do
         | not hear this much!
        
         | jp42 wrote:
         | Over the time I can see my dad getting that feeling. He is 76,
         | it took him years to make peace with that feeling. Apparently
         | it's unfortunate reality that we all have to go through it.
        
       | adamnemecek wrote:
       | Gian-Carlo Rota is probably the best combinatorist of the 20th
       | century.
        
         | spennant wrote:
         | Personal story: I sat in his office as an undergrad and he
         | presented a problem to me concerning counting balls in boxes
         | that had applications to quantum theory. It blew my freshman
         | mind.
        
         | mamonster wrote:
         | Is there any coherent argument for him to be considered more
         | important than Lovasz(considering that Lovasz did most of his
         | heavy work in the 80s)?
        
           | adamnemecek wrote:
           | He is generally considered to be responsible for creating
           | modern combinatorics.
        
       | richrichie wrote:
       | > The etiquette of old age does not seem to have been written up,
       | and we have to learn it the hard way. It de- pends on a basic
       | realization, which takes time to adjust to. You must realize that
       | after reach- ing a certain age you are no longer viewed as a
       | person. You become an institution, and you are treated the way
       | institutions are treated. You are expected to behave like a piece
       | of period furni- ture, an architectural landmark, or an incunab-
       | ulum.
       | 
       | This hits home hard. It is depressing to see that "boomer" is a
       | derogatory term :)
        
         | groby_b wrote:
         | You _can_ avoid this. It seems (based on my experience, at
         | least), a duration-of-tenure problem, not an age problem.
         | Switching fields when you're heading towards "landmark" status
         | does seem to do the trick. It's scary as heck, but you can
         | avoid that corner for a while longer.
        
       | teddyh wrote:
       | > _Write Informative Introductions_
       | 
       | > _Nowadays reading a mathematics paper from top to bottom is a
       | rare event. If we wish our paper to be read, we had better
       | provide our prospective readers with strong motivation to do so._
       | 
       | True.
       | 
       | > _A lengthy introduction, summarizing the history of the
       | subject, giving everybody his due, and perhaps enticingly
       | outlining the content of the paper in a discursive manner, will
       | go some of the way towards getting us a couple of readers._
       | 
       | That does not sound like a very good way to accomplish this.
       | 
       | I would instead recommend the approach explained here:
       | 
       | <https://www.youtube.com/watch?v=vtIzMaLkCaM>
       | 
       | (It's Larry McEnerney's lecture _The Craft of Writing
       | Effectively_ )
        
         | crazygringo wrote:
         | I suppose it depends on whether you're looking for readers
         | outside of your sub-sub-field, or readers within it.
         | 
         | If you're looking for readers _outside_ your sub-sub-field,
         | then it definitely sounds like a good way to me.
        
           | teddyh wrote:
           | No, I think that's a common fallacy. The lecture I linked
           | uses the example of someone writing a paper to get grants,
           | etc. This is not "outside your field". Other academicians in
           | your field are regular people too, and _all_ readers (who are
           | not your immediate teachers) will benefit from the techniques
           | described.
        
       | reaperducer wrote:
       | _" In the summer of 1979, while attending a philosophy meeting in
       | Pittsburgh..."_
       | 
       | Too many people in the tech industry get tunnel vision and think
       | that they should only focus on learning one thing. One
       | discipline. One science. It becomes one truth. One religion.
       | 
       | The true "smartest people in the room" are the ones who are well-
       | rounded in a lot of disciplines and able to apply knowledge from
       | one to another.
       | 
       | The smartest people I know - whether they work at NASA, USC, or
       | BNY Mellon - all started out in fields other than the one they
       | ended up in, and bring a diversity of knowledge to what they do
       | every day.
        
       ___________________________________________________________________
       (page generated 2024-06-27 23:00 UTC)