Proposal for 'Sticky' for certain issues that come up again and again.

[studiot]

This proposal is a result of my noticing how often certain issues crop up and was prompted by the following posts, which come from different threads.

Before offering a draft version I would like to ensure two things.

Assurance from the moderators that this is in order and will not lead to being called out as a blog.

The opportunity for interested other members to participate in the drafting; I do not pretend to have all the answers.

  

On 10/6/2019 at 6:20 AM, Sensei said:

On 10/6/2019 at 3:17 AM, Mordred said:

In physics a dimension is a mathematical term meaning an independent variable or other mathematical object such as a group or tensor. In particle physics it often related to an effective degree of freedom.

Maybe you should make article and make it sticky what dimension means in physics.. so they won't confuse it with sci-fi vision of other dimensions..

  

3 hours ago, studiot said:

I would just like to add in some words of caution here.

Dimensions are often identified with degrees of freedom.

Both have a (numerical) value.

These concepts are not the same, although sometimes their values coincide. They are all too often confused with each other.

Further it is important to identify the 'space' in which you are working - phase space, configuration space, geometric space and so on.

The dimensions of these different spaces can (and often do) differ for the same 'system'.

  

5 hours ago, Mordred said:

Sigh it never fails to amaze me how many posters want to invoke other universes to develop a Toe when they cannot describe how our universe evolves. 

A TOE as I mentioned in your other thread requires the relevant mathematics. The few equations you have do not even begin to describe how particles interact. They do not describe particle generations. The Pauli exclusion principle or apply any of the conservation laws in particle physics which is a primary importance for a TOE.

 

So I am suggesting two main areas for inclusion

1) Dimensions and degrees af freedom.

2) The Relations of Constitution and the Conditions of Compatibility and their implications for any proposed Theory of Everything (TOE).

 

Please have you say here so that the final post can be transposed to the locked sticky.

Edited June 29, 2020 by studiot

[Ghideon]

I guess this is intended for the physics section and should focus on physics? 

(I've seen confusion about dimensions in computer science, only loosely related to math and physics. Some clarifications I have in mind could maybe fit a general section sticky but probably not in physics.) 

[studiot]

14 minutes ago, Ghideon said:

I guess this is intended for the physics section and should focus on physics? 

(I've seen confusion about dimensions in computer science, only loosely related to math and physics. Some clarifications I have in mind could maybe fit a general section sticky but probably not in physics.) 

Please post them anyway.

(But only in outline form at this stage)

The purpose of a sticky is to be useful to as many as possible for reference.

 

Edited June 29, 2020 by studiot

[Mordred]

I have no problem with a sticky for this. It would certainly make a good time saver. I'm still unclear which forum would be most applicable. I'm thinking the modern physics forum may be suitable however one of the math may also be an option. As the term has is applicable in a number of fields including engineering, statistics, computer science as well as physics.

[joigus]

I think it's a good idea. +1. Modern and Theoretical Physics & Astronomy and Cosmology are especially affected in what physics is concerned.

Speculations could be another one, because much of what starts on the above ones ends up there.

This forums are very interdisciplinary, so maybe there are nuances between our respective current definitions, but I see no reason why I couldn't be worked out.

[Ghideon]

Here is rough idea for a layout.

Description of what a dimension is in physics and maybe math.

Followed by 

List of short descriptions/comparisons related to other sciences, for instance computer science.

Example to illustrate; partly taken from Mordred :

In this forum "dimension" have a specific meaning. In physics a dimension is a mathematical term meaning an independent variable or other mathematical object such as a group or tensor. In particle physics it often related to an effective degree of freedom.

Other areas of science may have related but not identical definition and usage of "dimension":
-Computer science
...

 

Edited June 29, 2020 by Ghideon
added example

[Mordred]

We can expand on the term degree of freedom as well the wiki link covers some of the essential aspects.

https://en.m.wikipedia.org/wiki/Degrees_of_freedom_(statistics)

Also tie this into vectors spinors matrices and tensors.

[studiot]

Many thanks to all who replied sor far.

I do not think where the sticky is finally placed is currently all that important. I'm sure it end result will speak for itself and it will be linkable in any case.

I do think, though, that the description and examples should be short enough, simple enough and clear enough for as many readers as possible (unlike Wikepedia).

To start here is a possible description and example for my posher phrases

Quote

2) The Relations of Constitution and the Conditions of Compatibility and their implications for any proposed Theory of Everything (TOE).

 

When analysing a situation or a problem we can divide the known information into two camps.

The Relations of Constitution refer to the Science (Physics ?) of the issue.
These may be suitable Laws, Principles etc that must be obeyed by the system in question.
Whilst these are often expressed as equations, they may not be which is why a more general term 'Relations' is used.
For example neither the Second Law of Thermodynamics nor the Uncertainty Principle are equations, but inequalities.
Even when we have equations (as in the worked example to follow) they may not allow solution of the problem or offer incorrect solutions. (There are an enormous number of such incorrect solutions to General Relativity)

So we also need a second set of defining information, usually specific to the problem and often geometric in nature.
Once again these often appear as equations but again they may not.
For a specific problem these can be every bit as important as the Relations of Constitution since once you have solved the Science you still may not have the answer.
This is also the difficulty any Theory of Everything must overcome.

So all that sounds very pompous here is a plain old example to make things a bt clearer.

A projectile is fired upwards at angle alpha to the horizontal with initial velocity V from the top of a 100m cliff, at a time t  = 0.

Calculate the time to splashdown in the ocean below.

The Science tells us that the equation of motion required is

h = V t sinα - 0.5gt²

Now this is a quadratic in t so it has two solutions.
For alpha = 30^o and V = 100m/s these are (nearest whole number) 12 seconds and -2 seconds.

This is where Compatibility rides to the rescue since it places the Condition that t is greater than  0 (time is non negative)

 

For the comparison of dimensions and degrees of freedom I was going to compare these for various plane frames (all of which have 2 dimensions but different degrees of freedom)

 

 

[Eise]

Not a bad idea at all. I was breeding on such a 'pin' for philosophy. I would like to see similar requirements to postings in other groups, so:

• opinions without (good?) arguments are not acceptable
• Questions, except completely nonsensical ("What is the colour of time?") are of course allowed
• Taking away some misunderstandings about what philosophy is (not wild speculations, not scientific speculations, but intelligibility problems)

I can try to write such a 'pinned post'.

Of course I also think about a pinned post about free will... I think I can  express me pretty neutrally. (Living in Switzerland for nearly 30 years now  )

[joigus]

On 6/30/2020 at 11:07 AM, Eise said:

Not a bad idea at all. I was breeding on such a 'pin' for philosophy. I would like to see similar requirements to postings in other groups, so:

• opinions without (good?) arguments are not acceptable
• Questions, except completely nonsensical ("What is the colour of time?") are of course allowed
• Taking away some misunderstandings about what philosophy is (not wild speculations, not scientific speculations, but intelligibility problems)

I can try to write such a 'pinned post'.

Of course I also think about a pinned post about free will... I think I can  express me pretty neutrally. (Living in Switzerland for nearly 30 years now  )

I applaud this idea too. +1 The only thing I find more difficult to establish from a practical POV is the "good" in "good" arguments. You seem to have an idea for when an argument is just too bad quality to be accepted as such... 🤔

[Mordred]

The difficulty with dimensions as opposed to degrees of freedom is a good topic to examine. There are factors that can reduce the needed degrees of freedom. I'm still looking into a simple way to highlight this detail.

5 hours ago, joigus said:

I applaud this idea too. +1 The only thing I find more difficult to establish from a practical POV is the "good" in "good" arguments. You seem to have an idea for when an argument is just too bad quality to be accepted as such... 🤔

I have no issues with pinned threads in philosophy but I am the worse philosopher lol. So I cannot contribute in that department.

[iNow]

51 minutes ago, Mordred said:

have no issues with pinned threads in philosophy but I am the worse philosopher lol. So I cannot contribute in that department.

Part of the challenge is that there are no correct answers in philosophy, only well reasoned, well supported, logically consistent positions. I suspect that like me you prefer conversations where 2+2=4, not where 2+2= ennui or potato salad. 

[Mordred]

Lol I prefer answers that can be proven via experimentation or mathematics. Any time it comes to opinion without recourse from belief then its not provable. At least in my opinion lol.

( however that is a distraction from thread topic which involves commonly misunderstood terms such as dimension or degrees of freedom)

Edited July 2, 2020 by Mordred

[MigL]

I don't know what the purpose of a 'sticky' on Philosophy would be; to tell people 'how' to think ?

As for dimension vs. degrees of freedom, I would think it would be sufficient to say that dimensions are degrees of freedom, while degrees of freedom are not necessarily dimensions, but can be other motions/aspects of the system. 
Or, would it be more simple to say dimensions relates to the space, degrees of freedom relates to the system ?

 

[Mordred]

Well let's try an example if you have two particles in 3d space it would take 6 dimension values to define their location. However you can reduce the degrees of freedom between the two particles to 5 via the constraint relation for two particles at a fixed distance.

This is the part that gets tricky as most examples are rigid bodies. However in GR there aren't rigid bodies.

These little sticky points is where I would need advise. Chemistry for example involves a different descriptive for degrees of freedom for a state than I would describe for a particle. Studiot would describe a more engineering aspect. Which involves more constraints due to application design so the effective degrees of freedom can be reduced due to the additional constraints.

 

 

Edited July 2, 2020 by Mordred

[Eise]

8 hours ago, joigus said:

The only thing I find more difficult to establish from a practical POV is the "good" in "good" arguments.

That's the reason I put 'good' between brackets, together with a question mark...

1 hour ago, iNow said:

Part of the challenge is that there are no correct answers in philosophy, only well reasoned, well supported, logically consistent positions.

Well, at least we have that: 'well reasoned, well supported, logically consistent positions'. And while 'correct answers' is definitely not a workable concept in philosophy, there are a lot of answers that are definitely wrong. 

43 minutes ago, MigL said:

I don't know what the purpose of a 'sticky' on Philosophy would be; to tell people 'how' to think ?

Partially, yes. Truth claims should be supported. Opinions without supportive arguments are definitely not philosophy. There is a strong parallel with science: philosophy is just missing the touchstone of experiments and observations. But logic and good and relevant arguments are just as important in philosophy as in science. So I do not want to tell people how to think: but I do want to tell how to think if they want to 'do philosophy'. You would not accept stupid arguments in a scientific discourse, do you? Scientific thinking must learned, and is essential when doing science. Same for philosophy.

[studiot]

2 hours ago, Eise said:

Partially, yes. Truth claims should be supported. Opinions without supportive arguments are definitely not philosophy. There is a strong parallel with science: philosophy is just missing the touchstone of experiments and observations. But logic and good and relevant arguments are just as important in philosophy as in science. So I do not want to tell people how to think: but I do want to tell how to think if they want to 'do philosophy'. You would not accept stupid arguments in a scientific discourse, do you? Scientific thinking must learned, and is essential when doing science. Same for philosophy.

This reminds me of a long established tradition in English schools in answer to the question

"Why do the English study English in school ?"

In my day there was a subject called 'Use of English'
Later in my daughter's day she studied 'Critical Thinking'

The point of these was how to read and extract (useful) information from different pieces of english text and logically evaluate them.

Of course the ambit was wider than Philosophy, but it always amazed me how clear thinking (university) graduates of English are.

[joigus]

3 hours ago, Mordred said:

I have no issues with pinned threads in philosophy but I am the worse philosopher lol. So I cannot contribute in that department.

 

4 hours ago, iNow said:

Part of the challenge is that there are no correct answers in philosophy, only well reasoned, well supported, logically consistent positions. I suspect that like me you prefer conversations where 2+2=4, not where 2+2= ennui or potato salad. 

2 hours ago, MigL said:

I don't know what the purpose of a 'sticky' on Philosophy would be; to tell people 'how' to think ?

Well, I wouldn't be very good at summing up criteria of philosophical goodness myself, but I cannot deny that there are significant things to be said. Somehow I picture @Eise as the most knowledgeable person I know around here, at least of those I've interacted with.

Some of the stickies on the forums rules already cover a number of common fallacies or what an argument in good faith is.

Other fallacies could be added, like the argument of authority, or the idola fori (Francis Bacon); that is "many people say or think". If not as explicit prohibitions, at least to make people aware of common sources of error or weak arguments.

On the other hand, there are certain philosophical topics that are of interest to science and I think have become universal quality standards for scientific thought:

Operationalism (ultimate reference to measurable quantities)

Ockam's razor (economy or parsimony of systems of ideas)

Falsifiability (K. Popper) --> road to experiments

2 hours ago, MigL said:

As for dimension vs. degrees of freedom, I would think it would be sufficient to say that dimensions are degrees of freedom, while degrees of freedom are not necessarily dimensions, but can be other motions/aspects of the system. 
Or, would it be more simple to say dimensions relates to the space, degrees of freedom relates to the system ?

This is a very good point, because if anything, it shows that the distinction is sometimes difficult.

I think that dimensions (at least overlapping with @Ghideon, @Mordred) is a concept that generally refers to the ambient space, or space of independent variables, while DOF generally refers to dependent variables that make up the mathematical concept of state, generally a function of the first. So to describe the state of a system you set up a functional dependence Y(t,x), with #DOF = number of independent Y₁, Y₂,...Y_n that you can fix. Any other function of the state would be numerically determined.

System, state, variables of state, ambient space I think are the concepts that shape the question. Although there are cases when the distinction can become blurry for several reasons. One of them appears in classical thermodynamics, where the ambient space disappears altogether, and you're left with an implicit relation among the state variables (equation of state): f(P,V,T,n) etc. There you have some kind of cyclicity, in which you can pick any number of these variables to describe the change of the others, and trajectories as abstract (timeless) motions in that surface of state.

Then we've got field theory. There the concept of DOF is the set of field variables, so F_a(t,x) would itself be the degree of freedom. A vector field, like the vector potential, mirrors the properties of the ambient space itself,

\[A^{\mu}\left(t,x\right)\]

but other "internal field variables", like e.g., Yang-Mills fields, have a representation space that is richer.

As to GR, you've got the manifold (independent variables) plus a set of fields: g(x), metric; R(x), Riemann; T(x), matter; all of them would add up to the state (dependent variables) as a function of the x's (independent variables).

As to classical dynamics, I see the DOFs as the specification of (x₁,...,x_n,p₁,...p_n) because, once you fix those, there's nothing else to fix unless you re-define what your system is. But another complication is that there is an existing tradition to call just (x₁,...,x_n) your DOFs.

Then there is @studiot's comments about the equations of constitution. The thing does ring a bell to me, but I don't remember what that is about, so I'd be thankful if he reminded me.

[studiot]

3 hours ago, MigL said:

Or, would it be more simple to say dimensions relates to the space, degrees of freedom relates to the system ?

I would go along with this as a simple but solid opening statement.

Thank you.

The interesting question comes when you ask "Can a clear line between them be drawn ?"

How do we include fractional  dimensions of the space? whilst allowing only integer degrees of freedom (I can't see how any DOF can be fractional)

[joigus]

3 minutes ago, studiot said:

How do we include fractional  dimensions of the space? whilst allowing only integer degrees of freedom (I can't see how any DOF can be fractional)

This is another very good point. On my part, I will brood over it for a while longer, plus go over everybody's comments.

[studiot]

9 minutes ago, joigus said:

Then there is @studiot's comments about the equations of constitution. The thing does ring a bell to me, but I don't remember what that is about, so I'd be thankful if he reminded me.

Thank you, this is what I want to find out because it shows my example was not clear enough.

Traditional examples of the difference between the physics and the maths  are usually drawn from fluid mehcanics - I will think about it.

 

[Eise]

When making such sticky posts, I think it is important to think about what their purpose is. From that purpose one can derive who the audience for these sticky post is, and with that at what abstraction level is used.

For its purpose, I think it is to avoid that the same arguments must be repeated again and again, just because a member is new. Ideally a new member would be guided to it ('Before posting, read this'). But it would also serve its purpose when we can just link to the sticky post, when applicable.

The audience will be most of the time some science fan or some science critic. Most of them will have their 'knowledge' from popular science books, sites, or articles in the press. So I think that is the level of speech we should use too. That means we should not be too abstract, drifting into too many technical details.

So e.g. when we would decide to make an entry about 'Einstein was wrong', I would only remark, very globally, that relativity has much developed since Einstein, is empirically proven many many times, and forms the basis for many understood phenomena (colour of gold, existence of magnetism, muons getting at the earth's surface, etc) and for technologies (GPS, LHC); all maybe with useful links for who is interested in the details.

And I would close the sticky thread to keep it clean. If somebody wants to discuss some topic from the sticky post, she can open a new thread for that.

And when I would write such a 'sticky introduction' to philosophy, I'll need a native English proof reader... Isn't it, Studiot? 

Edited July 2, 2020 by Eise

[studiot]

7 minutes ago, joigus said:

This is another very good point. On my part, I will brood over it for a while longer, plus go over everybody's comments.

Your other points in the rest of your previous post bring out very nicely soemthing I often say.
"We are really considering the geometry of graphs or plots of the connections between the variables."

Now this has implications if some property of the graph or plot space is not mirrored by the variables.

Here are my thoughts about fractal dimensions. Just take plane 2D for simplicity.

2D is 'made up' of points say x and y.

Now Euclid tells us that a point has zero dimension.

So are both the dimensions and the degrees of freedom of a fixed point or attractor zero ?

Variables and definite connections between them (equations) allow a point to move about in xy space again matching dimensions and degrees of freedom to 2.

Fractals are different. They have no equations to follow, they are procedural processes.
Take the Koch curve and snowflake.
The procedure involves taking points on the curve and moving them a small displacement in x and y.
So points in the xy space are no longer on the curve in a finer scale or iteration of the curve.

This process is different from taking two numbers on the number line and finding another number between them (continuity)
since all points encountered are always on the line