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Comment by mathgenius | Hacker News Reader

Here's a pro-tip: "I don't understand XYZ" this is the humble-brag of academia. And the more basic XYZ is, the more points you win. Try the following: "I don't understand 1+1=2." Sit back and enjoy your collaborators as they stare in wonderment at your sage lack of understanding.

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I don't think good mathematicians confuse rigorous understanding with intuitive understanding as you suggest; rather, they are complements of each other

Further reading: https://terrytao.wordpress.com/career-advice/theres-more-to-...

That's a great, yet easily forgotten distinction

Saying that you intuitively do not understand XYZ often requires intellectual honesty as well as understanding it rigorously, even more so in academia. So saying that you intuitively do not understand XYZ can be used as a signal.

This reminds me of a dinner party game described in a David Lodge book where highly competitive literature professors could only score points by naming books that they haven't read, but which everyone else has.

I have noticed that more often than not, when I say "I don't understand XYZ" I actually mean "Are you really, really sure that you understand XYZ, because what you say makes no sense whatsoever"

Yes, it's a challenge to the person you're speaking to.

It's a great way just to learn without losing face if you need to. The alternative sentiment is "I'm lost, please help" which may not be accurate.

There does need to be some way to express, "I am competent enough to understand this, I do not understand this, so something is going wrong and it isnt my stupidity".

One hazard I am still learning to adapt to after many years is saying this to US based colleagues. They tend to interpret it literally. I have to switch grammars in that context and speak much more directly.

It took a bit of work to understand what was going on here though: "From this proposition it will follow, when arithmetical addition has been defined, that 1 + 1 = 2." https://en.wikipedia.org/wiki/Principia_Mathematica#/media/F...

It's not just academic topics. It also works if you express mystification of some aspect of popular culture that any "normal" person understands. Even if you are genuinely mystified by it.

Like how is it that so many people can effortlessly memorize the names of hundreds of actors and recognize them on sight, and why do they bother?

Can something be effortless and a bother at the same time?

spent a minute trying to figure out if this is a meta humble-brag

Whatever do you mean, Socrates? Surely all men know the meaning of XYZ?

While I agree with your sentiment, the more I learn the more I realize there are some profound subtleties that are glossed over by people teaching them and people claiming they understand it. I think it's a sign of maturity to realize that even seemingly simple and well studied problems aren't very well understood by most people.

I've been humbled many times thinking I know something when in fact I really had a shallow understanding. Here are a few examples:

* Stable [1] in place sort. Merge sort requires an extra O(n) space, Quicksort isn't stable. The solution is either Grailsort [2] or Wikisort [2], both of which I still don't understand to this day.

* Gaussian elimination. Turns out Gaussian elimination might blow up exponentially (afaik, still an open problem whether it actually does) in intermediate bit complexity and other methods have to be employed to guarantee a polynomial bit length. [4]

* Fast Fourier Transform. How many bits do you need? When does using 64-bit floating point fail and why? The bit complexity is polynomial and understood but it turns out the most straight forward methods to figure this out uses modular arithmetic to get a handle on the complexity. Also, what's minimum known bit complexity? I'm not sure I know what's bleeding edge for this. [5]

* Dynamic programming. Only recently has it been shown that, unless P=NP, O(n^2) is basically optimal. [6] Also, what if you're comparing similar strings? What are the best algorithms in terms of edit distance and other efficiencies. Ukkonnen [7] Hirschberg [8] and checkpointing [9], but boy did it take me a while to get a good description of all of them, with checkpointing still unclear to me.

I've heard, and agree with, that 95% of programming doesn't require any deep CS knowledge. The flip side of that is 5% of the time you will and for those 1/20 times you encounter a problem that requires theory, you're dead in the water unless you know how to identify it, how to solve it or where to look for solutions to it.

These are just a few. The more I learn the more I realize how little I actually know.

[1] https://en.wikipedia.org/wiki/Sorting_algorithm#Stability

[2] https://github.com/Mrrl/GrailSort

[3] https://github.com/BonzaiThePenguin/WikiSort

[4] Chee K. Yap, "Fundamental Problems in Algorithmic Algebra", Chapter 10, Linear Systems, 10.3 Matrix Inversion

[5] Chee K. Yap, "Fundamental Problems in Algorithmic Algebra", Chapter 1, Arithmetic, 1.4 Modular Fast Fourier Transform

[6] https://rjlipton.wordpress.com/2015/06/01/puzzling-evidence/

[7] https://www.cs.helsinki.fi/u/ukkonen/InfCont85.PDF

[8] https://en.wikipedia.org/wiki/Hirschberg%27s_algorithm

[9] https://github.com/drpowell/sequence-alignment-checkpointing

> Dynamic programming. Only recently has it been shown that, unless P=NP, O(n^2) is basically optimal. [6]

This is about a dynamic programming approach to the edit distance problem. Not dynamic programming itself, which is a vague term (I think it's basically "use a bottom-up approach and avoid doing the same work twice")

Yep. It's a complete oversimpliification to consider all DP problems at O(n^2). Anybody familiar with modern algorithms will tell you that certain DP problems can even be O(nloglogn)!

https://en.wikipedia.org/wiki/Van_Emde_Boas_tree

For example, implementing VEB trees or even (countably distinct length) dictionary-based tries can speed up execution by orders of logn/n

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