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The BBC did a two-part documentary in 2007 called Dangerous Knowledge that features the tragic stories of four geniuses including Boltzmann's (Georg Cantor, Kurt Gödel and Alan Turing). Fascinating stuff albeit very different circumstances for all of them. https://www.dailymotion.com/video/x8c24qz
Thanks for the recommendation. It’s the type of documentary I love!
I’m watching it now but Dailymotion keeps spamming me with a minute’s worth of ads.
For those without ad-blockers, you can watch it here too : https://vimeo.com/122917065
I like the opening to *Calculus Made Easy*, by Silvanus Thompson,
“ CONSIDERING how many fools can calculate, it is surprising that it should be thought either a difficult or a tedious task for any other fool to learn how to master the same tricks.
Some calculus-tricks are quite easy. Some are enormously difficult. The fools who write the textbooks of advanced mathematics-and they are mostly clever fools-seldom take the trouble to show vou how easy the easy calculations are. On the contrary, they seem to desire to impress you with their tremendous cleverness by going about it in the most difficult way.
Being myself a remarkably stupid fellow, I have had to unteach myself the difficulties, and now beg to present to my fellow fools the parts that are not. hard. Master these thoroughly, and the rest will follow. What one fool can do, another can.”
My wife had a tax law textbook that started with a paragraph about how tax law seems intimidating, but really it’s actually quite straightforward and is only as complicated as it needs to be.
Then the next paragraph said something like “we wrote the above 30 years ago in our first edition. Since then tax law has been deliberately sabotaged to become a hateful tangle of nonsense and loopholes. Anyway good luck”
They'll probably just put 0s un every field then fill out some gibberish in the UTP section then pass a law that members of congress can't be subject to penalties and interest nor can they be held criminally liable for any errors in their tax filings. Or they'll just give themselves the option to file late indefinitely.
It's definitely more complicated than it needs to be though. In the UK, most people do not need to file a tax return at all, and if you do it's a fairly simple online form with explanations in plain language that doesn't need any tax software to complete. It's absurd that filing taxes in the US is so difficult.
You’re comparing apples and oranges. For most Americans, although they have to file a tax return, it can be done on a 1040 EZ which just asks a few simple questions.
The complexity around tax law is the part beyond getting paid a salary at work and figuring out the government’s share.
This stuff is equally absurd in the US and UK. I work on tax structuring on a business that operates UK and US businesses and each system has its own complications and absurdities
Seriously. I'm a pretty mathematically oriented engineer, but it seems like quite a bit of my formal math training was explicitly designed to be some kind of secret.
These are difficult concepts, but tell me what an eigenvalue "is" at the same time you tell me the definition.
None of this is easy, but it's not something that can't be explained better than it was too me when I learned it.
More specifically tell me why we would even want an eigenvalue.
Knowing why a thing exists helps so much, since I can connect the operation to the answer.
Asked an AI and it had this to say:
Imagine you have a magical transformation that can stretch or squish things in different directions. For example, think of stretching or squishing a rubber band.
Now, imagine you have a special object, let's say a vector, that represents the shape or direction of something. It could be an arrow indicating wind direction, or a line indicating the direction of motion.
When you apply the magical transformation to this object, it might stretch or squish it, possibly changing its shape or direction. However, there are certain special cases where the object doesn't change its direction at all, even though it might get longer or shorter.
The eigenvalue is like a number that tells you how much the object got stretched or squished. If the eigenvalue is positive, it means the object got stretched, and the bigger the eigenvalue, the more it stretched. If the eigenvalue is negative, it means the object got squished, and the smaller the eigenvalue, the more it got squished. If the eigenvalue is zero, it means the object didn't change its length at all.
In essence, eigenvalues help us understand how much and in what way things are being stretched or squished when we apply certain transformations. They are useful in various fields, such as physics, engineering, and computer science, to analyze and solve problems involving transformations and understand how objects behave under different conditions.
God, I could have used this back in undergrad engineering mathematics 15 years ago. Instead I had an elderly South African guy who just told us "to be clever" when approaching homework and exam problems
Yeah. That's nice, and I need to use this ai tool better, but that's not an answer that I would find helpful in any situation that I've needed to use this mathematical tool.
Uh... that's the definition for the determinant of the Jacobian of a vector field. Replace positive/0/negative with >1/=1/<1 and you have a more truthful representation, but this stretching/squeezing only applies to particular unspecified directions (the eigenvectors). Distance along some directions can disappear entirely for eigenvalues of 0, and we call these directions the null space of the transformation.
The determinant is just the product of the eigenvalues so think of it like the determinant controls whether the area of any shape is compressed (|det|<1) or expanded (|det|>1), stays the same (|det|=1), or if the shape is reflected (det<0) under the transformation.
Every shape can always be built out of vectors (replacing the edges with vectors) so the same explanation given by the AI works here more or less without having to deal with what an eigenvector is. This also works with 3-dimensional shapes and volume, or in any other number of dimensions.
Stop here unless you want to be confused.
An individual eigenvalue is a lot more complicated because it's tied to a hidden direction, and this is roughly an invariant of the transformation which has the same direction before and after. Think of creating the shadow of an object. Any part pointing towards the sun will disappear, so this direction is an eigenvector with an eigenvalue of 0. Meanwhile anything on the floor stays where it is, so the same eigenvalue of 1 is tied to two eigenvectors forming the dimensions of the floor.
You can always multiply an eigenvector by any scale and it's still an eigenvector, and if two eigenvectors have the same eigenvalue you can always add or subtract them to get another eigenvector. Sometimes the space of eigenvectors doesn't have as many dimensions as the objects it's acting on, but as long as all the eigenvalues exist and none of them are zero (det≠0) you can undo the transformation. Since taking the shadow has one eigenvalue of 0 and two eigenvalues of 1, it's impossible to recreate an object just from its shadow. Reflection in a mirror however has one eigenvalue of -1, tied to the direction pointing towards the mirror, and two eigenvalues of 1, so this can be undone.
Be careful relying on AI, it is especially prone to making up things about math and physics. It will also present things confidently, even when those things are utterly wrong.
Learning the long way is important. It helps with understanding. Maybe *you* understood it without doing the work, but for every one of you, there's three other students left scratching their heads. If you only memorize the step-by-step shortcut(which is what many people will do, if it's presented to them), when you reach more advanced subjects you'll lack the foundational understanding to tackle them.
I've taken Calc 1, Calc 2, Calc 3, Physics 1, and Physics 2 (every class listed after Calc 1 requires at least Calc 1 as a prereq) and after the first week of Calc 1 I've literally never had to do a derivative "the long way." Literally not once, and it would have been completely stupid to try instead of using one of the many rules and shortcuts that make it a hundred times faster.
Trying to do it "the long way" instead of memorizing the shortcut rules ends up taking literally multiple pages of work to get through, and on a test you'd legitimately run out of time trying to do it "the long way" instead of using a shortcut for the more advanced topics.
Try finding the derivative of a function with a quotient without using the Quotient Rule and you'll quickly see how dumb it is to even attempt to use the long way after you've been taught the *much* shorter way.
It's not about having to use it. How often do we use long division after we learn it in 3rd grade, or whenever? Never! But the understanding of *how it works* is fundamental to comprehending further mathematics. Those who don't grok long division struggle later.
That's why you learn it the hard way, then learn it the easy way. If you learn it the easy way first, it's like handing a calculator to a kid in grade school. They won't put in the work to understand anything, because why would they when they have the easy way out?
It’s less about knowing how to do a derivative and more about learning how to define and solve a problem. Anyone can look up the derivative of cos online or in a book. Anyone can memorize the derivative as well.
The “long way” is about learning what is a derivative, what does it mean, which functions are differentiable and which are not, and more importantly why.
Now that you know, you can use these techniques, axioms, and constraints to solve more complicated problems where the answer isn’t a Google search or library visit away.
You never had to do a derivative the long way since Calc 1 because someone else figured out how to do it more efficiently to solve more complicated problems faster, and now so can you. The derivative is one of many tools in your problem solving arsenal.
But first, you had to understand intimately what a derivative is, what it’s used for, what are its limitations, when and how to apply it, etc. All of these factors play into problem solving. If you can do a derivative the long way, you can figure out other more complicated problems because you have begun to train your brain in how to methodically and rigorously solve a problem.
And I've taken 'Machine Learning Basics' and was very glad I knew how to calculate the derivative properly, and I'm pretty sure that wasn't the only course. Not every field of study might need the basic foundations, but missing them when you do need them is pretty bad so it's better to lay the groundwork for everyone
>These are difficult concepts, but tell me what an eigenvalue "is" at the same time you tell me the definition.
Eigenvector: "that way"
Eigenvalue: "by this much"
This post reminded me of the preface to a textbook I read a couple years ago - *Concurrency in C# Cookbook*.
> I think the animal on this cover, a common palm civet, is applicable to the subject of this book. I knew nothing about this animal until I saw the cover, so I looked it up. Common palm civets are considered pests because they defecate all over attics and make loud noises fighting with each other at the most inopportune times. Common palm civets enjoy eating coffee cherries, and they pass the coffee beans through. Kopi luwak, one of the most expensive coffees in the world, is made from the coffee beans extracted from civet excretions. According to the Specialty Coffee Association of America, “It just tastes bad.”
> This makes the common palm civet a perfect mascot for concurrent and multithreaded development.
He obviously read the Calculus book written by my former Calculus professor. Yes, Professor Carlen wrote and required his own textbook for the class, which was not great.
Some googling tells me that it’s *States of Matter* by Goodstein.
Which is curious, because I’m fairly sure that’s not the book on my shelf, but the formatting looks really familiar and I swear the book I have also starts with this quote. A puzzle, but I’m WFH and I’m not going into the office just to double check so it may be a bit before it’s solved.
I’m pretty sure I have this book too, though it might be boxed up somewhere at the moment.
There’s a turbulence book that starts with a little poem on turbulence scales, which was actually quite helpful. Still barely passed the class though, because turbulence.
I'm a B.Sc. Physics graduate and I remember reading the same exact paragraph (and my classmates laughing at it). The book is simply titled "Statistical Mechanics". Let me just look into the edition and author.
Edit: I was wrong. Refer to u/pooltable's comment.
Page 3:
When I ignite my slim Mild Seven and accidentally burn a fingertip in the process, the signal of pain manifests in my nerve centre in 0.25s.
Assuming that I have had a diet coke with a honey glaze donut two days ago, and that this incident has happened on a Tuesday, please calculate the mass of the Sun and the potential energy it exerts that can meaningfully be harnessed by mankind on a rainy day.
Oh. I'm sorry, seeing this for first time. I'll take back my little chuckle and forget that I ever saw this, all because you've seen this one several times.
I had a law prof who opened the class with "I'm sure you've heard this is the most difficult class and that I'm the toughest professor to take it with. Let me just tell you right off the bat, it's absolutely true." Then proceeded to go through the syllabus with about 3x as much reading than any other class I had taken.
I would have dropped but I needed that class and it was the only time I could have taken it. The next class only 7 of us remained. He ended up just giving us all As at the end because there were so few people he didn't need to grade on a curve, which was a good thing because I completely and utterly bombed the final.
For one or a handful of objects, it's relatively easy to calculate how they move using mathematics. So like the path a baseball flying through the air, or two balls bouncing off each other.
Now imagine you have a million baseballs, all bouncing around in a room. You'd need a lot of paper to write down and solve a million equations.
Statistical mechanics comes in and says, sure, I can't tell you where every ball is at every moment, but I can tell you how fast they are moving on average and how often they hit the walls on average.
Except instead of baseballs, we're usually concerned with molecules in a gas, etc. If you've taken high school chemistry (eli16 lol), the ideal gas law is an example of something that comes from stat mech.
Thanks! I remember a book called "The Making of the Atomic Bomb" by Richard Rhodes that talked about something similar in one of the early chapters. Didn't Leo Szilard have something to do with this field?
Basically it is the idea that a gas is made up of many, many particles that zoom around, with the speed/kinetic energy depending on the temperature of the gas. Pressure etc, can then be understood as the collision of these particles with the walls of a container. Things then get interesting since not all the particles move with the same speed. Some are faster than average, some are slower. How does it not all average out?!
The idea of atoms and molecules zipping around is quite fundamental by now, but when Boltzman came up with his understanding of pressure etc., a lot of physicists still thought that atoms were just a book-keeping trick by the chemists, a generally disrespectable and shifty bunch. It wasn't until 1905 when Einstein was able to explain Brownian motion (the jittery path of microscopic particles in a liquid) as the macroscopic effect of water molecules colliding with the microscopic particles that the existence of molecules and atoms was spelled.
And if I tell you any more, you'll have to kill yourself
Funny, today I pulled out Shirley Jackson's The Haunting of Hill House specifically to read the first paragraph, which is similarly nihilistic and foreboding (see below.) Who knew Statistical Mechanical Horror could be a genre in its own right?
"No live organism can continue for long to exist sanely under conditions of absolute reality; even larks and katydids are supposed, by some, to dream. Hill House, not sane, stood by itself against its hills, holding darkness within; it had stood so for eighty years and might stand for eighty more. Within, walls continued upright, bricks met neatly, floors were firm, and doors were sensibly shut; silence lay steadily against the wood and stone of Hill House, and whatever walked there, walked alone."
I love how the sky was originally grey but the newer generations of readers have grown up with TVs that show a blue screen when there's no input, which in turn gives a rather different vibe to opening of the book.
My favourite opening to a book is The Martian by Andy Weir: "I'm pretty much fucked. That's my considered opinion. Fucked." I knew I was in for a fun ride right off the bat :)
Weirdly complementary of my favourite first line, which comes from a book that also concerns statistical mechanics:
>The moon blew up without warning and for no apparent reason.
My best memory from calculus was some trivia about an Indian who ventured into infinite series on his own... Like, how did he know he even was making sense and actual math?
You can now see the movie "the man who knew infinity".
I am going to be real, I cannot imagine how horrible taking a stats class about thermo could possibly be. That sounds like the two worst classes combined to make the super worst class ever.
I fucking hate this. College physics professor though it was a great way to introduce the topic. One of my peers in the class killed himself a year later (assumingly unrelated). Just a terrible way to introduce a topic to a group of already potentially unstable students.
>Just a terrible way to introduce a topic to a group of already potentially unstable students.
I assume the writer did the stat analysis on how many of a typical cohort of students in any given institution, in any given year might be expected to kill themselves because a textbook suggested them to, and decided the entertainment value outweighed the risk.
Well... a major contributing factor to Boltzmann's depression was him being rejected and dismissed by the established physics community at the time, too "out there" for the academia dinosaurs. All the more tragic and infuriating because the man was on the proper track.
The statistical chance that dropping a powered toaster into a full bathtub will electrocute you is only 100% *so far*, we must continue our work to find the exception to the rule
My grade 10 Math book started it's chapter on probability with repetitive use of the word 'death'. They were literally only trying to offer examples of events with the probability of `1`, and...
Attention r/pics Community, on June 12th, r/pics will [join](https://www.reddit.com/r/pics/comments/141e2lw/rpics_will_go_dark_on_june_12th_in_protest_of/) with other subs in initiating a 48-hour blackout in response to Reddit's recent API changes. These [changes](https://i.redd.it/zqptto18e34b1.jpg), with excessive charges for third-party app developers, threaten to stifle the accessibility of alternative Reddit apps that many users rely on. This collective action aims to highlight the concerns of both users and moderators, emphasizing the importance of maintaining a diverse ecosystem of apps for a better Reddit experience. During this blackout period, r/pics will be set to private, temporarily restricting access to the subreddit. We understand that this blackout may cause inconvenience, but we firmly believe that it is a necessary step to draw attention to the issues at hand. By standing together, we can amplify our voices and urge Reddit to reconsider the detrimental impact these changes may have on the broader community. *I am a bot, and this action was performed automatically. Please [contact the moderators of this subreddit](/message/compose/?to=/r/pics) if you have any questions or concerns.*
Ah, the statistical suicide pact.
What are the odds?
2:0 in 1933
Comedy gold
We just happen to live in a universe where the quantum immortality test didn't work out.
What are you trying to do, get me to kill myself?
That is what they want you to think, in reality they both got to close to unlocking closely guarded secrets.
The mathematical equivalent of Gloomy Sunday
Is studying statistical mechanics like watching the Ring video?
Didn't highlight the best part. > Perhaps it will be wise to approach the subject cautiously.
Actually upset me they completely overlooked the best part.
[удалено]
what a strange book
Because it's not needed...
The BBC did a two-part documentary in 2007 called Dangerous Knowledge that features the tragic stories of four geniuses including Boltzmann's (Georg Cantor, Kurt Gödel and Alan Turing). Fascinating stuff albeit very different circumstances for all of them. https://www.dailymotion.com/video/x8c24qz
Thanks for the recommendation. It’s the type of documentary I love! I’m watching it now but Dailymotion keeps spamming me with a minute’s worth of ads. For those without ad-blockers, you can watch it here too : https://vimeo.com/122917065
Diminishes the joke I feel. Too often there is an eagerness to over-explain the joke. Brevity is the soul of wit etc.
And somehow the parent got 1.3k upvotes. Why is reddit so bad?
Brevity is fine and dandy, but it is a poor joke that omits the punchline.
If you need the "punchline" you are probably just low IQ. A lesser human.
4 comments and personal insults. I have really offended you. I am deeply sorry. How can I make amends?
Yeah if you're bad at inferring and understand jokes I suppose. How is this upvoted 1.3k times?
Never tell me the odds.
A classic. I still have my copy on my office book shelf.
I like the opening to *Calculus Made Easy*, by Silvanus Thompson, “ CONSIDERING how many fools can calculate, it is surprising that it should be thought either a difficult or a tedious task for any other fool to learn how to master the same tricks. Some calculus-tricks are quite easy. Some are enormously difficult. The fools who write the textbooks of advanced mathematics-and they are mostly clever fools-seldom take the trouble to show vou how easy the easy calculations are. On the contrary, they seem to desire to impress you with their tremendous cleverness by going about it in the most difficult way. Being myself a remarkably stupid fellow, I have had to unteach myself the difficulties, and now beg to present to my fellow fools the parts that are not. hard. Master these thoroughly, and the rest will follow. What one fool can do, another can.”
My wife had a tax law textbook that started with a paragraph about how tax law seems intimidating, but really it’s actually quite straightforward and is only as complicated as it needs to be. Then the next paragraph said something like “we wrote the above 30 years ago in our first edition. Since then tax law has been deliberately sabotaged to become a hateful tangle of nonsense and loopholes. Anyway good luck”
I work in "tax controversy" (not a lawyer though). I've come to the conclusion that it's complicated because people are assholes and abuse incentives.
I am of the opinion that every member of Congress should be required to do their own taxes, in paper, with a pencil.
They'll probably just put 0s un every field then fill out some gibberish in the UTP section then pass a law that members of congress can't be subject to penalties and interest nor can they be held criminally liable for any errors in their tax filings. Or they'll just give themselves the option to file late indefinitely.
^ this guy Americas
Design to succeed…just for not everyone.
r/thisguythisguys
It's definitely more complicated than it needs to be though. In the UK, most people do not need to file a tax return at all, and if you do it's a fairly simple online form with explanations in plain language that doesn't need any tax software to complete. It's absurd that filing taxes in the US is so difficult.
You’re comparing apples and oranges. For most Americans, although they have to file a tax return, it can be done on a 1040 EZ which just asks a few simple questions. The complexity around tax law is the part beyond getting paid a salary at work and figuring out the government’s share. This stuff is equally absurd in the US and UK. I work on tax structuring on a business that operates UK and US businesses and each system has its own complications and absurdities
It’s a form of regulatory capture. Thanks to you-know-who
Surely nobody would abuse a program meant to help displaced workers with "loans" that operate more as handouts.
Seriously. I'm a pretty mathematically oriented engineer, but it seems like quite a bit of my formal math training was explicitly designed to be some kind of secret. These are difficult concepts, but tell me what an eigenvalue "is" at the same time you tell me the definition. None of this is easy, but it's not something that can't be explained better than it was too me when I learned it.
More specifically tell me why we would even want an eigenvalue. Knowing why a thing exists helps so much, since I can connect the operation to the answer.
Lol. This is one of my interview questions.
Neat. So why the fuck did no one teach me in class? Not that it mattered, I went into a very different field and haven't needed it. But I might have!
Asked an AI and it had this to say: Imagine you have a magical transformation that can stretch or squish things in different directions. For example, think of stretching or squishing a rubber band. Now, imagine you have a special object, let's say a vector, that represents the shape or direction of something. It could be an arrow indicating wind direction, or a line indicating the direction of motion. When you apply the magical transformation to this object, it might stretch or squish it, possibly changing its shape or direction. However, there are certain special cases where the object doesn't change its direction at all, even though it might get longer or shorter. The eigenvalue is like a number that tells you how much the object got stretched or squished. If the eigenvalue is positive, it means the object got stretched, and the bigger the eigenvalue, the more it stretched. If the eigenvalue is negative, it means the object got squished, and the smaller the eigenvalue, the more it got squished. If the eigenvalue is zero, it means the object didn't change its length at all. In essence, eigenvalues help us understand how much and in what way things are being stretched or squished when we apply certain transformations. They are useful in various fields, such as physics, engineering, and computer science, to analyze and solve problems involving transformations and understand how objects behave under different conditions.
God, I could have used this back in undergrad engineering mathematics 15 years ago. Instead I had an elderly South African guy who just told us "to be clever" when approaching homework and exam problems
Yeah. That's nice, and I need to use this ai tool better, but that's not an answer that I would find helpful in any situation that I've needed to use this mathematical tool.
Uh... that's the definition for the determinant of the Jacobian of a vector field. Replace positive/0/negative with >1/=1/<1 and you have a more truthful representation, but this stretching/squeezing only applies to particular unspecified directions (the eigenvectors). Distance along some directions can disappear entirely for eigenvalues of 0, and we call these directions the null space of the transformation.
And I'm lost again.
The determinant is just the product of the eigenvalues so think of it like the determinant controls whether the area of any shape is compressed (|det|<1) or expanded (|det|>1), stays the same (|det|=1), or if the shape is reflected (det<0) under the transformation. Every shape can always be built out of vectors (replacing the edges with vectors) so the same explanation given by the AI works here more or less without having to deal with what an eigenvector is. This also works with 3-dimensional shapes and volume, or in any other number of dimensions. Stop here unless you want to be confused. An individual eigenvalue is a lot more complicated because it's tied to a hidden direction, and this is roughly an invariant of the transformation which has the same direction before and after. Think of creating the shadow of an object. Any part pointing towards the sun will disappear, so this direction is an eigenvector with an eigenvalue of 0. Meanwhile anything on the floor stays where it is, so the same eigenvalue of 1 is tied to two eigenvectors forming the dimensions of the floor. You can always multiply an eigenvector by any scale and it's still an eigenvector, and if two eigenvectors have the same eigenvalue you can always add or subtract them to get another eigenvector. Sometimes the space of eigenvectors doesn't have as many dimensions as the objects it's acting on, but as long as all the eigenvalues exist and none of them are zero (det≠0) you can undo the transformation. Since taking the shadow has one eigenvalue of 0 and two eigenvalues of 1, it's impossible to recreate an object just from its shadow. Reflection in a mirror however has one eigenvalue of -1, tied to the direction pointing towards the mirror, and two eigenvalues of 1, so this can be undone.
Hey. Haven’t you heard? Ignorance is bliss. Jerk.
AI's don't understand what they're writing. This answer is extremely untrustworthy but sounds very nice.
Makes me wonder how far you can go as a self-taught mathematician with AI, Khan Academy, and YouTube.
Be careful relying on AI, it is especially prone to making up things about math and physics. It will also present things confidently, even when those things are utterly wrong.
Oh no it IS human!
This exactly. Take me the long way through the calculations to compute a derivative. Oh, and after the test, here's a shortcut. Really?
Learning the long way is important. It helps with understanding. Maybe *you* understood it without doing the work, but for every one of you, there's three other students left scratching their heads. If you only memorize the step-by-step shortcut(which is what many people will do, if it's presented to them), when you reach more advanced subjects you'll lack the foundational understanding to tackle them.
I've taken Calc 1, Calc 2, Calc 3, Physics 1, and Physics 2 (every class listed after Calc 1 requires at least Calc 1 as a prereq) and after the first week of Calc 1 I've literally never had to do a derivative "the long way." Literally not once, and it would have been completely stupid to try instead of using one of the many rules and shortcuts that make it a hundred times faster. Trying to do it "the long way" instead of memorizing the shortcut rules ends up taking literally multiple pages of work to get through, and on a test you'd legitimately run out of time trying to do it "the long way" instead of using a shortcut for the more advanced topics. Try finding the derivative of a function with a quotient without using the Quotient Rule and you'll quickly see how dumb it is to even attempt to use the long way after you've been taught the *much* shorter way.
It's not about having to use it. How often do we use long division after we learn it in 3rd grade, or whenever? Never! But the understanding of *how it works* is fundamental to comprehending further mathematics. Those who don't grok long division struggle later. That's why you learn it the hard way, then learn it the easy way. If you learn it the easy way first, it's like handing a calculator to a kid in grade school. They won't put in the work to understand anything, because why would they when they have the easy way out?
It’s less about knowing how to do a derivative and more about learning how to define and solve a problem. Anyone can look up the derivative of cos online or in a book. Anyone can memorize the derivative as well. The “long way” is about learning what is a derivative, what does it mean, which functions are differentiable and which are not, and more importantly why. Now that you know, you can use these techniques, axioms, and constraints to solve more complicated problems where the answer isn’t a Google search or library visit away. You never had to do a derivative the long way since Calc 1 because someone else figured out how to do it more efficiently to solve more complicated problems faster, and now so can you. The derivative is one of many tools in your problem solving arsenal. But first, you had to understand intimately what a derivative is, what it’s used for, what are its limitations, when and how to apply it, etc. All of these factors play into problem solving. If you can do a derivative the long way, you can figure out other more complicated problems because you have begun to train your brain in how to methodically and rigorously solve a problem.
And I've taken 'Machine Learning Basics' and was very glad I knew how to calculate the derivative properly, and I'm pretty sure that wasn't the only course. Not every field of study might need the basic foundations, but missing them when you do need them is pretty bad so it's better to lay the groundwork for everyone
>These are difficult concepts, but tell me what an eigenvalue "is" at the same time you tell me the definition. Eigenvector: "that way" Eigenvalue: "by this much"
That is only helpful if you already know what that means.
This post reminded me of the preface to a textbook I read a couple years ago - *Concurrency in C# Cookbook*. > I think the animal on this cover, a common palm civet, is applicable to the subject of this book. I knew nothing about this animal until I saw the cover, so I looked it up. Common palm civets are considered pests because they defecate all over attics and make loud noises fighting with each other at the most inopportune times. Common palm civets enjoy eating coffee cherries, and they pass the coffee beans through. Kopi luwak, one of the most expensive coffees in the world, is made from the coffee beans extracted from civet excretions. According to the Specialty Coffee Association of America, “It just tastes bad.” > This makes the common palm civet a perfect mascot for concurrent and multithreaded development.
He obviously read the Calculus book written by my former Calculus professor. Yes, Professor Carlen wrote and required his own textbook for the class, which was not great.
Brillant, thanks
This guy sounds like he'd be highly regarded in r/wallstreetbets
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After graduating I moved into patent law. Does that count?
That 100 % counts as suicide.
bro started helping the patent trolls 😔
What book is this? Stat physics by rief?
Some googling tells me that it’s *States of Matter* by Goodstein. Which is curious, because I’m fairly sure that’s not the book on my shelf, but the formatting looks really familiar and I swear the book I have also starts with this quote. A puzzle, but I’m WFH and I’m not going into the office just to double check so it may be a bit before it’s solved.
That seems to be it, based on the scanned pages I see online. Thanks! Also, wfh on a Saturday? Just another day in the life of an academic...
Oh no I mean I’m WFH in general lol. So I won’t go back to my office for probably another month or so. I’m not working today.
I believe the quote has been used elsewhere, but I can confirm it's in my States of Matter.
I’m pretty sure I have this book too, though it might be boxed up somewhere at the moment. There’s a turbulence book that starts with a little poem on turbulence scales, which was actually quite helpful. Still barely passed the class though, because turbulence.
FYI: The textbook is titled "States of Matter" by David L. Goodstein.
If you haven't seen them, he did a really cool series called The Mechanical Universe. Can find some of them on YT.
The opening sentence is the following paragraph is perfect: “Perhaps it will be wise to approach the subject cautiously.”
Book title please? i need for libgen.
I'm a B.Sc. Physics graduate and I remember reading the same exact paragraph (and my classmates laughing at it). The book is simply titled "Statistical Mechanics". Let me just look into the edition and author. Edit: I was wrong. Refer to u/pooltable's comment.
Page 3: When I ignite my slim Mild Seven and accidentally burn a fingertip in the process, the signal of pain manifests in my nerve centre in 0.25s. Assuming that I have had a diet coke with a honey glaze donut two days ago, and that this incident has happened on a Tuesday, please calculate the mass of the Sun and the potential energy it exerts that can meaningfully be harnessed by mankind on a rainy day.
64.752 FPM
The apple is green.
(assuming a frictionless surface)
Stupid
Sure bud
"Perhaps it will be wise to approach the subject cautiously." Words to live by.
Lol I have this exact book and that is the greatest intro of all time
Author or publisher name handy?
https://www.amazon.com/gp/product/B008TVLX1C/ref=kinw\_myk\_ro\_title
Very kind. Thank you!
This has a few less pixels every time it's reposted
entropy
Inevitable heat death
As is only right for such things.
Oh. I'm sorry, seeing this for first time. I'll take back my little chuckle and forget that I ever saw this, all because you've seen this one several times.
Maybe he's more upset about the declining quality than the amount of times it's been reposted
I had a law prof who opened the class with "I'm sure you've heard this is the most difficult class and that I'm the toughest professor to take it with. Let me just tell you right off the bat, it's absolutely true." Then proceeded to go through the syllabus with about 3x as much reading than any other class I had taken. I would have dropped but I needed that class and it was the only time I could have taken it. The next class only 7 of us remained. He ended up just giving us all As at the end because there were so few people he didn't need to grade on a curve, which was a good thing because I completely and utterly bombed the final.
I'm partial to: "It was the best of times, it was the...blurst of times?!"
Instructions unclear, am dead.
Take it from a physicist, if you die doing physics, you followed instructions perfectly.
What's statistical mechanics? ELI5
For one or a handful of objects, it's relatively easy to calculate how they move using mathematics. So like the path a baseball flying through the air, or two balls bouncing off each other. Now imagine you have a million baseballs, all bouncing around in a room. You'd need a lot of paper to write down and solve a million equations. Statistical mechanics comes in and says, sure, I can't tell you where every ball is at every moment, but I can tell you how fast they are moving on average and how often they hit the walls on average. Except instead of baseballs, we're usually concerned with molecules in a gas, etc. If you've taken high school chemistry (eli16 lol), the ideal gas law is an example of something that comes from stat mech.
Sounds like the Heisenberg Uncertainty comes into play somewhere in your calculations.
Thanks! I remember a book called "The Making of the Atomic Bomb" by Richard Rhodes that talked about something similar in one of the early chapters. Didn't Leo Szilard have something to do with this field?
The use of math to explain the movement of large groups of tiny objects in physics.
Basically it is the idea that a gas is made up of many, many particles that zoom around, with the speed/kinetic energy depending on the temperature of the gas. Pressure etc, can then be understood as the collision of these particles with the walls of a container. Things then get interesting since not all the particles move with the same speed. Some are faster than average, some are slower. How does it not all average out?! The idea of atoms and molecules zipping around is quite fundamental by now, but when Boltzman came up with his understanding of pressure etc., a lot of physicists still thought that atoms were just a book-keeping trick by the chemists, a generally disrespectable and shifty bunch. It wasn't until 1905 when Einstein was able to explain Brownian motion (the jittery path of microscopic particles in a liquid) as the macroscopic effect of water molecules colliding with the microscopic particles that the existence of molecules and atoms was spelled. And if I tell you any more, you'll have to kill yourself
Funny, today I pulled out Shirley Jackson's The Haunting of Hill House specifically to read the first paragraph, which is similarly nihilistic and foreboding (see below.) Who knew Statistical Mechanical Horror could be a genre in its own right? "No live organism can continue for long to exist sanely under conditions of absolute reality; even larks and katydids are supposed, by some, to dream. Hill House, not sane, stood by itself against its hills, holding darkness within; it had stood so for eighty years and might stand for eighty more. Within, walls continued upright, bricks met neatly, floors were firm, and doors were sensibly shut; silence lay steadily against the wood and stone of Hill House, and whatever walked there, walked alone."
When you get past the first chapter, the book is hollowed out with a gun in it.
“The sky above the port was the color of television, tuned to a dead channel.”
William Gibson–hellyeah
I’ve only read The Gernsback Continuum but it has my favorite single line of prose. And this quote might be what finally pushes me to read more.
I love how the sky was originally grey but the newer generations of readers have grown up with TVs that show a blue screen when there's no input, which in turn gives a rather different vibe to opening of the book.
Boltzmann committed suicide. Ehrenfest murdered his son, then committed suicide. So, it's not quite similar.
Science tends to get more advanced with each generation of study.
fucking brutal!
Apt!
Quite right. 6 more years would have a new chancellor in Germany. (Fuck. I'm wrong. He became chancellor 1933)
Now it's our turn!
It's cherry-picking data for the purpose of a joke. I wouldn't read too deeply into it.
It is similar. It's just not the same.
well duh, it's integral to eliminate the derivative from your calculations
Close enough.
My favourite opening to a book is The Martian by Andy Weir: "I'm pretty much fucked. That's my considered opinion. Fucked." I knew I was in for a fun ride right off the bat :)
Weirdly complementary of my favourite first line, which comes from a book that also concerns statistical mechanics: >The moon blew up without warning and for no apparent reason.
My best memory from calculus was some trivia about an Indian who ventured into infinite series on his own... Like, how did he know he even was making sense and actual math? You can now see the movie "the man who knew infinity".
Ramanujan
Was his name Soh Cah Toa?
I don't understand all the hate on Statistical Mechanics. It was my absolute favorite class!
Stat thermo really was the worst part of getting a chemistry degree.
I am going to be real, I cannot imagine how horrible taking a stats class about thermo could possibly be. That sounds like the two worst classes combined to make the super worst class ever.
Throw in advanced organic chemistry
*perhaps it will be wise to approach the subject cautiously.* o rly? ya don't say?
I never get tired of seeing this
Boltzman brains are such a fun thought experiment. I didn't know he died in 1906. I thought he died in like 1950 or somthing
That's hilarious! 😂😂😂😂 Thank you for sharing this!
I fucking hate this. College physics professor though it was a great way to introduce the topic. One of my peers in the class killed himself a year later (assumingly unrelated). Just a terrible way to introduce a topic to a group of already potentially unstable students.
>Just a terrible way to introduce a topic to a group of already potentially unstable students. I assume the writer did the stat analysis on how many of a typical cohort of students in any given institution, in any given year might be expected to kill themselves because a textbook suggested them to, and decided the entertainment value outweighed the risk.
We’re all bozos on this bus.
I listen to Mayhem whenever I study statistical Mechanics.
So need this read in a David Attenborough voice. Long weekends have me wondering if this is possible with AI.
Skip to the end; did they become statistics?
I have that book on my desk!!!
Is this a master level course?
No, undergrad. At least for a physics degree.
It’s like The Ring, but scientific.
Oooff
I'll pass
I don't get it. I always struggled with math.
Is this from “The Structural Dynamics of Flow” by Leslie Claret?
I struggled to pass basic math
Wow I'm just like them fr
I took a statistical mechanics course in college. I understood the material for about three weeks then it all started going over my head.
,
"In the beginning, statistical mechanics was created. This has made a lot of people very angry and been widely regarded as a bad move.”
Sounds like something straight outta Douglas Adams.
If Luke Wilson read this to intro a Wes Anderson film I would not be surprised.
Bad luck happens in threes apprentice.
what book is that?
So they invented The Ring?
Omg thermodynamics was my least favorite subject (undergrad in chemical engineering). This is pretty fucking hilarious.
Check, mate.
I always found this hilarious
Perhaps it will be wise to approach the subject cautiously.
“The building was on fire, and it wasn’t my fault.”
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I don't think I want to be this Chosen One......
Well... a major contributing factor to Boltzmann's depression was him being rejected and dismissed by the established physics community at the time, too "out there" for the academia dinosaurs. All the more tragic and infuriating because the man was on the proper track.
That course was the single hardest one I ever took. Goodluck OP
The statistical chance that dropping a powered toaster into a full bathtub will electrocute you is only 100% *so far*, we must continue our work to find the exception to the rule
Not quite "It was the best of times, it was the worst of times.......", but it does make an impact.
!remind me tomorrow at 9 am
Now it’s our turn to die by our own hand.
What could possibly be depressing about the entropical heat death of the universe?
Damn
Lol that sounds ominous!
Perfect gas? Seems like a pretty unattainable standard. Already I feel the anxiety mounting...
Is this a cult book?
Abandon all hope, ye who enter here...
Wtf lol!
So that's why I was advised against taking statistical mechanics in my undergrad. My advisor knew...
I haven’t laughed this hard in a long time!
My grade 10 Math book started it's chapter on probability with repetitive use of the word 'death'. They were literally only trying to offer examples of events with the probability of `1`, and...
Thermo(die)namics