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Lessons I Wish I Had Been Taught (1996) [pdf]

xanderlewis
33 replies
1d5h

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.

velcrovan
13 replies
1d5h

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
3 replies
1d4h

And a light foot is a nanosecond. Think about it…

daynthelife
1 replies
1d3h

Beat me to it!

tutipop
0 replies
1d2h

a light nanosecond is a foot :)

daynthelife
2 replies
1d3h

Working in HFT, my favorite is 1 nanosecond ≈ 1 foot

anal_reactor
2 replies
1d3h

I think the beauty of "microcentury" is that things that take 50 minutes indeed feel like a "microcentury"

eleveriven
0 replies
22h17m

The feeling of how long certain tasks can feel!

dingnuts
0 replies
20h59m

my mind immediately went to college classes, which were almost always exactly 1 microcentury

perfect

rzzzt
0 replies
18h30m

15 minutes = 1 centiday

myself248
0 replies
20h33m

Saturating 100Mbps will move about 1TB/day.

gniv
13 replies
1d5h

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
6 replies
1d4h

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.

082349872349872
3 replies
23h11m

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
1 replies
21h41m

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.

yazantapuz
0 replies
7h44m

Ghost in the Shell (1995) is 85 minutes long, just perfect.

endofreach
0 replies
19h43m

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...)

meristohm
0 replies
1d2h

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.

eleveriven
0 replies
22h15m

It seems like movies have been getting longer. Streaming platforms has influenced movie lengths I think in some ways.

tialaramex
4 replies
1d4h

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
2 replies
1d4h

fifty minutes per talk, ten minutes break between

Yes, I suspect that's the real reason.

dylan604
1 replies
1d2h

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
0 replies
22h56m

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
0 replies
22h12m

That's why Pomodoro Technique works great..

WalterBright
0 replies
21h14m

In lectures in college, I always looked at my watch 35 minutes in, and it was downhill from there.

vismit2000
1 replies
13h15m

π seconds is a nanocentury: 1 year = 3.155 × 10^7 seconds (Programming Pearls by Jon Bentley)

mikhailfranco
0 replies
2h40m

This allows you to calculate the Earth's orbital velocity per second, as the orbital diameter in millions, divided by 10.

So if you think the radius is 93m miles, you get 18.6 mile/sec, but if you are not American, you think the radius is 150m km, so 30 km/s.

https://en.wikipedia.org/wiki/Earth's_orbit

jihadjihad
0 replies
1d4h

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

jeffwass
0 replies
1d5h

And on a similar note :

Pi seconds is a nanocentury!

eleveriven
0 replies
22h18m

Love that! One nanocentury - about 3.16 seconds

robinhouston
12 replies
1d5h

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
10 replies
1d5h

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
5 replies
1d5h

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
3 replies
1d5h

Um... am I missing something? Legalities aside, how does one download a car? Is that actually a thing?

RobRivera
0 replies
12h0m

If it were, I would

almostgotcaught
0 replies
22h9m

no one will ever be able to convince me that i should feel bad for using https://libgen.is/

robinhouston
1 replies
1d4h

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
0 replies
1d2h

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.

eleveriven
0 replies
22h9m

Thank you for suggesting it!

Frummy
8 replies
1d6h

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
3 replies
1d5h

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
1 replies
1d4h

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
0 replies
1d2h

Ahh ok. I think my source was someone else, but it sounds like they were probably citing Feynman. Good to know.

pm215
0 replies
1d4h

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
2 replies
1d4h

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
1 replies
1d2h

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
0 replies
1d1h

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
0 replies
1d2h

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.

kkfx
7 replies
1d4h

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
4 replies
1d4h

teach like universities from the start

Do you know of any research suggesting that would be an effective way of teaching first graders?

screye
1 replies
1d1h

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
0 replies
23h43m

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...

Miraltar
0 replies
1d3h

I'm wondering as well, because it seems to me that it would just cause most children to drop school very early

JackFr
0 replies
1d3h

"Sticking Crayons Up Noses: A longitudinal study"

jimhefferon
1 replies
23h27m

I wonder if you have any experience in teaching at the primary level?

kkfx
0 replies
21h33m

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.

adamnemecek
3 replies
1d3h

Gian-Carlo Rota is probably the best combinatorist of the 20th century.

mamonster
1 replies
23h32m

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
0 replies
22h8m

He is generally considered to be responsible for creating modern combinatorics.

spennant
0 replies
1d1h

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.

teddyh
2 replies
1d1h

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
1 replies
1d

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
0 replies
21h34m

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.

richrichie
2 replies
1d1h

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
1 replies
23h43m

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.

richrichie
0 replies
16h42m

That's a good point.

dang
0 replies
1d1h

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)

bambax
0 replies
1d5h

Yes it does come back on HN frequently; it's worth a re-read every time though! ;-)

dotancohen
2 replies
1d4h

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
0 replies
1d1h

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
0 replies
21h5m

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.

reaperducer
0 replies
22h33m

"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.

fscaramuzza
0 replies
19h15m

Running overtime is the one unforgivable error a lecturer can make. This is so true. It has happened too often that a professor has decided to explain the most difficult topic in 5 minutes overtime. Before lunch. What a mistake.
anon3242
0 replies
6h50m

At least a portion of this paper appeared in "The Princeton Companion to Mathematics" ed. Timothy Gowers