Mathematics - 2017-06-27 (page 1 of 6)

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12:00 AM

If I localize a ring at just the neutral element, I get the same ring again, right?

12:11 AM

Wait, by neutral element, do you mean the additive or multiplicative identity? Just to be clear.

Sorry, I mean the multiplicative identity

for the additive identity we get the zero ring

Right, right.

I should think so, actually.

okay, thanks!

At least it's something isomorphic to it I think

I sometimes don't really know if I should say "it's the same" or "it's isomorphic"

Checking the definition, you want $(m,1)$ and $(n,1)$ to be equivalent if $1(1n - 1m) = 0$, or $m = n$, so you're creating a ring isomorphic to $R$ whose elements could be written as $\frac{r}{1}$.

Unless you're still working with the exact same objects, saying "it's isomorphic" is more precise.

Okay

12:16 AM

In the case of localization, you're constructing a new thing--namely, a ring structure on $R \times S$, so it's different, but isomorphic.

Yeah

I think my Professor is not so strict with the notation etc.

In that case, you'd be fine either way. After all, two isomorphic objects are basically the same thing, up to relabeling, so conceptually you wouldn't be wrong.

Just that there's a pedantic way to look at it.

Yeah

and I guess if we kept track of the correct notation all the time, then algebraic geometry wouldn't be much fun

That I can't speak to as much--I don't have the right background for algebraic geometry yet. Though I really want it!

Haha me too

it's a tough way though :D

12:23 AM

man I have a confrontation today with my supervisor

12:42 AM

why?

He was always rude to me so I changed to someone else

you mean you had a confrontation?

yeah

He was being super rude to me and not being friendly

so I wanted to see if I could change him and I did end up working with someone else

lol, the tense conveys meanings other than time

if you have a confrontation, it sounds like you planned it

yeah i guess

12:54 AM

Damn, sorry

Hope your new adviser is better

me 2 I know one guy who I want to work with, so I hope he accepts me.

Oh, wait so you don't yet know if you'll get that new adviser? What happens then?

@Daminark my old advisor was very rude to me and if I made a small mistake he would like throw a fit and wouldn't explain to me what is wrong or anything like that.

@Daminark I will see what will happen. I just don't think about it until this potential advisor emails back.

Alright, good luck

thanks

12:59 AM

Which year are you in grad school now?

Or I guess, which did you just finish?

@Daminark yeah I am in grad school atm

No I mean, are you a first year student, second year, what?

first year @Daminark

user image

wtf is $\sigma$?

1:14 AM

I see

@Twink a function

anyway I am happy I changed now I wouldn't be able to take it to work with him @Daminark

Akiva Weinberger

1:27 AM

1

reddit.com/r/tifu/comments/2livoo/…

2

reddit.com/r/AskReddit/comments/6jix5j/…

.

(Remind me to send the first link to my English teacher when I wake up.)

Yeah for sure

Send the first link to your English teacher when you wake up

1:48 AM

@Twink If you like, $\sigma(w)\equiv \dfrac{f(z+w)-f(z)}{w}-f'(z)$

which goes to $f'(z)-f'(z)=0$ as $z\to 0$.

why they only seem to think of it as a function of $w$...hrm.

I can't quite make sense of what they're doing, alas.

blah, should have been "as $w\to 0$" above

@Twink It's the terms (to be multiplied by $w$ later) in the Taylor expansion of $f(z+w)$, excluding the first 2 terms (one of which cancels $f(z)$ and the other is just $f'(z)w$

wait

I'd need to see this

why are they even doing this. I've not seen such a derivation of Cauchy Riemann equations before

2:34 AM

If I had to guess, they're just suppressing the $z$-dependence for the purposes of their argument.

2 hours later…

4:05 AM

Hello

user84215

4:24 AM

For a point of a regular surface with positive Gaussian curvature, if it is a local maximum for one of the principal curvature and a local minimum for the other one, why are these principal curvatures equal to each other ?

Any topologists around who could help me with this? math.stackexchange.com/q/2336320/169780

Hey everyone!

@Daminark sup dank

How's it going?

4:41 AM

Alright, drinking beer and eating mac

You?

Btw , it's possible to derive all of algebra from PDEs

Theoretically at least

That sounds suspicious

And I'm doing alright, thanks

4:59 AM

@Daminark well , you can simulate Newtonian mechanics with PDEs, so all we have to do is simulate the body of grothendieck, and then we can have all he produces, we can even do better and simulate the perfect algebraist

Iff such an algebraist exists

The essence is that you can derive ANYTHING from PDEs

Lol, free will tho

What about it?

You can't predict the actual results of algebra

Well I see two arguments here, are they the same?

am not sure what you mean by free will but for predicting algebra, all I have to do is simulate grothendieck and run different variations of him

or just simulate grothendieck and feed him different problems

You can't run a simulation of Grothendieck is the problem

5:10 AM

Why not?

Like, you can't replicate a human being because the actions aren't determined by Newtonian mechanics

Lol

Come on

What else? Magic?

Thought

user84215

For a point of a regular surface with positive Gaussian curvature, if it is a local maximum for one of the principal curvature and a local minimum for the other one, why are these principal curvatures equal to each other ?

@Daminark that vague

5:19 AM

Well, for what it's worth I'm leaning more to pluralist than physicalist

You took this from the realm of science and math to philosophy, where things are based on intuition and unsupported by either reason or experiments

I mean, you can't prove via experiment whether pluralism or physicalism works

so why adopt any of those?

We know that there is science and it obviously works

Why not just live within that frame work?

But if our thoughts were determined by initial conditions at the big bang, then that would undermine their validity, including the thought that this was the case

Why would you say this??

How does that undermines our thinking?

5:27 AM

Because then, that which we come to believe cannot be said to derive from reason, it was determined by some initial random conditions at the beginning of the universe that are not necessarily bound to lead people in the right direction

Perhaps we were determined to think that truth values acted in a certain way when they really did not, crippling reason itself. Anyway, beyond all that speculation, there's really not much to say if that were the case, everything halts

user image

And when you were mentioning that we know science, so why adopt the anything in the physicalist vs pluralist debate, making the claim that one could find a few PDEs floating around and simulate Grothendieck perfectly is necessarily adopting a physicalist position

Can someone help me with this question? It's difficult.

Look up the questions, am sure there is dozens of similar ones to it

@Zee nope

5:31 AM

Try the physics chat

Ok

@Daminark I don't see how other philosophical positions can bring back free will, aside from some form of supernatural world

Additionally, note that even if you could conduct this simulation, that doesn't mean that algebra derives from PDE

Okay perhaps free will is an iffy way of putting it, let's say ability to reason

Whether those two are the same, maybe, haven't thought about that much yet

Well any result of algebra that has been discovered can be simulated , and any result that could have been discovered by a human as well

And I mean, if supernatural means aphysical, then I mean sure.

5:35 AM

@Abcd no units, no answer...

id pick e

@Zee its a math problem...

No, it's not that , super natural means some kind of magical thing that we can't explain, aka black box, but a black box can explain anything so it's not really fair to use it

And the result itself is not simulated or contained, merely its derivation by someone is, in retrospect. Epistemologically those two are different

@Typhon Assume SI units...

@Abcd that's still unsolvable.

how do i know the answer is in seconds, milliseconds, minutes, or hours?

I mean, so we don't know if our sense perception is even correct, and that our subjective experience has any truth value to it at all

5:38 AM

@Typhon All that has to be assumed

...no

To engage in thought whatsoever, things need to be black boxed on basis of plausibility

1 hour = 60 minutes

for instance

@Typhon See this: clay6.com/qa/52505/…

One of those things which is plausible is that we have the ability to reason about things, that's no more of a black box than science, and perhaps maybe even less

5:38 AM

But I can't understand that...

so the answer could be in a different unit and therefore differ by a multiplicative constant

@Typhon Much ado about nothing

@Abcd wat. 60 minutes is an hour.

@Typhon Did you see the solution I linked you to?

thats not relevant

5:41 AM

So then given our apparent ability to reason, we ask whether we know it works out properly if we are to suggest that thought is determined by the laws of physics versus random or based on some actual ability humans have, which may derive from a non-physical reality, to reason. The answer is that we don't know. And neither claim is on a metaphysically stronger basis than the other

@Abcd no. it cannot be answered properly. all of those answers could be either right or wrong because they are not measurements.

suppose it is hours

Testing

and you answered for minutes

ASSUME SI units @Typhon

@Abcd hours and minutes are si units dumbass.

5:43 AM

@Daminark you bring many points, I can't really address all of them at once...

@Typhon second is SI unit for Time

SI units are not single unit

Hence, we do not really have particularly good reason to believe that PDE contains algebra in the way you say, and again, that's epistemologically distinct from derivation, the way that you can derive the implicit function theorem from the inverse function theorem

Lolol, fair, I tend to write this stuff in a very train of thought style

I can even do better than my original argument

Let's hear it

5:44 AM

@Abcd that is beyond narrow minded. so is hours, minutes, and days.

@Typhon They aren't.

International System of Units

The International System of Units (French: Système international d'unités pronounced: [sistɛm ɛ̃tɛʁnasjɔnal dynite]; abbreviated as SI) is the modern form of the metric system, and is the most widely used system of measurement. It comprises a coherent system of units of measurement built on seven base units. The system also establishes a set of twenty prefixes to the unit names and unit symbols that may be used when specifying multiples and fractions of the units. The system was published in 1960 as a result of an initiative that began in 1948. It is based on the metre-kilogram-second system of...

Have a look at the table.

Let's say you wanna solve some kind of algebraic symbolic relation

@Typhon ASSUME - m/s, s, m . I hope that's better.

You just simulate the symbols on the complex plane and simulate all possible movements of those symbols that correspond to the algebraic rules, and then just see if any PDE would give you such a result

I mean this depends strictly on choice of notation, and again is epistemologically different from derivation

A priori you have no idea which PDE would work, even with notation given

5:47 AM

sure but you can standardize the notation

The only way you could know is by already knowing the algebraic results

Which defeats the purpose of this

Well you have both sides of the equation, you wanna prove it

So you keep moving the left side in a way until it gives the same image as the right side

@Abcd you missed my point altogether. the thing you linked is a trick question. In true physics, the lack of a unit means just a number, so all four answers are incorrect. Even if they are some mystery unit assuming seconds is without justification and incredibly narrow-minded. SI is a system of units, and not just one unit for every measurement.

Then you take such a PDE, and "slow it down" and see how it maps the symbols at each T

so... you're still left with seeing which answer is if the form k*x = y where y is your solution and k is some constant. That's just silly.

is this college physics?

i sure hope not

5:49 AM

If you're just homotoping the symbols directly then you're not even generating algebraic results. If you're doing it under rules of manipulation, then again, you fail to have information about algebraic results from the PDE because verification involves testing it against the algebra, which you have to know already

It's about finding the proof

You have the result you want to find out how to manipulate the symbols to get the proof

@Typhon No High School (Grade 11) Physics.'

Sure, and what would the process be to do this?

Formalize the symbols as a figure on the complex plane

mumbles curses about Obama and educational budget cuts

5:51 AM

And then formalize the symbolic manipulations as geometric mappings on the plane

Which symbolic manipulations?

What ever your working with, if I wanna find a fact about a polynomial, it would have to follow the algebraic rules for manipulating polynomials

By fact , I mean a formula

You gotta stop being so skeptical of the world

Alright, so using my knowledge of PDE and the fact that I don't know any algebra (let's say we're trying to derive the very first result), how shall I figure out whether a given symbolic manipulation is legal or not?

@Abcd alrighty. let me correct a few things, because I know a bit more and you are mistaken, kid. First of all SI units refers to the usage of things like using meters and centimeters over inches and feet. It doesnt mean assume it is in meters. In fact assuming units is always wrong to do unless it is a very general identity in which case that is ok. Secondly, units are always required. At the higher math level they are elements of a abstract number rings which means...

idk at that point...

I was teasing you with PDEs you know...

5:56 AM

that their formulae and manipulations only apply to the units and NOT to the numbers. It's like forgetting i with imaginary numbers. You technically end up doing it wrong bug time.

Oh I know but I'm just bored so I actually wanted to pursue this

So... um.

It's fun

I still don't see the problem with simulating grothendieck...

please keep in mind that 11th grade is primarily teaching you horrible physics. XD

@Abcd anyways good luck.

Ring (mathematics)

In mathematics, a ring is one of the fundamental algebraic structures used in abstract algebra. It consists of a set equipped with two binary operations that generalize the arithmetic operations of addition and multiplication. Through this generalization, theorems from arithmetic are extended to non-numerical objects such as polynomials, series, matrices and functions. The conceptualization of rings started in the 1870s and completed in the 1920s. Key contributors include Dedekind, Hilbert, Fraenkel, and Noether. Rings were first formalized as a generalization of Dedekind domains that occur in...

5:58 AM

I mean, basically that you don't really know that this should work, and if you did know

Wait, you can try different axioms, and then simulate them to see which ones give you the desired algebraic relations you want and don't want in a system

You'd still have the problem that you're using the fact that someone has already derived the results, and also knowledge of physics, to pull algebra out of PDE

@Abcd second is SI base unit, hour is SI derived unit, both are SI units

^^

@Typhon Ok. Thanks.

5:59 AM

This is different than using reason to derive formal results from other formal results

@LeakyNun Oh. I intended to say: SI base units.

@Daminark you gotta be more creative, I would just simulate myself now, and then see what algebra would the PDE give me

@LeakyNun they claim that if it isnt listed on the wiki Page for "SI", then it isnt a unit in SI.

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