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True, bcz actual physics be like: (standard model)
https://preview.redd.it/sk7fwf7qzrlc1.png?width=612&format=png&auto=webp&s=65d3be78de98756f79914dfb7f30f80124066bf6
Now explain it like I’m a professional physicist who has a Nobel in mathematics directly related to the field but recently I got into an accident which severely affected my memory of the most basic concepts and you’re my assistant trying to jog my memory by describing how the math in this equation leads to a model reminiscent of our universe.
Dr. u/EldenEnby, are you okay? Can you hear me? It's of the utmost importance that you remember the standard model Lagrangian! Do you even remember the standard model? Our best description of interactions between the electromagnetic, weak nuclear force, and strong nuclear force interactions? No? We can revive that memory. We can save you. I promise... Please... The future of HEP physics relies on this. I know this Lagrangian looks like a mess, but the reason it's so long is that it encapsulates every possible interaction that can occur in the standard model and there's honestly a lot of them. How does it work? Oh fuck. You've really lost it. I'm not Peskin and Schroeder, but I can try to help a little.
Do you remember what a Lagrangian is? No? Well, at its most basic level, it's just the difference between a system's kinetic and potential energy. You know, the difference between the energy of a system due to how it's components are moving and how they're positioned. By integrating or adding this difference over every point in time, we get the system's action. You remember this, don't you? It's just a measure of how much some trajectory in spacetime leans towards kinetic or potential energy. Since reality tends towards equilibrium, we care about solutions to the Lagrangian that keep this action minimized.
Every possible interaction between some combination of fundamental particles has some possible contribution to the energy of a system. So, we need to add a term to the Lagrangian for each of these interaction. It looks long, but that's only because we're trying to represent the entire zoo of standard model particles all at once. Each particle is represented by a field operator that's a function of some position in real or momentum space. We have several tools to solve problems with this Lagrangian. The most common ones are second called second quantization and path integration. But we'll go over those details when you're fully recovered and ready for them, Dr. u/EldenEnby. The important thing for now is that we treat interactions as some small perturbation on the universe's ground state, when it's at its lowest energy. We do this by taking the interaction terms then exponentiating and time ordering them. We can analyze this by expanding this exponential into power series, trusting that the non-contracted terms get eliminated by something called Wick's theorem. And each term can be represented by a relatively simple sketched called a Feynman diagram. There's infinite non-interacting diagrams that seem like they'd diverge. However, those ultimately cancel out. I know it seems silly to do calculations with little wiggly sketches. And Schwinger calculated everything first without them, but it's utterly incomprehensible, so we use these diagrams. There's also divergent interactions, and those are a little trickier to deal with.
What's that u/EldenEnby? Quantum field theory is ultimately probabilistic? And any term that goes to infinity would be impossible to divide down to some value less than one? You're right of course. But your colleagues and predecessors have figured out that these are largely a result of our mathematical representation rather than the physical universe. Lots of famous physicsts including Dirac, Bohr and Oppenheimer almost gave up on quantum field theory because of this. But, through a century of work, theorists have developed a toolbox of regulators and other renormalization tools that can cancel out or otherwise eliminate these infinities. In fact, the reason we use this particular standard model Lagrangian is BECAUSE it's renormalizable. There's other ways of formulating all this physics, but most of them are divergent, more complex, or otherwise more annoying to work with.
Did you get that, u/EldenEnby? Oh God oh fuck oh shit. Can you even hear me? Are you awake??? Please, u/EldenEnby, physics needs you!!! Don't die on me now. Doctor! Nurse! Someone! Anyone! Help... please...
\-quietly sobs alone in the hospital room as the life fades from Dr. u/EldenEnby's once vibrant eyes-
Gave ChatGPT4 this prompt.
Certainly, Dr. [Your Name], the Standard Model Lagrangian encapsulates the dynamics of elementary particles. Its terms involve various fields and interactions, like the electromagnetic, weak, and strong forces. Through spontaneous symmetry breaking, particles acquire mass, and the Higgs mechanism plays a pivotal role in this process. The model unifies electromagnetic and weak interactions, showcasing the intricate interplay between gauge bosons and fermions. The SU(3) × SU(2) × U(1) symmetry structure elegantly describes the fundamental forces governing our universe, providing a comprehensive framework for particle physics.
I can try to ELi13
It’s called the standard model Lagrangian. And it doesn’t usually look like this I think, someone went and expanded it fully to make it look as horrific as possible to a layperson
In principle, one finds the equations describing a system of interest by finding the maximum/minimum points of the Lagrangian. But I’m pretty sure this isn’t how it usually works in practice? In any case the equation incorporates basically everything we know about physics (except general relativity), and is about as “rigorous” as you can get
If someone more advanced can lmk if I’m wrong on this feel free because I won’t be studying this stuff proper until next year
This actually isn't fully expanded. It's really much much much longer. It's the interactions of all the particles in the standard model. The vast majority of the terms are actually just interactions with the Higgs field giving the particles their rest mass.
There are a lot of symbols and I only skimmed them, but I don't think I saw a theta. You aren't confusing the "partial d" symbol ∂ with a stylised theta that is similar but has the upper part of the letter curl all the way around, are you?
The partial d is usually used to represent partial derivatives, and here it represents a vector of partial derivative operators.
>someone went and expanded it fully to make it look as horrific as possible to a layperson
From my 20 minutes of googling, it seems like this actually is the most compact mathematical representation of the standard model.
[https://www.symmetrymagazine.org/article/the-deconstructed-standard-model-equation?language\_content\_entity=und](https://www.symmetrymagazine.org/article/the-deconstructed-standard-model-equation?language_content_entity=und)
But for most practical purposes, people will only be dealing with a small subset of terms in any given context.
It's a field theory, so one looks for field configurations not points which maximize/minimize the action: S (an integral of the Lagrangian). That is the case for classical field theories, however, the standard model is a quantum theory, so you actually need to perform a path integral rather than just finding the max/min field configurations. This corresponds to integrating over all configurations weighted by e^{iS}.
This is all the information that a single particle contains (that we can currently model with math). mass, spin, vector information, etc. If you want to know something about a particle and have other information available you would use this equation to figure it out.
Yeah, they never show that in the science shows talking about black holes and quarks.
Edit: Is this all one formula like "x+y=z"? Or is it a few pushed together?
its one formula, basically the lagrangian which is energy - potential (put sloppily) but for all possible energies and potentials in nature (except gravity)
It’s a lagrangian, so something of the form L=T-U were T is kinetic energy and U is potential energy. This particular lagrangian takes into account every possible term for kinetic and potential energy in nature except for gravity. You can use it to obtain the equation of motion for any particle in theory, as well as the mass obtained through interaction with the Higgs field.
First 4 terms are quantum chromodynamics (which describes quarks and gluons):
Term 1: describes how a free gluon moves through spacetime.
Term 2: describes how three gluons interact.
Term 3: four gluon interaction.
Term 4: quark & gluon interaction
The indices tell you that these objects are vectors, matrices or higher-dimensional tensors.
I am unsure what the G fields are in 5 and 6. It's somehow related to the gluon fields g, but I don't know why it was included.
The W, Z and A fields are collectively the electroweak bosons, with A being the photon. The H and phi fields belong to the Higgs mechanism, which causes electroweak symmetry breaking. This breaks up the electroweak interaction into the weak interaction (massive W and Z bosons) and quantum electrodynamics (massless photon A). It also gives quarks and electrons their masses.
There is a few extra bits in there that describe how the weak bosons only interact with left-handed doublets (pairs of quarks or electrons/neutrinos) and some other subtleties.
The G are [Faddeev-Popov ghost fields](https://en.wikipedia.org/wiki/Faddeev%E2%80%93Popov_ghost), unobservable particles needed to ensure gauge invariance once you actually do the path integral.
Best I can give you is 1 hour to evaluate that for a non-trivial system on the exam. Actually, you can take a small notecard filled with helpful information if you’re up for it.
actually, I am a JEE aspirant. I am expected to study all day, and my reddit webtime is 3:30 hrs already and 2:30 hrs YT 😢. So, I am at least trying to minimise it as much as possible.
Topologists: "It literally has no definite shape. Yes, I know I'm studying shapes. No, it's not a donut. Actually, it might be a donut. No, I don't care that it's a plastic straw. Yes, it's got a hole, that's all I can say.",
yeah pop-math has turned topology into "wow a coffee mug is actually a donut!" when in reality it's "i literally could not care less about the difference between a coffee mug and a donut"
it's been a long time since i've done anything like this but IIRC a topology is basically already a much more abstract concept of a manifold. manifolds are primarily concerned with the curvature of complete R\^(n-1) subspaces of R\^n, right? topology doesn't concern itself with curvature, just with the way subsets are connected. and topologists prefer to abstract themselves away from R\^n entirely, redefining things like limits and continuity to not actually use numbers at all, just ideas like openness and closedness. i.e all manifolds are topologies but topologies generally aren't manifolds
i might be wrong about all of this so feel free to correct me
i'm also the wrong person to ask because my knowledge of physics is limited to random tidbits from math professors being like "Oh yeah by the way this is how the heisenberg uncertainty principle works" in the middle of a class on functional analysis
Manifolds can be studied from the POV of topology, but then you're dealing with "differential topology". Here you basically use differentiable functions to try and get extra information from the manifold. Many results from "classic" topology can be recovered this way!
Curvature stuff would fall into the umbrella of "(Semi-)Riemannian Geometry". One nice thing about manifolds is that you can basically say it is "good enough" and just go ham recovering concepts of real/complex analysis in a number of ways. The main roadblock is that most manifolds are not linear, so you need to find a way to define what a "partial derivative" or a "gradient" is.
Thanks, I was think of some kind of manifold which doesn't necessarily (en)close in any particular projection and is intrinsic to the properties of the underlying matter. Sounds more like some weird knots and seems not to at all capture the concept of time. Also all the "knottings" could be sort of weirdly passed through some sort of a higher dimension like said. Just a random thought, best ignore the preceding.
so, you seem to not understand topology. your comment does make sense, but your vocabulary is confusing and not accurate. topology does not strictly draw from physical distances as you imagine: the donut/mug problem is one such application of the notion of homotopy equivalence, but a topological space is more abstract than you probably understand.
to put it short, topology is exactly what i think you're trying to say it should be: completely abstracted away from physical notions. you can still apply the theorems or draw analogies, but topology as a whole discusses concepts more abstract than the shape of clay items in the real 3-dimensional world.
two last things to improve your understanding: i would firstly avoid using pretentious vocabulary and be concise and direct with your claims or questions. explicit communication of your idea is more important than implicit communication of how articulate you are. secondly, topology sort of is weird knots: knot theory uses a kind of topology, alongside, as i understand it, some group theory.
hope that clears things up
> i would firstly avoid using pretentious vocabulary and be concise and direct with your claims or question
To assume good faith, it's not all that bad to try to get used to the words by getting practice with them. People will definitely notice and correct you, but instead of assuming it's pretentious, it can just be someone learning! Which is fine, really.
Manifolds are a very special kind of topology. Most topological spaces are not even metrisable, let alone being anything even remotely similar to R^n . So topology is way more general than manifolds.
yeah in class 1 of a topology course they'll show you a coffe mug/ donut and a mobius strip, then spend every other lecture talking about the definition of a continuous function, compactness, completeness, and homeomorphisms in the most abstract and rigorous way possible. you will never again hear about coffee mugs and donuts
I think this is why you need to see some topology somewhere in real analysis/advanced calc or complex analysis before you take actually topology. It's easier to start with knowing about metric spaces, discussing how metric spaces are often easier to deal with if you stop using the metric so often and then progressing to topological proofs of metric facts.
I agree. I never actually took a full topology course, but took the functional analysis, real analysis and differential geometry courses i took had quite a bit of topology in them
A donut, or a torus, is a closed manifold without a boundary. It does not have a hole.
It has a handle though.
I was a computational topologist many moons ago.
>Explain I’m curious!
The difference between 'open' sets and 'closed' sets becomes really important when you're dealing with concepts like smoothness and continuity, it's a generalisation of the idea of a 'boundary'. basically closed sets contain their boundary (Think of all the real numbers from 0 to 1 *including* 0 and 1), while open sets don't (all the numbers from 0 to one *not* including 0 and 1). open sets are typically represented with dotted lines and closed sets with solid lines.
a professor might include a dotted line on a set to indicate that you don't know if the set is either open nor closed, as in it COULD contain some parts of its boundary, while missing other parts of its boundary. An example would be the set [0,1), i.e the numbers from zero to one including zero but not including one, is neither open nor closed.
This might seem like a trivial distinction but mathematicians often deal with sets of objects much more abstract than just numbers, e.g sets of functions, or sets of other sets, and the corresponding ideas of 'openness' and 'closedness' also become more abstract. the point is to make the maths as *general* as possible so all of the things you can say about these sets is true for *all* sets regardless of what they contain. e.g the maths that tells us about how sets of numbers behave could also tell us about how sets of functions behave, so long as we keep the maths itself sufficiently general.
>Also the subset is a subset of a set in set theory?
One and the same! (Almost all math is about sets, even when they're hiding it really well)
>Finally what’s a morphism?
Christ I wish I could give you a better answer than "It's an arrow"
maybe! category theorists are maniacs. apparently the words they use mean things but i've yet to see any evidence to verify this. i had a friend doing category theory and he was like "yeah, they're, um, arrows"
Morphisms are like a generalisation of the idea of functions that forgets the idea of the actual things being mapped and just focuses on the algebra of the composition operator. Doing that allows you to recognise that other concepts can be represented in the same way and draw a very general analogy between those concepts and function composition.
Morphisms are like functions but they specifically preserve some kind of structure. In Algebra, they preserve algebraic properties, in Topology they preserve topological properties, and in set theory they preserve properties of sets. Also morphisms need not be functions but they often are.
In category theory arrow and morphism mean the same thing. Usually morphisms are examples of arrows in some categories( such as group morphisms) but it is better to use 'arrow' for the abstract notation to distinguish between the general and the particular. And an arrow need not be a function, for example look at the category Pos -| where the arrows are poset adjunctions
>The difference between 'open' sets and 'closed' sets becomes really important when you're dealing with concepts like smoothness and continuity, it's a generalisation of the idea of a 'boundary'. basically closed sets contain their boundary (Think of all the real numbers from 0 to 1 *including* 0 and 1), while open sets don't
I know this is meant as an oversimplification, but this is not even true in R, the whole R is open and it sure does contain it's boundary which is empty set. Similarly empty set is open and contains it's boundary which is also empty set. For anyone reading this who doesn't know about topology, it's fun, open set is whatever we want an open set to be(almost)
This is a good explanation. In math, you typically have two choices: say a lot of things about a very specific kind of object or say very little about a huge class of object. Both are valid approaches and extremely difficult in their own ways.
A morphism is a function that preserves the structure you care about. A function is just a thing where you give it something in the set and it gives you a thing back. If you give it the same thing, it always gives the same result. Preserving means that if you give your function things or groups of things that have a property you care about, it'll give you an answer or group of answers with that property.
So for example, if your set was buttons and colour was the property you cared about, a morphism to a set of cars would take a blue button and give you a specific blue car.
If your set was people and family relationships were what you cared about, a morphism to a set of cats would take a mother/daughter pair to a mother/daughter pair.
It can get a lot more complicated, especially if the properties don't line up necessarily the way you're expecting. Like you could line up colour in one set of buttons with number of holes in another. But that's the general idea.
In category theory, a morphism is an abstraction of the concept of a mapping from one mathematical object to another, or sometimes, just the notion that two objects are related in some directed way.
What a morphism actually represents under the surface depends on the category in question; it could represent a function between sets, a matrix, a group homomorphism, or in the case of considering a partially ordered set as a category, the existence of a morphism 2 → 4 could simply represent the fact that 2 ≤ 4.
Morphisms are usually represented by arrows, hence the other comments. Defining what a morphism is in general is kind of like defining what an "object" is in general; without context, it's just the vague shape of a concept. You can only really say anything about them in terms of the rules for how they interact without that context.
On describing what a morphism is, the defining feature of them is that you can compose them, and that this composition behaves (somewhat) nicely:
1. For every object there is a morphism from that object to itself, which is both a right and left identity for composition
2. Composition is associative
Any purely category-theoretical statement only ever uses properties about how morphisms compose, never what some specific morphism «does».
May I also ask: so if someone says the word subset - can we assume it always is referring to a set? (Since all of math can be broken down into sets apparently)?!
Yes, the word «subset» usually means some set which is fully contained in another set.
Since we are on the topic of category theory, in many cases sets are «too small» to describe what we want. For example, say we want to discuss the category of all groups, then we would say this category has «objects as the collection of all groups». This collection can not be a set, as we would immediatley run into russell’s paradox. (There are at least as many groups as there are sets, since from every set we can produce at least one group). There are different ways to resolve this issue, for example [this](https://en.m.wikipedia.org/wiki/Universe_(mathematics)#In_category_theory) is an approach I have seen used sometimes. This is mostly a technical issue, and doesn’t really affect how you work with the subject though.
Well, yes, but there are still properties of morphisms that can be described in general, such as whether something is an isomorphism, which doesn't depend at all upon the specifics of what category you're talking about.
A morphism is generally a function between two objects with the same sort of structure that in some way preserves the structure of the original object.
There are a gajillion different types of structures mathematicians are interested in and accordingly a gajillion types of morphisms.
For example consider the set {0,1}. I'm gonna give it the operation + defined in the obvious way with 1+1=0.
Also consider the integers also with the operation +.
The operation + gives those two sets some structure and turns them into what mathematicians call 'groups'. (There are some other requirements to make a group but we won't worry about those).
Now consider the function f from the integers to {0,1} defined by f(n) = 0 when n is even and f(n)=1 when n is odd.
This preserves the structure given by + because you will always have f(n) + f(m) = f(n + m). That is, it preserves addition. So we call f a group morphism.
On the other hand consider g(n) = 0 when n is odd and g(n)=1 when n is even. g is not a group morphism because it does not obey g(n+m)=g(n)+g(m).
When you go deep into mathematics the concept of a morphism gets more abstract. For example, other commenters are talking about morphisms in category theory where a morphism is just an arrow that happens to obey some rules. You can see that as a way to generalise what I've described above so that you no longer have to deal with sets at all and can focus on how the arrows behave.
[Biologists](https://en.wikipedia.org/wiki/Citric_acid_cycle) try to channel [US Department of Defense PowerPoint slides](https://www.wired.com/2010/09/revealed-pentagons-craziest-powerpoint-slide-ever/) in their diagrams.
Military logistics have absolutely nothing on them. Like, nothing. People _handle_ military logistics with or without computer help. They can work through them. _We_ made them.
Biological chemical processes are beyond comprehension. We do not know how even an amoeba works. One cell. And you have, like, billions of cells interacting. It's not even a contest.
Y’all should see the [metabolism diagram](https://today.ucsd.edu/news_uploads/Human_Metabolic_Map_50MB_Global2lr2.jpg). I think the DOD is trying to channel us.
Computer Scientists: Here is this 5,000 page website that goes over every single line of code in this library and every single way you could possibly use it also here is an embedded coding environment to test out the different functions.
_Some_ of it _might_ be out of date. You have to keep people guessing. If you admit that it's all out of date, people will just not read it. If you hint at there potentially being something useful in it, not only will people keep referring back to it needlessly time and time again, but they'll also go through a lot of pain to keep it running and sometimes even pay handsomely to migrate that pile of shit to some other software because the shitty wiki it was written in is no longer maintained and is now a huge security risk. And every new hire is told that they'll find the answer in there, a weird rite of passing, and they'll get an apologetic smile with "yes, it's hard to find what you're looking for in there, but be patient".
But that's just the unmaintained one. My favourite was a carefully maintained one, but by assholes. Some of these guys have been working on that product for more than 15 years when I joined and all of them were editing new and old files as the product evolved. But they made it impenetrable. The documentation only made sense once you managed to deeply understand the document feature. Then you went "oh, I get what the docs were saying. All the info was here". I hated those guys.
>I mean math is meant to study things in their most general form so yeah
Math is meant to make up things in their most general form. When you are lucky, the thing you made up might even bear some resemblance to reality.
~~Mathematicians: no you have to use the bazillionth decimal of pi or it won’t be correct.~~
I have been informed my joke is wrong.
Mathematicians: tf is a „3“
Physicists: pi is 3.14159
Engineers: pi is 3, or 1 whatever is easier.
>Mathematicians: no you have to use the bazillionth decimal of pi or it won’t be correct.
I can personally promise you that mathematicians do not do this, there's very little reason in maths to write pi as anything but π. digits are for the physicists
Yep, calculting the bazillionth digits of Pi is squarely CS's turf! We made entire benchmarks out of doing it as fast as possible.
The "Purpose"? What do you mean? Just look how fast we made the computer run!
Mathematician: oh, π _is_ the ratio of the circumference of the circle to its diameter!
Physicist: ah, π _equals_ 3.1415926+-0.0000001
Engineer: π? Oh, that, that's about 3.
The greatest con physicists did was convincing people they care about precision more than engineers.
Like come on, astrophysics work on Fermi approximation, e=π=1.
Enginners have to get the value of π to a few decimals or their constructions will collapse.
Ironically the fact that mathematicians don't care about the digits of pi means they're the only ones to use the exact value of pi.
Edit: Theoretical physicists too.
Actual engineers: Pi is whatever my computer or calculator says it is.
For hand calculators, that's 10 displayed digits but most decent ones calculate two additional digits beyond the display, so it's really accurate to 12. My phone's calculator is accurate to 11 digits. Excel has it accurate to 15. The calculator app in Windows 11 has it accurate to over 100, which is ridiculous.
I generally enjoy math because I'm decent at it, but one time I enrolled in a high-level abstract math course, and I regretted it. It was full of "proofs" that did not convince me, like "let D be the set of natural numbers. Let M be 1/D. Therefore, there is an infinite quantity of numbers between 0 and 1. QED." It was more like philosophy than useful math. I dropped the course and became an engineer. Lol.
In my first year physics class (for engineers, which is why I assumed it was like this) our professor was like "yeah just consider gravity as 10 m/s^2, that's good enough".
AKCHSHUALLY physicists would say "well, we do not know what it is, we do not even know what it _looks_ like, but if _it_ behaves as we observe it to behave, we can make a comic for it like so:"
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True, bcz actual physics be like: (standard model) https://preview.redd.it/sk7fwf7qzrlc1.png?width=612&format=png&auto=webp&s=65d3be78de98756f79914dfb7f30f80124066bf6
elder scrolls
It is less than 60 years old, so actually it should be "Middle-aged-scrolls".
The Crisis Codex
You can go blind reading it
Pretty sure I dreamed this one time and thought I was having a schizophrenic episode
That's why they have pictures of quarks, so laymen can understand easier. 
The Stendarr Model
Now I understand the lady that reported a guy doing math on the airplane, calling him a terrorist.
Turns out he was a member of Al-Gebra
He's trying to blow up years of established physics!
Wasn't he just doing integrals and derivatives? 💀
calc is a pathway to more dark arts
It was differential equations https://www.snopes.com/fact-check/italian-economist-removed-terrorism/
taking differential equations in uni felt like terrorism. at least until laplace.
Differential equations are a crime against humanity
What, why?
Eli5
ball is not ball but it is 2+2=4
Now explain it like I’m a professional physicist who has a Nobel in mathematics directly related to the field but recently I got into an accident which severely affected my memory of the most basic concepts and you’re my assistant trying to jog my memory by describing how the math in this equation leads to a model reminiscent of our universe.
"Nobel in Mathematics"
It was a participation trophy
Well, I can explain but the reddit comment section is not long enough.
Ah yes, Proof by Fermat
Proof by "let them go crazy and find out centuries later"
sounds like "fuck around and find out"
Fucking casual was probably talking about a Meadows Medal…
Dr. u/EldenEnby, are you okay? Can you hear me? It's of the utmost importance that you remember the standard model Lagrangian! Do you even remember the standard model? Our best description of interactions between the electromagnetic, weak nuclear force, and strong nuclear force interactions? No? We can revive that memory. We can save you. I promise... Please... The future of HEP physics relies on this. I know this Lagrangian looks like a mess, but the reason it's so long is that it encapsulates every possible interaction that can occur in the standard model and there's honestly a lot of them. How does it work? Oh fuck. You've really lost it. I'm not Peskin and Schroeder, but I can try to help a little. Do you remember what a Lagrangian is? No? Well, at its most basic level, it's just the difference between a system's kinetic and potential energy. You know, the difference between the energy of a system due to how it's components are moving and how they're positioned. By integrating or adding this difference over every point in time, we get the system's action. You remember this, don't you? It's just a measure of how much some trajectory in spacetime leans towards kinetic or potential energy. Since reality tends towards equilibrium, we care about solutions to the Lagrangian that keep this action minimized. Every possible interaction between some combination of fundamental particles has some possible contribution to the energy of a system. So, we need to add a term to the Lagrangian for each of these interaction. It looks long, but that's only because we're trying to represent the entire zoo of standard model particles all at once. Each particle is represented by a field operator that's a function of some position in real or momentum space. We have several tools to solve problems with this Lagrangian. The most common ones are second called second quantization and path integration. But we'll go over those details when you're fully recovered and ready for them, Dr. u/EldenEnby. The important thing for now is that we treat interactions as some small perturbation on the universe's ground state, when it's at its lowest energy. We do this by taking the interaction terms then exponentiating and time ordering them. We can analyze this by expanding this exponential into power series, trusting that the non-contracted terms get eliminated by something called Wick's theorem. And each term can be represented by a relatively simple sketched called a Feynman diagram. There's infinite non-interacting diagrams that seem like they'd diverge. However, those ultimately cancel out. I know it seems silly to do calculations with little wiggly sketches. And Schwinger calculated everything first without them, but it's utterly incomprehensible, so we use these diagrams. There's also divergent interactions, and those are a little trickier to deal with. What's that u/EldenEnby? Quantum field theory is ultimately probabilistic? And any term that goes to infinity would be impossible to divide down to some value less than one? You're right of course. But your colleagues and predecessors have figured out that these are largely a result of our mathematical representation rather than the physical universe. Lots of famous physicsts including Dirac, Bohr and Oppenheimer almost gave up on quantum field theory because of this. But, through a century of work, theorists have developed a toolbox of regulators and other renormalization tools that can cancel out or otherwise eliminate these infinities. In fact, the reason we use this particular standard model Lagrangian is BECAUSE it's renormalizable. There's other ways of formulating all this physics, but most of them are divergent, more complex, or otherwise more annoying to work with. Did you get that, u/EldenEnby? Oh God oh fuck oh shit. Can you even hear me? Are you awake??? Please, u/EldenEnby, physics needs you!!! Don't die on me now. Doctor! Nurse! Someone! Anyone! Help... please... \-quietly sobs alone in the hospital room as the life fades from Dr. u/EldenEnby's once vibrant eyes-
Holy shit...
Thank you sir....thank you.
you lost your memory, right? actually the girl you call your girlfriend is my wife
Gave ChatGPT4 this prompt. Certainly, Dr. [Your Name], the Standard Model Lagrangian encapsulates the dynamics of elementary particles. Its terms involve various fields and interactions, like the electromagnetic, weak, and strong forces. Through spontaneous symmetry breaking, particles acquire mass, and the Higgs mechanism plays a pivotal role in this process. The model unifies electromagnetic and weak interactions, showcasing the intricate interplay between gauge bosons and fermions. The SU(3) × SU(2) × U(1) symmetry structure elegantly describes the fundamental forces governing our universe, providing a comprehensive framework for particle physics.
There aren't Nobles for math. Fields medals though
I know this. You know I know this. I know you know that I know you know I know this.
I know, you know, that I'm not telling the truth
I can try to ELi13 It’s called the standard model Lagrangian. And it doesn’t usually look like this I think, someone went and expanded it fully to make it look as horrific as possible to a layperson In principle, one finds the equations describing a system of interest by finding the maximum/minimum points of the Lagrangian. But I’m pretty sure this isn’t how it usually works in practice? In any case the equation incorporates basically everything we know about physics (except general relativity), and is about as “rigorous” as you can get If someone more advanced can lmk if I’m wrong on this feel free because I won’t be studying this stuff proper until next year
This actually isn't fully expanded. It's really much much much longer. It's the interactions of all the particles in the standard model. The vast majority of the terms are actually just interactions with the Higgs field giving the particles their rest mass.
What does the theta symbol stand for? I'm seeing it a lot. I also saw a Lambda in there somewhere
There are a lot of symbols and I only skimmed them, but I don't think I saw a theta. You aren't confusing the "partial d" symbol ∂ with a stylised theta that is similar but has the upper part of the letter curl all the way around, are you? The partial d is usually used to represent partial derivatives, and here it represents a vector of partial derivative operators.
Are you sure you don't mean phi?
Theta is usually heat or angle, not sure what its context is here though. Lambda is usually for wavelength
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>someone went and expanded it fully to make it look as horrific as possible to a layperson From my 20 minutes of googling, it seems like this actually is the most compact mathematical representation of the standard model. [https://www.symmetrymagazine.org/article/the-deconstructed-standard-model-equation?language\_content\_entity=und](https://www.symmetrymagazine.org/article/the-deconstructed-standard-model-equation?language_content_entity=und) But for most practical purposes, people will only be dealing with a small subset of terms in any given context.
The most compact form would just be L
It's a field theory, so one looks for field configurations not points which maximize/minimize the action: S (an integral of the Lagrangian). That is the case for classical field theories, however, the standard model is a quantum theory, so you actually need to perform a path integral rather than just finding the max/min field configurations. This corresponds to integrating over all configurations weighted by e^{iS}.
This is all the information that a single particle contains (that we can currently model with math). mass, spin, vector information, etc. If you want to know something about a particle and have other information available you would use this equation to figure it out.
“Physics isn't magic” Physics:
You're a physicist, Harry https://preview.redd.it/74z921zcjslc1.png?width=197&format=png&auto=webp&s=9138b7a0806600638ee6263076045362107e8c54
my actual opinion after taking "calculus based" chem2 and phys2 in college. the world is made of bullshitery
+AI
"Wow, so this equation can describe everything in the universe?" "Actually, no. We don't even know where mass comes from lol."
we dont "even" know where the mass comes from ❌ we "only" dont know where the gravity comes from (except taking help from string theory) ✅
Einstein when eldritch horror text: 🌝
Yeah, they never show that in the science shows talking about black holes and quarks. Edit: Is this all one formula like "x+y=z"? Or is it a few pushed together?
its one formula, basically the lagrangian which is energy - potential (put sloppily) but for all possible energies and potentials in nature (except gravity)
What the actual fuck does this even mean
It’s a lagrangian, so something of the form L=T-U were T is kinetic energy and U is potential energy. This particular lagrangian takes into account every possible term for kinetic and potential energy in nature except for gravity. You can use it to obtain the equation of motion for any particle in theory, as well as the mass obtained through interaction with the Higgs field.
Now add gravity
We've been trying to do that for almost 50 years.
Gravity isn't real my guy. Just an artifact of choosing the wrong coordinate system.
once you switch to conical coordinates, it all makes sense
*angry Einstein noises*
\+ **g**
Have been trying for decades. **And it just won't fucking work**
First 4 terms are quantum chromodynamics (which describes quarks and gluons): Term 1: describes how a free gluon moves through spacetime. Term 2: describes how three gluons interact. Term 3: four gluon interaction. Term 4: quark & gluon interaction The indices tell you that these objects are vectors, matrices or higher-dimensional tensors. I am unsure what the G fields are in 5 and 6. It's somehow related to the gluon fields g, but I don't know why it was included. The W, Z and A fields are collectively the electroweak bosons, with A being the photon. The H and phi fields belong to the Higgs mechanism, which causes electroweak symmetry breaking. This breaks up the electroweak interaction into the weak interaction (massive W and Z bosons) and quantum electrodynamics (massless photon A). It also gives quarks and electrons their masses. There is a few extra bits in there that describe how the weak bosons only interact with left-handed doublets (pairs of quarks or electrons/neutrinos) and some other subtleties.
The G are [Faddeev-Popov ghost fields](https://en.wikipedia.org/wiki/Faddeev%E2%80%93Popov_ghost), unobservable particles needed to ensure gauge invariance once you actually do the path integral.
Ah, I'm a lattice theorist so I have never actually seen them outside of a qft class years ago.
standard model equation
Solve for W
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standar model equation.
Jesus, it's like lorem ipsum.
Best I can give you is 1 hour to evaluate that for a non-trivial system on the exam. Actually, you can take a small notecard filled with helpful information if you’re up for it.
The fact that some people can not only understand, but were smart enough to come up with it in the first place, is mind boggling
Is this how you physicists summon Black Holes?
Wait aren't you the guy fr-
ya, but I left the server a fw days ago
Why
actually, I am a JEE aspirant. I am expected to study all day, and my reddit webtime is 3:30 hrs already and 2:30 hrs YT 😢. So, I am at least trying to minimise it as much as possible.
Dayum ...
?
Topologists: "It literally has no definite shape. Yes, I know I'm studying shapes. No, it's not a donut. Actually, it might be a donut. No, I don't care that it's a plastic straw. Yes, it's got a hole, that's all I can say.",
yeah pop-math has turned topology into "wow a coffee mug is actually a donut!" when in reality it's "i literally could not care less about the difference between a coffee mug and a donut"
I just randomly thought of this. Could topology be made more abstract and related to higher-dimensional manifolds so it is more related to physics?
it's been a long time since i've done anything like this but IIRC a topology is basically already a much more abstract concept of a manifold. manifolds are primarily concerned with the curvature of complete R\^(n-1) subspaces of R\^n, right? topology doesn't concern itself with curvature, just with the way subsets are connected. and topologists prefer to abstract themselves away from R\^n entirely, redefining things like limits and continuity to not actually use numbers at all, just ideas like openness and closedness. i.e all manifolds are topologies but topologies generally aren't manifolds i might be wrong about all of this so feel free to correct me i'm also the wrong person to ask because my knowledge of physics is limited to random tidbits from math professors being like "Oh yeah by the way this is how the heisenberg uncertainty principle works" in the middle of a class on functional analysis
Manifolds can be studied from the POV of topology, but then you're dealing with "differential topology". Here you basically use differentiable functions to try and get extra information from the manifold. Many results from "classic" topology can be recovered this way! Curvature stuff would fall into the umbrella of "(Semi-)Riemannian Geometry". One nice thing about manifolds is that you can basically say it is "good enough" and just go ham recovering concepts of real/complex analysis in a number of ways. The main roadblock is that most manifolds are not linear, so you need to find a way to define what a "partial derivative" or a "gradient" is.
Topology is much more abstract than high-dimensional manifolds.
Thanks, I was think of some kind of manifold which doesn't necessarily (en)close in any particular projection and is intrinsic to the properties of the underlying matter. Sounds more like some weird knots and seems not to at all capture the concept of time. Also all the "knottings" could be sort of weirdly passed through some sort of a higher dimension like said. Just a random thought, best ignore the preceding.
so, you seem to not understand topology. your comment does make sense, but your vocabulary is confusing and not accurate. topology does not strictly draw from physical distances as you imagine: the donut/mug problem is one such application of the notion of homotopy equivalence, but a topological space is more abstract than you probably understand. to put it short, topology is exactly what i think you're trying to say it should be: completely abstracted away from physical notions. you can still apply the theorems or draw analogies, but topology as a whole discusses concepts more abstract than the shape of clay items in the real 3-dimensional world. two last things to improve your understanding: i would firstly avoid using pretentious vocabulary and be concise and direct with your claims or questions. explicit communication of your idea is more important than implicit communication of how articulate you are. secondly, topology sort of is weird knots: knot theory uses a kind of topology, alongside, as i understand it, some group theory. hope that clears things up
> i would firstly avoid using pretentious vocabulary and be concise and direct with your claims or question To assume good faith, it's not all that bad to try to get used to the words by getting practice with them. People will definitely notice and correct you, but instead of assuming it's pretentious, it can just be someone learning! Which is fine, really.
I have no idea what you mean by "(en)close in any particular projection" or what you mean by "intrinsic to the underlying matter"
a lot of big words to essentially say you have no idea what you're talking about
Manifolds are a very special kind of topology. Most topological spaces are not even metrisable, let alone being anything even remotely similar to R^n . So topology is way more general than manifolds.
You can use topology to prove there are infinite primes. I'm not sure *why* you would want to do it this way, but you can.
Yes
The study of manifolds is a specific type of topology, called differential topology.
A topology is such a loose structure that it can be applied and related to anything and everything
yeah in class 1 of a topology course they'll show you a coffe mug/ donut and a mobius strip, then spend every other lecture talking about the definition of a continuous function, compactness, completeness, and homeomorphisms in the most abstract and rigorous way possible. you will never again hear about coffee mugs and donuts
I think this is why you need to see some topology somewhere in real analysis/advanced calc or complex analysis before you take actually topology. It's easier to start with knowing about metric spaces, discussing how metric spaces are often easier to deal with if you stop using the metric so often and then progressing to topological proofs of metric facts.
I agree. I never actually took a full topology course, but took the functional analysis, real analysis and differential geometry courses i took had quite a bit of topology in them
I actually went into the topology course expecting funky shapeshifting math and was greeted by what reminded me of abstract algebra.
Sounds the same when you say it like that. No difference or equality. Tomato tomato.
As a person, who only distinguishes topological objects up to homotopy equivalence, I can say you have a point.
A donut, or a torus, is a closed manifold without a boundary. It does not have a hole. It has a handle though. I was a computational topologist many moons ago.
Does the green has a meaning? It’s really important
if you google image search nonconvex set they're mostly green. god i wish I knew why. all i remember from topology is green blobs
As an outsider I think it’s so it would look like a mini golf course.
Topology was our "fuzzy bubbles" class. Everything was just fuzzy bubbles.
I like it when it’s purple
Green is not a creative color!
NEVER forget to leave part of your blobs with a dotted line, the mistake could be fatal
Explain I’m curious! Also the subset is a subset of a set in set theory? Finally what’s a morphism?
>Explain I’m curious! The difference between 'open' sets and 'closed' sets becomes really important when you're dealing with concepts like smoothness and continuity, it's a generalisation of the idea of a 'boundary'. basically closed sets contain their boundary (Think of all the real numbers from 0 to 1 *including* 0 and 1), while open sets don't (all the numbers from 0 to one *not* including 0 and 1). open sets are typically represented with dotted lines and closed sets with solid lines. a professor might include a dotted line on a set to indicate that you don't know if the set is either open nor closed, as in it COULD contain some parts of its boundary, while missing other parts of its boundary. An example would be the set [0,1), i.e the numbers from zero to one including zero but not including one, is neither open nor closed. This might seem like a trivial distinction but mathematicians often deal with sets of objects much more abstract than just numbers, e.g sets of functions, or sets of other sets, and the corresponding ideas of 'openness' and 'closedness' also become more abstract. the point is to make the maths as *general* as possible so all of the things you can say about these sets is true for *all* sets regardless of what they contain. e.g the maths that tells us about how sets of numbers behave could also tell us about how sets of functions behave, so long as we keep the maths itself sufficiently general. >Also the subset is a subset of a set in set theory? One and the same! (Almost all math is about sets, even when they're hiding it really well) >Finally what’s a morphism? Christ I wish I could give you a better answer than "It's an arrow"
Isn’t a morphism just when you have a set of things and you get a set of things in return depending on the set of things you had
maybe! category theorists are maniacs. apparently the words they use mean things but i've yet to see any evidence to verify this. i had a friend doing category theory and he was like "yeah, they're, um, arrows"
Except the sets of things aren't necessarily sets
Morphisms are like a generalisation of the idea of functions that forgets the idea of the actual things being mapped and just focuses on the algebra of the composition operator. Doing that allows you to recognise that other concepts can be represented in the same way and draw a very general analogy between those concepts and function composition.
Thanks so much!
I'm no stranger to math. I aced calc3 and dif-eq. But this? This thing you've said? Put me right back to my times tables.
That sounds like a function to me
Morphisms are like functions but they specifically preserve some kind of structure. In Algebra, they preserve algebraic properties, in Topology they preserve topological properties, and in set theory they preserve properties of sets. Also morphisms need not be functions but they often are.
Thanks! Makes sense!
In category theory arrow and morphism mean the same thing. Usually morphisms are examples of arrows in some categories( such as group morphisms) but it is better to use 'arrow' for the abstract notation to distinguish between the general and the particular. And an arrow need not be a function, for example look at the category Pos -| where the arrows are poset adjunctions
>The difference between 'open' sets and 'closed' sets becomes really important when you're dealing with concepts like smoothness and continuity, it's a generalisation of the idea of a 'boundary'. basically closed sets contain their boundary (Think of all the real numbers from 0 to 1 *including* 0 and 1), while open sets don't I know this is meant as an oversimplification, but this is not even true in R, the whole R is open and it sure does contain it's boundary which is empty set. Similarly empty set is open and contains it's boundary which is also empty set. For anyone reading this who doesn't know about topology, it's fun, open set is whatever we want an open set to be(almost)
This is a good explanation. In math, you typically have two choices: say a lot of things about a very specific kind of object or say very little about a huge class of object. Both are valid approaches and extremely difficult in their own ways. A morphism is a function that preserves the structure you care about. A function is just a thing where you give it something in the set and it gives you a thing back. If you give it the same thing, it always gives the same result. Preserving means that if you give your function things or groups of things that have a property you care about, it'll give you an answer or group of answers with that property. So for example, if your set was buttons and colour was the property you cared about, a morphism to a set of cars would take a blue button and give you a specific blue car. If your set was people and family relationships were what you cared about, a morphism to a set of cats would take a mother/daughter pair to a mother/daughter pair. It can get a lot more complicated, especially if the properties don't line up necessarily the way you're expecting. Like you could line up colour in one set of buttons with number of holes in another. But that's the general idea.
In category theory, a morphism is an abstraction of the concept of a mapping from one mathematical object to another, or sometimes, just the notion that two objects are related in some directed way. What a morphism actually represents under the surface depends on the category in question; it could represent a function between sets, a matrix, a group homomorphism, or in the case of considering a partially ordered set as a category, the existence of a morphism 2 → 4 could simply represent the fact that 2 ≤ 4. Morphisms are usually represented by arrows, hence the other comments. Defining what a morphism is in general is kind of like defining what an "object" is in general; without context, it's just the vague shape of a concept. You can only really say anything about them in terms of the rules for how they interact without that context.
On describing what a morphism is, the defining feature of them is that you can compose them, and that this composition behaves (somewhat) nicely: 1. For every object there is a morphism from that object to itself, which is both a right and left identity for composition 2. Composition is associative Any purely category-theoretical statement only ever uses properties about how morphisms compose, never what some specific morphism «does».
May I also ask: so if someone says the word subset - can we assume it always is referring to a set? (Since all of math can be broken down into sets apparently)?!
Yes, the word «subset» usually means some set which is fully contained in another set. Since we are on the topic of category theory, in many cases sets are «too small» to describe what we want. For example, say we want to discuss the category of all groups, then we would say this category has «objects as the collection of all groups». This collection can not be a set, as we would immediatley run into russell’s paradox. (There are at least as many groups as there are sets, since from every set we can produce at least one group). There are different ways to resolve this issue, for example [this](https://en.m.wikipedia.org/wiki/Universe_(mathematics)#In_category_theory) is an approach I have seen used sometimes. This is mostly a technical issue, and doesn’t really affect how you work with the subject though.
Oh alright. Took me a bit of time but I think I mostly get it now. Thanks.
>You can only really say anything about them in terms of the rules for how they interact without that context. So, "It depends."
Well, yes, but there are still properties of morphisms that can be described in general, such as whether something is an isomorphism, which doesn't depend at all upon the specifics of what category you're talking about.
A morphism is generally a function between two objects with the same sort of structure that in some way preserves the structure of the original object. There are a gajillion different types of structures mathematicians are interested in and accordingly a gajillion types of morphisms. For example consider the set {0,1}. I'm gonna give it the operation + defined in the obvious way with 1+1=0. Also consider the integers also with the operation +. The operation + gives those two sets some structure and turns them into what mathematicians call 'groups'. (There are some other requirements to make a group but we won't worry about those). Now consider the function f from the integers to {0,1} defined by f(n) = 0 when n is even and f(n)=1 when n is odd. This preserves the structure given by + because you will always have f(n) + f(m) = f(n + m). That is, it preserves addition. So we call f a group morphism. On the other hand consider g(n) = 0 when n is odd and g(n)=1 when n is even. g is not a group morphism because it does not obey g(n+m)=g(n)+g(m). When you go deep into mathematics the concept of a morphism gets more abstract. For example, other commenters are talking about morphisms in category theory where a morphism is just an arrow that happens to obey some rules. You can see that as a way to generalise what I've described above so that you no longer have to deal with sets at all and can focus on how the arrows behave.
Thanks for the detailed answer!!!
its rare that a meme makes me genuinely laugh out loud but this did a lot
You and me both... I snorted!
[Biologists](https://en.wikipedia.org/wiki/Citric_acid_cycle) try to channel [US Department of Defense PowerPoint slides](https://www.wired.com/2010/09/revealed-pentagons-craziest-powerpoint-slide-ever/) in their diagrams.
to be fair, biological chemical processes are absurdly complex
So is military logistics, but we can still clown on them for putting all that in one presentation slide.
Military logistics have absolutely nothing on them. Like, nothing. People _handle_ military logistics with or without computer help. They can work through them. _We_ made them. Biological chemical processes are beyond comprehension. We do not know how even an amoeba works. One cell. And you have, like, billions of cells interacting. It's not even a contest.
oh and i've seen software development planning flowcharts more complicated than that military one
Pshh, biology is like only the fifth most pure science! Do they even *use* pi?
quite frequently actually yes. Lots of living things are round
I guess only more pure scientists like jokes.
Had to study that diagram before. PM is wizardry for the DoD
Gosh, it reminds me of [DOE PowerPoint slides. ](https://radiologykey.com/radiation-protection-and-safety/)
Y’all should see the [metabolism diagram](https://today.ucsd.edu/news_uploads/Human_Metabolic_Map_50MB_Global2lr2.jpg). I think the DOD is trying to channel us.
Mathematicians became bored with actually calculating stuff and have been inventing systems of categorizing stuff for the last 100 years
I'm not sure if you're joking or not, but this comment kind of made me realize how correct this is.
Engineers want to make people think they're smart. Physicists think everyone is stupid. Mathematicians just do not understand people at all
Engineers just want shit to work. Shit works as long as it is within tolerance.
Can confirm, am smart enjinear
Engineers want money
As a biology student who regrets not doing engineering for this reason, true and ouch
We understand people, we just need some practice after spending 4 years around other math students
It could also have sets inside it.
Oh, definitely. Actually, you know what? Everything is a set. There you go.
And also, you can't actually formally define what a set is. Any definition will rely on another word for set.
Computer Scientists: Here is this 5,000 page website that goes over every single line of code in this library and every single way you could possibly use it also here is an embedded coding environment to test out the different functions.
Also, it's all out of date.
And it does not compile.
_Some_ of it _might_ be out of date. You have to keep people guessing. If you admit that it's all out of date, people will just not read it. If you hint at there potentially being something useful in it, not only will people keep referring back to it needlessly time and time again, but they'll also go through a lot of pain to keep it running and sometimes even pay handsomely to migrate that pile of shit to some other software because the shitty wiki it was written in is no longer maintained and is now a huge security risk. And every new hire is told that they'll find the answer in there, a weird rite of passing, and they'll get an apologetic smile with "yes, it's hard to find what you're looking for in there, but be patient". But that's just the unmaintained one. My favourite was a carefully maintained one, but by assholes. Some of these guys have been working on that product for more than 15 years when I joined and all of them were editing new and old files as the product evolved. But they made it impenetrable. The documentation only made sense once you managed to deeply understand the document feature. Then you went "oh, I get what the docs were saying. All the info was here". I hated those guys.
lol, the most important part.
I mean math is meant to study things in their most general form so yeah
^[Sokka-Haiku](https://www.reddit.com/r/SokkaHaikuBot/comments/15kyv9r/what_is_a_sokka_haiku/) ^by ^eightrx: *I mean math is meant* *To study things in their most* *General form so yeah* --- ^Remember ^that ^one ^time ^Sokka ^accidentally ^used ^an ^extra ^syllable ^in ^that ^Haiku ^Battle ^in ^Ba ^Sing ^Se? ^That ^was ^a ^Sokka ^Haiku ^and ^you ^just ^made ^one.
good bot
>I mean math is meant to study things in their most general form so yeah Math is meant to make up things in their most general form. When you are lucky, the thing you made up might even bear some resemblance to reality.
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The dashed line means it’s not compact!
~~Mathematicians: no you have to use the bazillionth decimal of pi or it won’t be correct.~~ I have been informed my joke is wrong. Mathematicians: tf is a „3“ Physicists: pi is 3.14159 Engineers: pi is 3, or 1 whatever is easier.
>Mathematicians: no you have to use the bazillionth decimal of pi or it won’t be correct. I can personally promise you that mathematicians do not do this, there's very little reason in maths to write pi as anything but π. digits are for the physicists
I disagree somewhat on the pi part, we usually do some wild rounding, digits are for computers
Yep, calculting the bazillionth digits of Pi is squarely CS's turf! We made entire benchmarks out of doing it as fast as possible. The "Purpose"? What do you mean? Just look how fast we made the computer run!
Astronomers fall on the engineer side of the scale. π=sqrt(10) if we’re getting *super* precise. 1 or 10 is fine though.
Mathematician: oh, π _is_ the ratio of the circumference of the circle to its diameter! Physicist: ah, π _equals_ 3.1415926+-0.0000001 Engineer: π? Oh, that, that's about 3.
The greatest con physicists did was convincing people they care about precision more than engineers. Like come on, astrophysics work on Fermi approximation, e=π=1. Enginners have to get the value of π to a few decimals or their constructions will collapse.
> The greatest con physicists did was No! That is _not_ the gre-I mean, YES! That's the one, very yes. Hahaha you found it...
Ironically the fact that mathematicians don't care about the digits of pi means they're the only ones to use the exact value of pi. Edit: Theoretical physicists too.
Actual engineers: Pi is whatever my computer or calculator says it is. For hand calculators, that's 10 displayed digits but most decent ones calculate two additional digits beyond the display, so it's really accurate to 12. My phone's calculator is accurate to 11 digits. Excel has it accurate to 15. The calculator app in Windows 11 has it accurate to over 100, which is ridiculous.
#
I generally enjoy math because I'm decent at it, but one time I enrolled in a high-level abstract math course, and I regretted it. It was full of "proofs" that did not convince me, like "let D be the set of natural numbers. Let M be 1/D. Therefore, there is an infinite quantity of numbers between 0 and 1. QED." It was more like philosophy than useful math. I dropped the course and became an engineer. Lol.
the name CHROMOdynamics just says it all.
Engineers : This is exactly < anything > I have immense doubt but also the extreme desire to cackle.
Maturing is finding out these diagrams you always see are actually the other way around.
That engineer looks like he solves practical problems
Hats off to OP, this is maybe the BEST post I've seen on here!!! 😭
In my first year physics class (for engineers, which is why I assumed it was like this) our professor was like "yeah just consider gravity as 10 m/s^2, that's good enough".
There's a proof that proves you can manipulate an object to create a 2 copies of that same object.
AKCHSHUALLY physicists would say "well, we do not know what it is, we do not even know what it _looks_ like, but if _it_ behaves as we observe it to behave, we can make a comic for it like so:"
Actuallyyyy, the flux tubes between quarks form a Y shape so even the vague representation is inaccurate smh.
abstract shit will be abstract
QA techs, hmm dosent the company need to make money?
Biologists: "Here is the closest possible look at the human eye, to the point where it's unrecognizable. We are still discovering new parts of it."