The Naked Scientists

The Naked Scientists Forum

Author Topic: What physics and math topics do people find hardest to grasp?  (Read 18207 times)

Offline dlorde

  • Neilep Level Member
  • ******
  • Posts: 1441
  • Thanked: 9 times
  • ex human-biologist & software developer
    • View Profile
Yes, I agree. Let me put it this way though, when I think of randomness then I do it from chaos. Maybe that's not correct but to me they become equivalent, although you might want to define randomness to superpositions microscopically, as a example of how I think :) versus chaos macroscopically. Even though you can call chaos deterministic, as in if we only knew all parameters we could describe it, I personally relate it to a randomness.
Well, 'deterministic' means 'non-random' by definition, so perhaps 'pseudo-random' is a better description for the results of chaotic functions.

Quote
Maybe I could express it as I don't think there ever will a possibility of knowing the whole history, of anything. It seems to go through all physics that one, no matter what scales you look at it from?
'Having no history' - that could almost pass as a definition of randomness that leaves the question of knowledge open - i.e. can one distinguish a chaotic sequence from a random sequence without knowing the prior history of the system? If I recall correctly, a characteristic of chaotic systems is that islands of order may appear at regular intervals among the apparent randomness, so it should be possible to distinguish randomness from chaos for long enough sequences. How long 'long enough' might be is an open question...
« Last Edit: 17/05/2013 17:36:10 by dlorde »
 

Offline yor_on

  • Naked Science Forum GOD!
  • *******
  • Posts: 11999
  • Thanked: 4 times
  • (Ah, yes:) *a table is always good to hide under*
    • View Profile
A intriguing idea dlorde. And yes, assuming Feigenbaums constant one should be able to assume a fractal behavior to chaos giving you mystical attractors and some regularity in that randomness. But then the question becomes how to prove what is random, doesn't it? Haven't thought of that one :) but it seems to become a mathematical concept defined by what circumstances, degrees of freedom etc something have. In flipping the coin we then have three possibilities, the coin giving us head tail and its edge. Of those we ignore the edge defining it as head and tail, and define it as a 50/50 chance for each throw. The randomness referred to here is not something able to make the coin disappear, it's a mathematical definition of what 'choice' of two it may make landing.
 

Offline yor_on

  • Naked Science Forum GOD!
  • *******
  • Posts: 11999
  • Thanked: 4 times
  • (Ah, yes:) *a table is always good to hide under*
    • View Profile
Now, as far as I remember, although Feigenbaums constant give you a regularity, somethings bifurcations (splits) can not be back-tracked. What does that make it, a random behavior? What is random here? Normally used I would refer to something random as something I can't foresee, meaning its exact outcome. Although I might expect myself able to back-track it after a outcome. But that isn't perfectly correct, is it :) thinking of that coin throw. Even though I couldn't foresee it, after its outcome I sincerely doubt myself to be able to define exactly why it gave me a 'tail', but, should I be able too? If knowing all parameters?
=

This one is nice http://www.imho.com/grae/chaos/chaos.html
==

Then again, assuming a time symmetry. if I can back-track it I also should be able foresee it, using the same presumption (knowing all parameters). So that one doesn't really say anything. Well, it do state something, if we define it as being of two choices.

Determinism relative indeterminism. Then what we have found so far is not determinism as I think, that as I see no real experimental proof for it. Historically we've used determinism though as a leading star, expecting a linear causality to define the universe, as some clock work. And working from an assumption of the universe wanting it to be as simple as possible, indeterminism must win :)
« Last Edit: 18/05/2013 13:47:09 by yor_on »
 

Offline yor_on

  • Naked Science Forum GOD!
  • *******
  • Posts: 11999
  • Thanked: 4 times
  • (Ah, yes:) *a table is always good to hide under*
    • View Profile
So, either we define it as a 'random behavior' inherent in Chaos equations, or we call them deterministic. If they really are deterministic then we should be able to simplify a chaotic system to the degree where we can control all parameters, and so 'predict' its outcomes. But we can't do that, as far as I know. So that leaves us a randomness, but is it a same randomness as in the coin throws?

Put another way, you're part of a chaotic system, population wise, environmental, Earth itself. As you throw that coin, the coin also must become a parameter in chaos.
=

And what more, well, if one believe in a absolute time symmetry, how do one explain indeterminism? And 'randomness'. I define time symmetry to a logic. I can also use Feigenbaums constant to define a logic, but inside that logic we find randomness and, as I think, also a description of indeterminism. Time symmetry works as a logic because we need it, it gives us a past and and a present and a future. But it's no proof of a arrow able to go backwards, not as long as you use your local clock defining that experiment proving your concept.
« Last Edit: 18/05/2013 14:00:31 by yor_on »
 

Offline dlorde

  • Neilep Level Member
  • ******
  • Posts: 1441
  • Thanked: 9 times
  • ex human-biologist & software developer
    • View Profile
So, either we define it as a 'random behavior' inherent in Chaos equations, or we call them deterministic. If they really are deterministic then we should be able to simplify a chaotic system to the degree where we can control all parameters, and so 'predict' its outcomes. But we can't do that, as far as I know. So that leaves us a randomness, but is it a same randomness as in the coin throws?
As I previously said, chaos is deterministic, not random. It is unpredictable because of sensitive dependence on initial conditions. For example, this means that given the initial parameters, we can't predict on which wing of Lorentz's butterfly we'll find ourselves after n iterations. To discover this, we must iterate the function n times with those initial parameters. In the real world, we can't obtain the initial parameters for chaotic processes with sufficient precision to obtain useful results by iterating the function(s) even if we know it(them). Hence the Monte-carlo simulations for weather, where even for chaotic states there is some hope of identifying the major attractors (although this may mean predicting, say, a 40% chance of stormy, wet weather and a 60% chance of clear, sunny weather!).

The real world has both chaotic and random components. Chaotic because of non-linear dynamic processes, and random because of quantum indeterminacy. The contribution of quantum indeterminacy to chaotic processes in the real world introduces a clouding degree of randomness at small scales, but should be statistically averaged out for macro-scale processes.
 

Offline yor_on

  • Naked Science Forum GOD!
  • *******
  • Posts: 11999
  • Thanked: 4 times
  • (Ah, yes:) *a table is always good to hide under*
    • View Profile
Are you telling me that we can't define a smallest chaotic system to experimentally define its 'determinism' :)
And therefore it becomes deterministic?

Ah well :)

I think I would say that any system unable to be deterministically defined have a very little probability to be proven deterministic, other than theoretically. After all, we should use experiments to define theory, not the other way around.
=

On the other hand, theory do define experiments, to test a theory. and that's what I would like to see here :) Determinism being proven by carefully chosen initial parameters. Otherwise it seems to me that no matter how small those initial parameters are we still won't prove a systems determinism, although we can show a 'deterministic' constant repeating itself. So one might then be able to say that even though outcomes are unpredictable, its pattern is mathematically predictable.

Doesn't it remind you about the discussion of 'free will' too? I know it does to me, statistical trends relative individual choices..
« Last Edit: 19/05/2013 00:03:29 by yor_on »
 

Offline Pmb

  • Neilep Level Member
  • ******
  • Posts: 1838
  • Physicist
    • View Profile
    • New England Science Constortium
I'm very displeased that this thread has been taken so off topic that the actual topic is no longer being addressed.
 

Offline yor_on

  • Naked Science Forum GOD!
  • *******
  • Posts: 11999
  • Thanked: 4 times
  • (Ah, yes:) *a table is always good to hide under*
    • View Profile
Yes, afraid you're right Pete. Maybe we should split it?
You better talk with a moderator, to agree on where, as you're the originator of the thread.
 

Offline dlorde

  • Neilep Level Member
  • ******
  • Posts: 1441
  • Thanked: 9 times
  • ex human-biologist & software developer
    • View Profile
I'm very displeased that this thread has been taken so off topic that the actual topic is no longer being addressed.
You may be right; but perhaps the direction of the thread is evidence that the difference between randomness and chaos (which involves both physics and maths) is a topic that's hard to grasp?

Personally, I'd rather have a live thread than a dead one - unless someone has some other hard-to-grasp topic to discuss?
 

Offline yor_on

  • Naked Science Forum GOD!
  • *******
  • Posts: 11999
  • Thanked: 4 times
  • (Ah, yes:) *a table is always good to hide under*
    • View Profile
Wrote this, and thought it made sense at the time :)

"One can think of it this way maybe, the pattern of a thousand tails is no more uncommon that any other combinations of set patterns like tail - tail  - head, if repeated over and over, for a thousand flips. Which then just should make one thousand tails, or heads, uncommon, because it is so easy to recognize for us. That will make the one defining it as being 'reset' with each new flip the one making most sense.

What i mean is that if you count the way a pattern evolve over time, flipping a coin, then all patterns possible should have a equal chance of evolving, singling out no pattern as the one, more probable. And a pattern would then be whatever way you found head and tails arrange themselves over a thousand throws."

Still think it makes sense, but read this..

"In contrast, you wouldn’t expect all of the dice to be 4 at the same time, or otherwise assume one particular pattern.  That would be a very unlikely and low entropy outcome." http://www.askamathematician.com/2011/12/q-why-does-the-entropy-of-universe-always-increase-and-what-is-heat-death-of-the-universe/

So a unordered sequence is then more probable?
What makes it so?

Stupid question :)
You got a larger probability (number) of 'unordered sequences' than 'ordered'. Then again, we are the ones defining them as ordered or unordered, isn't that so? We mark them, and so define them.

In 'reality' no pattern should be more probable, as I think?
Maybe it's a stupid question, but there seems a slight difference to me? What we define as a probability relative a logic. Or maybe it's just me not thinking it through.
=

(Sorry Pete, forgot, still, this is a rather good thread I think, 'organically growing' if you see how I read it.)
« Last Edit: 30/05/2013 19:26:09 by yor_on »
 

Offline CliffordK

  • Neilep Level Member
  • ******
  • Posts: 6321
  • Thanked: 3 times
  • Site Moderator
    • View Profile
I think there was a moderator discussing the numerical theory.  Anyway, if more posts are on that subject, we can split, if not, I'll leave it alone.   Certainly there would be benefits of discussing probability and numerical theory.  And, I'm quite rusty on my factorials and "Choose" equations.

I saw this puzzle online.
What is next in this series? 1, 4, 10, 19, 31, _   (no need to post the answer here).

It reminds me of the old SAT questions (Scholastic Aptitude Test).  Anyway, there may be benefits of discussing how to approach determining an unknown sequence or series.

Another, more well known series:
1, 1, 2, 3, 5, 8, 13, ...
 

Offline bizerl

  • Sr. Member
  • ****
  • Posts: 279
    • View Profile
I'm very displeased that this thread has been taken so off topic that the actual topic is no longer being addressed.

That's a shame Pete, because I really wanted to talk about the Monty Hall problem again. I got all excited because after reading this thread, I finally get it. But I'll address the topic first and say that Maths never really bothered me much at the fairly low levels I studied it at.

What always baffled me was "particle" physics and what a "particle" actually consists of. I think that trying to simplify it diagrams of an atom made of billiard balls actually makes it harder to grasp on a deeper level of what is actually happening.

Now, Monty Hall. I find it interesting that you can think of the situation of 100 doors, where you are asked to choose a door, but then you are asked to decide whether the door has the prize, or a goat. Probability at that stage would say that you've probably chosen a goat, which is why when you are given the opportunity to change in the original scenario, you would.

What interests me is that if at the stage of having 98 goats staring out of opened doors and 2 closed doors, one of which has a prize, someone new enters the studio and is asked to choose a door, would he (or she) be given any advantage by asking what the previous person chose?
 

Offline damocles

  • Hero Member
  • *****
  • Posts: 756
  • Thanked: 1 times
    • View Profile
From bizerl:
Quote
What interests me is that if at the stage of having 98 goats staring out of opened doors and 2 closed doors, one of which has a prize, someone new enters the studio and is asked to choose a door, would he (or she) be given any advantage by asking what the previous person chose?
The answer to that is yes -- it is extra information that modifies the odds from 50:50 to 99:1.

From pmb:
Quote
I'm very displeased that this thread has been taken so off topic that the actual topic is no longer being addressed.
I apologize Pete for my part in this, although I think you can see that Probability and Combinatorics is a part of Maths that both fascinates and confuses many people.

One part of advanced Maths/Physics that confuses me is how to relate the character tables of say trigonal groups like C3v or D3 to that of the underlying C3 group (there are other examples of the same sort of thing where a degenerate representation might consist of a pair of complex conjugates or a conventional E type representation with a character of 2 for the identity.)
 

Offline evan_au

  • Neilep Level Member
  • ******
  • Posts: 4126
  • Thanked: 247 times
    • View Profile
I just discovered the Khan Academy, https://www.khanacademy.org/

This covers a number of areas of Maths & Science in a progressive and clear manner (I needed a statistics refresher).

...although I am puzzled about how & why they combine "Science & Economics" into a single category??
 

Offline damocles

  • Hero Member
  • *****
  • Posts: 756
  • Thanked: 1 times
    • View Profile
I just discovered the Khan Academy, https://www.khanacademy.org/

This covers a number of areas of Maths & Science in a progressive and clear manner (I needed a statistics refresher).

...although I am puzzled about how & why they combine "Science & Economics" into a single category??

The reason for this is because physics and econometrics are the major areas of application of advanced mathematics, and because (at least in Canberra) there were a huge number of postdocs in physics at ANU who could not find employment in physics when their contracts ran out, but they were easily able to move across and develop the field of econometrics with jobs in the public service (perhaps explaining why econometrics has not turned out to be particularly successful). I do not know about the situation in other countries, but can imagine it was much the same.
 

The Naked Scientists Forum


 

SMF 2.0.10 | SMF © 2015, Simple Machines
SMFAds for Free Forums