/sci/ - Science & Math

[Anonymous No.15012234]

>I LOVE SCIENCE
>can’t do basic calculus

[Anonymous No.15012246]

>>15012234
Calculus isn't real. 0.999... = 1 infinite precision doesn't exist. The only math you need is linear algebra and geometry. Everything else is literally just so "academic" types can circle jerk to how "clever" they are. Calculus has never had any real applications.

[Anonymous No.15012278]

Calculus dont provide any understanding btw.

Coordinates in general and ((((ameritizable analysis))) was made for parrots to deceive themselves into thinking they understood some maths.

There's a reason why Newton choose coordinate free geometrical arguments for his magnum opus instead of fluxions.

[Anonymous No.15012294]

>>15012246
And dimensionless points exist?

[Anonymous No.15012329]

>I LOVE CALCULUS
>can't do basic science

[Anonymous No.15012341]

>>15012329
Ngmi

[Anonymous No.15012350]

>>15012294
No a point has 1 dimensions. Pseud.

[Anonymous No.15012352]

>>15012246
>calculus isn't real
Yes it is it's the study of infinitesimals...

lim dx--> 0 of f(x)-f(x-dx)/dx

[Anonymous No.15012379]

>>15012234
I agree that understanding some models used in science absolutely requires understanding the mathematics they employ on an intuitive/fairly deep level.

That said, there are lots of areas where people very clearly get all tied up because they understand the mathematics but not what it is supposed to be modeling. This is made worse by the siloing of the natural sciences, mathematics, and philosophy. The latter of these has made itself irrelevant by choosing to focus on chronological slogs through the "great names," instead of anything applied. Contrast this with the 19th century and first half of the 20th, where philosophers and mathematicians were deeply involved in the sciences with many luminaries making a mark in all three.

People substitute mathematical notation for demonstrating how they understand nuanced concepts that are open to interpretation, and then unwittingly give explanations that result in contradictions if you think then through.

I see this the most with thermodynamics and information theory, also with computation, particularly when cognitive scientists and biologists are using the concepts. Then you also have a huge problem with people using statistics for inductive reasoning, but never having been taught anything about induction or abduction aside from a brief definition. This is made worse by most stats textbooks just skipping over interpretations of probability, either awkwardly glossing over the subject, or just asserting rout frequentism, which is simply incoherent in many contexts. A lot of people using stats for publications simply cannot explain why they are a good/valid tool for what they are doing.

You need mathematics, logic, and epistemology to do science. You don't need to be an expert, but you should have some level of comfort with them. In some fields people only get the first, and in many they get an insufficient amount of all three in many cases.

[Anonymous No.15012396]

[eqn]f(x)=x^2[/eqn]
slope of [math] f(x)= [/math]
[eqn]{f(x)-f(x-d) \over d}={x^2 - (x^2 -2xd + d^2) \over d}={2xd - d^2 \over d}[/eqn]
which any bloke can take the limit of as d goes to 0

[Anonymous No.15012402]

[math] d^2 [\math] gets infinitely smaller than [math] 2xd [\math], thus the second term goes to 0... the first term clearly remains equal to [math] 2x [\math] no matter how small [math] d [\math] gets.. thus we can make [math] d [\math] as theoretically small as we want

[Anonymous No.15012406]

[math] d^2 [/math] gets infinitely smaller than [math] 2xd [/math], thus the second term goes to 0... the first term clearly remains equal to [math] 2x [/math] no matter how small [math] d [/math] gets.. thus we can make [math] d [/math] as theoretically small as we want

[Anonymous No.15012424]

Limit logic: We can't compute d=0, but we can analyze what happens for ANY extremely small d, thus we can make d as small as we want

[Anonymous No.15012432]

If you can compute [math]f(x)-f(x-d) \over d [/math] for ANY small d, then you can analyze the function as close to zero as you... so basically solving limits is just solving an equation with a new variable that we have an estimate for

[Anonymous No.15012441]

Instead of plugging in d=0, you treat d as a new variable

[Anonymous No.15012444]

>>15012352
It's 0/0 it's undefined. Calculus is the study of things that are not real. It has no real world applications.

[Anonymous No.15012451]

>>15012444
It's not undefined. Treat dx like a new variable which could be anything except 0. Then we can see exactly what the result will be for ANY small dx

[Anonymous No.15012453]

>>15012451
>which could be anything except 0
Exactly, calculus doesn't work.

[Anonymous No.15012457]

>>15012444
You think too broadly. If we consider the equation [eqn]{f(x) - f(x-d) \over d }[/eqn] for x in the Real Numbers and d in Real Numbers but unequal to 0, then we can analyze precisely the equation for any small d

[Anonymous No.15012459]

As long as f(x) is defined for all x in Real Numbers then so is f(x-d), and we can analyze the slope for any d unequal to 0.

Some functions like [eqn]x^2[/eqn] will simplify a lot in the slope equation and the result for small d and any x will be clear

[Anonymous No.15012460]

Taking the limit as d goes to 0 is just the same as analyzing the result for any small d

[Anonymous No.15012463]

>>15012453
See my last post. Taking the limit is not magical. It is just the analysis for ANY small d.

[Anonymous No.15012523]

>>15012379
>they understand the mathematics but not what it is supposed to be modeling
What would be an example of this?

[Anonymous No.15012655]

>>15012523
Me whenever I have to do any amount of calculus in my engineering classes

[Anonymous No.15012711]

>>15012396
0/0 undefined

[Anonymous No.15012713]

>>15012432
Okay use that to compute the derivative of (sin(x^3))^2

[Anonymous No.15012733]

>i love math
>doesnt know what a banach space is

[Anonymous No.15012797]

>>15012713
[eqn]R(x)=f(g(h(x))))=(sin(x^3))^2[/eqn]
chain rule.... allows for
[eqn]{A^2 - (A-d)^2 \over d }{sin(B)-sin(B-d) \over d}{ x^3 - (x-d)^3 \over d }[/eqn]
A = sin(x^3)
B = x^3

because slope of f(g(x)) equals [eqn]{df(g(x)) \over dg(x)}{dg(x) \over dx}[/eqn]

so [eqn](2A - d)(cos(B))(3x^2 - d)[/eqn] (derivative of sin(u) is by just examining the finite graph)(and the d is as small as need be)

[Anonymous No.15012809]

>>15012234
that should be classed as retarded at this point in history, like not understanding division

[Anonymous No.15012823]

>>15012797
>chain rule
Wrong. Use the definition and only the definition provided in the earlier post.

[Anonymous No.15012833]

>>15012797
>Uses things unproven
>Introduced opaque, undefined notation
What is this "dy/dx" of which you speak and why do you claim some weird stuff like the derivative acts like a fraction? Just admit you can't do it homie.

[Anonymous No.15012841]

THe chained rule is based on [eqn]{df(g(x)) \over dg(x)}{dg(x)\over dx}[/eqn] .... a rate of change multiplied by another rate of change yields the rate of change of the composition...

[eqn]R1 * R2 = R3[/eqn]where R3 represents the composition

[Anonymous No.15012868]

>>15012841
Derivatives aren't fractions. You can't "cancel" anything like what you tried to do.

[Anonymous No.15013063]

>>15012868
yes he can, and yes they are, just limits of fractions. Are you one of those finitist retards?

[Anonymous No.15013086]

>>15013063
They can be considered without using a limit

The rate of change is based on

dx implies dg(x) implies df(g(x))

for finite dx...

We want to show [math] df(g(x))/dx == (d(f(g(x))/df(x)) * (df(x)/dx) [/math]

[Anonymous No.15013106]

ITT /sci/ schizos argue about a math debate that's literally 3,000 years old.

[Anonymous No.15013110]

>>15013063
We have

[math]dx \implies dg(x)[/math]

[math]dg(x) \implies df(g(x))[/math]

so [math]dx \implies df(g(x)) [/math]

We also have [math]dx*R1=dg(x)[/math] and [math]dg(x)*R2=df(g(x))[/math]

so [math]dx*R1*R2=df(g(x))[/math] thus R1*R2 is the slope of f(g(x))

[Anonymous No.15013117]

>>15012234
Pop science is fun.
Real science is fucking awful... or so I think.

[Anonymous No.15013309]

>>15012246
The area under the curve (integral) is real. The slope of the tangent line of a point (derivitive) is also real

[Anonymous No.15013311]

>>15012234
The universe doesn't think in calculus, making it completely irrelevant

[Anonymous No.15013312]

>>15012823
>>15012833
We can't provide proofs for every aspect of calculus. Look up "proof for chain rule"

[Anonymous No.15013316]

>>15013312
>We can't provide proofs
Ignorance sure is bliss

[Anonymous No.15013362]

>>15012246
>can't do basic calculus
>MATHS IS WRONG

[Anonymous No.15013398]

>>15013362
>can't describe the universe without making up shit that doesn't exist

[Anonymous No.15013404]

>>15012246
Philosophy major pls go

[Anonymous No.15013405]

>>15013316
There is a word limit on 4chan posts, plus it would take an unfeasible amount of time to prove all of calculus. We understand the proofs but it would be impossible to communicate it to you in this medium

[Anonymous No.15013468]

>>15013405
If you can't explain it simply...

[Anonymous No.15013508]

>>15012523
Not him, but most stuff in quantum mechanics and a large proportion of stuff involving information theoretic approaches to the sciences has this problem.

Arguably this is a problem in economics too, since people will insist their models are valid even after observation keeps falsifying them.

Loads of people use significance testing with no real knowledge of probability theory as >>15012379 points out.

[Anonymous No.15014161]

>>15012523
A woman in the UK got sent to prison for killing her two infant children largely on the testimony of a renowned doctor who did a ton of stats work. He said that the chance of two kids from a family as wealthy as her's dying of SIDS was 1:14 million or something, based on a regression analysis.

She was released after people who actually know probability theory pointed out that the statistics that are relevant were: given both children died in x manner, what is the chance that their mother murdered them.

At first this seems like simple base rate neglect. The doctor ignored that it is extremely rare for a mother to kill two children, and for her to do so in ways that didn't leave evidence. He also was ignoring the correlation between having one SIDS death in a family and another (essentially, mutual information). He was also making the common mistake of picking a low likelyhood null hypothesis and saying if not H0 then H1. Really, this sort of thing needs a prior used or some other way to correct for this.

But the deeper logical flaws that even the doctors critics tended to miss is that the question he even was attempting to answer was formulated wrong, besides any of the above critiques. He wanted to answer, "what is the probability that these two children died of SIDS?" All else aside, the question is: "given both children are dead, what is the probability they both died of SIDS?

These aren't the same question, right? But actually a ton of science supposed they absolutely are the same question. This is the root problem of the replication crisis and why nothing is fixing it that well.

Essentially, this is the consequence of only working through incredibly simple frequentist examples with coin tosses and dice, then moving on to notation and abstract concepts, and never looking back to see what your math actually implies is true.

[Anonymous No.15014171]

>>15012234
Why is calculus so kino and statistics so shit? They're like opposite ends of how intuitive it is to understand them?? 2r88p8

[Anonymous No.15014172]

>>15012234
My witch doctor can study the natural world too, sweaty.

[Anonymous No.15014179]

>>15012234
I can do basic calculus, but I’m a brainlet. I literally can’t apply anything I learn, but it’s very simple to do the tests for convergence and divergence and draw conclusions. Taking derivatives literally only require basic arithmetic, remembering a few special derivatives (sin, cos, e^x), and product rule/chain rule.

The true filter is probably understanding high level physics and engineering.

[Anonymous No.15014196]

>I hate science
>Master of Quantum Chromodynamics, Differential Geometry, Conformal groups, and Path Integral Formalism.

Explain

[Anonymous No.15014227]

You can conceive a function with a geometrical rational slope that can be constructed which will be also the result of a limit. Is it just a coincidence the two are the same?

[Anonymous No.15014269]

>>15013311
did you ask the universe?

[Anonymous No.15014302]

>>15012234
>I LOVE MATH!
>Can't do basic predicate calculus.

[Anonymous No.15014309]

>>15014302
>I LOVE LOGIC
>Can't do basic dialectical

[Anonymous No.15014352]

>>15014171
I think it's the blending of deductive and indictive reasoning in stats that makes it so difficult to conceptualize. You're using deduction to say things about induction but keeping the two threads apart is challenging.

Parts of stats are so intuitive you can teach them to children. That's what makes it so tricky though.