Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

I realized that derivatives are linear

codesmoothie.com

Post reply on HN
Print view View original

61–70 of 76 posts

Re: I realized that derivatives are linear

#61

Post by fwdpropaganda »

steamer25 wrote: post #56
fwdpropaganda wrote: post #50

Earlier quoted context omitted.

That aside I think there's something bigger here. I think learning is really hard work, and so most people's first reaction to hard work is to say No, and then go and construct an a posteriori rationale for why actually they shouldn't do that hard work (it's not that useful, you're never gonna use it, you're an expert at something else, etc). Similar story for why asking data structures in job interviews is a bad ide…

Yeah it seems analogous to bike shedding or Paul Graham's 'blub' paradox. I.e., "we don't understand that and haven't [realized that we've] needed it to date therefore it's probably not important and certainly not of interest". I like your conservation-of-mental-energy interpretation.

TIL about the Blub paradox https://en.wikipedia.org/wiki/Blub_paradox#The_Blub_paradox

Thanks for that.

Re: I realized that derivatives are linear

#62

Post by minhazm423 »

msie wrote: post #60
sampo wrote: post #5

The derivative is a linear operator, but it's not a bounded operator. That is, for example, the vector norm of f(x) = k·sin(x/k) → 0 when k→0, but the norm of d/dx f(x) does not. This also means that it's not continuous. Of the mappings between vector spaces, the most well behaving are the bounded linear operators, and the derivative doesn't belong to these. But yes, it's linear. Edit: Originally wrote f(x) = k·sin(k…

So what level of mathematics is needed to understand the following thread? Undergrad real analysis? Grad math courses?

hoping for an answer to this too

Re: I realized that derivatives are linear

#63

Post by sampo »

msie wrote: post #60
sampo wrote: post #5

The derivative is a linear operator, but it's not a bounded operator. That is, for example, the vector norm of f(x) = k·sin(x/k) → 0 when k→0, but the norm of d/dx f(x) does not. This also means that it's not continuous. Of the mappings between vector spaces, the most well behaving are the bounded linear operators, and the derivative doesn't belong to these. But yes, it's linear. Edit: Originally wrote f(x) = k·sin(k…

So what level of mathematics is needed to understand the following thread? Undergrad real analysis? Grad math courses?

> So what level of mathematics is needed to understand the following thread?

First course in functional analysis.

Before that, people usually take linear algebra, all the calculus courses, some kind of theorem-proving course for calculus (either analysis or real analysis or really rigorous versions of the calculus courses) and measure theory, maybe also topology.

Re: I realized that derivatives are linear

#66

Post by dang »

fwdpropaganda wrote: post #39

HN continues to confuse me to no end. Mention some mathematically advanced idea: out come the pitchforks about how you don't need that, all you need is code/market size/scalability/product fit/investment/execution. Mention a banality that anyone who studied algebra knows: frontpage.

Could you please not post like this? It's a shallow dismissal and it's tediously meta.

There's nothing wrong with the OP at all—someone sharing the excitement of discovering something for themselves.

Re: I realized that derivatives are linear

#68

Post by rs86 »

fwdpropaganda wrote: post #39

HN continues to confuse me to no end. Mention some mathematically advanced idea: out come the pitchforks about how you don't need that, all you need is code/market size/scalability/product fit/investment/execution. Mention a banality that anyone who studied algebra knows: frontpage.

My sentiments exactly. I see how the author felt thrilled by his discovery. But hn is getting less interesting each month. Otoh lobsters and Lbda the ultimate keep going strong.

Re: I realized that derivatives are linear

#69

Post by rs86 »

viraptor wrote: post #49
fwdpropaganda wrote: post #39

HN continues to confuse me to no end. Mention some mathematically advanced idea: out come the pitchforks about how you don't need that, all you need is code/market size/scalability/product fit/investment/execution. Mention a banality that anyone who studied algebra knows: frontpage.

You may be overestimating the banality. I studied CS with many math courses and some of the article goes over my head. (It would be clearer 10y ago) I don't expect many people here actually studied math as their main goal.

This is completely banal mathematics....
Post reply on HN