Curious results from interferometer experiments

[Obvious Leo]

But the mathematics used in those laws is just as non-linear as anything else.

Then how come physics is the only science that uses these tools to model natural systems?

Surely one of the fundamental principles of mathematics is that it must be a logically self consistent system, isn't it?

Disproven by Godel.

[Steve3007]

Then how come physics is the only science that uses these tools to model natural systems?

How do you mean? Do you mean how come physics is the only science that uses non-linear mathematics?

Disproven by Godel.

OK. So to pick a concrete example, do you think that, say, the non-linear mathematics which describes the Mandelbrot set is fundamentally incompatible with the non linear equations that describe the movements of mutually gravitating bodies in the Newtonian model of gravitation?

[Sy Borg]

... do you think that, say, the non-linear mathematics which describes the Mandelbrot set is fundamentally incompatible with the non linear equations that describe the movements of mutually gravitating bodies in the Newtonian model of gravitation?

Now THAT's a helluva question to put to someone.

My Harbalesque answer to this would be "They are both non linear so maybe there's a connection somewhere?"

[Steve3007]

Good Harbalesque answer. My attempt at a Harbalesque answer: "That's a question that often keep me awake at night worrying too."

-- Updated Thu Apr 09, 2015 12:21 pm to add the following --

My attempt at a Fanmanesque answer: "Nota bene: Logically speaking, I find that question insulting and demeaning and will therefore, hereinafter notwithstanding never be communicating with yourself again."

[Sy Borg]

Haha. I think you read his mind. Or maybe "It's not something you'd ask in polite company".

I'll behave now and allow serious discussion of things I know bugger all about to continue.

-- Updated 09 Apr 2015, 06:26 to add the following --

Oh no, the Big F would definitely say "What are you talking about?". Or ignore it.

[Obvious Leo]

How do you mean? Do you mean how come physics is the only science that uses non-linear mathematics?

I mean other sciences which model natural systems cannot use linear mathematics to model the whole system, only subsets of it and then only approximately. Biology is the most obvious example but geology and meteorology are other prominent examples. Obviously the sciences related to engineering and computing aren't included because these are linearly determined according to a plan. Linearly deterministic systems need a mind to determine them. However my sister-in-law is a high-powered computer geek who researches non-linear computation using evolutionary algorithms. I know very little about this science but these algorithms look very much like fractal geometry to me. You would obviously know more about this than me. However since our universe is quite obviously evolving then surely it can only be modelled holistically by using such algorithms.

do you think that, say, the non-linear mathematics which describes the Mandelbrot set is fundamentally incompatible with the non linear equations that describe the movements of mutually gravitating bodies in the Newtonian model of gravitation?

I'd have to declare myself unqualified to be absolutely certain about it but I would say yes. Believe me, the thought did cross my mind to try the Fanman approach.

[Steve3007]

But physics surely does that too. Most of the equations of physics which purport to describe physical systems are non-linear. Linear approximations are then used to describe small parts of them or approximations to them. A simple example: the pendulum. Its movement can be approximated as (linear) simple harmonic motion by making the "small angle approximation" - that for small angles the sine of an angle is approximately equal to the value of the angle itself (in radians).

-- Updated Thu Apr 09, 2015 12:45 pm to add the following --

On evolutionary algorithms: I think I mentioned before that I briefly worked on them too and, yes, I see the parallel there with fractal geometry in the sense that evolutionary algorithms continuously feed the results of calculations back in as the starting point for the next calculation. i.e. they are iterative.

[Bohm2]

When Bohm2 says:

we can't get to the "real" world in any other way except using mathematics.

you seem to interpret that as him saying that mathematics is the real world. So you presumably see him as doing the old "confusing the map with the territory" thing. But he's not saying that is he? All he seems to be saying there is that we have no way of knowing the "real" world other than through some kind of logically structured language. Surely that's true, isn't it?

Yes, that is my view. I always considered my perspective as more in line with epistemic structural realism or even pyrrhonian skepticism; that is, we can have knowledge only about the structure of the physical world but not about the "objects" that implement the structure in question. Physics is simply silent on the question of the intrinsic, non-structural nature of matter as pointed out by Strawson/Russell:

If someone asks what an electron is, all we can say is that is a ‘particle’ with a certain mass (9.10938188 × 10-31 kilogram), electric charge -1, spin ½, etc. Each of these attributes can only be defined relationally and all we know about them is what these relations provide. A mass of m is just that property such that something with it will obey the relation that m = F/a for a force F and acceleration a, and so on. Another way to put this, in line with the way Russell views things, is that all that science provides, or can provide, is structural or purely mathematical information about the world...[Or as Russell says]: ‘the only legitimate attitude about the physical world seems to be one of complete agnosticism as regards all but its mathematical properties’ .

The only exception is the experiential part that we all have, where we are basically getting an 'insider's look" of some matter as Lockwood points out:

But, according to the line of thought I am now pursuing, we do, in a very limited way, have access to content in the material world as opposed merely to abstract casual structure, since there is a corner of the physical world that we know, not merely by inference from the deliverances of our five senses, but because we are that corner. It is the bit within our skulls, which we know by introspection. In being aware, for example, of the qualia that seemed so troublesome for the materialist, we glimpse the intrinsic nature of what, concretely, realizes the formal structure that a correct physics would attribute to the matter of our brains. In awareness, we are, so to speak, getting an insider's look at our own brain activity.

And I don't see how "energy" is immune to this view as Feynman pointed out:

It is important to realize that in physics today, we have no knowledge of what energy is. We do not have a picture that energy comes in little blobs of a definite amount. It is not that way. However, there are formulas for calculating some numerical quantity and when we add it together it gives “28″—always the same number. It is an abstract thing in that it does not tell us the mechanisms or the reasons for the various formulas...It states that there is a certain quantity, which we call energy, that does not change in the manifold changes which nature undergoes. That is a most abstract idea, because it is a mathematical principle; it says that there is a numerical quantity which does not change when something happens. It is not a description of a mechanism, or anything concrete; it is just a strange fact that we can calculate some number and when we finish watching nature go through her tricks and calculate the number again, it is the same.

What is energy?
http://www.feynmanlectures.caltech.edu/I_04.html

[Steve3007]

Bohm2, On the definition of energy, and that Feynmamn quote: I started a topic/thread on that very subject a while ago here in which I tried to keep it simple by considering kinetic versus gravitational potential energy.

As Feynman says, energy is perhaps more of an abstraction than people might realize.

[Jklint]

It seems the Universe consists only of relationships and nothing which is bluntly materialist. It's not a new idea but one which is becoming ever more clear. At its lowest level it is nothing more than a gathering of forces and energies morphing into separate paradigms to create both the beholder and what is beheld. The more one looks backward the more tenuous materials become.

[Obvious Leo]

It seems the Universe consists only of relationships and nothing which is bluntly materialist. It's not a new idea but one which is becoming ever more clear. At its lowest level it is nothing more than a gathering of forces and energies morphing into separate paradigms to create both the beholder and what is beheld. The more one looks backward the more tenuous materials become.

I think this point comes the closest to the one I seek to make and the last few posts seem to show us as being in broad agreement. I use the term energy as a matter of convenience because we all know what we mean by it but my model is fundamentally an information model and when I refer to energy and matter I'm actually referring to organised information. There isn't actually a "thing as it is" to get a conceptual handle on in this paradigm but I'm certainly not suggesting that an objective reality doesn't actually exist.

My paradigm is an "it from bit" idea in which I define the universe as a computer and I intend this statement to be taken absolutely literally. However this is the point at which I venture way above my pay grade because it's not an information processing computer but an information generating computer. I've covered this idea elsewhere when I referred to Conway's Game of Life as a perfect model of how this works on the Planck scale but this is about as far as I'm willing to go with the idea because I can only conceive of it in generalities and not in the specifics.

The idea of the universe as a reality Maker is not really one that physics is equipped to deal with so in a sense what I'm talking about lies beyond physics in the science of computation. I'm in no doubt that the algorithm for such a universal computation is an evolutionary one and that the processing speed of it is the speed of light. Since the continuum of gravity and time defines the speed of light as variable all the way down to the Planck scale this computation can then best be thought of as a modulated one-dimensional bit-stream. However to get a mental picture of this is no more possible than it is to get a mental picture of the 4D space-time continuum which the observer then constructs from it. However this is exactly what I mean when I speak of the difference between the map and the territory. One is essentially the temporal mirror image of the other.

I realise I'm not explaining myself very well because this is the most abstract part of my model and non-linear computation is not my strong suit. However the model is perfectly represented by the Universal Turing Machine, the eternal reality maker which programmes its own input and forms the central plank of the philosophy of computation. I'll leave it there for the moment and invite comment from those who know more about computation than I do, which is probably everybody.

Regards Leo