>the latter is his actual name.
In Greek no, in Latin and German transliterations yes. In greek the ευ is pronounced as a short e and a french u combined into one diphthong, not even close to german or latin eu. Once again europoors display their ignorance
how would one pronounce it using the lucian pronunciation? >europoors
why the classism?
2 years ago
Anonymous
>lucian pronunciation
the lucian pronunciation is not a reconstructed pronunciation, it’s an attempt to make something that pleases as many people as possible and sounds good because he wants it to be adopted as the standard for modern people who for some reason are trying to create a modern ancient greek speaking community. his pronunciation is closer to modern greek than ancient greek. However it’s probably pronounced the same in lucian pronunciation since most of the differences between lucian and reconstructed pronunciation are in other letters and sounds. I think he uses the proper sound for upsilon and epsilon
He didn't invent a single theorem. He only made more complicated and less comprehensible proofs (the ones you were given) instead of clear and simple ones (picrelated)
Probably he was one of the first entanglers of science. There is no royal path to geometry my ass (did I mention that he also was a homosexual, just as all academia is? And by academia I meant the Plato's school of pederasty from which catholic church originated to control the science to this day)
Oh well, the good thing about 0^0 = 1^1 is that you can write it in different ways and it is still true.
okay, I thought you're a little crazy, but it seems to be a little more complicated: > Zero to the power of zero, denoted by 00, is a mathematical expression with no agreed-upon value. The most common possibilities are 1 or leaving the expression undefined, with justifications existing for each, depending on context. In algebra and combinatorics, the generally agreed upon value is 00 = 1, whereas in mathematical analysis, the expression is sometimes left undefined. Computer programming languages and software also have differing ways of handling this expression.
But what is the meaning of that? It's not even nothing taken nothing times which would be 0*0 but what is it? Why is n^0 = 1? I don't understand even that, other than the graph tells that it is kinda so, but I have some dubts that the graphs are defined at that very point.
What about https://en.wikipedia.org/wiki/Translation_(geometry) don't you understand?
>did I mention that he also was a homosexual, just as all academia is? And by academia I meant the Plato's school of pederasty from which catholic church originated to control the science to this day
I dare you to show me a reddirrt thread speaking of that. Or is it your userpic and you're shocked?
That's not a proof. It's a kindergarten-level "fit-the-patterns" argument. A proof requires several things. You would have to prove that the lengths of corresponding lines are the same. You would have to prove that translation and rotation don't change anything. You would have to lay out your assumptions, i.e., Euclidean geometry and so on.
You put together colored shapes and wrote lengths at the sides, hoping everybody would just believe they're correct because everything fits so nicely. >but the reader can easily compute for herself that all corresponding lines have the same length!
Yeah, so it's not a proof.
2 years ago
Anonymous
>You would have to prove that the lengths of corresponding lines are the same.
Why are you not supposed to do the same in this over-the-ass proof?
2 years ago
Anonymous
You do. That's an unfounded "illustration" of Euclid's proof. Euclid didn't illustrate it like that. He wrote a formal proof.
2 years ago
Anonymous
He probably did, and you probably even memorized it. But almost nobody who did cannot repeat it. I'm pretty sure Pythagoras had his proofs alright, but we'll never read it (unlest some palimpsest resurfaces) because platonic school (to which both Euclid and catholic church belonged) are known to burn the books of their opponents.
Your proof is akin to showing that the angles in a triangle add up to 180 by cutting the corners off a triangle and arranging them such that they lie in a straight line. Whilst a demonstration of the concept, the proof is not rigorous. It should instead be approached by drawing a line through C parallel to AB, then using the parallel postulate to show the angles add to 180.
2 years ago
Anonymous
The fact that this method can be abused doesn't make this method invalid. You can entertain sophistry in verbal form as well.
They're actually allowing shit like that in math departments now in "woke" universities in progressive urban areas. Last year I graduated from the University of Washington in Seattle, which is obviously a major shitlib hub, and even in upper division, proofs-based classes like real analysis and abstract algebra, they were allowing students to submit "visual proofs" and "diagrams" for credit. Standards have really dropped a lot, especially in the last 5-10 years. When I started my undergrad back in 2016 they still had some objective standards, and we were regularly assigned graded homeworks and exams but by the time I graduated in 2021, a lot of teachers had switched to grading based on "completion" and all of our exams had become bullshit "take home" exams without no supervision or oversight. COVID was a big part of it, but the rise of "distance learning" (which is completely ineffective for actual learning) and platforms like blackboard have also played a major role, and well as the rise in woke policies that promote arbitrary grading standards.
It's not just grading either. A lot of universities are switching to admissions criteria that downplay the significance of academic credentials like GPA and SAT/GRE scores in favor of more subjective measures like legacy status, letters of rec., and extracurriculars. This is nominally intended to create a more "holistic" admissions process that places less emphasis on narrow quantitative measures of academic ability like GPA, and I completely understand those concerns, but the reality is that these new standards are not an improvement. In fact, they're making it worse, and we know that because there's plenty of data available on college admissions. When colleges downplay more objective metrics like GPA and SAT scores, it actually harms disadvantaged students, since the people with legacy status and access to extracurriculars and impressive letters of recommendation tend to come from wealthy, educated families.
A big part of this is dramatic decline in college enrollment. Making it harder isn't a good way to entice new students to enroll.
2 years ago
Anonymous
>A big part of this is dramatic decline in college enrollment.
They have pretty well made it a toxic environment for anyone who is more interested in ideas than conformity---it makes the medieval University, where you might have had to go to Church and mouth the words to some ceremony, but otherwise would explore almost everything seem an open intellectual arena.
A few years ago, almost every university required SAT/GRE scores. Now most of them have removed the requirement altogether. Some admissions FAQ pages even tell applicants explicitly not to send test scores.
>did I mention that he also was a homosexual, just as all academia is? And by academia I meant the Plato's school of pederasty from which catholic church originated to control the science to this day
I mean, they're interesting from a math history perspective and there's a reason it's been printed so much.
I know the Greeks basically threw out everything prior to Euclid's texts because they liked his explanations more. He didn't really theorize anything himself, but he's basically the first math textbook author and really cemented the concept of a textbook into STEM. At some level, the textbook surpasses and becomes more fundamental than the original work which is why most people don't really waste time reading original work in STEM unless it's cutting edge.
> most people don't really waste time reading original work in STEM because they're too lazy to read more accurate primary sources and are content with the soundbite version which has been filtered for them and made politically correct by an industry approved textbook author
oh yeah, reading the primary source is a total waste of time, is that why the science geniuses keep on repeating the same mistakes over and over again? >i'm too smart to read primary sources, i'm so smart i know whats in them without reading them
Not really the issue in mathematics, where review papers and textbooks can contribute by producing clearer, more elegant expositions of the same results than the original research paper.
This. It's precisely the reason Euclid blew up in popularity. He btfoed the competition, not because he came up with original theories, but because his formating and explanations and connections were so much more clear and clearly laid out that you didn't NEED the original work. You could just read Euclid instead. Again, this is common in math and physics. I know very few people who read the original papers unless they're cutting edge shit or they're interested in them from a historical perspective.
Actually a lot of mathematical progress is really just about more explicitly identifying important results and connecting them together. Usually when a new field is emerging, many of the problems and basic results have been circulating for decades, but nobody put them together in a systematic way. Calculus is a great example of this, since there were results anticipating it's development for centuries, but nobody was able to connect it all together. People were researching sequences and sums and infinite series and rates of change and interpolation and stuff like that since ancient times, and it really picked up during the renaissance. What Newton and Leibniz did was just connect it all together.
The same thing also happened with basic group theory/modular arithmetic, logic, and non-Euclidean geometry. There were bits and pieces of all these subjects scattered here and there, but nobody pieced them together.
Even modern mathematical physics and topology and algebraic geometry and differential geometry are still studying the same things that Euclid was 2500 years ago. Over simplifying of course, but mathematical physics is basically the study of circles and spheres, since that's what a Lie Group is. We just developed a much more organized and systematic language for doing so, but the objects of study are still the same. Things have just gotten more systematic.
2 years ago
Anonymous
>study of circles and spheres
These were the hardest shapes for me to internally compute. Anything with edges and verticies was really intuitive.
Decoding this image has been difficult, only partially "seen". Most other similar pictures are fairly easy.
2 years ago
Anonymous
I 100% agree, but I would go a step further. Even these leaders are not read anymore. No one reads Newton or Leibniz, they read calculus textbooks ultimately derived from these works, but basically no one reads the original texts.
Everyone knows Maxwell's equations, but no one has read Maxwell. Everyone know Fourier expansion, but no one reads him. Euler is like the only mathematician that I sometimes see read.
Again, STEM is very unique in this respect. Transfer of knowledge of concepts do not require the original papers to understand, in fact the original papers could be more confusing than anything.
All other fields you almost feel obligated to read the original texts because a textbook is full of many interpretations.
2 years ago
Anonymous
Yes, this is a good point, and I think the way science is driven by research papers is probably one of the main drivers of the phenomenon I was talking about. In the body of research papers that are published over the years, you see a lot of the organizational development that I was talking about. A lot of papers are centered around the introduction of a new definition or other mathematical or scientific concept. And as fields develop over decades, their definitions often change slowly, and in a progressive manner. Definitions tend to become more and more abstract. Theorems are generalized. Pre-existing theories or problems are proven to be equivalent. Old concepts take on new life.
If you look at any mathematical subject, and you go back more than a few decades it starts to get really difficult to read because the notation and the definitions change so much. Even the writing style and the way proofs are worded changes.
2 years ago
Anonymous
>No one reads Newton or Leibniz
False. Learn Latin so I could read those old works (it was to read Gauss's book), they are hard as frick, but damn, when you read Newton you learn how amaxing he was. Still took me a long time to understand his book, though.
2 years ago
Anonymous
>Everyone knows Maxwell's equations, but no one has read Maxwell
Those 4 equations were not formulated by Maxwell in his book, it was done by Heaviside. Maxwell's book is horrible to read, even more when you learn he use quartenions (I believe it was in 2nd edition, first edition was as just equations for x, y and z) unlike Heaviside who knew how great vectors are. And he was right, given that we use vectors in physics and not quartenions.
No not all. Math doesn't really become "outdated". Now is Euclid's work still at the forefront of modern mathematical research? Of course not, but it's by no means outdated. It's simply more elementary, and hence not at the level of contemporary research, but it's by no means outdated. In fact, much of the material in Euclid is still covered in high school geometry classes, and actually it will generally be presented in a simplified form. Calling Euclid outdated is like say high school algebra is outdated. Furthermore, modern research mathematics actually follows the same definition-axiom-theorem format pioneered by Euclid, so his presentation of the material is actually more similar to modern research mathematics than what you would see in a standard high school geometry textbook.
I would argue that Euclid is probably a better way to teach math to middle schoolers, high schoolers, and undergrads. Most math education is based on rote memorization of formulas and equations without any understanding of their logical or conceptual underpinnings. First of all, this method is extremely boring, and usually more difficult. Secondly, teaching in this way means that most math education is basically a waste of time, since any math you will encounter if you go into any STEM, or even careers in finance, economics and the social sciences, is completely different. You'll never have to memorize a formula or equation in your life. That's not what math is like when you're actually working in math or biology or economics or any other field. In the real world, math is actually both more fun and more creative than that. Instead of memorizing formulas, the emphasis will be on axioms, definitions, proofs, and theorems if you're working in a more abstract setting, and on models if you're working in a more applied setting. In either case, the main issue will not be memorizing formulas, but rather on identifying and formalizing properties of whatever you're trying to study.
ligma thread
well its served the best and still around after 2000 years. most would recommend to read Heath. or you might take a look at Hartshorne.
>formalize geometry with simple definitions, axioms and postulates.
nothing personal kid
Musk read it when he was a littling.
Parallel postulate chads rise up
anons, is it pronounced yooclid or oyclid?
The former if you're a murrican pleb, the latter is his actual name.
>the latter is his actual name.
In Greek no, in Latin and German transliterations yes. In greek the ευ is pronounced as a short e and a french u combined into one diphthong, not even close to german or latin eu. Once again europoors display their ignorance
how would one pronounce it using the lucian pronunciation?
>europoors
why the classism?
>lucian pronunciation
the lucian pronunciation is not a reconstructed pronunciation, it’s an attempt to make something that pleases as many people as possible and sounds good because he wants it to be adopted as the standard for modern people who for some reason are trying to create a modern ancient greek speaking community. his pronunciation is closer to modern greek than ancient greek. However it’s probably pronounced the same in lucian pronunciation since most of the differences between lucian and reconstructed pronunciation are in other letters and sounds. I think he uses the proper sound for upsilon and epsilon
歐幾里得
pronounced Ou chi li te, in brave land dpeech
Εὐκλείδης
>oy clay eedes
Its pronounced eh-oo--clid---es
eh oo sounds like how people in dublin say ow
F-klii-(this)
>t.greek
he's a dumbass. his proof of pons asinorum is a shining example. and the principle of 'superposition'
>tries to axiomatize geometry
>line segments join points
>no postulates saying points exist in the first place
Pretty shit system really.
Definition 1
Apointis that which has no part.
σημεῖόνἐστιν,οὗμέροςοὐθέν.
Not good enough for you? Because it is negative?
He didn't invent a single theorem. He only made more complicated and less comprehensible proofs (the ones you were given) instead of clear and simple ones (picrelated)
Probably he was one of the first entanglers of science. There is no royal path to geometry my ass (did I mention that he also was a homosexual, just as all academia is? And by academia I meant the Plato's school of pederasty from which catholic church originated to control the science to this day)
I like you.
00 = 11
Aww, my superscripts did not format properly. How sad.
Oh well, the good thing about 0^0 = 1^1 is that you can write it in different ways and it is still true.
>0^0
Do you actually understand it? I thought o^o^ is undefined.
okay, I thought you're a little crazy, but it seems to be a little more complicated:
> Zero to the power of zero, denoted by 00, is a mathematical expression with no agreed-upon value. The most common possibilities are 1 or leaving the expression undefined, with justifications existing for each, depending on context. In algebra and combinatorics, the generally agreed upon value is 00 = 1, whereas in mathematical analysis, the expression is sometimes left undefined. Computer programming languages and software also have differing ways of handling this expression.
But what is the meaning of that? It's not even nothing taken nothing times which would be 0*0 but what is it? Why is n^0 = 1? I don't understand even that, other than the graph tells that it is kinda so, but I have some dubts that the graphs are defined at that very point.
n^0 = 1 so that the rule x^a * x^b = x^{a+b} applies even when a or b is 0. Of course, if the base is 0, this doesn't really apply any guidance.
Thanks. Makes sense.
>proof by picture
and suddenly, the IQ level in this thread dropped even further
What about https://en.wikipedia.org/wiki/Translation_(geometry) don't you understand?
I dare you to show me a reddirrt thread speaking of that. Or is it your userpic and you're shocked?
That's not a proof. It's a kindergarten-level "fit-the-patterns" argument. A proof requires several things. You would have to prove that the lengths of corresponding lines are the same. You would have to prove that translation and rotation don't change anything. You would have to lay out your assumptions, i.e., Euclidean geometry and so on.
You put together colored shapes and wrote lengths at the sides, hoping everybody would just believe they're correct because everything fits so nicely.
>but the reader can easily compute for herself that all corresponding lines have the same length!
Yeah, so it's not a proof.
>You would have to prove that the lengths of corresponding lines are the same.
Why are you not supposed to do the same in this over-the-ass proof?
You do. That's an unfounded "illustration" of Euclid's proof. Euclid didn't illustrate it like that. He wrote a formal proof.
He probably did, and you probably even memorized it. But almost nobody who did cannot repeat it. I'm pretty sure Pythagoras had his proofs alright, but we'll never read it (unlest some palimpsest resurfaces) because platonic school (to which both Euclid and catholic church belonged) are known to burn the books of their opponents.
Your proof is akin to showing that the angles in a triangle add up to 180 by cutting the corners off a triangle and arranging them such that they lie in a straight line. Whilst a demonstration of the concept, the proof is not rigorous. It should instead be approached by drawing a line through C parallel to AB, then using the parallel postulate to show the angles add to 180.
The fact that this method can be abused doesn't make this method invalid. You can entertain sophistry in verbal form as well.
I don't understand which explicit translation you've used in the proof. Can you clarify and quantify, please?
They're actually allowing shit like that in math departments now in "woke" universities in progressive urban areas. Last year I graduated from the University of Washington in Seattle, which is obviously a major shitlib hub, and even in upper division, proofs-based classes like real analysis and abstract algebra, they were allowing students to submit "visual proofs" and "diagrams" for credit. Standards have really dropped a lot, especially in the last 5-10 years. When I started my undergrad back in 2016 they still had some objective standards, and we were regularly assigned graded homeworks and exams but by the time I graduated in 2021, a lot of teachers had switched to grading based on "completion" and all of our exams had become bullshit "take home" exams without no supervision or oversight. COVID was a big part of it, but the rise of "distance learning" (which is completely ineffective for actual learning) and platforms like blackboard have also played a major role, and well as the rise in woke policies that promote arbitrary grading standards.
It's not just grading either. A lot of universities are switching to admissions criteria that downplay the significance of academic credentials like GPA and SAT/GRE scores in favor of more subjective measures like legacy status, letters of rec., and extracurriculars. This is nominally intended to create a more "holistic" admissions process that places less emphasis on narrow quantitative measures of academic ability like GPA, and I completely understand those concerns, but the reality is that these new standards are not an improvement. In fact, they're making it worse, and we know that because there's plenty of data available on college admissions. When colleges downplay more objective metrics like GPA and SAT scores, it actually harms disadvantaged students, since the people with legacy status and access to extracurriculars and impressive letters of recommendation tend to come from wealthy, educated families.
A big part of this is dramatic decline in college enrollment. Making it harder isn't a good way to entice new students to enroll.
>A big part of this is dramatic decline in college enrollment.
They have pretty well made it a toxic environment for anyone who is more interested in ideas than conformity---it makes the medieval University, where you might have had to go to Church and mouth the words to some ceremony, but otherwise would explore almost everything seem an open intellectual arena.
A few years ago, almost every university required SAT/GRE scores. Now most of them have removed the requirement altogether. Some admissions FAQ pages even tell applicants explicitly not to send test scores.
I.47 was his greatest blunder, but he's still great.
>did I mention that he also was a homosexual, just as all academia is? And by academia I meant the Plato's school of pederasty from which catholic church originated to control the science to this day
Cute picture. How do I know it's correct?
There is not much info about who Euclid was but most scholars agree that he compiled existing work instead of claiming the theorems as original.
The books are reportedly the most printed publication ever.
The books pissed of Bertrand and exposed him as a brainlet.
>whiney crybaby nerd voice: Can we have a thread about Euclid?
I mean, they're interesting from a math history perspective and there's a reason it's been printed so much.
I know the Greeks basically threw out everything prior to Euclid's texts because they liked his explanations more. He didn't really theorize anything himself, but he's basically the first math textbook author and really cemented the concept of a textbook into STEM. At some level, the textbook surpasses and becomes more fundamental than the original work which is why most people don't really waste time reading original work in STEM unless it's cutting edge.
> most people don't really waste time reading original work in STEM because they're too lazy to read more accurate primary sources and are content with the soundbite version which has been filtered for them and made politically correct by an industry approved textbook author
oh yeah, reading the primary source is a total waste of time, is that why the science geniuses keep on repeating the same mistakes over and over again?
>i'm too smart to read primary sources, i'm so smart i know whats in them without reading them
Not really the issue in mathematics, where review papers and textbooks can contribute by producing clearer, more elegant expositions of the same results than the original research paper.
This. It's precisely the reason Euclid blew up in popularity. He btfoed the competition, not because he came up with original theories, but because his formating and explanations and connections were so much more clear and clearly laid out that you didn't NEED the original work. You could just read Euclid instead. Again, this is common in math and physics. I know very few people who read the original papers unless they're cutting edge shit or they're interested in them from a historical perspective.
Actually a lot of mathematical progress is really just about more explicitly identifying important results and connecting them together. Usually when a new field is emerging, many of the problems and basic results have been circulating for decades, but nobody put them together in a systematic way. Calculus is a great example of this, since there were results anticipating it's development for centuries, but nobody was able to connect it all together. People were researching sequences and sums and infinite series and rates of change and interpolation and stuff like that since ancient times, and it really picked up during the renaissance. What Newton and Leibniz did was just connect it all together.
The same thing also happened with basic group theory/modular arithmetic, logic, and non-Euclidean geometry. There were bits and pieces of all these subjects scattered here and there, but nobody pieced them together.
Even modern mathematical physics and topology and algebraic geometry and differential geometry are still studying the same things that Euclid was 2500 years ago. Over simplifying of course, but mathematical physics is basically the study of circles and spheres, since that's what a Lie Group is. We just developed a much more organized and systematic language for doing so, but the objects of study are still the same. Things have just gotten more systematic.
>study of circles and spheres
These were the hardest shapes for me to internally compute. Anything with edges and verticies was really intuitive.
Decoding this image has been difficult, only partially "seen". Most other similar pictures are fairly easy.
I 100% agree, but I would go a step further. Even these leaders are not read anymore. No one reads Newton or Leibniz, they read calculus textbooks ultimately derived from these works, but basically no one reads the original texts.
Everyone knows Maxwell's equations, but no one has read Maxwell. Everyone know Fourier expansion, but no one reads him. Euler is like the only mathematician that I sometimes see read.
Again, STEM is very unique in this respect. Transfer of knowledge of concepts do not require the original papers to understand, in fact the original papers could be more confusing than anything.
All other fields you almost feel obligated to read the original texts because a textbook is full of many interpretations.
Yes, this is a good point, and I think the way science is driven by research papers is probably one of the main drivers of the phenomenon I was talking about. In the body of research papers that are published over the years, you see a lot of the organizational development that I was talking about. A lot of papers are centered around the introduction of a new definition or other mathematical or scientific concept. And as fields develop over decades, their definitions often change slowly, and in a progressive manner. Definitions tend to become more and more abstract. Theorems are generalized. Pre-existing theories or problems are proven to be equivalent. Old concepts take on new life.
If you look at any mathematical subject, and you go back more than a few decades it starts to get really difficult to read because the notation and the definitions change so much. Even the writing style and the way proofs are worded changes.
>No one reads Newton or Leibniz
False. Learn Latin so I could read those old works (it was to read Gauss's book), they are hard as frick, but damn, when you read Newton you learn how amaxing he was. Still took me a long time to understand his book, though.
>Everyone knows Maxwell's equations, but no one has read Maxwell
Those 4 equations were not formulated by Maxwell in his book, it was done by Heaviside. Maxwell's book is horrible to read, even more when you learn he use quartenions (I believe it was in 2nd edition, first edition was as just equations for x, y and z) unlike Heaviside who knew how great vectors are. And he was right, given that we use vectors in physics and not quartenions.
Aren't his books outdated as frick?
kind of
But now they come in all the other forms with advanced set of functions.
I'm yet to see a good audio version of a science text book
No not all. Math doesn't really become "outdated". Now is Euclid's work still at the forefront of modern mathematical research? Of course not, but it's by no means outdated. It's simply more elementary, and hence not at the level of contemporary research, but it's by no means outdated. In fact, much of the material in Euclid is still covered in high school geometry classes, and actually it will generally be presented in a simplified form. Calling Euclid outdated is like say high school algebra is outdated. Furthermore, modern research mathematics actually follows the same definition-axiom-theorem format pioneered by Euclid, so his presentation of the material is actually more similar to modern research mathematics than what you would see in a standard high school geometry textbook.
I would argue that Euclid is probably a better way to teach math to middle schoolers, high schoolers, and undergrads. Most math education is based on rote memorization of formulas and equations without any understanding of their logical or conceptual underpinnings. First of all, this method is extremely boring, and usually more difficult. Secondly, teaching in this way means that most math education is basically a waste of time, since any math you will encounter if you go into any STEM, or even careers in finance, economics and the social sciences, is completely different. You'll never have to memorize a formula or equation in your life. That's not what math is like when you're actually working in math or biology or economics or any other field. In the real world, math is actually both more fun and more creative than that. Instead of memorizing formulas, the emphasis will be on axioms, definitions, proofs, and theorems if you're working in a more abstract setting, and on models if you're working in a more applied setting. In either case, the main issue will not be memorizing formulas, but rather on identifying and formalizing properties of whatever you're trying to study.
Eh-ooh-clay-desu.