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[WealthyRadish]

Any time you have an absolute value (or other "norm", in higher dimensions) there's very little you can do algebraically with the contents of that expression, beyond proving some bounding values that the result lies within using inequalities (or proving that the absolute value can be dropped over the interval, for instance by showing that those two functions never intersect).

To compute the value itself in the general case, you would need to split the interval up and first solve for the roots of "f(x)-g(x)=0", which by itself could easily be impossible to solve analytically even for relatively simple-appearing functions. You would basically need to write a computer program implementing a root-finding algorithm and some method of numerical quadrature to approximate the answer, except in contrived examples that can be done by hand.

[McTraveller]

Your teacher is correct - you cannot, in general, say that the absolute value of the integral of f(x)-g(x) is the same thing as the absolute value of the integral of g(x)-f(x).  The quantity you get from an integral is "area like", but it is not always a quantity that represents real area.  Even if the units end up being "area", the integral may not represent a physical area either.

There are many situations in which the sign of the integral is important - the energy output of an engine is computed as the integral of the difference of two functions, and the sign absolutely is important because that sign tells you if the engine is producing energy or consuming it.

(I think this is the same thing that Ulfarr is saying...)

[bloop_bleep]

Integral is more of a generalization of summation than area computation; the symbol for integrals commonly used is derived from the letter "S". Integral gives "signed" area, not nonnegative area. Parts where f-g changes sign would change the sign of the area being added. So integral of f - g on two lines like the following on the shown interval:

Code: [Select]

\      /
 \    /
  \  /
   \/
   /\
  /  \
 /    \
/      \

would give a value of zero. In general you can't just flip the sign of an integral. There is no absolute value implied for integrals, if that's in your application you'd write out the absolute value symbols.

[Vector]

firm handshakes all around to the five (5) mathematicians who descended on this thread like a cloud of piranhas

[Naturegirl1999]

firm handshakes all around to the five (5) mathematicians who descended on this thread like a cloud of piranhas

Idk why but I chuckled when reading this

[methylatedspirit]

Very versatile, this thread. One day, I'm asking about computers and math, the next day, someone's talking about Norwegian death metal. No focus on any particular topic, just like Bay12 itself. We have a very loose concept of being "on-topic", and I love it.

[Kagus]

firm handshakes all around to the five (5) mathematicians who descended on this thread like a cloud of piranhas

Breaking News: Math groups around the world suddenly decimated by exponential increase in COVID cases

Very versatile, this thread. One day, I'm asking about computers and math, the next day, someone's talking about Norwegian death metal. No focus on any particular topic, just like Bay12 itself. We have a very loose concept of being "on-topic", and I love it.

Norwegian Death Mathel

[methylatedspirit]

If there were animals with our level of intelligence, but they did not have any concept of sex, nor different sets of genitals to base sex on, would their society that would inevitably form have any concept of gender as a cultural given, rather than just a scientific concept? Gender's primarily a cultural concept that's predicated on sex, so I think there's merit in considering a sexless society and if all sexless societies must necessarily be genderless too.

Like, Patrick in Spongebob, as far as I know, is a member of an asexually-reproducing species, but he's explicitly referred to as male, and he embodies traits that we see as masculine. But I'd argue that it's because of the society that he lives in; Bikini Bottom is predominantly fish, which reproduce sexually most of the time, so a concept of gender exists there, and because of that, Patrick have given himself the gender of "male" by being in that society. (I'd use Spongebob too, but there's an episode where he's been shown to be an embryo, which makes it real hard to say if he has a sex or not)

So then, if Patrick was born in a society of asexual creatures like he is, would he still call himself a "he", or would he adopt gender-neutral pronouns?

[Vector]

I recently had a convo with a friend where I said that they should do a Kinsey scale for if you prefer to argue with women or with men.

..... anyway, I tend to see gender in general as surrealist humor. I'm aware that most people aren't of that opinion, but I thought I would share.

[wierd]

If there were animals with our level of intelligence, but they did not have any concept of sex, nor different sets of genitals to base sex on, would their society that would inevitably form have any concept of gender as a cultural given, rather than just a scientific concept? Gender's primarily a cultural concept that's predicated on sex, so I think there's merit in considering a sexless society and if all sexless societies must necessarily be genderless too.

Like, Patrick in Spongebob, as far as I know, is a member of an asexually-reproducing species, but he's explicitly referred to as male, and he embodies traits that we see as masculine. But I'd argue that it's because of the society that he lives in; Bikini Bottom is predominantly fish, which reproduce sexually most of the time, so a concept of gender exists there, and because of that, Patrick have given himself the gender of "male" by being in that society. (I'd use Spongebob too, but there's an episode where he's been shown to be an embryo, which makes it real hard to say if he has a sex or not)

So then, if Patrick was born in a society of asexual creatures like he is, would he still call himself a "he", or would he adopt gender-neutral pronouns?

I would say the society would stratify on levels of submissiveness/dominance instead.  You would still have Tops and Bottoms, in the loose sense. It just would not be based on sexual characteristics, since all the creatures would have the same toolkit.

There might be some other outward physical trait that is closely associated with behavioral defaults, (think something like bright vs dull plumage), that might get used instead, for the same purposes.


Jockeying for heirarchy, and differences of opinion on how to approach a heirarchy, are going to be endemic of any intelligent social system (that does not have straight up telepathy, or a technological surrogate for same)

[Rose]

It's been a running joke among my friends group to declare various things like long cloaks as being a gender.

[methylatedspirit]

I'm very inclined to see gender as a "bullshit concept", but I maintain support for it because other people care about it; it's not quite "deprecated" to me, but I would love to put it there. I think we're on the same page here. I threw my own gender out the window because I thought it wasn't worth keeping around. I keep a little emulator with my birth gender on it for safety and because it's funny, but that's all that's left.

Also, Kinsey scale for gender preference of arguments? Geez, talk about pointless gendering. Maybe it's by gender expression, by the traits that are often expressed by a certain gender... but that's still dubious as hell in my book. Why not rate it by personality characteristics?

[scriver]

If there were animals with our level of intelligence, but they did not have any concept of sex, nor different sets of genitals to base sex on, would their society that would inevitably form have any concept of gender as a cultural given, rather than just a scientific concept? Gender's primarily a cultural concept that's predicated on sex, so I think there's merit in considering a sexless society and if all sexless societies must necessarily be genderless too.

Like, Patrick in Spongebob, as far as I know, is a member of an asexually-reproducing species, but he's explicitly referred to as male, and he embodies traits that we see as masculine. But I'd argue that it's because of the society that he lives in; Bikini Bottom is predominantly fish, which reproduce sexually most of the time, so a concept of gender exists there, and because of that, Patrick have given himself the gender of "male" by being in that society. (I'd use Spongebob too, but there's an episode where he's been shown to be an embryo, which makes it real hard to say if he has a sex or not)

So then, if Patrick was born in a society of asexual creatures like he is, would he still call himself a "he", or would he adopt gender-neutral pronouns?

I'd argue that trying to analyse cartoon characters, of an absurdism-driven style to the extent that Spongebob is at that, to be an exercise in complete futility.

Patrick is not given a gender or masculinity or anything by Bikini Bottom society. His society is made up. He was given a gender and masculinisation by the people who created the Spongebob show and the gender norms of "Bikini Bottom society" likely didn't even enter into the minds of those creates when they made him up.

[Arx]

Yeah Spongebob is definitely not the place for literary analysis. It's been a while since I last read it, but Ursula Le Guin's The Left Hand of Darkness takes place in an either agender or genderfluid (can't remember) society and does a little bit get into it. Dunno what the modern consensus is on its quality etc.

[Ulfarr]

Can someone explain to me what's the big deal with pronouns and/or gendered words?

A quick search in the net results mainly in articles about how you shouldn't misgender a person because it's oppresive, but don't really explain why or how it does that. I always understood that some words are gendered merely out of convinience, so that people don't need to specify everything or repeat themselves all the time. Then, through common usage, certain words got a "default" gender for when gender is either unknown or irrelevant.

To give an example, the phrase "this woman" is basicaly just the short version for "this human that appears to be female". Now, one could argue that this implies that there is a certain understanding of "what is a female" in the first place,  but it doesn't really force said person to conform by that definition. It merely reflects what the one who used the phrase percieve as a woman.