Physics is Just a Model

[SelfSim]

... So the idea that our perceptions refer to anything real beyond our own minds is just a belief like any other, for example, like the belief in the resurrection of Jesus?

This is the point at which I need to produce a usable definition of 'belief'. As follows:

'A belief is that which I hold to be true out of preference, that does not follow from objective tests and is not beholden to the rules of logic'.

Try testing the mind-model of 'the resurrection of Jesus' against this definition and then compare the results with the same test on the mind-model of 'the existence of a mind independent reality'.
Is there a difference when using my above operational definition as the criterion?
(Ie: given that both are objectively untestable?)

I dont buy that, in that the reality of something real "out there" (even if its quite different than our perceptions indicate) is the baseline mode of understanding which we all share as human animals prior to the exertions required for religious or ideological belief-building.

Its called philosophical 'Realism' ... there are many other philosophically held '-isms' that pertain to reality, so I don't think you can assert that on behalf of all human thinkers .. but I do agree that its a very commonly held philosophical model (based on a belief) to have in the back of one's mind. (Popper for instance was notorious for it).

In other words belief in the real is the opposite of a slippery slope downward to any old crazy belief. Its more like the rut we're stuck in

Maybe .. but its still based on a belief which is objectively untestable.

Oh .. and I'm not going to attempt to 'push' this notion onto anyone who doesn't claim their knowledge reality as being some kind 'privileged' knowledge .. nor on anyone who's basis of argument is distinguished by them as as being a belief. Assumed, undistinguished believed-in posits are also a problem where education in science can help, (IMO).

 

[durangodawood]

...I once heard someone on this forum (and an atheist to boot) say they accept a reality apart from themselves because that's the way it appears......

Its the position that requires the least effort-of-belief. Add to it that our perception must coordinate somewhat to actually reality. If not, we'd have quite short lives as we make our way through it (whatever it "really" is.)

 

[J_B_]

Its the position that requires the least effort-of-belief.

Yeah. I know you weren't referring to belief in God, but it is an odd conversation when someone brings in Occam's Razor to try to make the case that believing in God is not the most parsimonious position. That is just an opinion. Quantifying what is most parsimonious is a sticky wicket.

 

[durangodawood]

Yeah. I know you weren't referring to belief in God, but it is an odd conversation when someone brings in Occam's Razor to try to make the case that believing in God is not the most parsimonious position. That is just an opinion. Quantifying what is most parsimonious is a sticky wicket.

Having one explanation for all problems sounds parsimonious at first. But then when you really think about what youre adding to the picture of reality. Wow, its a lot!

 

[durangodawood]

This is the point at which I need to produce a usable definition of 'belief'. As follows:

'A belief is that which I hold to be true out of preference, that does not follow from objective tests and is not beholden to the rules of logic'.

Try testing the mind-model of 'the resurrection of Jesus' against this definition and then compare the results with the same test on the mind-model of 'the existence of a mind independent reality'.
Is there a difference when using my above operational definition as the criterion?
(Ie: given that both are objectively untestable?)

Ressurection.
1. yes, preference
2. yes, does not follow from objective tests
3. maybe not beholden to the rules of logic? (not totally sure if logic is broken, or if just new premises are introduced)

Mind independent reality.
1. no, its typically our naïve understanding before we even consider if we like it. Its the human "thats life" default.
2. yes, does not follow from objective tests (Im still toying with this one tho)
3. yes, is beholden to the rules of logic.

Conclusion: they are different to me in some regard using your test.

Maybe .. but its still based on a belief which is objectively untestable.

Out-there reality seems the least "activated" of any belief you could hold on the matter. The belief that mind independent reality might be unreal seems to involve more believing effort. You have to really work yourself into that mood and drive your imagination pretty hard.

 

[durangodawood]

....Maybe .. but its still based on a belief which is objectively untestable.....

Lets turn the question around:

Is mind-dependent reality objectively testable?

(Good discussion, SelfSim. Gotta take a break but will think on this.)

 

[J_B_]

Having one explanation for all problems sounds parsimonious at first. But then when you really think about what youre adding to the picture of reality. Wow, its a lot!

I was about to say something similar ... though I'm not sure we mean the same thing in saying it.

 

[SelfSim]

My take on that test against my definition:

Ressurection.
1. Preference
2. Does not follow from objective tests
3. Logic can be compliant but is still applied to an assumed belief as a posit, (which nullifies this as a determining sub-criteria, in this case).

Mind independent reality.
1. Preference
2. Does not follow from objective tests
3. Logic is usually compliant but is still applied to an assumed belief as a posit, (which nullifies this as a determining sub-criteria, in this case).

Conclusion: Both qualify as beliefs.

Compare with:
Mind Dependent Reality.
1. Not a preference
2. Does follow from objective tests
3. Logic is consistent.

Conclusion: Not a belief.

 

[SelfSim]

Lets turn the question around:

Is mind-dependent reality objectively testable?

It is when the hypothesis is stated in a slightly more 'consumable' way.

 

[SelfSim]

Out-there reality seems the least "activated" of any belief you could hold on the matter. The belief that mind independent reality might be unreal seems to involve more believing effort. You have to really work yourself into that mood and drive your imagination pretty hard.

It takes mental effort, but I note you're making it a belief there, in order to make your point though .. and I'm demonstrating that it doesn't appear so.
(Thus, Occam's doesn't apply there, demonstrably due to the vastly dissimilar quantity of results on both sides, obtained by testing the hypothesis .. Ie: abundant verifying for mind dependency and zip for mind independence).

One can always suspend one's beliefs for a moment .. but in to order to do that, one has to firstly come to terms with how to distinguish a belief .. hence the definition.
(Oh, and that definition is, of course, subject to change with new objective evidence .. provisional and contextual).

 

[sjastro]

Lagrangian mechanics revolutionized physics in the 20th century so a brief treatise of the subject is given here.
It’s assumed the reader has a basic understanding of calculus.
I will break the treatise into two posts and Johann Bernoulli’s solution into a third post.

In my previous post Johann Bernoulli posed a problem to Isaac Newton about the curve taken by a particle so it would fall in the least time.
This could be the shape of a wire which is frictionless with a bead sliding down the wire under gravity.

The problem can be analysed by considering three alternative shapes.

If A is some point x₁ and B is x₂ then particle slides down the wire from x₁ to x₂.
If the shape of the wire is given by the function y(x) then the shortest time taken occurs when y(x) satisfies the condition;

I[y(x)] is not a function but a functional and takes on a stationary or extreme value.

Let’s consider a general case for a pathway of the particle where y(x) is the extremal curve as I[y(x)] is stationary.

y(x,ε) = y(x) + εη(x)

Next post.

 

[SelfSim]

Lagrangian mechanics revolutionized physics in the 20th century so a brief treatise of the subject is given here .. {etc}

.. a warmly welcomed break .. thank you!

 

[J_B_]

Lagrangian mechanics revolutionized physics in the 20th century ...

I don't doubt it. I used Lagrange for my master's thesis* because it made things so much easier than Newton. But in what particular way are you saying it revolutionized physics?

*edit: P.S. I remember debating this choice with my professor, and he wanted me to demonstrate I would be properly handling Coriolis effects - something that gave me no end of headaches. I'm sure it's nothing for the brilliant mathematicians here, but at the age of 24 I was just beginning to come to grips with some of the math involved.

 

[durangodawood]

...Ie: abundant verifying for mind dependency and zip for mind independence...

For example...?

 

[sjastro]

Continued from my previous post.
y(x,ε) = y(x) + εη(x)

This function is not extremal and the endpoints (x₁, y₁) and (x₂, y₂) correspond with y(x).
η(x) is a random function with the property η(x₁) = η(x₂) since the endpoints coincide with y(x).
ε is a small parameter and δy = εη(x) is called the variation of y(x).

The variation can be weak or strong as illustrated.

C₀ is the extremal curve.
The neighbouring curve C₁ has a weak variation since the difference between the gradients of C₀ and C₁ is small at any given point.
In other words δy' = d/dx(δy) is small.
The curve C₂ on the other hand has a strong variation since although δy is small, the derivative δy' is not small.

The functional can be expressed as.

Whence

Using the Taylor expansion

and simplifying δI(ε) gives

Integrating the second term by parts gives

Since η(x₁) = η(x₂) the term in the square brackets is zero hence

From elementary calculus to find if the function f(x) is extreme at x₀ then f '(x₀) = 0.

Similarly for the functional I[y(x)] to be extreme δI(ε) = 0 hence

Since η(x) is an arbitrary function we can select η(x) such that

Hence for I[y(x)] to become extreme the equation

needs to be met.

This equation is known as the Euler-Lagrange equation and will be used in my next post to solve Johann Bernoulli’s problem.

 

[SelfSim]

For example...?

A demonstrative example illustrating the generation of evidence through the application of a test of MDR hypothesis was given in post#18.

Another might be say, when people say they can tell a stone exists independently from their minds. When they kick one, (their test for mind independence), and it hurts, they are inexplicably ignoring the fact that it is their mind that's telling them it hurts. (That's mind dependence, again).

The 'abundance' claim comes from the myriad of such simple examples. All that has to be queried is what someone means by something (or their descriptions of something) and the mind dependence evidence appears (with zip for mind independence).

Look we could go on ad-nauseum about this .. but I have no reason to 'push' this hypothesis/test/results. At the end of the day, one's preferred philosophical viewpoint (such as Realism), makes zero difference on the production of objective results anyway, (because all philosophies are posited on assumed true beliefs and science can't test these, so they're ignored .. and the testing process proceeds). Adjusting perspectives using various philosophical viewpoint however, highlights some of these rather surprising results and exposes untestable truisms people claim as being 'part of science' (and they demonstrably just aren't).

I'd rather learn some more about Langrangian mechanics .. Cheers

 

[sjastro]

Before the dealing with the Johann Bernoulli problem the Euler-Lagrange equation

can exist in different formats.
Since f ≡ f(x,y,y') the format can change depending on the presence on the variables x, y and y'.
If y is explicitly absent the first term vanishes and integrating the Euler-Lagrange equation takes the form.

where C is the integration constant.

If x is explicitly absent then

The total differential with respect to x is

Multiplying the Euler-Lagrange equation by y' gives

Combining with the above equation gives

This can be simplified to

On integrating Euler’s –Lagrange equation becomes

The final case is when y’ is absent.

The Euler-Lagrange equation reduces to

We can now solve the problem which is the next post.

 

[sjastro]

We are now in a position of solving the Johann Bernoulli problem using Lagrangian mechanics.

Since the wire is frictionless and gravity is a conservative field T (kinetic energy) + V (potential energy) is a constant.
By definition T = 0.5mv² and V = mgy where v is the velocity, g is the acceleration, m is the mass and y is the distance from the zero PE level.
At the midpoint T = V and therefore v = √2gy.
PP' around the midpoint (=δs) is a small element of length of the wire.

For the bead to travel this distance in time δT is
δT = δs/√2gy = √(1+y'²)δx/√2gy
Since δs² = (1+y'²) δx² using Pythagoras theorem.

Hence the total time T to travel from 0 to A(x₁,y₁) is the integral;

The equation is in the form

The exercise is to find y(x) so that T is a minimum.
Note that x is explicitly absent hence we can use the Euler-Lagrange equation in the form as shown in the previous post.

Where

The Euler-Lagrange equation is therefore

This can be simplified to;

Using the substitution y =cot(θ)

This is the parametric equation for a cycloid which is unintuitive as one would have expected a straight line for the bead to fall in the shortest time.

Both Bernoulli and Newton came to the same conclusion using pages of mathematics.
Lagrangian mechanics considerably simplified the problem.

 

[Mountainmike]

Whether they are objectively testable does not make them objective reality.

We model in terms of the limited senses we have in the limited dimensions we percieve.

So the model is an illfitting suit on a higher dimensional body of which we cannot know the entireity. ie the lower dimension circle we percieve, measure and model can clearly be a projection of a sphere into our sensor space in reality. (extrapolate that analogy to infinite possible dimensions...)

Therefore, physics is a model of behaviour not of existence of how the observed behaviour of things repeat, or can be made to repeat, limited to our own sensor space . Otherwise it has little to say.

There are enough paradoxes in these models to demonstrate they are not the underlying reality, however model development may assymptotically approach how some of it usually behaves

I could point to many - but take "does the moon exist before you look at it?"
The model of physics presumes as foundation that the universe is objective, causal and deterministic. Yet the quantum models derived from those assumptions violate all three of those tenets of the models foundation. Quantum physics attitude to this philosophical contradiction is "shut up and calculate". It is a useful model of what we percieve by senses. Not an objective reality.

Hawking eventually got there. Having long postulated a fundamental theory of everything - his last book contradicted that at philosophical level by including the concept of "model dependent reality" - that is multiple irreconcilable models may be needed, requiring choice depending on circumstance. Whether Hawking realised he had blown his own philosophical foundation to bits is hard to say.

Everything we perceive, once described using language, (which includes math descriptions), becomes a model. Modelling is what our minds do, once we use language.

All of science's models, (including all of its definitions), however are objectively testable, either in theory, or in practice.

Reality in Physics is the meaning we assign to models which 'test out' (objectively).
Reality can also be assigned a meaning by way of beliefs.
Regardless of either of these ways we go about it, objective evidence of active minds having been at work, remains .. (ie: the mind's fingerprints are all over reality).
All we have to do is look for it.

 

[chilehed]

(Never mind)