> 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.
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.
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.
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.
I think you're confusing your kiloseconds with megaseconds.
* 60 seconds per minute
* 60 minutes per hour: 3600 seconds per hour
* 1 kilosecond = 16 minutes and 40 seconds
* 24 hours per day: 86,400 +/- 1 seconds per day
* 1,000,000 / 86,400 ~= 11.57
I love giving metric-using friends a hard time whenever they criticize imperial units of measure. I always tell them that I will happily embrace metric when they give up their irrational attachment to an archaic system of time-telling.
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.
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.
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"?
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...)
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.
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.
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.
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
> 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.
"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.
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.
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!
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.
- 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.
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%.
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...
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.
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.
> 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.
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.
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.
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
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. "
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.
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.
> 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 :)
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.
> 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:
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.
> 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.
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.
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.
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.
no one will ever be able to convince me that i should feel bad for using https://libgen.is/
Um... am I missing something? Legalities aside, how does one download a car? Is that actually a thing?
It's a reference to this old PSA: https://www.youtube.com/watch?v=P-pYiWGSN8w
Related IT Crowd bit
https://youtu.be/ALZZx1xmAzg
If it were, I would
Open library has it. https://openlibrary.org/books/OL22471553M/Indiscrete_thought...
Or use the direct link https://archive.org/details/indiscretethough0000rota/ (I am happy to know this book is not in the 500,000+ books we have lost access to)
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.
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.
Thank you for suggesting it!
> 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.
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
Working in HFT, my favorite is 1 nanosecond ≈ 1 foot
grace hopper would carry around nanosecond-long wires, for demonstrations
https://youtu.be/ZR0ujwlvbkQ?si=aAj2OkbS8cj_MeGo&t=2707
My favorite from What if? (xkcd):
20 miles per gallon ≈ 0.1 mm²
https://www.wolframalpha.com/input/?i=1%2F%2820+mile%2Fgallo...
I think the beauty of "microcentury" is that things that take 50 minutes indeed feel like a "microcentury"
The feeling of how long certain tasks can feel!
my mind immediately went to college classes, which were almost always exactly 1 microcentury
perfect
Saturating 100Mbps will move about 1TB/day.
I like going the other way, too. My personal favorite:
kilosecond: 11.57 days
and fun to say, but never useful:
gigasecond: 31.68 years
I think you're confusing your kiloseconds with megaseconds.
* 60 seconds per minute
* 60 minutes per hour: 3600 seconds per hour
* 1 kilosecond = 16 minutes and 40 seconds
* 24 hours per day: 86,400 +/- 1 seconds per day
* 1,000,000 / 86,400 ~= 11.57
I love giving metric-using friends a hard time whenever they criticize imperial units of measure. I always tell them that I will happily embrace metric when they give up their irrational attachment to an archaic system of time-telling.
Also attoparsec [1] ≈ 3 cm.
[1]: https://youtube.com/@attoparsec
And a light foot is a nanosecond. Think about it…
a light nanosecond is a foot :)
Beat me to it!
You will like this: https://www.youtube.com/watch?v=9eyFDBPk4Yw
15 minutes = 1 centiday
I love GNU Units for stuff like this, it's just such a fun utility:
And on a similar note :
Pi seconds is a nanocentury!
π seconds is a nanocentury: 1 year = 3.155 × 10^7 seconds (Programming Pearls by Jon Bentley)
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
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.
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.
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"?
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...)
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.
Ghost in the Shell (1995) is 85 minutes long, just perfect.
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.
[dead]
It seems like movies have been getting longer. Streaming platforms has influenced movie lengths I think in some ways.
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.
> fifty minutes per talk, ten minutes break between
Yes, I suspect that's the real reason.
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
> 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.
That's why Pomodoro Technique works great..
In lectures in college, I always looked at my watch 35 minutes in, and it was downhill from there.
Love that! One nanocentury - about 3.16 seconds
"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.
> 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.
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!
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.
(1997)
The last time it was discussed, four years ago: https://news.ycombinator.com/item?id=23722803
Yes it does come back on HN frequently; it's worth a re-read every time though! ;-)
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)
[dead]
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.
>teach like universities from the start
Do you know of any research suggesting that would be an effective way of teaching first graders?
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%.
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...
[dead]
I'm wondering as well, because it seems to me that it would just cause most children to drop school very early
"Sticking Crayons Up Noses: A longitudinal study"
I wonder if you have any experience in teaching at the primary level?
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.
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.
> 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.
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.
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.
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
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. "
> heard somewhere awhile back:
This is verbatim how Feynman describes it in "surely you're joking" (the chapter with spinning plate and QED iirc).
Ahh ok. I think my source was someone else, but it sounds like they were probably citing Feynman. Good to know.
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.
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Gian-Carlo Rota is probably the best combinatorist of the 20th century.
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.
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)?
He is generally considered to be responsible for creating modern combinatorics.
> 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 :)
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.
That's a good point.
At least a portion of this paper appeared in "The Princeton Companion to Mathematics" ed. Timothy Gowers
Love these reflections from Gian-Carlo Rota
In the past, similar discussions have occured: https://hn.algolia.com/?q=Gian-Carlo+Rota
> 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)
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.
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.
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It hit "delve" on the penultimate point.
Having read that article, I have to say that is spot on!