The h Bar

heather

1:56 AM

hello

DanielSank

2:22 AM

Hi

heather

when we left off yesterday, was 0 incorrect?

Wildcard

2:38 AM

I have what may be a very silly question about the scientific community's conception of the burden of proof and falsifiability....

heather

@Wildcard, ask away =)

Wildcard

I understand in general that a theory, to be considered a scientific theory, must be possible to falsify; i.e. there must be a possibility of information existing which could in itself indicate that a theory is false.

But, that hardly seems sufficient to call a theory "scientific"—and how could a theory be proved, ultimately, other than heuristically?

For instance: "Nothing can go faster than the speed of light."

I suppose this is falsifiable, because if I were to go faster than the speed of light it would be shown to be false.

heather

well, you could also say that if theories are inconsistent, one must be false.

Wildcard

But, if I were to say something stupid such as, "No person can have six legs," it is falsifiable for the same reason—and yet the absence of a readily visible person with six legs hardly indicates that this is scientific.

@heather That's fair. I was still writing out my thoughts. ;)

I'm a little unclear how falsifiability relates to the burden of proof.

It seems that the best one can achieve is to make an internally self-consistent theory....

But then how does that fit with "burden of proof"?

For instance, "There is a Creator," is "not a scientific theory" because you cannot demonstrate that there is not a Creator, so it's not falsifiable.

heather

well, I'm honestly not the best person to answer these questions. however, i would point out that whenever physics has been thought to be solidly established (aristotelian physics, newtonian physics, etc) it has been swept away or refuted by new discoveries.

Wildcard

2:44 AM

@heather I guess that's where I'm really going with this.

heather

also, in terms of a Creator, by that same argument the multiverse/many worlds theory is not a scientific theory, yet it is treated as one.

Wildcard

I suppose it has a lot to do with the relationship of science to philosophy.

@heather Perfect example. String Theory is an even worse example of the same thing.

Mew

@heather many worlds theory isn't thought of as a scientific theory though by most physicists

Wildcard

I could sidestep the whole thing by concluding, "People will believe what they want to believe, including scientists, and they will invent yardsticks for the validity of theories which will assert that they are right."

But that's not really helpful either (even if true.)

Mew

the interpretation of QM is considered to be outside of physics scope currently as no experiment can distinguish between them

it is more philosophy

only physics when experiments are proposed to differentiate them

Wildcard

2:47 AM

@Mew Reminds me of blogs.scientificamerican.com/cross-check/…

Mew

@Wildcard no theory can be proven true

@Wildcard the goal of string theorists is to come up with a prediction that can be tested

but until they do so, string theory isn't a mainstream scientific theory

heather

and now we say darn philosophy and keep studying physics =)

Wildcard

@Mew Okay, I suspected as much. (Or rather, that's what I had concluded, and am attempting to reconcile with the idea of a "burden of proof.")

Mew

@Wildcard science doesn't have a burden of proof

heather

but there is a sort of line between scientific theory and non-scientific though admittedly it is hard to define (for me at least).

Mew

2:49 AM

@heather yes, a scientific theory must be falsifiable

at least in principle

and it must be consistent with observations to date

and we usually use ocaam's razor as a guiding principle

Wildcard

@Mew But ultimately, it can never be proven true with the sort of conclusiveness that is achieved in mathematics. Correct?

(Because in mathematics, things are true by definition.)

Mew

@Wildcard correcvt

it is about getting the best approximation of reality we can

our theories are never 100% true

they are always evolving over time

from Newton to Einstein to Schrodinger

better approximations over time

heather

@Mew, but many-worlds theories or string theory...

Mew

and I"m sure this trend will continue

Wildcard

@Mew And the idea of sampling bias, and so forth, but those are questionable theoretical ideas (compared to the scientific method itself).

@Mew This makes sense to me.

Mew

2:52 AM

@heather most physicists agree many wolrds is an "interpretation" not a scientific theory

heather

and string theory?

Mew

most physicists are also sskeptical of string theory

because at present there are no experiments to verify it

heather

true

Mew

but a physicist can still work on it if they believe eventually they can come up with a falsifiablle prediction

heather

thanks for the conversation, very interesting

i have to go now =)

so good night everyone.

Mew

2:53 AM

but if it turns out there can never be a falsifiable prediction, string theory will be buried for sure

Wildcard

@heather Okay, thanks! :)

heather

@Wildcard, not a problem, glad you asked =)

always feel free to just ask, no need to ask to ask.

Wildcard

@Mew Buried as a scientific idea, perhaps, but it sure doesn't mean people won't still believe it.

Mew

@Wildcard but by occams razor why would you believe in it?

most rational people won't believe in something where there is no reason to do so

why believe say invisible fairies pushing planets around causes gravity when there is no reason to do so

Wildcard

@Mew Ask Richard Dawkins.

@Mew If you take a personal dislike of religion as a reason, then he certainly has a reason. :)

Mew

2:55 AM

people will always believe different things, but that isn't relevant for determing what is a good scientific theory

Wildcard

@Mew I agree with you. The most important trait for a good researcher, in my opinion, is the ability to see past one's own personal prejudices. And to change them.

Mew

Personal beliefs don't even need to come into play when doing research

A belief in god doesn't mean you can't do good work in QM

Wildcard

@Mew When one is researching, one is using one's mind.

Mew

I think a good scientist can separate beliefs from observations and reasoning

everyone has beliefs of some kinds, they are essential for getting by in life

Wildcard

All other aspects of research are secondary to the ability to use one's mind well. Notes, equipment, case studies....

@Mew Agreed.

Mew

2:59 AM

but as you said a good scientist won't include these beliefs in their work, only observations and reasoning

user116211

@JohnRennie An explicit point-wise explanation on JD's stand for the first-time; hope he reads that. I was expecting such post to come there; that was somewhat fulfilled by Gennaro, but this is a neat record on his deeds here. Although I'm sure, it wouldn't change his opinion, but I'm eager to see his response, if any; +1.

Wildcard

@Mew And predictions. Don't forget that.

Beliefs can play a VERY important role.

user116211

@AccidentalFourierTransform Just enjoying learning new things!

user116211

@DanielSank o/

Wildcard

Successfully challenging a widespread assumption of the impossibility of a certain task is, I would contend, NEVER otherwise than the result of one's personal belief that the task is possible.

If we ever do exceed the speed of light, you can bet it won't be conceived of and implemented by someone who believes it's impossible to go faster than the speed of light.

Most major scientific breakthroughs (not mere feats of engineering in applying existing knowledge, but NEW discoveries) were widely considered as impossible before they were accomplished.

More succinctly: Evidence is only found through observation.

@Mew Actually, I think "reasoning" has very little to do with scientific accuracy. Reasoning can ALWAYS be overturned by observation. "It still moves."

Secret

3:42 AM

Current chat occupancy
$$\lvert \textrm{Me}\rangle = \frac{1}{N}(\lvert \hbar \rangle + \lvert \textrm{maths}\rangle+\lvert \textrm{Mos Eisley}\rangle)$$

user116211

@Secret Why did you go to Mos?

Secret

Recently I have a harry potter question

user116211

Rogue One?

user116211

@Secret oh

Secret

nope, I plan to watch Rogue one on thursday

user116211

3:44 AM

okay

Secret

In other news, when trying to formulate a way to organise Light's associativity test, G. Bergeron found I might have used the set builder notation wrongly, and Tobias Kildetoft does not quite understood what I am trying to do.

I am not sure what goes wrong, but it might be I have used the cartesian product in a wrong way when defining a set that depends on elements in such set

(details to be reposted in seconds)

2 days ago, by Secret

Def. 1. All elements in a Cayley table

Given a magma $(M,\circ)$, Let $S=\{s_1,s_2,\dots,s_n\}$ be the ordered set obtained by imposing an order $\mathcal{O}$ onto M. Then the cayley table $T$ is given by $T=\{\ x\lvert \forall (a,b) \in S \times S, a\circ b=x\}$. The tranpose is defined by $T^\textrm{T}=\{\ x\lvert \forall (b,a) \in S \times S, a\circ b=x\}$.

Def 2. Rows and columns and collections

A row $R_i \subset T$ is given by $R_i= \{\ x\lvert \exists i \in S,\forall (a,i) \in S \times S, a\circ i=x\}$. Similarly, a column $C_i=\{ x\lvert \exists i \in S,\forall (i,b) \in S \time…

The whole thing in plain english: I have a magma. Def 1

tries to impose an ordering to the underlying set of the magma (which has n elements , thus the magma has $n^2$ elements in total including the products)

T thus gives the cayley table under $\circ$

which can be transposed by swapping the ordered pair around

Def. 2, fixes one of the entries of that ordered pair so that you get rows and columns of a cayley table instead. Def. 3 uses multiplication by elements in a magma elementwise to the rows and columns so it maps rows to rows and columns to columns

Theorem 1 than give the criteria for the magma to be associative is that when rows can always be map to rows without leaving the set of all rows of the cayley table

and Lemma 2 showed that proving all rows are closed under the magma action is sufficient to show associativity because rows and column operations are related by the transpose

DanielSank

3:59 AM

@MAFIA36790 \o

user228700

@JohnRennie: And this has been sitting here, all along... (::facepalm::)

user228700

7

Q: Justification for Freezing Point Depression & Boiling Point Elevation in Solutions?

I was wondering if the following justification for freezing point depression and boiling point elevation are conceptually correct. The reason why I ask this question is because I have been self studying chemistry for a course I will be taking this fall, and I don't have a human reference to check...

user116211

So, you are all in a voyage to show the magma is a semigroup @secret?

Secret

yeah, and if the above can be formulated rigorously and (more importantly) understandable to those in the field, then it is potentially powerful because you can actually check by looking at the cayley table whether the structure is associative, and where exactly will the associativity will break if it is not a semigroup

that is, the above attempt will end up putting the two tables of light's associativity test on top of each other, thus if the row and columns in the cayley table are closed under that "magma" action, then the magma is associative and hence a semigroup

David Z

0

Q: Hypergeometric Function: Differential Equation

In Birrel Davies: QFT in curved spacetime it is written that the following differential equation can be solved in terms of hypergeometric functions. $$(\partial_t^2 +(k^2+c(t)m^2))\phi(t)=0$$ But there is no reference and no method listen. Could somebody please help me solve this equation for $c(...

qft-in-curved-spacetime

send to Mathematics?

Secret

4:11 AM

@DavidZ right now it is too maths oriented. Either suggest the user to put more physical context to the question or sent it to maths

Mew

@Wildcard yes reasoning isn't good for determing accuracy but it's good for coming up with theories to then test experimentally

@Wildcard e.g. Einstein's special relativity was derived through reasoning but thne tested with observation. Of course like you say, if observation didn't reconcile with the theory the theory would need to be discarded despite reasoning being in its favour

@Kaumudi.H how is the new laptop?

user116211

@DavidZ I would say it's not fit for here; but would wait for the community.

user116211

In anyway, it looks like homework.

David Z

@MAFIA36790 you are the community :-P

user116211

I'm a part of the community.

user228700

4:37 AM

@Mew It's excellent and still waiting at Customs (-_____-)

user228700

@JohnRennie: Morning, morning! :-) I've a quick question. The definition of the freezing point of a liquid is given as:

user228700

> "The temperature at which the vapour pressure of the solid becomes equal to the vapor pressure of the liquid"

user228700

Why is this the definition?

user116211

4:53 AM

@Kaumudi.H And why do you feel it should be otherwise?

user228700

Uhh, I don't. I'm unable to understand why this definition makes sense.

user228700

@Mew: I've just learned about osmosis and have figured out why my two fish died, all those years ago. I was a kid, how was I s'posed to know?! :-(

Secret

5:27 AM

Row- and column-major order

In computing, row-major order and column-major order describe methods for arranging multidimensional arrays in linear storage such as random access memory. In row-major order, consecutive elements of the rows of the array are contiguous in memory; in column-major order, consecutive elements of the columns are contiguous. Array layout is critical for correctly passing arrays between programs written in different languages. It is also important for performance when traversing an array because accessing array elements that are contiguous in memory is usually faster than accessing elements which are...

I found it very hard to phrase my ideas in precise mathematical language because I often think in terms of arrays, and trying to find set builder notations that can give me the ordering of arrays

user228700

5:39 AM

If anybody in interested in the following article about demystifying osmosis, please give it a read and let me know if u agree with the writer's hypothesis:

user228700

alienryderflex.com/osmosis

John Rennie

5:50 AM

@Kaumudi.H It's true, but not a wonderfully useful definition.

The free energy of the molecules in the solid and the free energy of the molecules in the vapour above the solid are equal because they always are when there is equilibrium.

And likewise for the liquid: the free energy of the molecules in the liquid and the free energy of the molecules in the vapour above the liquid are also equal.

user228700

And since free energy is directly proportional to pressure, it makes sense to use this definition, yeah..?

John Rennie

So if the free energies of the vapour above the solid and the vapour above the liquid are equal that must mean the free energies of the molecules in the liquid and solid are equal.

@Kaumudi.H I wouldn't have said it's a very useful definition.

user228700

Alrighty. I've another quick question (which may lead to a bigger question, oops). Shall I go on..?

John Rennie

Yes, go ahead

user228700

Is it OK to think "Osmosis occurs due to a concentration gradient"? I've come across other explanations but haven't really understood any of them properly. Is it worth the time or should I just accept this and move along..?

John Rennie

6:02 AM

Well molecules bounce around randomly due to thermal motion.

And the number of molecules bouncing randomly past any point will be proportional to the concentration of molecules near that point.

user228700

Right, right, but look at what this person is suggesting:

user228700

> "Yes, the concentration of water is lower on the right side, but what does that mean to any individual pore? If a sugar molecule is not nearby the pore, the water concentration is the same on both sides of the pore, and if a sugar molecule is close enough to the pore to prevent water molecules from escaping right-to-left, it is also blocking water molecules from entering left-to-right. When a sugar molecule blocks a pore, it blocks water flow in both directions, indiscriminately."

user228700

(Source: alienryderflex.com/osmosis)

John Rennie

I find it hard to raise much enthusiasm for that argument. The sugar molecules don't block pores

user228700

What about this:

user228700

6:06 AM

> "If a sugar molecule is not nearby the pore, the water concentration is the same on both sides of the pore"

DanielSank

@JohnRennie why are you taking to a cat?

John Rennie

The flow of water through the semipermeable membrane has nothing to do with sugar molecules blocking the pores in the membrane.

@DanielSank it's a NAND cat!!

user228700

@JohnRennie THANK YOU!! @DanielSank: x-(

user228700

@JohnRennie Right...

DanielSank

Lolol

user228700

6:09 AM

I too found it a little difficult to believe what the O.P is saying.

John Rennie

@Kaumudi.H that's also meaningless. Concentration is an average property and it's averaged over a large number of molecules. Osmosis is a net flow where we average the flow rates over a large number of molecules.

To talk about individual molecules is meaningless.

You've finally found a source even worse than your textbook :-)

user228700

Why, tho? Why is it entirely meaningless?

user228700

@JohnRennie The level of suck that my textbook contributes to this world is now a well-known fact hereabouts :-P Nothing can beat my textbook's expertise in this field.

Secret

is so tempted to star that

user228700

:-)

John Rennie

6:14 AM

In a sugar in water solution the molecules are all buzzing around randomly and there will be local variations in the densities of water and sugar molecules just due to random chance.

user228700

Riight...

user228700

(Sorry about that. My mum needed me)

user228700

Can u pls go on..? Why is the O.P's argument addressing individual particles meaningless..?

user228700

Hiya @Mew :-)

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