Mathematics - 2017-07-07 (page 4 of 8)

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12:00 PM

well, I guess it varies. For my co-supervisors and part of the chem school, their sabbatical ends on 1 June 2018

though some of them continue to work during the summer holidays and other going to conferences

3 mins ago, by Secret

Indeed, and supervisors like to take sabbaticals during this period

Perhaps the better way to phrase this is, they like to pick a starting date for the sabbatical somewhere in this period, which coincides with the mid year break of the undergrads

You know what would be a great idea? If you had a good friend who you really trusted, and you gave them your rent for the next month, and you make them promise not to give it to you until you've finished something :P That would be a good deadline.

@Sha I'm slightly concerned about that

Unfortunately, my nearest good friends is 1.5 hours of train away

I mean

lol ever heard of bank transfer?:P

12:04 PM

Make sure to tell your friend that you'd rather accept a late fee as a fine for not finishing on time

(Assuming this is actually the case)

Maybe I could ask my MOM!!!!!!!!

Also do make sure that this doesn't go so long that you get evicted

I trust her!

:P

I mean, friend or mom, either way, you want it to be totally clear what your priorities are

@Daminark hahahahahah that's the point! I need the pressure :P

my priorities are that I do math this summer!

12:06 PM

Speaking about pressure, I am like a pH plot of enzymes

too little pressure I slack off,

too much pressure, I choked and my brain stops working

the catch: The optimial pressure range is very narrow

This is true, but like, the specific ordering of doing math, paying late fees, or going homeless

@Secret hm, I can handle normal and too much pressure, though not for too long. If the pressure continues for more than 4-6 months, I'm fried :P

I was fried at the end of this year. I failed a lot of tests in the past two months. But up until then my grades were fantastic. So I want to correct all that stuff, which is what I am. going. to. do. this summer, with the help of the pressure of going homeless :P

I hope this chat stays alive!

this chat really makes maths (and physics) so much more fun and interactive for me

If you are actually willing to go the whole way, then props (though a friend/mom would be insanely guilty for being responsible, so keep that in mind)

And lol, I hope so as well

we have to make sacrifices for math :P It is worth the guilt and the pain

Lmao

'tis true

12:14 PM

yeah, maths is a subject that takes a lot of time to understand and then master. It is not as conceptually and (insert word) difficult as physics, but it take a lot of practice and time before the definitions, theorems etc. all sink in

yea the thing with math is, once you've passed some threshold, it just really gets fun and "easy" to master the details. I think I've passed this threshold with all my subjects (i.e., I've mastered the basics and I know the ideas), so it should be all fun from here on

@Secret Yeah my main problem in physics was that I couldn't visualize for shit, which choked me in most problems

I mean, "visualize" might be the wrong word, more like, handling motion

For me, my problem is that while I can visualise it, I am quite reluctant to let go of rigor and take assumptions thus I miss out the physical conditions needed for the problem

We'll call it "physical intuition"

I have mixed emotions when it comes down to physics :P

12:16 PM

"$\sin(x) = x$"

I did physics for two entire months without doing any maths. that really made me question the validity of my existence

but I love the close relationship between scifi settings and physics. It is one of the bridges that makes scifi real

@Dami dude that is a bad example, because we know how it actually works. the worst thing is when you don't even know how it is supposed to work, and you have to go with the physics flow

that was the nightmare I was in in the beginning of this year, when I hadn't had any introductory math

user84215

I think there is no distinction between physics and mathematics.

One example of an assumption is to discard one of the general solution of the particle in a box problem, because it blows to infinity once the physics are taken account of

12:18 PM

lol are you just trying to be controversial @amin :P

If you stay purely in maths, nothing will tell you that solution will blow up

but do you find that a problem @Secret?

@ShaVuklia I mean, I was under the impression that even all these approximations were made, they were only done so after they were mathematically known not to screw you up too badly, so ideally none of them should be at least qualitatively worse than something over the sort

user84215

@ShaVuklia jus tryin to be cotroversial?!

I don't know if I'm tired or your sentence is just way too long :P @Dami

12:21 PM

@ShaVuklia Well, back in my 2nd year, it prevented me from completing an assignment until very late because of not realising I can do that, and I have pages of algebra by treating the problem as a ODE problem, but my peers can solve it in 1 sheet

@aminliverpool the notion that math and physics are identical seems absurd. Physics is a study of nature, and if you tweak some stuff, the whole subject flips on its head

@aminliverpool Well, for that I have an interesting perspective. One reason why the maths I have done so far in the chat is weird (modulo that some of these are from my dreams) is because I actually treat mathematical objects as real as physical objects, so whenever I am doing maths, I am actually modelling some physics in an alien universe

Or put it in another way, I do physics problem like a mathematician does, but I do pure maths like an engineer and physicist (and sometime chemist)

Math is a study of formal objects, so even though our choices in what types of objects to study is often inspired by nature, the truth values of the statements made are independent.

That mindset is one reason I found abstract algebra quite visual, even though it is supposed to be abstract

@ShaVuklia My sosc teachers have complained about my long sentences, some of them clocking in at over 100 words. But given that fatigue is such a common thing I'll say that both are true

12:24 PM

don't worry, I have much longer sentence problems pointed out in my thesis writing

it does not help that I read like a computer and thus I don't need to resume from the last fullstop if I stop reading a sentence

I think my schtick is that I often have a sentence not just as a complete thought, but as a self-contained thought.

that makes it hard for me to detect long sentences

@Secret lol I think it's fair to not compare chat sentences to thesis sentences :P

^

user84215

in physical theories, you add the implicit axiom, "physical theories must be consistent with nature's behaviors", to math theories. So they may seem different in one axiom, but they are actually the same.

12:28 PM

I mean, so in the process of writing a paper there's definitely a sort of idea-based interdependency between the various sentences (it'd be rather weird if it weren't), but somehow, I am not inclined to have a "blah blah blah is true. This is because blah blah blah" construction, instead preferring that this is "blah blah, due to blah blah", which really makes some sentences kinda long.

Crap I did that in this sentence, didn't I...

indeed indeed

lol, I thought I spotted a period, but that's when you said you didn't do that :P

I mean I write how I think both in chat and in a paper so merp.

I say "I mean" way too much... :P

hahah, that's better than inserting "like" everywhere

(but not much better, I have to add :P)

But yeah so, @aminliverpool the point in physics is that you're taking nature as your object of study, and then finding what can be modeled mathematically, which in some sense is doing what you're doing, but adding a new contingency on the truth values of your claims which is not present in math.

This strikes me as being a very significant difference

12:33 PM

I am mixed: I treat both reality and the math world as equally real universes, observed their laws. When I start doing theorems and stuff, I am actually modelling those laws

@ShaVuklia I'll take what I can get

user84215

that is a nextra axiom like other axioms which exist in mathematical theories

user84215

like the axiom of infinity

Tobias Kildetoft

@aminliverpool Most mathematicians would not be happy having to add any additional axioms to the ones they are using

For me, anything is real to me once I understood what happens when it interact with something else

Tobias Kildetoft

12:34 PM

They have a fixed set they use and no others. Not that most think of them at all

Hence relational existence = physical existence fallacy for me

To be fair, that was an unfortunate wording on my part. The better way to say it is that this axiom makes experiment into a generator of "likely extendable truth"

user84215

and some mathematicians think that some axioms like the axiom of infinity is an extra one.

I am happy to nuke or unnuke axioms if I need to, while being careful not to invalidate too many proven results

Tobias Kildetoft

@aminliverpool Very few serious mathematicians do. And the ones that do are generally the ones that study very foundational stuff.

12:37 PM

In fact, in a sense, similar to gene knocking experiments, One way I understood some axioms is to knock them out

and then see how things fell apart, realise the mess I caused ,and then restore the axiom

Additionally, I find that people often are alright with countable sets, the metaphysical sketchiness comes in more with uncountable sets, where doing things explicitly is a problem.

Axioms are axiomatically true :P

But even then, I think many will just be unconcerned and think of it as truth in the correctly defined model given by the axioms and just roll with it

My issue with uncountable sets is that I often mistakenly end up counting elements, as Tobias noticed in some of my past proofs that I pick out two elements from an uncountable set, but I only need to pick one

user84215

Now, there are many mathematicians called physicists that put the axiom of consistency with nature in their logical axioms.

Tobias Kildetoft

12:40 PM

@aminliverpool Now you are just redefining terms to make what you say true

Mathematical physicists or applied mathematicians?

Tobias Kildetoft

(which makes you a mathematician I guess)

user84215

naming is not important. They are all mathematicians.

The issue here is that you've literally changed the form of the object you're studying when you move to physics

Nature and physical reality cannot be axiomatically defined, and its behavior inferred purely from the axioms, the way a set can

Rajesh Dachiraju

Hi All

12:45 PM

Actually, here's a philosophical (?) question for the mathematicians here: What will a physical law be like that cannot be modelled with maths?

Hi

Rajesh Dachiraju

is there anyone good with ode here

are atleast who think they are good

Askaway

That's tricky, if we're going to include probability it's hard to imagine something which can't even fall under that scope

What do you mean by "law"?

A law follows rules.

Rules can be described mathematically.

user84215

12:52 PM

So mathematics and physics are the same

12

Q: Mathematical Universe Hypothesis

What is the current "consensus" on Max Tegmark's Mathematical Universe Hypothesis (MUH) which claims every concievable mathematical structure exists, including infinite different Universes etc. I realize it's more metaphysics than physics and that it is not falsifiable, yet a lot of people seem ...

mathematical-physics cosmology mathematics

Not always.

The issue is this: I have no idea what a non mathematical universe is like, as the most unpredictable events can still be encapsulated by probability and statistics

They look the same sometimes.

@aminliverpool you're failing to adequately respond to our points so I don't think this conclusion holds

12:54 PM

and even non computability does not rule out the ability of maths to model laws

-1

Q: What are the consequences of a non-computable universe?

I have seen that is is debated if the universe is digital, computable or non-computable. what specific consequence could this have in the format of the laws of physics? Or would that mean that we will not be ever capable or writing equations?

soft-question universe simulations

So what is non-mathematical reality? I really have no idea...

Mathematics is the language of Physics. It is not Physics itself.

French is not France.

user84215

Physics = Mathematics + Axiom of consistency with nature

I know there's a difference between maths and physics, but I have no idea what can disprove that mathematical universe hypothesis

Tobias Kildetoft

@aminliverpool For many physicists you also need to remove some rules or at least allow for some much less strict reasoning

Physics - axiom of consistency with nature =/= math

user84215

12:58 PM

Prove the above inequality.

(to add to that equation) There are consistent things that are false, btw

The LHS does not exist.

Math exists.

user84215

Consider physics as a logical system.

It maybe depending on its stage of development.

Physics has labs.

Math has computers.

Simply Beautiful Art

@Secret Mmm, I immediately think about ordinal universes

user84215

1:03 PM

labs are constituents of the consistency axiom.

@SimplyBeautifulArt that's still mathematical, though

You can discover new theories in a lab.

user84215

You also can discover math theories in a lab.

Physics is not a logical system, it requires knowing nature which is not axiomatically derived

Math discoveries are made purely theoretically.

Rajesh Dachiraju

1:09 PM

ok here is my ODE I am trying : mathoverflow.net/q/273906/14414

Tobias Kildetoft

@Justwinbaby Except experimental math

Rajesh Dachiraju

assume the case d = 2.

What? Give me an example of experimental math

Rajesh Dachiraju

I am gueassing atleast how the solution looks like

user84215

But you can form it as a logical system. In math you first put axioms and then develop a structure; in physics you first discover the theorems then find the required axioms. Both lead to the same result.

Tobias Kildetoft

1:10 PM

@Daminark Look it up (it is an actual thing)

Rajesh Dachiraju

its definitely not sine wave

There's always an exception to the "rule" @TobiasKildetoft

Experimental mathematics

Experimental mathematics is an approach to mathematics in which computation is used to investigate mathematical objects and identify properties and patterns. It has been defined as "that branch of mathematics that concerns itself ultimately with the codification and transmission of insights within the mathematical community through the use of experimental (in either the Galilean, Baconian, Aristotelian or Kantian sense) exploration of conjectures and more informal beliefs and a careful analysis of the data acquired in this pursuit." As expressed by Paul Halmos: "Mathematics is not a deductive science...

I do this all the time

user84215

A deeper question: Math is created in mind and physics is discovered in nature. Can you prove that nature exists independently from human's minds?

Can you disprove it?

user84215

1:14 PM

No. But I can say that the description of nature is made by mind

Simply Beautiful Art

Saying anything is easy. Can you prove it?

The proof of the pudding is in the eating.

So, the vibe I'm getting is that experimental math is basically, try things out to see if certain ideas are believable and if we should try to prove them. A large scale analog of trying something on the number 6 just to make sure you don't immediately get rekt

user84215

My last words do not need to prove. The fact is obvious

Simply Beautiful Art

Obvious? You are saying they are axioms?

1:18 PM

And the description of nature that we use is in the mind, this is true, if only because knowledge must factor through the mind

user84215

^

Simply Beautiful Art

So what if we all died due to some tragic accident

as did all living beings in the universe

Like, your perception of nature is precisely your subjective experience, and a description is either that or based on that. The issue is then whether our perception of nature is inspired by an actually existing nature

Simply Beautiful Art

Does 'nature' exist? Or will the universe exist regardless of whether or not someone can observe it?

the proof of the pudding is in the eating

== English == === Etymology === This proverb dates back at least to the 14th century as "Jt is ywrite that euery thing Hymself sheweth in the tastyng", and William Camden stated it in 1605 in Remaines of a Greater Worke, Concerning Britaine as "All the proofe of a pudding, is in the eating", per Rogers' Dictionary of Cliche and the Oxford Dictionary of Quotations. A 1682 translation of Nicolas Boileau-Despréaux Le Lutrin (written between 1672 and 1674) renders it "The proof of th' pudding's seen i' the eating." The current phrasing is generally attributed to the 1701 translation by Peter...

1:20 PM

My stuff on this chat is basically (half baked) universal experimental algebra

user84215

Yes. It exists

Simply Beautiful Art

Hm, I want some chocolate pudding

Actually, I think the best way to put it, and this applies to both nature if it really does exist objectively or if it's only in perception, is that in either case, knowledge of physics is a posteriori.

Experience informs your pursuit in math, but the knowledge itself is a priori

3

hi chat

Simply Beautiful Art

hi

1:28 PM

Hey Balarka!

what nu

Las Vegas Raiders

chillin, u?

That explains the distinction between maths and physics well (as well it is a language) .

now, I just need one counterexample to the mathematical universe hypothesis

@Daminark However, pursuit is itself a math in experience, even though knowledge is not.

How many oracles do I need to solve that problem...?

1:31 PM

@Secret about 90

:P

over 9000

lol, that's much less than I expected, I thought it is at least $\omega$

@Balarka do you consider engaging in rational thought to automatically be "an experience"?

@Daminark I do not consider engaging in rational thought

Question. Let's say we had

1:33 PM

"All rational thoughts must be exterminated" - William S. Burroughs

$$f(x) = \left ( \frac{1}{-118} \right ) ^{\frac{2}{2.4}}$$

Are all of f(x)'s derivatives positive?

"William Burroughs must be exterminated" -all rational thoughts

Makes sense; William S. Burroughs was after all an exterminator in early life.

Tobias Kildetoft

Finally. I now have proper internet again rather than relying on using my phone as a hotspot.

But yeah I mean, if rational thought is to be taken as an experience, I would question whether existence itself is an experience. I don't see how that would not be the case and presume the answer is yes, in which case this notion of experience is a poor differentiation.

1:38 PM

@SirCumference uh, that's a number...

Ugh, I'm stupid

$$f(x) = \left ( \frac{1}{1 - \frac{-3(-1.8) - 3}{2} \times 70x} \right ) ^{\frac{2}{-3(-1.8) - 3}}$$

Actually no need to make the existence jump, all knowledge would be some mix of rational thought and observation and would thus have an experience-based person pursuit. If rational thought in itself isn't an experience, the fact that it is for us is contingent on our being human, and surely the epistemological nature of the subject can't be based on that

But I imagine this room tires of my ramblings of the sort so I'll leave it at that

simplify some of the expressions first e.g. (-3(-1.8)-3)/2=1.2

@Daminark Your philosophical taste is too technical for me. I like to think about concrete things; for example, philosophy of various kinds of artistic works.

Just to clarify why I have no constructive input on what you say.

What's an experience?

1:43 PM

Entirely fair

@Secret Right:

$$f(x) = \left ( \frac{1}{1 - 84x} \right ) ^{\frac{2}{2.4}}$$

I think an experience is some time chunk of my sensory input.

Though what you think is in some sense sensory input

since you know you are thinking it.

I prefer to think about metaphysics, since they are as real as physical objects to me

@SirCumference 2/2.4=1.2. You should be able to differentiate that and note the pattern i.e., you should see its signs flipping every odd number of derivatives

Interesting proposition @PVAL

@Secret Uh, 2.4/2 = 1.2

Not the other way around

1:47 PM

ah yes, sorry

anyway 1/1.2=1(6/5)=5/6

O btw guys, it is interesting that we somewhat touched upon consciousness in our today's philosophical discussion because tmr in sydney there's this:

Well, I was graphing this function:

user image

You can see it's asymptotic

I don't think though that when you consider something like rational thought, generally you aren't concerned with only the self-observation of rational thought (the agents experience while thinking rationally) but other much less abstract notions.

user image

The first, second, third, fourth and fifth derivatives are positive. My question is, are all the derivatives positive?

@PVAL What else would you be concerned with?

Okay that came off as somehow an argumentative/skeptical question, for reference I am asking about it out of curiosity at this point

1:51 PM

Rationality of a rational thought is relevant to the consistency of the thought with the various practicalities of the observed functional life around you, isn't it?

I think I am more concerned with the changes in the mind itself, and more concerned with how rational thought leads to ethical changes (which in my opinion lead to better outcomes).

I think those are the less abstract notions PVAL had in mind

yeah I think that is essentially the second thing I am saying.

By less abstract I mean notions which aren't terribly concerned with divisions of the mind, the agent and the observer.

If that makes any sense.

Hi @PVAL

Hi @Mike

1:56 PM

@SirCumference $$f(x) = \left ( \frac{1}{1 - 84x} \right ) ^{\frac{2}{2.4}}=(1 - 84x)^{-\frac{5}{6}}$$ Differentiate this and the power keep going down to -ve (which means each differentiation a negative number pops up. however because of the chain rule on the 1-84x, you also have a negative number pop up. These two negative signs cancel, thus your derivative is always positive

That sounds reasonable, I'd say. Does any thought necessarily induce certain said ethical changes? It's something I've been wondering

@Secret Beautiful

I would say that depends on what you mean by ethical change.

(well, of course if your x > 1/84, then those regions you always have negative derivatives)

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