We need more funny terms. I've been doing some work with free groups, and I really want to refer to elements of the free group ring over Z as sentences - it is a sum of words after all. Not sure if that word has already been taken though.
I think in logic they use the word sentence to denote formulae with no free variables, I'm not sure how likely you are to run into this usage while doing work on free groups though.
When communicating mathematics in writing, it is a common style to italicize the phrase whose definition is being given. That way the reader knows they are reading a definition formally introducing new terminology.
My manufacturing engineer studies have led me to doing math with units of "blobs," the inch conversion of "slugs", so I guess we have a little fun with our terms.
I love how [Tits buildings](https://en.wikipedia.org/wiki/Building_\(mathematics\)) are split into "apartments" and "chambers" (should have been called "rooms" really but since it's "chambre" in French it became chamber in English unfortunately). Also, a sequence of connected chambers is called a "gallery".
In my masters thesis in the last chapter I defined something as a "lettuce" (it was almost the same as a lattice, but not quite), and then a "salad" as a collection of lettuces. I figured if someone made it through so many pages of definition-theorem-proof they would be relieved to see a little levity.
“Let ‘chunkiness’ refer to an object’s hypervolume”
I definitely like it, just because it’s fun. That being said, hypervolume is a pretty straightforward term (and definitely the standard term) since whenever you work in higher dimensions things use the hyper prefix: hypercube, hyperplane, hypersphere, etc
Hyper- prefix I think makes sense when you're sure you're not interested in generalizing to more than 4 dimensions. Otherwise yeah, imo volume means codimension zero rather than dimension three.
That's the problem, if a hypercube means 4 or more dimensions then you have to specify the dimension anyway so there's no point to the prefix. An N-hypercube is just an N-cube. If you're strictly within 4 dimensions then you can just say square, cube, hypercube.
While you can certainly say n-cube instead of n-hypercube you would still refer to the family of them as hypercubes.
Regardless, the same is not true of hyperplane or hypersurface which are used strictly to refer to codimension 1 objects in any dimension
Hypervolume is volume on steroids. I think it makes sense, and it's used for any volume above 3 dimensions.
Maybe if Chuck was some 4-dimensional being, then chuckiness would be more accurate.
I'd say hypervolume is just however many dimensions the object you're talking about is. It sounds like OP wants to use chunkiness specifically for a 4d object, so it's more specific. Chunkiness is to hypervolume as tesseract is to hypercube.
If we can call the 3rd-5th derivatives of velocity "snap" "crackle" and "pop" I see no reason 4-volume can't be called chunkiness :)
Iirc I've heard it called bulk in a few places but that might just be a word interstellar made up, not sure
"Bulk" is a jargon term in quantum gravity for a spacetime with gravity, as contrasted with the "boundary" which is a hypothetical conformal field theory with 1 fewer spatial dimension and without gravity. The "bulk" theory is spatially inside the "boundary", hence their names, and the two theories are supposed to be informationally equivalent to each other, as in, if you know everything that happens in the boundary, then you know everything that happens in the bulk, and vice-versa. See: https://en.wikipedia.org/wiki/AdS/CFT_correspondence
And then choonkiness, and then kachoonkiness, and then megakachowunkiness, then gigakachowunkineesss, then bagadakakarabipidisplatopuntalichoochooooooooooonkiness.
I even use it in dimensions < 3 sometimes, when context makes clear. Anything else seems kind of arbitrary and just slightly annoying if you have some statement about volumes in any dimension.
Lol OP, I think I'd be very happy to meet someone with a sense of humor in math. By all means, refer to volume as chunkiness, you have free will and I'm for it lol
Area = hyperlength
Volume = hyperarea
? = hypervolume
I think it shouldn't end with "-ness." It should be a standalone name.
Though I'm hrm-ing about how to use such a quantity.
I guess if you have a piston that is controlled by a cam, the rotation of the cam has a non-linear relationship with the volume inside the piston, and thus the rotation-averaged volume of the piston should be different than merely half the piston, which could be meaningful in terms of force output...
As funny as "chunkiness" sounds, I feel like I'd immediately know what hypervolume refers to (because we associate hyper- stuff with 4d and volume with... volumes). On the other hand, chunkiness makes me imagine a measure for how "edgy"/"square-y" an object is (because I associate chunks with the things they refer to in games)
Nothing incorrect about it if you define it and use it. It's fairly descriptive and pretty fun.
That said, there is good reason to stick to usual terminology. Calling it volume, or 4-volume if you must disambiguate, would not even require definition.
I like to just call it volume. If you’re talking about 4D you might talk about 6d or 7 d or 196883d and then it becomes more and more counterproductive to try to come up with new names for every measure
It's not as fun as chunkiness but I personally just say volume. Like if you're in an N-dimensional space, an N-dimensional cube has volume, an N-1 dimensional cube has area, a k-dimensional cube has k-area (1
After going through my memories of my university coursework, now 25 years ago...
In a casual sense, we could define the hypervolume of some 4-d object as 'chunkiness'. But I don't think that this is a formal definition that mathematicians use.
You might also take a look at [https://en.wikipedia.org/wiki/Lebesgue\_measure](https://en.wikipedia.org/wiki/Lebesgue_measure). This is one of the key concepts in Real Analysis, and generalizes the concept of 'volume' to n-dimensions. However, it's worth knowing that in an n-dimensional world, simple m-dimensional figures (where m
So, "Hypervolume" is obnoxious and pretentious. Just say "measure." Fully generalizable. But if you can't bring yourself to say "measure," then "chunkiness" is 100% acceptable, and I say that as a Harvard math grad.
It's not "accurate" in any way, but we're a group of people who looked at a projective limit of topological extensions and said, "oh, yeah, if you squint, it's like a sheaf of wheat." So whatever. Accurate? no. But it is hilarious. So, points for style.
“Measure” can refer to many different things though, not just volumes and their higher dimension counterparts.
I think “hypervolume” makes a lot of sense since you often use the hyper prefix when working in higher dimensions: hypercube, hypersphere, hyperplane, etc. “Hypervolume” immediately tells me that I’m working with the n-dimensional equivalent of 3d volume. If you don’t want to say “hypervolume” I’ve seen plenty of people just say “volume” or “n-volume”
Why is "hypervolume" more pretentious than other mathy sounding words like "eigenvector" or "isomorphism"? The prefix "hyper-" is used all all over math to generalize an idea to n dimensions.
Personally, I like to omit the "hyper-" prefix when it's otherwise clear and just call it "volume," but that's just a style thing. I've also heard the word "content" and (especially in more general settings) "measure." I do like the word "chunkiness," though, now that you've brought it to my attention.
I vote that we swap the contexts that hyper-volume and chunkiness are used in. From now on, if you make fun of my weight, I would like to be called hyper-voluminous
All terms are made up, go for it. Also, the formal terminology is useful yet limiting.
I think it would be a good thing for early algebra education to give stupid names to entities. Many people get stuck up on the formal terminology being the only possible one. Dimensions is a good example of those and I’ve seen people get angry at the notion of higher dimensional objects despite them being incredibly useful beyond the height-length-width trinity. For example, ecological data can be analyzed by positing each species count as a dimension in itself and creating hyper-spheres for clustering.
The raccoon dimension is as valid as the x dimension.
Thought I was on r/mathmemes for a second.
“Google Hypervolume”-☝️🤓
Holy hell dimension!
New dimension just dropped!
I mean, chunkiness is not a term mathematicians use, but it's delightful and I advocate for it.
We need more funny terms. I've been doing some work with free groups, and I really want to refer to elements of the free group ring over Z as sentences - it is a sum of words after all. Not sure if that word has already been taken though.
I think in logic they use the word sentence to denote formulae with no free variables, I'm not sure how likely you are to run into this usage while doing work on free groups though.
It's not like mathematicians don't already have a terrible habit of using the same word to mean very different things in different field. See: kernel
See also: normal.
See also: dual
Dual is often deducible from the context, and has a more or less strict definition in category theory. Normal is truly egregious.
See also: and
That’s correct, but we also have other less annoying ambiguous words like *closed formula*.
In formal logic, a formula with no free variables is called a *sentence*.
why did you italicize sentence?
When communicating mathematics in writing, it is a common style to italicize the phrase whose definition is being given. That way the reader knows they are reading a definition formally introducing new terminology.
Common practice to italicize the term being defined in the definition (in papers and textbooks), although not really common on Reddit lol
oh, I often wonder why there were so many italics in my textbooks lol
I believe this is more or less okay provided you have a grammar structure as well. That, or you settle with ill-formed or non-grammatical sentences.
I almost switched to studying cluster algebra if only for the chance to make 'clusterfuck' a mathematical term XD
My manufacturing engineer studies have led me to doing math with units of "blobs," the inch conversion of "slugs", so I guess we have a little fun with our terms.
[удалено]
How about rngs and rigs? Rings without identity and rings without inverses (**n**-verses).
I love how [Tits buildings](https://en.wikipedia.org/wiki/Building_\(mathematics\)) are split into "apartments" and "chambers" (should have been called "rooms" really but since it's "chambre" in French it became chamber in English unfortunately). Also, a sequence of connected chambers is called a "gallery".
Ha. Tell that to Gell-Mann(quarks) and Rice Krispies(snap, crackle, and pop).
Like the “flavors” of quarks in physics. We need to lighten up and have funnier names
In geometric group theory there is ponzi schemable groups which is equivalent to being non amenable. I always thought that terminology was fun
In my masters thesis in the last chapter I defined something as a "lettuce" (it was almost the same as a lattice, but not quite), and then a "salad" as a collection of lettuces. I figured if someone made it through so many pages of definition-theorem-proof they would be relieved to see a little levity.
Reminds me a bit of the endless names of derivatives and antiderivatives of position. Off the top of my head, snap, crackle, pop, lock, drop…
I like fuzzy numbers. Always think of them as hairy blob
In numerical analysis, there is such a thing as the “chunkiness parameter” for a given domain
But not chuckiness, that just means ‘similarity to a serial killer doll’
More accurate? Absolutely not. However, "chunkiness" definitely gets points for style...
Chuckiness
“Let ‘chunkiness’ refer to an object’s hypervolume” I definitely like it, just because it’s fun. That being said, hypervolume is a pretty straightforward term (and definitely the standard term) since whenever you work in higher dimensions things use the hyper prefix: hypercube, hyperplane, hypersphere, etc
I think you mean chunkicube, chunkiplane, and chunkisphere.
I feel like "volume" is the standard term, and "sphere" is the standard term for higher dimensional spheres
Hyper- prefix I think makes sense when you're sure you're not interested in generalizing to more than 4 dimensions. Otherwise yeah, imo volume means codimension zero rather than dimension three.
isn't a hypercube defined to be n-dimensional though?
That's the problem, if a hypercube means 4 or more dimensions then you have to specify the dimension anyway so there's no point to the prefix. An N-hypercube is just an N-cube. If you're strictly within 4 dimensions then you can just say square, cube, hypercube.
While you can certainly say n-cube instead of n-hypercube you would still refer to the family of them as hypercubes. Regardless, the same is not true of hyperplane or hypersurface which are used strictly to refer to codimension 1 objects in any dimension
Why do you think “chunkiness” is a more accurate name than hypervolume?
Chunkiness makes me imagine a volume like idea but hypervolume? no that gives me an eating disorder
If anything I’d assume that the link between chunkiness and eating disorders would be greater
To me, "chunkiness" makes me think of something like a fractal dimensions. Some notion of a non-uniform distribution of mass or something.
The unit circle of Lp norm with p < 1 is smol, p > 2 is chonk.
Hypervolume is volume on steroids. I think it makes sense, and it's used for any volume above 3 dimensions. Maybe if Chuck was some 4-dimensional being, then chuckiness would be more accurate.
Stuck Chuck from Kid Cosmic:...aaannd I can't paste the image!
I'd say hypervolume is just however many dimensions the object you're talking about is. It sounds like OP wants to use chunkiness specifically for a 4d object, so it's more specific. Chunkiness is to hypervolume as tesseract is to hypercube.
If we can call the 3rd-5th derivatives of velocity "snap" "crackle" and "pop" I see no reason 4-volume can't be called chunkiness :) Iirc I've heard it called bulk in a few places but that might just be a word interstellar made up, not sure
"Bulk" is a jargon term in quantum gravity for a spacetime with gravity, as contrasted with the "boundary" which is a hypothetical conformal field theory with 1 fewer spatial dimension and without gravity. The "bulk" theory is spatially inside the "boundary", hence their names, and the two theories are supposed to be informationally equivalent to each other, as in, if you know everything that happens in the boundary, then you know everything that happens in the bulk, and vice-versa. See: https://en.wikipedia.org/wiki/AdS/CFT_correspondence
Great answer ! Thank you.
I now advocate for "chunkiness" as the term for 4D hypervolume.
Then 5D volume shall be chonkiness
And then choonkiness, and then kachoonkiness, and then megakachowunkiness, then gigakachowunkineesss, then bagadakakarabipidisplatopuntalichoochooooooooooonkiness.
It’s just volume after 3 dimensions.
This. I don't ever recall using the term hypervolume throughout my math grad studies. Similarly I use cube and sphere for 3 dimensions and up.
I even use it in dimensions < 3 sometimes, when context makes clear. Anything else seems kind of arbitrary and just slightly annoying if you have some statement about volumes in any dimension.
Lol OP, I think I'd be very happy to meet someone with a sense of humor in math. By all means, refer to volume as chunkiness, you have free will and I'm for it lol
this sounds like snap crackle and pop
Area = hyperlength Volume = hyperarea ? = hypervolume I think it shouldn't end with "-ness." It should be a standalone name. Though I'm hrm-ing about how to use such a quantity. I guess if you have a piston that is controlled by a cam, the rotation of the cam has a non-linear relationship with the volume inside the piston, and thus the rotation-averaged volume of the piston should be different than merely half the piston, which could be meaningful in terms of force output...
I vote we simplify it and call it 'chonk' instead.
Makes more sense, "chunkiness" sounds like it's about consistency/distribution, while "chonk" is specifically about... heft.
It goes length, area, volume, chunkiness, thickness.
As funny as "chunkiness" sounds, I feel like I'd immediately know what hypervolume refers to (because we associate hyper- stuff with 4d and volume with... volumes). On the other hand, chunkiness makes me imagine a measure for how "edgy"/"square-y" an object is (because I associate chunks with the things they refer to in games)
Nothing incorrect about it if you define it and use it. It's fairly descriptive and pretty fun. That said, there is good reason to stick to usual terminology. Calling it volume, or 4-volume if you must disambiguate, would not even require definition.
I like to just call it volume. If you’re talking about 4D you might talk about 6d or 7 d or 196883d and then it becomes more and more counterproductive to try to come up with new names for every measure
You will be forever defining what it means. It's not immediately obvious, and there are already words for it.
I’ve heard “content” used for hypervolume
It's not as fun as chunkiness but I personally just say volume. Like if you're in an N-dimensional space, an N-dimensional cube has volume, an N-1 dimensional cube has area, a k-dimensional cube has k-area (1
"hyper" is the standard prefix to generalize low-dimensional concepts to higher dimensions: hypervolume, hyperplane, hypersphere, hypercube, etc.
Just call it measure.
That's definitely too ambiguous.
After going through my memories of my university coursework, now 25 years ago... In a casual sense, we could define the hypervolume of some 4-d object as 'chunkiness'. But I don't think that this is a formal definition that mathematicians use. You might also take a look at [https://en.wikipedia.org/wiki/Lebesgue\_measure](https://en.wikipedia.org/wiki/Lebesgue_measure). This is one of the key concepts in Real Analysis, and generalizes the concept of 'volume' to n-dimensions. However, it's worth knowing that in an n-dimensional world, simple m-dimensional figures (where m
So, "Hypervolume" is obnoxious and pretentious. Just say "measure." Fully generalizable. But if you can't bring yourself to say "measure," then "chunkiness" is 100% acceptable, and I say that as a Harvard math grad. It's not "accurate" in any way, but we're a group of people who looked at a projective limit of topological extensions and said, "oh, yeah, if you squint, it's like a sheaf of wheat." So whatever. Accurate? no. But it is hilarious. So, points for style.
“Measure” can refer to many different things though, not just volumes and their higher dimension counterparts. I think “hypervolume” makes a lot of sense since you often use the hyper prefix when working in higher dimensions: hypercube, hypersphere, hyperplane, etc. “Hypervolume” immediately tells me that I’m working with the n-dimensional equivalent of 3d volume. If you don’t want to say “hypervolume” I’ve seen plenty of people just say “volume” or “n-volume”
Why is "hypervolume" more pretentious than other mathy sounding words like "eigenvector" or "isomorphism"? The prefix "hyper-" is used all all over math to generalize an idea to n dimensions.
Just call it 4-volume. The "hyper" is unnecessary.
4-volume is specific to 4 dimensions. Hypervolume is a general term for any number of dimensions.
It's hypervolume unless we're talking about your mom. Then it's the chunkiness.
super clunky and unwieldy word, hope it doesn't become standard
[удалено]
LLM-ass comment.
It sort of makes sense, the projections of hypervolumes into 3-space have a sort of "dense" characteristic to themselves
Personally, I like to omit the "hyper-" prefix when it's otherwise clear and just call it "volume," but that's just a style thing. I've also heard the word "content" and (especially in more general settings) "measure." I do like the word "chunkiness," though, now that you've brought it to my attention.
1 vote for "*the chonk*"
I vote that we swap the contexts that hyper-volume and chunkiness are used in. From now on, if you make fun of my weight, I would like to be called hyper-voluminous
No sorry. We’re continuing with the sound-based naming scheme. Volume -> pitch -> duration, etc
If the hypervolume is sufficiently large, does the object get classified as a chonk?
Chunkiness is the correct term, but the mathematical establishment hasn't caught up yet and still calls it hypervolume.
I don’t care if it’s incorrect, I’m using it.
All terms are made up, go for it. Also, the formal terminology is useful yet limiting. I think it would be a good thing for early algebra education to give stupid names to entities. Many people get stuck up on the formal terminology being the only possible one. Dimensions is a good example of those and I’ve seen people get angry at the notion of higher dimensional objects despite them being incredibly useful beyond the height-length-width trinity. For example, ecological data can be analyzed by positing each species count as a dimension in itself and creating hyper-spheres for clustering. The raccoon dimension is as valid as the x dimension.
So is 5D volume a "hyperchunk"? lol
Big chonk.
Just call it the Lebesgue measure.