Listen here, Little Dicky
from fossilesque@mander.xyz to science_memes@mander.xyz on 01 Jul 17:55
https://mander.xyz/post/33193418

#science_memes

threaded - newest

benignintervention@lemmy.world on 01 Jul 17:59 next collapse

I found math in physics to have this really fun duality of “these are rigorous rules that must be followed” and “if we make a set of edge case assumptions, we can fit the square peg in the round hole”

Also I will always treat the derivative operator as a fraction

MyTurtleSwimsUpsideDown@fedia.io on 01 Jul 18:58 next collapse

2+2 = 5

…for sufficiently large values of 2

Quill7513@slrpnk.net on 01 Jul 19:38 next collapse

i was in a math class once where a physics major treated a particular variable as one because at csmic scale the value of the variable basically doesn’t matter. the math professor both was and wasn’t amused

Lemmyoutofhere@lemmy.ca on 01 Jul 22:11 next collapse

Engineer. 2+2=5+/-1

jaupsinluggies@feddit.uk on 01 Jul 22:51 next collapse

Statistician: 1+1=sqrt(2)

InternetCitizen2@lemmy.world on 02 Jul 04:19 next collapse

pi*pi = g

gandalf_der_12te@discuss.tchncs.de on 02 Jul 13:43 collapse

units don’t match, though

umbraroze@slrpnk.net on 02 Jul 07:21 next collapse

Computer science: 2+2=4 (for integers at least; try this with floating point numbers at your own peril, you absolute fool)

gandalf_der_12te@discuss.tchncs.de on 02 Jul 13:44 next collapse

comparing floats for exact equality should be illegal, IMO

callyral@pawb.social on 02 Jul 17:01 next collapse

0.1 + 0.2 = 0.30000000000000004

socsa@piefed.social on 03 Jul 21:01 collapse

Freshmen engineer: wow floating point numbers are great.

Senior engineer: actually the distribution of floating point errors is mindfuck.

Professional engineer: the mean error for all pairwaise 64 bit floating point operations is smaller than the Planck constant.

WR5@lemmy.world on 02 Jul 14:00 collapse

I mean as an engineer, this should actually be 2+2=4 +/-1.

bhamlin@lemmy.world on 02 Jul 18:25 collapse

Found the engineer

sepi@piefed.social on 02 Jul 04:58 next collapse

is this how Brian Greene was born?

bhamlin@lemmy.world on 02 Jul 18:25 collapse

I always chafed at that.

“Here are these rigid rules you must use and follow.”

“How did we get these rules?”

“By ignoring others.”

KTJ_microbes@mander.xyz on 01 Jul 18:50 next collapse

Little dicky? Dick Feynman?

Worx@lemmynsfw.com on 01 Jul 18:58 next collapse

It’s not even a fraction, you can just cancel out the two "d"s

Worx@lemmynsfw.com on 01 Jul 18:58 collapse

"d"s nuts lmao

vaionko@sopuli.xyz on 01 Jul 19:05 next collapse

Except you can kinda treat it as a fraction when dealing with differential equations

prole@lemmy.blahaj.zone on 01 Jul 21:12 next collapse

Oh god this comment just gave me ptsd

JustAPenguin@lemmy.world on 01 Jul 22:55 next collapse

Only for separable equations

socsa@piefed.social on 03 Jul 21:02 collapse

And discrete math.

rudyharrelson@lemmy.radio on 01 Jul 19:05 next collapse

Derivatives started making more sense to me after I started learning their practical applications in physics class. d/dx was too abstract when learning it in precalc, but once physics introduced d/dt (change with respect to time t), it made derivative formulas feel more intuitive, like “velocity is the change in position with respect to time, which the derivative of position” and “acceleration is the change in velocity with respect to time, which is the derivative of velocity”

Lemmygradwontallowme@hexbear.net on 01 Jul 19:37 next collapse

yea, essentially, to me, calculus is like the study of slope and a slope of everything slope, with displacement, velocity, acceleration.

Prunebutt@slrpnk.net on 01 Jul 21:06 collapse

Possibly you just had to hear it more than once.

I learned it the other way around since my physics teacher was speedrunning the math sections to get to the fun physics stuff and I really got it after hearing it the second time in math class.

But yeah: it often helps to have practical examples and it doesn’t get any more applicable to real life than d/dt.

exasperation@lemmy.dbzer0.com on 02 Jul 18:10 collapse

I always needed practical examples, which is why it was helpful to learn physics alongside calculus my senior year in high school. Knowing where the physics equations came from was easier than just blindly memorizing the formulas.

The specific example of things clicking for me was understanding where the “1/2” came from in distance = 1/2 (acceleration)(time)^2 (the simpler case of initial velocity being 0).

And then later on, complex numbers didn’t make any sense to me until phase angles in AC circuits showed me a practical application, and vector calculus didn’t make sense to me until I had to actually work out practical applications of Maxwell’s equations.

iAvicenna@lemmy.world on 01 Jul 20:07 next collapse

Look it is so simple, it just acts on an uncountably infinite dimensional vector space of differentiable functions.

gandalf_der_12te@discuss.tchncs.de on 02 Jul 13:45 collapse

fun fact: the vector space of differentiable functions (at least on compact domains) is actually of countable dimension.

still infinite though

iAvicenna@lemmy.world on 02 Jul 17:17 collapse

Doesn’t BCT imply that infinite dimensional Banach spaces cannot have a countable basis

gandalf_der_12te@discuss.tchncs.de on 03 Jul 11:59 collapse

Uhm, yeah, but there’s two different definitions of basis iirc. And i’m using the analytical definition here; you’re talking about the linear algebra definition.

iAvicenna@lemmy.world on 03 Jul 13:51 collapse

So I call an infinite dimensional vector space of countable/uncountable dimensions if it has a countable and uncountable basis. What is the analytical definition? Or do you mean basis in the sense of topology?

gandalf_der_12te@discuss.tchncs.de on 03 Jul 14:07 collapse

Uhm, i remember there’s two definitions for basis.

The basis in linear algebra says that you can compose every vector v as a finite sum v = sum over i from 1 to N of a_i * v_i, where a_i are arbitrary coefficients

The basis in analysis says that you can compose every vector v as an infinite sum v = sum over i from 1 to infinity of a_i * v_i. So that makes a convergent series. It requires that a topology is defined on the vector space fist, so convergence becomes well-defined. We call such a vector space of countably infinite dimension if such a basis (v_1, v_2, …) exists that every vector v can be represented as a convergent series.

gandalf_der_12te@discuss.tchncs.de on 03 Jul 14:11 next collapse

i just checked and there’s official names for it:

  • the term Hamel basis refers to basis in linear algebra
  • the term Schauder basis is used to refer to the basis in analysis sense.
iAvicenna@lemmy.world on 03 Jul 16:16 collapse

Ah that makes sense, regular definition of basis is not much of use in infinite dimension anyways as far as I recall. Wonder if differentiability is required for what you said since polynomials on compact domains (probably required for uniform convergence or sth) would also work for cont functions I think.

gandalf_der_12te@discuss.tchncs.de on 04 Jul 05:43 collapse

regular definition of basis is not much of use in infinite dimension anyways as far as I recall.

yeah, that’s exactly why we have an alternative definition for that :D

Wonder if differentiability is required for what you said since polynomials on compact domains (probably required for uniform convergence or sth) would also work for cont functions I think.

Differentiability is not required; what is required is a topology, i.e. a definition of convergence to make sure the infinite series are well-defined.

Zerush@lemmy.ml on 01 Jul 20:22 next collapse

When a mathematician want to scare an physicist he only need to speak about ∞

corvus@lemmy.ml on 02 Jul 05:49 next collapse

When a physicist want to impress a mathematician he explains how he tames infinities with renormalization.

socsa@piefed.social on 03 Jul 21:04 collapse

Only the sith deal in ∞

Zerush@lemmy.ml on 03 Jul 22:16 collapse

…and Buzz Lightyear

chortle_tortle@mander.xyz on 01 Jul 21:12 next collapse

Mathematicians will in one breath tell you they aren’t fractions, then in the next tell you dz/dx = dz/dy * dy/dx

lmmarsano@lemmynsfw.com on 01 Jul 21:34 next collapse

Brah, chain rule & function composition.

Koolio@hexbear.net on 01 Jul 22:08 next collapse

Also multiplying by dx in diffeqs

gandalf_der_12te@discuss.tchncs.de on 02 Jul 13:41 collapse

vietnam flashbacks meme

marcos@lemmy.world on 02 Jul 04:08 next collapse

Have you seen a mathematician claim that? Because there’s entire algebra they created just so it becomes a fraction.

RvTV95XBeo@sh.itjust.works on 02 Jul 05:35 next collapse

(d/dx)(x) = 1 = dx/dx

Collatz_problem@hexbear.net on 02 Jul 07:19 next collapse

This is until you do multivariate functions. Then you get for f(x(t), y(t)) this: df/dt = df/dx * dx/dt + df/dy * dy/dt

jsomae@lemmy.ml on 03 Jul 17:35 collapse

Not very good mathematicians if they tell you they aren’t fractions.

devilish666@lemmy.world on 01 Jul 22:53 next collapse

Is that Phill Swift from flex tape ?

Kolanaki@pawb.social on 01 Jul 22:56 next collapse

De dix, boss! De dix!

moobythegoldensock@infosec.pub on 02 Jul 01:42 next collapse

It was a fraction in Leibniz’s original notation.

marcos@lemmy.world on 02 Jul 04:07 collapse

And it denotes an operation that gives you that fraction in operational algebra…

Instead of making it clear that d is an operator, not a value, and thus the entire thing becomes an operator, physicists keep claiming that there’s no fraction involved. I guess they like confusing people.

corvus@lemmy.ml on 02 Jul 05:40 next collapse

Chicken thinking: “Someone please explain this guy how we solve the Schroëdinger equation”

justme@lemmy.dbzer0.com on 02 Jul 12:03 next collapse

Division is an operator

Gladaed@feddit.org on 02 Jul 12:48 next collapse

Why does using it as a fraction work just fine then? Checkmate, Maths!

kogasa@programming.dev on 03 Jul 15:02 collapse

It doesn’t. Only sometimes it does, because it can be seen as an operator involving a limit of a fraction and sometimes you can commute the limit when the expression is sufficiently regular

Gladaed@feddit.org on 03 Jul 15:10 collapse

Added clarifying sentence I speak from a physicists point of view.

BoxOfFeet@lemmy.world on 02 Jul 13:32 next collapse

What is Phil Swift going to do with that chicken?

ArsonButCute@lemmy.dbzer0.com on 02 Jul 15:48 collapse

The will repair it with flex seal of course

BoxOfFeet@lemmy.world on 02 Jul 16:05 collapse

To demonstrate the power of flex seal, I SAWED THIS CHICKEN IN HALF!

shapis@lemmy.ml on 02 Jul 13:46 next collapse

This very nice Romanian lady that taught me complex plane calculus made sure to emphasize that e^j*theta was just a notation.

Then proceeded to just use it as if it was actually eulers number to the j arg. And I still don’t understand why and under what cases I can’t just assume it’s the actual thing.

zea_64@lemmy.blahaj.zone on 02 Jul 15:29 next collapse

I’ve seen e^{d/dx}

frezik@lemmy.blahaj.zone on 02 Jul 17:01 next collapse

Let’s face it: Calculus notation is a mess. We have three different ways to notate a derivative, and they all suck.

JackbyDev@programming.dev on 03 Jul 16:40 collapse

Calculus was the only class I failed in college. It was one of those massive 200 student classes. The teacher had a thick accent and hand writing that was difficult to read. Also, I remember her using phrases like “iff” that at the time I thought was her misspelling something only to later realize it was short hand for “if and only if”, so I can’t imagine how many other things just blew over my head.

I retook it in a much smaller class and had a much better time.

carmo55@lemmy.zip on 03 Jul 14:07 next collapse

It is just a definition, but it’s the only definition of the complex exponential function which is well behaved and is equal to the real variable function on the real line.

Also, every identity about analytical functions on the real line also holds for the respective complex function (excluding things that require ordering). They should have probably explained it.

shapis@lemmy.ml on 03 Jul 15:13 collapse

She did. She spent a whole class on about the fundamental theorem of algebra I believe? I was distracted though.

sabin@lemmy.world on 03 Jul 16:00 next collapse

It legitimately IS exponentiation. Romanian lady was wrong.

jsomae@lemmy.ml on 03 Jul 17:26 collapse

e^𝘪θ^ is not just notation. You can graph the entire function e^x+𝘪θ^ across the whole complex domain and find that it matches up smoothly with both the version restricted to the real axis (e^x^) and the imaginary axis (e^𝘪θ^). The complete version is:

e^x+𝘪θ^ := e^x^(cos(θ) + 𝘪sin(θ))

Various proofs of this can be found on wikipeda. Since these proofs just use basic calculus, this means we didn’t need to invent any new notation along the way.

shapis@lemmy.ml on 03 Jul 20:26 collapse

I’m aware of that identity. There’s a good chance I misunderstood what she said about it being just a notation.

jsomae@lemmy.ml on 04 Jul 01:11 collapse

It’s not simply notation, since you can prove the identity from base principles. An alien species would be able to discover this independently.

callyral@pawb.social on 02 Jul 16:59 next collapse

clearly, d/dx simplifies to 1/x

SaharaMaleikuhm@feddit.org on 02 Jul 17:47 next collapse

I still don’t know how I made it through those math curses at uni.

filcuk@lemmy.zip on 03 Jul 14:33 collapse

Calling them ‘curses’ is apt

LovableSidekick@lemmy.world on 02 Jul 18:14 next collapse

Having studied physics myself I’m sure physicists know what a derivative looks like.

[deleted] on 02 Jul 18:22 next collapse

.

bhamlin@lemmy.world on 02 Jul 18:22 next collapse

If not fraction, why fraction shaped?

Mubelotix@jlai.lu on 03 Jul 14:04 next collapse

We teach kids the derive operator being or ·. Then we switch to that writing which makes sense when you can use it properly enough it behaves like a fraction

olafurp@lemmy.world on 03 Jul 14:10 next collapse

The thing is that it’s legit a fraction and d/dx actually explains what’s going on under the hood. People interact with it as an operator because it’s mostly looking up common derivatives and using the properties.

Take for example ∫f(x) dx to mean "the sum (∫) of supersmall sections of x (dx) multiplied by the value of x at that point ( f(x) ). This is why there’s dx at the end of all integrals.

The same way you can say that the slope at x is tiny f(x) divided by tiny x or d*f(x) / dx or more traditionally (d/dx) * f(x).

kogasa@programming.dev on 03 Jul 15:00 collapse

The other thing is that it’s legit not a fraction.

jsomae@lemmy.ml on 03 Jul 16:29 collapse

it’s legit a fraction, just the numerator and denominator aren’t numbers.

kogasa@programming.dev on 03 Jul 17:11 collapse

No 👍

jsomae@lemmy.ml on 03 Jul 17:20 collapse

try this on – Yes 👎

It’s a fraction of two infinitesimals. Infinitesimals aren’t numbers, however, they have their own algebra and can be manipulated algebraically. It so happens that a fraction of two infinitesimals behaves as a derivative.

kogasa@programming.dev on 03 Jul 19:06 collapse

Ok, but no. Infinitesimal-based foundations for calculus aren’t standard and if you try to make this work with differential forms you’ll get a convoluted mess that is far less elegant than the actual definitions. It’s just not founded on actual math. It’s hard for me to argue this with you because it comes down to simply not knowing the definition of a basic concept or having the necessary context to understand why that definition is used instead of others…

jsomae@lemmy.ml on 03 Jul 19:49 collapse

Why would you assume I don’t have the context? I have a degree in math. I could be wrong about this, I’m open-minded. By all means, please explain how infinitesimals don’t have a consistent algebra.

kogasa@programming.dev on 03 Jul 20:22 collapse

  1. I also have a masters in math and completed all coursework for a PhD. Infinitesimals never came up because they’re not part of standard foundations for analysis. I’d be shocked if they were addressed in any formal capacity in your curriculum, because why would they be? It can be useful to think in terms of infinitesimals for intuition but you should know the difference between intuition and formalism.

  2. I didn’t say “infinitesimals don’t have a consistent algebra.” I’m familiar with NSA and other systems admitting infinitesimal-like objects. I said they’re not standard. They aren’t.

  3. If you want to use differential forms to define 1D calculus, rather than a NSA/infinitesimal approach, you’ll eventually realize some of your definitions are circular, since differential forms themselves are defined with an implicit understanding of basic calculus. You can get around this circular dependence but only by introducing new definitions that are ultimately less elegant than the standard limit-based ones.

Daft_ish@lemmy.dbzer0.com on 03 Jul 14:17 next collapse

1/2 <-- not a number. Two numbers and an operator. But also a number.

jsomae@lemmy.ml on 03 Jul 16:31 collapse

In Comp-Sci, operators mean stuff like >>, *, /, + and so on. But in math, an operator is a (possibly symbollic) function, such as a derivative or matrix.

Daft_ish@lemmy.dbzer0.com on 03 Jul 16:37 collapse

Youre not wrong, distinctively, but even in mathematics “/” is considered an operator.

en.m.wikipedia.org/wiki/Operation_(mathematics)

<img alt="" src="https://lemmy.dbzer0.com/pictrs/image/3b1247d0-ca8e-4241-94b7-7509bf33ccb0.webp">

jsomae@lemmy.ml on 03 Jul 16:43 collapse

oh huh, neat. Always though of those as “operations.”

voodooattack@lemmy.world on 03 Jul 17:48 next collapse

Software engineer: 🫦

socsa@piefed.social on 03 Jul 20:54 next collapse

The world has finite precision. dx isn't a limit towards zero, it is a limit towards the smallest numerical non-zero. For physics, that's Planck, for engineers it's the least significant bit/figure. All of calculus can be generalized to arbitrary precision, and it's called discrete math. So not even mathematicians agree on this topic.

Zerush@lemmy.ml on 04 Jul 00:58 next collapse

Headache for mathematicians

youtube.com/shorts/WSFkDNXOpMk

someacnt@sh.itjust.works on 04 Jul 10:12 collapse

But df/dx is a fraction, is a ratio between differential of f and standard differential of x. They both live in the tangent space TR, which is isomorphic to R.

What’s not fraction is \partial f / \partial x, but likely you already know that. This is akin to how you cannot divide two vectors.