Mathematics - 2017-07-06 (page 3 of 10)

Semiclassical

05:00

No, it's not.

Typhon

does anything even tip its hat towards that being possible?

Semiclassical

That's kinda my point, though. Quantum mechanics doesn't answer that question.

Typhon

i assumed that if something can be in two places at once, then anything can be in two places at once

Las Vegas Raiders

Not "logically"

Typhon

and therefore, there are objects in two places at once

Semiclassical

05:00

The question of what the particle is doing when we're not measuring it has no operational content.

As such, quantum mechanics shrugs its shoulders and says "that's not what I'm here to tell you."

Typhon

measurements merely record what is given off by a particle right?

or do we bounce things off them to see them?

Semiclassical

If you're talking particles at the quantum level, you pretty much have to interact with them directly in some fashion.

Las Vegas Raiders

We need light to see

Typhon

i mean, you don't surely expect me to believe that the human mind actually causes a particle to change fundamentally?

Semiclassical

Ugh, I hope not.

I hate hate hate "consciousness causes collapse" interpretations.

Typhon

05:03

@Semiclassical oh. I thought they gave off smaller electron dust or proton dust or whatever

Las Vegas Raiders

It could.

Daminark

@Secret not weird enou... What??

Typhon

or rays of some kind... on their own

Semiclassical

Eh, the problem is that anything a particle could 'emit' that we could detect would be a wave

and as such would carry both energy and momentum

Secret

Check the article on PR boxes, they are even more nonlocal correlations than entanglement

Typhon

05:04

@Semiclassical and why is that a problem?

Semiclassical

for instance, the state of an electron before it emits a photon will not be the same as after it does

which means at most we gain information about how the electron changed, not about what it was actually doing.

Typhon

so we are looking at the past?

oh..

darnit

if we only we had something that could just peer into the universe through the eyes of a deity.

as in... you somehow view it without altering it or bouncing light off

Semiclassical

Now, to some extent such issues have been 'understood' in terms of decoherence

Typhon

ok

but umm...

look

I am good with physics at the newtonian level

and I get what you are saying

and I am glad you enjoy your stuff

Semiclassical

Getting back to what I was saying about 'conservation of absurdity': any interpretation which manages to make some aspect of quantum mechanics seem not absurd will inevitably be absurd in some other way.

2

Typhon

05:06

but honestly, I don't understand much of what you are saying right now. XD

Semiclassical

Hell, you think I do?

Typhon

fair point

Secret

I actually like nonlocality due to my personality to be everywhere at the same time

Typhon

so it is as absurd as my geometry?

Secret

nonrealism is harder for me to accept

Typhon

05:07

or rather as absurd as claiming surfaces can be one sided?

Secret

though I eventually managed

Typhon

@Semiclassical surely points being at more than one point at once would be noticed at a large scale though. As then we would notice things like cars being in two places at once. Surely, it would impact the larger scale after a while?

or even somewhere in space i would think it does

Semiclassical

eh, not really.

Typhon

@Semiclassical I think defining my one sided surfaces will be my next large mathematical quest. See you in a few years with a definition.

Semiclassical

the problem is the length scales involved.

Typhon

05:11

probably something really obvious

in fact, if i run into a particular professor... i shall ask him

Semiclassical

in order to have quantum mechanical effects be substantial, you need the de Broglie wavelengths of the particles involved to be pretty big.

Typhon

(there's a few professors from the uni's who teach classes over the summer here)

Balarka Sen

i am gradually realizing my proof-writing ability is terrible

Typhon

i cannot explain it

Semiclassical

But the more momentum the particles have, the less de Broglie wavelength

and the more mass, the easier it is for them to have momentum.

Las Vegas Raiders

05:12

Does GR have philosophical measurement problems also? @Semiclassical

Typhon

I see

so...

Semiclassical

@LasVegasRaiders Less so, I think.

Typhon

if we managed to get something to absolute zero....

we'd see the effects?

Semiclassical

well, you're certainly right in one way: If you bring particles to near absolute zero, then quantum mechanical effects become far more significant and interesting.

Typhon

no

Semiclassical

05:13

Hence why superconductivity is a thing, for instance.

Typhon

i meant what if they went to being equal to absolute 0

Secret

Bose–Einstein condensate

A Bose–Einstein condensate (BEC) is a state of matter of a dilute gas of bosons cooled to temperatures very close to absolute zero (that is, very near 0 K or −273.15 °C). Under such conditions, a large fraction of bosons occupy the lowest quantum state, at which point microscopic quantum phenomena become apparent. A BEC is formed by cooling a gas of extremely low density, about one-hundred-thousandth the density of normal air, to ultra-low temperatures. This state was first predicted, generally, in 1924–25 by Satyendra Nath Bose and Albert Einstein. == History == Satyendra Nath Bose first sent...

Typhon

in theory....

if the effect is in a multiplicative relationship... the result would be in an infinite effect.

Secret

You cannot get to absolute zero without an infinite process. The 3rd law of thermodynamics have been mathematically proven just 2 years ago. Even if you can, the particles will still be in motion as they have zero point energy

Typhon

which.... perhaps explains absolute 0

Semiclassical

05:15

The joy of entropy.

Typhon

if particles exist in more places at once as the momentum descreases

then perhaps absolute 0 results in a particle becoming everywhere in the universe at once

and therefore it "ceases to exist"

Semiclassical

The other problem with this line of thinking is that, when you do an experiment, the system may go to fractions of a kelvin within absolute zero

Typhon

yeah

Semiclassical

But, of course, the environment which contains that system is not at absolute zero.

Typhon

but im referring to theory

the instant it hits absolute 0, what happens?

Semiclassical

05:17

Could not tell you.

Typhon

does it mean all motion has ceased? or do the particles cease to exist?

after all, absence of all matter or particles is at absolute zero

Semiclassical

Not really.

Typhon

by definition of energy in various forms.

if I have literally nothing

Semiclassical

Absence of temperature would just be absence of thermal fluctuations.

Typhon

how can it have heat?

it must be at 0 degrees

Semiclassical

05:18

Heat is not energy, heat is energy transfer.

Typhon

ugh

Secret

What is clear is that motion still exists at absolute zero as every quantum system has zero point energy

Semiclassical

^

Typhon

well it isn't giving off any heat

it's temperature is 0

@Secret err wat?

Semiclassical

The problem one also starts to run into is that the concept of temperature is ultimately a thermodynamic one.

It's really a statement about systems with enough particles to have meaningful statistics.

Typhon

05:19

temperature is the average kinetic energy

Semiclassical

No.

Typhon

so 0 temperature implies either no motion

or negative motion

Semiclassical

$T=\frac{\partial U}{\partial S}$ is the thermodynamic definition of temperature.

Typhon

im talking about the general definition

Semiclassical

That is the general definition.

Typhon

05:20

it is a measure of total kinetic energy

Semiclassical

That it matches the average kinetic energy of an ideal gas is a derived result. It is not a fundamental one.

Typhon

it is in relationship to kinetic energy then

Secret

Zero point energy is the energy of the lowest possible state of a quantum system. That exists because of the uncertainty principle

Typhon

in that kinetic energy increases with temperature

Semiclassical

Secret, again, has it.

Typhon

05:21

ugh

Semiclassical

Temperature is not a fundamental concept. It is a description of a system of many particles.

(Entropy, by contrast, is fundamental.)

Secret

Prepare have your mind blown

mpg.de/research/negative-absolute-temperature

Typhon

yeah and it is a description based on their kinetic energy?

Semiclassical

Ehh, that's cheating :P @secret

Though it is a physically relevant effect. (Huzzah for magnetic cooling!)

Secret

But it illustrates well where average kinetic energy is not temperature. Temperature is really a trade off between energy of an ensemble and it's entropy

Like how semi mentions earlier

Semiclassical

05:24

Plus, to have temperature you need to have a concept of equillibrium (or near equillibrium).

If you do out-of-equillibrium stuff (mesoscopics e.g.) you may not have a well-defined notion of temperature to begin with.

Typhon

oh my lord

let's end this discussion

it is late

Semiclassical

lol

Secret

Night

Typhon

oh im not heading to bed

i just cannot handle this paradox

between this and my geometry my mind needs a break from revelations

Secret

Welcome to weirdness which is real life

Typhon

05:30

nah

my thing makes me think of ye old legend of zelda ocarina of time trickery in the shadow temple

like how yo can walk through walls

Semiclassical

Funny, you say that and my brain immediately goes to the music from the Forest temple

Typhon

lol

Semiclassical

And now I find myself trying to think of what Zelda music I like best.

Probably the theme for Stone Tower Temple wins it, though.

Typhon

I'd have to say it is one of the following somewhat long list

the molgera battle from WW

the Volvagia battle in OOT

the bellum boss (any stage) in PH

ganon's theme in oot

yeah definitely those 4

ironically the boss theme for the stone temple boss is now stuck in my head

Semiclassical

I tend to remember the stage music better than the boss battles.

Isn't that also molgera?

The giant ones.

Typhon

05:35

dun dun.... dun dun dun

hopefully that gets it in your head

Semiclassical

Nope. I'm remembering boss battle music but I don't remember it being unique for the MM fights.

With the exception of Majora itself, of course.

Typhon

it never was

Las Vegas Raiders

This answer to the question "is looking at something a measurement" made me think that it was circular @Semiclassical

in The h Bar, 7 hours ago, by ACuriousMind

@0celo7 I guess the serious answer is "perhaps" ;P "A measurement" is some process that yields as a result some definite value of some observable. If by looking at something you can determine such an observable (e.g. position), I guess it qualifies as a measurement.

Semiclassical

Oh, sure.

My point was that I find the word 'interaction' more interesting than 'measurement.'

Contains the same problems but in wider scope.

Las Vegas Raiders

In what sense is it "wider"?

Typhon

05:38

@Semiclassical i forgot that music

until now

Semiclassical

Well, measurement typically presupposes one classical object as the measurement device, and another object as the system to be measured.

Typhon

ok

Semiclassical

But interaction can be either of these scenarios, or it can be between quantum systems.

But ugh. Measurement problem gives me a headache

Typhon

kk!

im out of here

XD

Semiclassical

later

Typhon

05:40

too much physics

Meow Mix

05:59

@Semiclassical did someone say 64-bit zelda

Las Vegas Raiders

Hi pal

Long time no see.

Meow Mix

how are you

Las Vegas Raiders

fine thanks, how are you doing?

Alessandro Codenotti

Hi @Zach

Meow Mix

im ok

just doing a lot of CS related stuff rather than math

Las Vegas Raiders

06:07

did you get into that math summer camp?

Meow Mix

hi @AlessandroCodenotti

@LasVegasRaiders oh i thought i told you, but apparently not. i didnt even get to apply

Las Vegas Raiders

:(

oh well, there's always next year

Meow Mix

probably not next year either

parents won't let me go on plane alone

Las Vegas Raiders

take a bus

or train

Meow Mix

lol that's not the point

it's the fact that i'm leaving home by myself

Las Vegas Raiders

06:10

tell them to travel with you

make it a family vacation trip

Meow Mix

its for a month

we barely go on vaacation as it is

we havent in a few years

Alessandro Codenotti

06:25

So will you self study some cool math in the summer?

Las Vegas Raiders

and try to relate it to the CS stuff you're doing

Alex K Chen

'allo ~~@Key Annul~~ err @LeakyNun are you here ?

Leaky Nun

@AlexKChen yes

Meow Mix

@AlessandroCodenotti i really don't know. everything i do is just based on my current interest

ill return to math when im interested in math

and ill stay doing CS until i want to do something else :]

Alex K Chen

@LeakyNun Why your weird name "Leaky Nun" ? It's hard to imagine a nun that's leaking.

Leaky Nun

06:30

just an anagram of my real name

Alessandro Codenotti

CS is also nice, what are you interested in in particular at the moment?

Meow Mix

operating system development

however

Balarka Sen

I can also see Keanu in there

Meow Mix

i'm also disassembling, documenting, and reverse engineering a game for the GBA

Las Vegas Raiders

Reverse engineering is cool stuff.

Secret

06:31

[history]

mathwithbaddrawings.com/2015/02/17/the-math-learners-checklist

2

Las Vegas Raiders

I wish they did more of it in schools.

Alessandro Codenotti

@Balarka have you seen my ping yesterday evening?

Balarka Sen

This?

Alessandro Codenotti

yeah

Alex K Chen

Hi @Blank Areas !

Balarka Sen

06:34

I am unsure what cardinality means.

Hi @Alex

Alessandro Codenotti

whether it's countable or not

Balarka Sen

Err. It's a sequence of natural numbers?

Of course it's countable?

Alessandro Codenotti

it's a set of sequences of natural numbers

Balarka Sen

Oh, the set.

Las Vegas Raiders

Blank Areas?

Alessandro Codenotti

06:35

I want to know how many such sequences are there

the real question is whether there is such a sequence which isn't the image of $\Bbb N$ through a polynomial

Alex K Chen

@BalarkaSen You should call me "Excel Khan" or "Chalk Enex" :P

Balarka Sen

I have no idea. The setting is interesting but I don't really think about cardinalities.

Alessandro Codenotti

(and if we're lucky and that set is uncountable we're done :P)

Balarka Sen

@AlessandroCodenotti Ok, that would be interesting.

@AlexKChen Excel Khan is a nice name.

Las Vegas Raiders

It's better than Your Highness :P

Alessandro Codenotti

06:37

@BalarkaSen sounds like a microsoft sponsored Mongol leader :P

Balarka Sen

lolol

Alex K Chen

@BalarkaSen If my name name was Alex K Sen, then it would be Ankle Sex. Not sure what that means, though.

:P

Balarka Sen

I can imagine what it means, sure, why not

Alex K Chen

Or An Elk Sex. Visualizing this is more concrete.

Leaky Nun

11 hours ago, by Alessandro Codenotti

Consider the set of sequences of natural numbers $\{a_n\}$ with "polynomial growth", in the sense that there is a polynomial $g(n)\in\Bbb N[x]$ such that $a_{n+1}-a_n\le g(n)$ for all $n\in\Bbb N$. What's the cardinality of this set?

consider $g(n)=x \mapsto x$

it is clear that there are $\mathfrak c$ many sequences satisfying the criterion for this $g$.

Alex K Chen

06:41

Lemme make some funny anagrams of well known people here.

Leaky Nun

@AlessandroCodenotti

or in a combinatorical sense, $1 \times 2 \times 3 \times \cdots = \mathfrak c$

Las Vegas Raiders

Username: abc...xyz contains all possible anagrams @AlexKChen :P

Leaky Nun

@LasVegasRaiders not really

e.g. aaa

Las Vegas Raiders

I'm allowing repeats.

Alessandro Codenotti

oh, right, of course

even most binary sequences will satisfy that requirenment for a lot of polynomials

Las Vegas Raiders

06:46

Including infinitely many repeats.

Alex K Chen

Ted Shifrin = Fiend Shirt = Hit Friends = Finders hit
Mike Miller = Milkier Elm = Milker Mile/Lime
Akiva Weinberger = A viewing breaker = A baking Reviewer = Braver weak genii
Semiclassical = Camels' Silicas = Classic Emails
Balarka Sen = Blank Areas = Nasal Break

@BalarkaSen @AkivaWeinberger ^

Alessandro Codenotti

what about my name? @Alex

Balarka Sen

For a constructive proof, @Alessandro: I am pretty sure primes have polynomial growth (this should be a very easy prime gap result). On the other hand, if $g$ was a polynomial which took all prime values, then $g$ must take a value in $[N, 2N]$ for any natural number $N$. But I am pretty sure that is impossible.

Alex K Chen

Couldn't find any good one :P

Las Vegas Raiders

How 'bout me?

Alessandro Codenotti

06:49

So, time for the actual question. Is there a simple example of a sequence $\{a_n\}$ such that $a_{n+1}-a_n\le g(n)$ for some polynomial $g$ but there exist no polynomial $f$ with $f(\Bbb N)=\{a_n,n\in\Bbb N\}$?

Balarka Sen

And yeah, I think something along that lines should def prove there is no polynomial $g$ such that $g(\Bbb N)$ contains all the prime numbers.

Not even equal to.

Alessandro Codenotti

@BalarkaSen ah, that's a good argument

Balarka Sen

It's all a growth argument.

A sequence with sufficiently slow, but chaotic, growth is all that's needed

Secret

Mar 10 '15 at 0:40, by Semiclassical

yeah, and it's pretty obvious in retrospect. the determinant, viewed as a function of its column vectors, is linear in each argument

Cool, never thought it as a vector function. That might be just the thing to get me through that permanent roadblock of 2 years ago

Alessandro Codenotti

It's also alternating

Alex K Chen

06:54

$Mathematics$ Recreational math games

For playing various recreational but mathematical games, e.g S...

Anybody can play anything there ^

Free advertisement :P

Balarka Sen

meh

Alex K Chen

Why ?

Leaky Nun

@AlessandroCodenotti increasing, I'd assume?

Alessandro Codenotti

Not necessarily

By the cardinality argument there is such a sequence even when allowing polynomials in any number of variables @Balarka

Secret

Mar 10 '15 at 1:19, by Semiclassical

for $n^2$, the first differences go like 1,3,5,...; the second differences go as 2,2,2,...

Balarka Sen

06:58

@Alessandro Ah I see

Secret

To be investigated sequence and their nested differences

Balarka Sen

Interesting though!

Secret

Conjecture: all sequence when repeatedly take their consecutive difference, will terminate at a constant sequence

Tobias Kildetoft

@Secret Clearly that is not true for all sequences without assuming they are given in some specific form

Alex K Chen

Numberphile and 3blue1brown together and has posted a new youtube video regarding polynomials with integer coefficients having prime values.

Tobias Kildetoft

07:02

@AlexKChen Those work better when the video does not have an add to start with

Alex K Chen

Eh ? I don't see any "add" ? I only see polynomials taking infinitely many prime values.

@BalarkaSen Are there any irreducible polynomials with coeff from integers whic are guarranteed to take finitely many prime values ?

Alessandro Codenotti

Irreducible where?

Alex K Chen

Over the integers.

Secret

Hmm? I though if you have any sequence a0 a1 a2 ... take its difference to form (a1-a0) (a2 - a1) .. and repeat the procedure many times the difference will get smaller?

Balarka Sen

What about $x^2 +x + 2$

$x(x+1)$ is always even

so any value of that is divisible by 2

it's also clearly irred

Secret

07:09

O wait, that does not work. a2 + a0 is a larger number

and a2 + a0 -2a1 is not necessary smaller than a(i+1) - ai

Mathmore

07:21

@LeakyNun Hi! I want to thank you for our previous conversation regarding logic. You suggested me various links about my confusion in truth of conditional statements.

Leaky Nun

@Mathmore how is it now?

Mathmore

Yeah sky is clear now. :D

it was funny to read the statements "pigs can fly" and "elephant laying eggs"

Leaky Nun

nice to hear that

@Mathmore comment on the truth of the following statement: "all even primes greater than 2 are perfect squares"

Mathmore

Should I consider it little embarassing that I have completed MSc and applying for PhD at institutes and still struggle in basic logic? :/

Leaky Nun

that's not a question I can answer

Mathmore

07:24

It is true statement.

Leaky Nun

@Mathmore why?

Mathmore

We can reframe this statement in if-then format as : If I have an even prime greater than $2$, then it is a perfect square.

Both are false statements

@LeakyNun Hence the conditional statement is true.

Leaky Nun

@Mathmore why is the latter false?

Mathmore

@LeakyNun Because prime numbers can not be perfect squares.

Leaky Nun

alright

Mathmore

07:28

passed the test hooray!!

Leaky Nun

are you familiar with symbols?

Mathmore

I should modify my second statement to "...then that prime number is a perfect square". That is exactly true.

Yeah $\exists$ and $\forall$

Leaky Nun

have you studied set theory?

Mathmore

Yes as in I have studied schroder bernstein theorem, unions, intersections, functions on unions and intersections, cantors theorem that there can not be surjection from a set to it's power set...

I have read about axion of choice once but now don't remember anything.

Leaky Nun

wow, that's a lot

Mathmore

07:33

Is it?

Tobias Kildetoft

@LeakyNun Actually, I would call that a bare minimum of set theory to know for a prospective PhD student

Leaky Nun

alright.

Tobias Kildetoft

(not that I would recomment most people learn more than the bare minimum unless their research takes them in that direction)

Alex K Chen

@BalarkaSen What's "irred" ? Anagram for "drier" ?

Tobias Kildetoft

@AlexKChen presumably irreducible

Mathmore

07:35

@TobiasKildetoft Thanks for your feedback. Highly appreciated.

@LeakyNun have something more in mind?

Leaky Nun

@Secret obviously false for $2^n$

it is a fixed-point under consecutive difference

@Mathmore thinking

Mathmore

@LeakyNun Waiting...

@TobiasKildetoft Surely. I am planning to study naive set theory by halmos. I hope it fulfills my set theory knowledge as a prospective PhD candidate.

Tobias Kildetoft

@Mathmore As I said, you already know the bare minimum, and you might not need any more than that

Leaky Nun

@Mathmore how do you prove any theorem without a sufficient knowledge of logic?

derive $p$ from $\neg p \implies p$.

Mathmore

@TobiasKildetoft Okay.

Tobias Kildetoft

07:46

My own set theory knowledge is only slightly more than what you mentioned (I have studied a little bit of axiomatic set theory and a bit more on the axiom of choice), but I don't think I have ever needed anything beyond it.

Mathmore

@LeakyNun I see patterns in various proofs presented in standard books

Leaky Nun

@Mathmore alright

Mathmore

like rudin, munkres, gallian, bartle sherbert, ote...dummit fo

Leaky Nun

are you thinking about my question?

Alex K Chen

Don't ask, just ask to ask, or even better, ask to ask to ask, or best, ask to ask to ask to ask.

:P

Mathmore

07:49

@LeakyNun Yes. I am thinking. Haven't done such kinda proofs. :/

@LeakyNun hey I see... $\neg p \implies p \iff p \or \neg p$. Thus we have $p$.

SteamyRoot

$p \vee \neg p$ is always true.

Leaky Nun

\lor

Mathmore

That is $(\neg p \implies p) \iff (p \lor \neg p) \implies p$?

Alex K Chen

@LeakyNun Is float s[100] sufficient for declaration when s is a list with floats (in C) ?

Mathmore

@TobiasKildetoft That's good to listen. Although I have yet not decided which area I love most in Mathematics to do research. I just enjoy studying algebra, analysis and topology. From me peers I hear that I should focus on only one of these trio. But I'm finding it difficult to study only one. :/ Is it normal?

Tobias Kildetoft

07:58

@Mathmore Sure, there is plenty of room to move in between those as well

Leaky Nun

@AlexKChen maybe

$Mathematics$ Recreational math games

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$Mathematics$ Mathematics