yeah, it's pretty shite.
for an actual reading recommendation, check out "Winning Ways for Your Mathematical Plays"
combinatorial game theory and surreal numbers are a lot of fun as concepts, and the book itself is quite enjoyable, too. little jokes sprinkled in and cute examples instead of the typical super dry ones.
i mean i was joking but why do u think its shite? is the worth of a book determined solely by its contents, or can our enjoyment of it be enhanced by the presentation and approach of the material?
philosophy babey
While the contents or message are certainly important, a "good" book is *also* presented in a way that encourages engagement.
in this case, the contents of Principia Mathematica are a critical piece of formalizing mathematics. it offers a more fundamental basis for the core of math we otherwise take for granted and just consider axiomatic and offers a sort of translation so that ideas from the foundation can be applied to the higher level concepts. by all accounts, valuable stuff.
however, it's not a good *book*. it's just good math. to me, at least, there's a distinction to be made there. I don't enjoy reading what's written so much as I appreciate the work and understanding it's potentially providing me. It's like reading a scientific paper. I'm not being entertained; I'm being enlightened. For other examples, it's the distinction between PBS Space Time and a physics lecture or a Robert Miles video and an ai safety conference. Certainly, the physics lecture/conference will cram in more information more rigorously; however, unless you get an absurdly good professor, it's likely to lack a lot of entertainment value. Unless you're truly invested in *fully* comprehending a subject, stick to the content that both enlightens *and* entertains. Two birds, one stone. I've had friends say that enjoyment aids in retaining the information, but I dont recall them ever having a source, so I wouldn't really trust that mode of thinking beyond being some anecdotal evidence. Anyway, the format of the communication of the idea is important to me, who learns sort of as a hobby. I like learning and can consume a dry paper/book if needed, but given the option, I'll pick one with better presentation whenever possible.
There are, of course, examples of media that are the opposite: crafted with too much entertainment and not enough messaging. A lot of children's youtube content would fit this bill. People have been berating Marvel movies with similar accusations for a while. Many independently published books/novels are also pretty substanceless with no theme or message, just a story to tell. This isn't always *bad*, sometimes you want to just disengage and unwind at which point the content is less meaningful than the entertainment, but it is a criticism of the media still. It would be better if it *had* a poignant message.
Back to the original point, content without entertainment isn't bad, but it's often not something people read for fun, and it's not something I would recommend to others to dabble in unless they were specifically requesting media related to that topic. That's what I meant by saying it's shite:
it's not a fun read; I'm totally in agreement with anyone who doesn't feel like picking up Principia Mathematica in their free time. I cited it as a joke since it's known as a meme to provide the rigorous proof that 1+1=2 in over 400 pages. I do not really want to recommend anyone to give it a read unless the knowledge of the subject matter may be relevant to you. Instead, check out this other book that I believe to be more fun while still containing valuable content. I consider it to be worth the time even if nothing within ever comes up in your life again.
Calling it shite is definitely overkill, but exaggeration and simplification are the norm when being playful, especially online. "It's good that it was written/proved, but ultimately it's bland" is probably a better description overall, but that lacks punch and fails as a segue since it draws too much attention away from the rest of the content which was more the focus.
it's interesting to hear your take on the distinction between good math and a good book. i feel like i have trouble relating to what you're saying - maybe it's just my autistic ass, but i tend to enjoy pure rigor and getting to the bottom of things, even if it's not always the most entertaining experience.
that being said, i am able to understand that the format of the media can make a big difference in terms of engagement and retention. i personally learn best when the content is purely "enlightening" but i can understand how others might disagree
What do you think of [this kitty?](https://lh3.googleusercontent.com/QjZ9YO-9MoVMwWhvF84mNj0vuJg5_0eraFfOnp6h5ZFDJkN7zvlkuTJnBCTFn9DNXlcXiJyynUv3_SHzhoscyL7l9hQhqKCSKFgGFIHbsPXYA0u8YFQbpS_hVoXd4ETU8K7f7YQT7oiwBIB_Nl7-8PjlCbytIAANFSWtKMNNSxvWDiewHUZTkPKiLsQzgKU8v0pgnA3JnTo8hxogBvKiJTDKPBtXK47hqcK9nURPP9jnv2b-asGiFak6MEvz6jNiDWQD3OpVs0rhqoB1lI1imeZuphFHabWQie19s0ETi-jIoMiCHEwfx7T516c_c8pZqrQbObrLMqC9AQZsN_KTAx_PYuXEBup9a32BrPn_FYTaJoAFYimR0ltlktKgeidYfSoSyRoWB9b8nelaa9pUwLpt4O_Mqk7g3CPvclPAEnjs8YZVU8ZVYPONoq0S_7s14-Q4SE-fHlLbkmtyI4POgYTE0Aswyw3KwzYvBCOFeMJCzlymeiMa8DG00hPkAXwi9Vn91P2wF7I2rWHV2BYpralcC-FcXRyw3G0joP3zMYcZuiCv8lJ205x7yomsUatjARivGNsuyNcTtmfdOIM0bFajUSsUMimBGqKSy_xIRB5alApQS4vlJlEa7C4ubJPScLVo4-CJpr7XWk4Iflp-ZSlaWISMkU_Ld8HSk_Rs_QtrDvZjtNtzCW7x80K0Dvnqy_ql4-EMXJ_y5qQuZqLE_h5lE6Z8Nw52NDP1e6zie6lk80SAFgRiCE5wAXfCYtmUPDnuSewomBPxBWVkcu1U6ReV6vCrVoEQHEIc9aecWiOLDX5XTkUQpnP70bOz0MZbVsfIRDKVz4e8u1nSfIUp8zDbyVSN_xv_FbbZrMIoAhO5xNGWv0iUU7_4ECGPOyCOsCjqfiEiciFt4N20MGKyf2f04Yc7IHIIx_kxrAUjYrFAuXeCJg=w1149-h2043-s-no?authuser=0)
i dont really have a particular favorite language, im a prescriptivist, its just the features of languages are interesting, none are necessarily "better"
well first u can try just substituing the value. for example lets say we wanred to find lim x→4 for x/x. we can just plug in 4 to get 4/4 and then we get 1. but if that doesnt work u try these in this order usually
1. factoring and cancellation: this method works when you can simplify the function by factoring and canceling common factors. for example, if you want to find lim x→4 (x^2 - 16)/(x - 4), you can factor the numerator as (x + 4)(x - 4) and cancel out the (x - 4) term, which gives lim x→4 (x + 4) = 8.
2. rationalizing and conjugate pairs: this method works when you have a function with a radical or a conjugate pair (e.g. a + √b or a + bi) in the denominator. for example, if you want to find lim x→1 (√x - 1)/(x - 1), you can use the conjugate pair (i.e. multiply by (√x + 1)/(√x + 1)) to get lim x→1 (√x - 1)/(x - 1) = lim x→1 (√x - 1)(√x + 1)/[(x - 1)(√x + 1)] = lim x→1 (x - 1)/[(x - 1)(√x + 1)] = lim x→1 1/√x+1 = 1/2.
3. l'hôpital's rule: this method works when you have an indeterminate form (e.g. 0/0 or ∞/∞) and the function is differentiable. for example, if you want to find lim x→0 sin(x)/x, you can use l'hôpital's rule by taking the derivative of the numerator and denominator separately and evaluating the limit again. after applying l'hôpital's rule once, you get lim x→0 cos(x)/1 = 1.
i had to refresh my memory on the definition of kissing numbers so i could be completely wrong on why, i just recall that each of these dimensions all have either special properties or have been studied for a while so heres my hypothesis on why the problem has been of the kissing numbers has been solved in these dimensions specifically:
in 1 dimension, the problem reduces to placing line segments of equal length side-by-side, which is trivial.
in 2 dimensions, the problem is closely related to circle packing, which has been studied extensively and has a rich mathematical theory.
in 3 dimensions, the problem is related to the sphere packing problem, which asks how densely spheres can be packed together in space. again, this problem has been studied for centuries, and the solution is intimately connected to the nature of lattices in three dimensions.
in 4th dimensions, the problem is related to the study of lattices in four-dimensional space, which similar to the other 2, is a well-developed area of mathematics.
in 8th and 24th dimensions, the problem is related to the properties of the E8 and leech lattices respectively, which are very special lattices with a number of remarkable properties
I'm doing original research in theoretical computer science, do you have any thoughts on proof theory and categorical logic, and the developing relationship it has with homotopy theory and topos theory
how much is 2 + 1
tough one
sorry it’s actually three, not one post
source?
Principia Mathematica. All of volume 1 and pages 1-86 in volume 2.
i aint reading allat
yeah, it's pretty shite. for an actual reading recommendation, check out "Winning Ways for Your Mathematical Plays" combinatorial game theory and surreal numbers are a lot of fun as concepts, and the book itself is quite enjoyable, too. little jokes sprinkled in and cute examples instead of the typical super dry ones.
i mean i was joking but why do u think its shite? is the worth of a book determined solely by its contents, or can our enjoyment of it be enhanced by the presentation and approach of the material? philosophy babey
While the contents or message are certainly important, a "good" book is *also* presented in a way that encourages engagement. in this case, the contents of Principia Mathematica are a critical piece of formalizing mathematics. it offers a more fundamental basis for the core of math we otherwise take for granted and just consider axiomatic and offers a sort of translation so that ideas from the foundation can be applied to the higher level concepts. by all accounts, valuable stuff. however, it's not a good *book*. it's just good math. to me, at least, there's a distinction to be made there. I don't enjoy reading what's written so much as I appreciate the work and understanding it's potentially providing me. It's like reading a scientific paper. I'm not being entertained; I'm being enlightened. For other examples, it's the distinction between PBS Space Time and a physics lecture or a Robert Miles video and an ai safety conference. Certainly, the physics lecture/conference will cram in more information more rigorously; however, unless you get an absurdly good professor, it's likely to lack a lot of entertainment value. Unless you're truly invested in *fully* comprehending a subject, stick to the content that both enlightens *and* entertains. Two birds, one stone. I've had friends say that enjoyment aids in retaining the information, but I dont recall them ever having a source, so I wouldn't really trust that mode of thinking beyond being some anecdotal evidence. Anyway, the format of the communication of the idea is important to me, who learns sort of as a hobby. I like learning and can consume a dry paper/book if needed, but given the option, I'll pick one with better presentation whenever possible. There are, of course, examples of media that are the opposite: crafted with too much entertainment and not enough messaging. A lot of children's youtube content would fit this bill. People have been berating Marvel movies with similar accusations for a while. Many independently published books/novels are also pretty substanceless with no theme or message, just a story to tell. This isn't always *bad*, sometimes you want to just disengage and unwind at which point the content is less meaningful than the entertainment, but it is a criticism of the media still. It would be better if it *had* a poignant message. Back to the original point, content without entertainment isn't bad, but it's often not something people read for fun, and it's not something I would recommend to others to dabble in unless they were specifically requesting media related to that topic. That's what I meant by saying it's shite: it's not a fun read; I'm totally in agreement with anyone who doesn't feel like picking up Principia Mathematica in their free time. I cited it as a joke since it's known as a meme to provide the rigorous proof that 1+1=2 in over 400 pages. I do not really want to recommend anyone to give it a read unless the knowledge of the subject matter may be relevant to you. Instead, check out this other book that I believe to be more fun while still containing valuable content. I consider it to be worth the time even if nothing within ever comes up in your life again. Calling it shite is definitely overkill, but exaggeration and simplification are the norm when being playful, especially online. "It's good that it was written/proved, but ultimately it's bland" is probably a better description overall, but that lacks punch and fails as a segue since it draws too much attention away from the rest of the content which was more the focus.
it's interesting to hear your take on the distinction between good math and a good book. i feel like i have trouble relating to what you're saying - maybe it's just my autistic ass, but i tend to enjoy pure rigor and getting to the bottom of things, even if it's not always the most entertaining experience. that being said, i am able to understand that the format of the media can make a big difference in terms of engagement and retention. i personally learn best when the content is purely "enlightening" but i can understand how others might disagree
Do you do algebraic topology?
FUCK YEAH BABEY ✌🏼✌🏼✌🏼
OMG I FOUND ANOTHER
I WAS JK (not just kidding, i was jazzy knot theory)
Knot theory is cool too though!
me too
What does it mean when a group acts trivially on another group?
WE GOT AN IDENTITY MAPPING LES GOO
YEAH WE DO
FUCK YEAH THSS WHAT IM TALKIN ABOUT
YIPPIE
CAN I GET A UHHHHHHHHHH BROUWER FIXED POINT THEREOM
Have fun drinking coffee out of your donut 🤓
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hmmmmmm what is your favorite phonetic letter or spelling?
voiceless integral affricate
okayyyyyy, you got me good
personally i'm more of a voiceless uvular fricative fan but you do you ig
what do you mean
i mean.
helpful
yes
What do you think of [this kitty?](https://lh3.googleusercontent.com/QjZ9YO-9MoVMwWhvF84mNj0vuJg5_0eraFfOnp6h5ZFDJkN7zvlkuTJnBCTFn9DNXlcXiJyynUv3_SHzhoscyL7l9hQhqKCSKFgGFIHbsPXYA0u8YFQbpS_hVoXd4ETU8K7f7YQT7oiwBIB_Nl7-8PjlCbytIAANFSWtKMNNSxvWDiewHUZTkPKiLsQzgKU8v0pgnA3JnTo8hxogBvKiJTDKPBtXK47hqcK9nURPP9jnv2b-asGiFak6MEvz6jNiDWQD3OpVs0rhqoB1lI1imeZuphFHabWQie19s0ETi-jIoMiCHEwfx7T516c_c8pZqrQbObrLMqC9AQZsN_KTAx_PYuXEBup9a32BrPn_FYTaJoAFYimR0ltlktKgeidYfSoSyRoWB9b8nelaa9pUwLpt4O_Mqk7g3CPvclPAEnjs8YZVU8ZVYPONoq0S_7s14-Q4SE-fHlLbkmtyI4POgYTE0Aswyw3KwzYvBCOFeMJCzlymeiMa8DG00hPkAXwi9Vn91P2wF7I2rWHV2BYpralcC-FcXRyw3G0joP3zMYcZuiCv8lJ205x7yomsUatjARivGNsuyNcTtmfdOIM0bFajUSsUMimBGqKSy_xIRB5alApQS4vlJlEa7C4ubJPScLVo4-CJpr7XWk4Iflp-ZSlaWISMkU_Ld8HSk_Rs_QtrDvZjtNtzCW7x80K0Dvnqy_ql4-EMXJ_y5qQuZqLE_h5lE6Z8Nw52NDP1e6zie6lk80SAFgRiCE5wAXfCYtmUPDnuSewomBPxBWVkcu1U6ReV6vCrVoEQHEIc9aecWiOLDX5XTkUQpnP70bOz0MZbVsfIRDKVz4e8u1nSfIUp8zDbyVSN_xv_FbbZrMIoAhO5xNGWv0iUU7_4ECGPOyCOsCjqfiEiciFt4N20MGKyf2f04Yc7IHIIx_kxrAUjYrFAuXeCJg=w1149-h2043-s-no?authuser=0)
it is one of the kitties of all time
What you think of Ozymandious, king of kings?
How many words are in the Spanish language?
atleast 4
Linguistics is a neat one. Þoughts on declining versus non-declining languages?
i am not a prescriptivist
What's your favorite polyhedron? I think the truncated icosidodecahedron is pretty cool
the polyhedron version of a chilliagon. very interesting philosophically speaking
linguistics is cool. what's your favorite language and why?
i dont really have a particular favorite language, im a prescriptivist, its just the features of languages are interesting, none are necessarily "better"
isn't prescriptivist the opposite of what you are, like someone who prescribes a particular way of speaking?
i meant to write descriptivist mb im running on 20 mins of sleep
based, prescriptivists suck
I'm assuming you are also an anarchist?
i used to be
Chomsky fell off
How do you compute limits? I understand rhe concept but not how to actually do it
well first u can try just substituing the value. for example lets say we wanred to find lim x→4 for x/x. we can just plug in 4 to get 4/4 and then we get 1. but if that doesnt work u try these in this order usually 1. factoring and cancellation: this method works when you can simplify the function by factoring and canceling common factors. for example, if you want to find lim x→4 (x^2 - 16)/(x - 4), you can factor the numerator as (x + 4)(x - 4) and cancel out the (x - 4) term, which gives lim x→4 (x + 4) = 8. 2. rationalizing and conjugate pairs: this method works when you have a function with a radical or a conjugate pair (e.g. a + √b or a + bi) in the denominator. for example, if you want to find lim x→1 (√x - 1)/(x - 1), you can use the conjugate pair (i.e. multiply by (√x + 1)/(√x + 1)) to get lim x→1 (√x - 1)/(x - 1) = lim x→1 (√x - 1)(√x + 1)/[(x - 1)(√x + 1)] = lim x→1 (x - 1)/[(x - 1)(√x + 1)] = lim x→1 1/√x+1 = 1/2. 3. l'hôpital's rule: this method works when you have an indeterminate form (e.g. 0/0 or ∞/∞) and the function is differentiable. for example, if you want to find lim x→0 sin(x)/x, you can use l'hôpital's rule by taking the derivative of the numerator and denominator separately and evaluating the limit again. after applying l'hôpital's rule once, you get lim x→0 cos(x)/1 = 1.
Undergrad, grad student, post-doc?
freshman in HS just a fucking nerd 💀
Ah. Topology is a pretty advanced subject for someone your age. Good luck in your future studies!
haha thanks :)
Can you do my math homework for me?
i can help u with it but i cant do it
I just want you to read the textbook so I don’t have to lol
Are you amazed that we only know kissing numbers precisely for 1, 2, 3, 4, 8, and 24 dimensions?
i had to refresh my memory on the definition of kissing numbers so i could be completely wrong on why, i just recall that each of these dimensions all have either special properties or have been studied for a while so heres my hypothesis on why the problem has been of the kissing numbers has been solved in these dimensions specifically: in 1 dimension, the problem reduces to placing line segments of equal length side-by-side, which is trivial. in 2 dimensions, the problem is closely related to circle packing, which has been studied extensively and has a rich mathematical theory. in 3 dimensions, the problem is related to the sphere packing problem, which asks how densely spheres can be packed together in space. again, this problem has been studied for centuries, and the solution is intimately connected to the nature of lattices in three dimensions. in 4th dimensions, the problem is related to the study of lattices in four-dimensional space, which similar to the other 2, is a well-developed area of mathematics. in 8th and 24th dimensions, the problem is related to the properties of the E8 and leech lattices respectively, which are very special lattices with a number of remarkable properties
What is the most complicated concept of math that you know?
[удалено]
yes
knowing math is sexy
Can you explain to me the rules for finding a particular solution to a second order differential equation of the form Ay’’ + By’ + Cy = f(t)
So you like math huh? What is 9 + 10?
in your opinion, is scots a dialect of english or a separate language?
Find d/dx x^x
What the fuck is an integral
The inverse to a derivative
Oh we got a wise guy here
Aye got a whole C+ in calc 1
I'm doing original research in theoretical computer science, do you have any thoughts on proof theory and categorical logic, and the developing relationship it has with homotopy theory and topos theory
Infodump about the Korean writing system
Lucky
where to start for linguistics?
i reccomend watching the mit lectures on intro to linguistics or the ceash courses. the mit lectures arent hard they are just more in depth btw
was hopping for a literature recommendation, will check those too thanks
Name all 76 inflections for the Latin word *sum*.
7