4 ms·

Not sure how feasible or necessary this is in general, but there are certainly some places for improvement. Some more modern examples than "isosceles": - Heav

Not sure how feasible or necessary this is in general, but there are certainly some places for improvement. Some more modern examples than "isosceles": - Heaviside function → step function (edit: though maybe this one is, amusingly, already descriptive by accident?) - Fourier domain → frequency domain While I'm here, just a couple suggestions from me: - Markov chain → memoryless chain - Lebesgue integral → horizontal integral

tomcam 6y ago
Was prepared to dislike these suggestions but I think they're all solid. Good thinking.
- mehrdadn 6y ago
  Thank you! :) Though I'd assume I'm not the first to think of them haha.
joshuamorton 6y ago
I'd be concerned that memoryless is misleading for markovian. A markov chain can be used to represent a fixed, nonzero memory, since if you have an n-state dfa D you can take the set of pairs of the states of D (or specifically D + null) and reweight them. The markov chain over D^2 has no memory over D^2, but does have memory over D, and this is often a useful property (bigrams). You repeat this operation to get more and more (but always a fixed constant maximum) history.
- mehrdadn 6y ago
  Memoryless isn't even something I came up with, it's practically in the first sentence of everyone's description of the Markov property, e.g.: https://en.wikipedia.org/wiki/Markov_chain#Definition https://en.wikipedia.org/wiki/Markov_chain#Definition Also see: https://en.wikipedia.org/wiki/Memorylessness https://en.wikipedia.org/wiki/Memorylessness ("memorylessness refers to the Markov property") All I'm doing is suggesting just using the existing description as the name itself. Even if there were some cases where it wouldn't apply, though, it wouldn't really matter. Fourier domain also applies to things other than time but that doesn't make frequency domain a bad term. It's just a name meant to carry some intuition; that's all. It's not meant to serve as the formal definition.
detaro 6y ago
Guess would need a different term for Markov chains of higher order. And I'm not sure if there's other concepts that could also be labeled "memoryless chains", where a distinct name might help.
OskarS 6y ago
Another example is Abelian groups, which should just be called commutative groups. Though that example brings up a decent counterargument to the thesis: ”groups”, ”rings” and ”fields” all have descriptive names, but that doesn’t help a bit, they’re still mad confusing. They’d almost be easier to pick apart if they were named after people.
- mehrdadn 6y ago
  +1 for commutative groups. Interesting point! So like we'd rename group theory to Galois theory? :)
kergonath 6y ago
I have seen 'reciprocal space' used for 'Fourier space'. It is quite descriptive, and has the advantage of also working with Legendre transforms. 'Horizontal integrals' does not work. It refers to one way of visualising functions (and even then, only of 1 or 2 variables, and only with specific conventions), and not to the integral itself.
- mehrdadn 6y ago
  > 'Horizontal integrals' does not work. It refers to one way of visualising functions (and even then, only of 1 or 2 variables, and only with specific conventions), and not to the integral itself. We already have "left" and "right" Riemann sums...
  - kergonath 6y ago
    Right, but left and right Riemann sums apply only to functions of a single variable; it breaks down in 2D spaces. It’s not a general concept like Riemann (or Lebesgue) integrals.
    - mehrdadn 6y ago
      One of your complaints was "It refers to one way of visualising function" right? Which is exactly what left and right sums do too.
      - kergonath 6y ago
        Well, yes, it’s bad, I am not defending it (and I have never seen it in the wild, even in class when I was taught Riemann integration). I am not sure how the supposed popularity of ‘right Riemann sum’ means that ‘horizontal integral’ would be any good.
        mehrdadn 6y ago
        I guess I'm saying it's not bad; you're just declaring it as such. People find them quite intuitive. I don't know about you but I've literally never seen someone get confused over silly things like "why is it called a left sum if I can plot the function in the other direction".

tomcam 6y ago

Was prepared to dislike these suggestions but I think they're all solid. Good thinking.

mehrdadn 6y ago
Thank you! :) Though I'd assume I'm not the first to think of them haha.

joshuamorton 6y ago

I'd be concerned that memoryless is misleading for markovian. A markov chain can be used to represent a fixed, nonzero memory, since if you have an n-state dfa D you can take the set of pairs of the states of D (or specifically D + null) and reweight them. The markov chain over D^2 has no memory over D^2, but does have memory over D, and this is often a useful property (bigrams). You repeat this operation to get more and more (but always a fixed constant maximum) history.

mehrdadn 6y ago
Memoryless isn't even something I came up with, it's practically in the first sentence of everyone's description of the Markov property, e.g.: https://en.wikipedia.org/wiki/Markov_chain#Definition https://en.wikipedia.org/wiki/Markov_chain#Definition Also see: https://en.wikipedia.org/wiki/Memorylessness https://en.wikipedia.org/wiki/Memorylessness ("memorylessness refers to the Markov property") All I'm doing is suggesting just using the existing description as the name itself. Even if there were some cases where it wouldn't apply, though, it wouldn't really matter. Fourier domain also applies to things other than time but that doesn't make frequency domain a bad term. It's just a name meant to carry some intuition; that's all. It's not meant to serve as the formal definition.

detaro 6y ago

Guess would need a different term for Markov chains of higher order. And I'm not sure if there's other concepts that could also be labeled "memoryless chains", where a distinct name might help.

OskarS 6y ago

Another example is Abelian groups, which should just be called commutative groups. Though that example brings up a decent counterargument to the thesis: ”groups”, ”rings” and ”fields” all have descriptive names, but that doesn’t help a bit, they’re still mad confusing. They’d almost be easier to pick apart if they were named after people.

mehrdadn 6y ago
+1 for commutative groups. Interesting point! So like we'd rename group theory to Galois theory? :)

kergonath 6y ago

I have seen 'reciprocal space' used for 'Fourier space'. It is quite descriptive, and has the advantage of also working with Legendre transforms. 'Horizontal integrals' does not work. It refers to one way of visualising functions (and even then, only of 1 or 2 variables, and only with specific conventions), and not to the integral itself.

mehrdadn 6y ago
> 'Horizontal integrals' does not work. It refers to one way of visualising functions (and even then, only of 1 or 2 variables, and only with specific conventions), and not to the integral itself. We already have "left" and "right" Riemann sums...
- kergonath 6y ago
  Right, but left and right Riemann sums apply only to functions of a single variable; it breaks down in 2D spaces. It’s not a general concept like Riemann (or Lebesgue) integrals.
  - mehrdadn 6y ago
    One of your complaints was "It refers to one way of visualising function" right? Which is exactly what left and right sums do too.
    - kergonath 6y ago
      Well, yes, it’s bad, I am not defending it (and I have never seen it in the wild, even in class when I was taught Riemann integration). I am not sure how the supposed popularity of ‘right Riemann sum’ means that ‘horizontal integral’ would be any good.
      - mehrdadn 6y ago
        I guess I'm saying it's not bad; you're just declaring it as such. People find them quite intuitive. I don't know about you but I've literally never seen someone get confused over silly things like "why is it called a left sum if I can plot the function in the other direction".