So, a real bridge is following instructions like in a video game? — Agent Smith

If you believe that the laws of physics are correct models in a context of the uniformity of nature, then I think yes. That's why folks went crazy for Newton, I think. He found God's source code (differential equations.)

n the simplest situation, the model will be fit to a set of measurements, which always refer to the past. — lll

How does that follow? If I'm plotting rocket path, then I'll obviously be relying on both Newtonian and relativitistic physics. How do they 'refer to the past'? There's something other than inductive logic at work here isn't there? Has anyone ever reported that force equaled something other than mass times acceleration?

I don't see how the mathematical 'necessity' can escape into the world and bind whatever is counted by x and y. — lll

We're sorrounded by the products of applied maths and physics. The very devices we're using to conduct this conversation rely on quantum physics (I'm foggy on how - I seem to recall that many of the fundamental breakthroughs in semi-computer design required application of quantum principles to micro-electronics.) The unreasonable effectiveness of mathematics in the natural sciences is writ large in most routine daily activities, we're sorrounded by it. And that relies on this interplay between mathematical conjecture, prediction, measurement and observation. So again I'm having trouble understanding why logical necessity and physical causation are regarded as separate domains, when our technology brings them together to such enormous effect.

'How is it possible that mathematics, a product of human thought that is independent of experience, fits so excellently the objects of physical reality?'

Einstein , 1934.

Differential equations, lll, are they part of load & stress equations in re bridges? Can you explain them to me, please? Simplify them, if you can or want to. — Agent Smith

I've never studied bridges in particular, unless it was a textbook problem. Definitely there are diffeqs 'in there' at some level of magnification. I spent more time with Maxwell's laws. But I won't dare to jump into vector calculus. Instead I'll give you the simplest example which is still beautiful.

In a differential equation, you are solving not for a number but for a function. They are 'differential' because the equation expresses relationships between the unknown function and its derivatives. A classic equation is $f = f'$. In other words, you are asked to find a function whose slope at x is equal to its height at x. This represents something whose growth rate is equal to its current size, which makes it (with some parameter sauce) a good model for things like a pile of germs in plenty of foodgoo. The solution is $f(x) = e^x$.

https://en.wikipedia.org/wiki/Exponential_function

How do they 'refer to the past'? — Wayfarer

The measurements refer to the past, as indicated by the grammar, unless you know something about time that I don't. <no rudeness intended, just saying>

There's something other than inductive logic at work here isn't there? — Wayfarer

It seems clear to me that we are projecting the structure of the past onto the future. Inductive, yes? This is how I understand the assumption of 'the uniformity of nature' in the Humean context. I can't doubt it any more than Hume can outside his study. But I can't deduce it either. That's why it's so gloriously weird ! It's 'irrational' and yet rationality itself.

Has anyone ever reported that force equaled something other than mass times acceleration? — Wayfarer

That was taught to me as a definition of force, but not all teachers do that. The larger issue is maybe whether 'laws' are ever proven wrong, and we've already discussed that Newton's model was wrong, though successful enough to give many the sense that they had the source code that moved both the planets and the apples on their trees.

It seems clear to me that we are projecting the structure of the past onto the future. — lll

If something is knowable a priori, then it's known independently of experience, so I don't see how the past comes into it. That really only applies to a posteriori propositions.

we've already discussed that Newton's model was wrong — lll

Not wrong. It's applicability is shown to be limited but within the range of applicability it's not wrong. Lunar landers rely on the calculations of both Newtonian and relativistic physics, don't they?

Not wrong. It's applicability is shown to be limited but with the range of applicability it's not wrong. — Wayfarer

Well now you're coming over to my filthy 'instrumentalist' camp which isn't so concerned with the really really real. From a realist perspective, and unless my rusty physics knowledge is betraying me (hopefully a physicist will jump in)... it's wrong, but the errors in its 'range of applicability' are so small that one can ignore them for practical purposes. Hence this range will itself be a function of how much precision is needed for a particular purpose. Recall also that measurement is always noisy. So folks back then didn't notice these errors and/or tried to explain away issues like the Mercury thing.

If something is knowable a priori, then it's known independently of experience, so I don't see how the past comes into it. — Wayfarer

We could make up all kinds of mathematical models without data even. We could then transform them according to the grammar of math and call it a priori knowledge (though actually we did need the experience of the moving the symbols around, and the 'ideality' of math is its own issue.) The only reason to rely on a model, however, would seem to be that it summarized past experience and therefore, given the assumption of the uniformity of nature, should be good for predicting the future (like the path of a rocket.)

But it also enables novel discovery - phenomena that haven’t ever been seen before.

(On that note, thank you for the thought-provoking discussion, and good evening.)

Yeah, I love the novel discovery part. I guess theoretical physicists are searching through the space of all possible video games for one that looks like ours (like the one we imagine behind the noise of our world, I should say.)

Have a good night!

You get an F! :smile:

May be I wasn't clear enough. Oh well! Your answer is, I'm certain, a notch above the rest.

May be I wasn't clear enough. Oh well! Your answer is, I'm certain, a notch above the rest. — Agent Smith

It takes some time to grok differential equations, so it was a bit of a fool's errand for me to even try to dish it out in a post (a fun one, though.) In a video game world, you can think of updating the position and the velocity and the acceleration of a pong ball at every tiny time step according to a rule that takes the current values of those attributes into account. Some might find that easier to understand. Imagine if your current acceleration is set to be equal to your current speed. That'd be quite a ride, if you start with a positive speed.

Swipe your fingers on the screen of your smartphone. Notice anything interesting/weird?

Not anything unexpected.

Here's one more answer to your question about what makes you you and me me. Also touches on qualia, I guess. All this seems very pre-Wittgensteinian to me. It's just that analytics shit their pants at the name of Hegel perhaps, so it took the mathy smelling guy to tell them.

It is by means of Empfindung or sense experience that sentient beings are able to distinguish individuals from one another, including, in some instances, individuals that share the same essence. The form of experience is temporality, which is to say that whatever is directly experienced occurs “now”, or at the moment in time to which we refer as “the present”. Experience, in other words, is essentially fleeting and transitory, and its contents are incommunicable. What we experience are the perceivable features of individual objects. It is through the act of thinking that we are able to identify those features through the possession of which different individuals belong to the same species, with the other members of which they share these essential features in common.

Unlike sense experience, thought is essentially communicable. Thinking is not an activity performed by the individual person qua individual. It is the activity of spirit, to which Hegel famously referred in the Phenomenology as “‘I’ that is ‘We’ and ‘We’ that is ‘I’” (Hegel [1807] 1977: 110). Pure spirit is nothing but this thinking activity, in which the individual thinker participates without himself (or herself) being the principal thinking agent. That thoughts present themselves to the consciousness of individual thinking subjects in temporal succession is due, not to the nature of thought itself, but to the nature of individuality, and to the fact that individual thinking subjects, while able to participate in the life of spirit, do not cease in doing so to exist as corporeally distinct entities who remain part of nature, and are thus not pure spirit.

https://plato.stanford.edu/entries/ludwig-feuerbach/

Not anything unexpected. — lll

:chin:

Wires crossed I'm afraid!

Does it help if I tell you I have a nice big quad HD monitor and not a smartphone, and I used that instead?

It's so late here that it's early again, so I gotta get to bed soon!

Does it help if I tell you I have a nice big quad HD monitor and not a smartphone, and I used that instead? — lll

No, not really. Forget I ever mentioned it.

I gotta get to bed soon! — lll

G'nite!

It takes some time to grok differential equations — lll

How much time did it take you?

But only one is realistic. — Wayfarer

Incidentally, I believe what I described is why the observations of quantum mechanics are so difficult to interpret. Because relativity principles are so deeply entrenched in modern physical theories, the consequence is that any interpretation is correct, but no interpretation is the true interpretation. As it turns out, Many Worlds becomes the best interpretation, but that's just a reflection of the logical consequences of staying true to the principles employed. The conclusions reflect the premises. And so it is a nonsense interpretation which denies the possibility of a real world, thrown out to us, because the principles plugged in, deny the possibility of a real world.

One answer I got on Stack Exchange was:

There is no causation in logic. Some formulas are equivalent to others, and common language confuses the issue with formulations like "this circle has circumference Pi because its diameter is 1", when in fact saying one proposition is the same as saying the other. It is not analogous to physical causation (I.e. The observation that some events often happen in succession).

I see the point, but I can't help but think there's something wrong with it. I mean, it seems to me science relies heavily on the application of logic to the analysis of causal relationships. And that 'natural law' is where these meet. You conjecture that if [x] then [y], and then carry out an experiment or make an observation that confirms or disconfirms it. So I'm considering the idea that scientific law is where logical necessity and physical causation intersect, but I've never heard anyone else say that. — Wayfarer

Actually there is causation at work in logical necessity, it is final cause. This is a very important philosophical principle to understand. It is Plato's "the good", described in "The Republic" as that which makes intelligible objects intelligible, like the sun makes visible objects visible. Why do we adhere to logic, and say that conclusions are necessary? Because it is good and useful to do that. Why do we understand "2+2=4"? Because it is good and useful to understand this. That is final cause at work.

We're sorrounded by the products of applied maths and physics. — Wayfarer

The "products" you mention here are "the goods" which the intelligible objects help to bring into existence as final causation. Notice that the intelligible objects themselves are not the actual cause. The desire for the good, what we call "intention" is the actual cause, and the intelligible objects are the means to that end. They become intelligible to the individual, because the individual has the desire for the end. That is why the good, as final cause or intention, is not the intelligible object itself, but that which makes the intelligible object intelligible, like the sun makes visible objects visible.

Plato exposed this principle, and it has a long history in theology. The revelation of the true nature of the good as a cause, final cause, is called "seeing the light" because of Plato's analogy. Why is there a world? Because God saw that it was good, final cause. Under this principle all human knowledge falls to pragmaticism. But then a higher form of knowledge is revealed to us, that which knows the truth, divine knowledge. And when we make "the truth" the good which is sought, we allow ourselves to be ruled by divinity, making human knowledge compatible with divine knowledge.

Yeah. The how questions are questions about material and efficient causality. The why questions go to formal and final cause. — apokrisis

It seems to me that "why" questions could be just as easily asking about causality. Formal and final causes are illusory in that the goal in the mind in the present is what is causing something to happen. Goals don't exist in the future, but are visions of the future in the present moment and it is always the state-of-affairs in the present that determine the future, not the other way around.

It's the search for a causal account. Every particular must be the product of something more general. — apokrisis

The general is the illusion that other events can be the same as another event and therefore lead to the same effects. Similar states-of-affairs lead to similar effects, not the same effects.

We're sorrounded by the products of applied maths and physics. The very devices we're using to conduct this conversation rely on quantum physics ( — Wayfarer

That's the usual defense in favor of the view that scientific, mathematical reality is a real one. We use it to construct technology with. But we can turn that around. We constructed a very limited reality, a subset of a more comprehensive one. Which we have transformed, broke up and divided by math and experimentally constructed as to conform to this image.

Occam's razor, :kiss: Men are simple folk. Women, no, they remind me of Rube Goldberg machines, they do! — Agent Smith

Men being a straight line is having a great privilige. Woman, in their curvy appearances, are anorexiously in search of the right metric, leading to creepy Kardashian-like appearances.

Why are things the way they are? — Luke

It depends on the objective reality one lives in. In the context of killer whale-gods, wasp-gods, red ant-gods, bonobo-, and even homo sapiens-gods, things are the way they are because they were fed up with eternally making love and hate. They created and developed very special particles to lay back eternally in their heavenly pastures to watch the creatures developing from them in a universe they created for them. The heavenly heavens can be considered a giant cinema screen.

About scientific law:

A piece of the context, from Feynman:

"You might ask why we cannot teach physics by just giving the basic laws on page one and then showing how they work in all possible circumstances, as we do in Euclidean geometry, where we state the axioms and then make all sorts of deductions. (So, not satisfied to learn physics in four years, you want to learn it in four minutes?) We cannot do it in this way for two reasons. First, we do not yet know all the basic laws: there is an expanding frontier of ignorance. Second, the correct statement of the laws of physics involves some very unfamiliar ideas which require advanced mathematics for their description. Therefore, one needs a considerable amount of preparatory training even to learn what the words mean. No, it is not possible to do it that way. We can only do it piece by piece. Each piece, or part, of the whole of nature is always merely an approximation to the complete truth, or the complete truth so far as we know it. In fact, everything we know is only some kind of approximation, because we know that we do not know all the laws as yet. Therefore, things must be learned only to be unlearned again or, more likely, to be corrected."

So we know that what we don't know all the laws yet. And therefore, everything we know is an approximation only. There is an expanding frontier of ignorance, and I think he means the frontier that exists when looking to small scales. Of course every expanding sphere of knowledge brings a frontier along. Separating what's outside that sphere and inside of it. There are more things outside of that domain than inside, and maybe each new piece of the domain of nature has its own laws.

We can't know everything, but it's imaginable that when we look to smaller and smaller scales, some ultimate truth can be found (Popper would call such a theory non-scientific, but how can you falsify something if you have hit rock bottom so to speak?).

You can't, obviously, just state the laws of nature. You have to grow into these laws, and once you're in you have to realize that what you've learned is an approximation only. Again, I'm not sure if he means the laws at the bottom or higher level laws, which are approximations always. They are still laws and they can operate quite independently of the laws deep down.

The laws on the smallest scale, which are what we call fundamental laws, can't be exactly right yet and we know it, according to Feynman. So we must let go what we have learned, or at least correct it and see it as an approximation to the deeper theory.

I'm not sure if he thinks that a final theory is possible. I don't see why not, and when we think we have found one, it will always be nature that makes the final call, like in all physical laws we create or find out about.

How much time did it take you? — Agent Smith

I think it was around my third semester, with my schedule full of math and physics all the way there, that I got the 'main idea' of differential equations. You can start with numbers as the basic objects and climb (in one direction) to where functions are the basic objects.

the Wikipedia article on the topic associates efficient cause with an Agent: — Luke

A carpenter is an organism and is indeed autonomous to the degree they embody all four causes. The carpenter can act with form, with purpose and with mechanical actions, like hammering and sawing, so as to craft the desired material outcome.

So you are confusing the wholeness of that definition of "an agent" with the part that is just the efficient cause - which is the immediate physical actions that bring about the material change (according to the constraints of form and purpose). So the agent in this sense is the carpentry, not the carpenter. The hammering and sawing is what caused the matter of the wood to become the form of the new chair that the carpenter wanted to sit on.

Goals don't exist in the future, but are visions of the future in the present moment and it is always the state-of-affairs in the present that determine the future, not the other way around. — Harry Hindu

This is why the nonlocality in quantum mechanics, and the principle of least action that grounds physics in general, are such a metaphysical problem for the reductionist point of view.

How does a particle know which path between two points is the shortest, even before it sets out on its journey? How can nature be ruled by the finality of least action before anything has begun to happen?

Physics just plugs this global finality in as a law. And it uses integration - inverse differentiation - to make the calculation. It is then silent on how all this fits into a view of reality as being merely the sum of its mechanical (ie: material + efficient) causes.

The general is the illusion that other events can be the same as another event and therefore lead to the same effects. Similar states-of-affairs lead to similar effects, not the same effects. — Harry Hindu

That would certainly be my constraints-based view. Top-down constraints only add context to restrict the local degrees of freedom.

So as Peirce argued, Nature is fundamentally tychic or probabilistic. Constraints can only limit the spontaneity, the contingency, of any part. Determinism is achieved only in the limit.

The laws of quantum mechanics and thermodynamics build this into their generalised accounts of Nature.

So generality is just as real as particularity. And just as unreal in that each is a bounding limit on reality, and so something that can only be approached with arbitrary closeness, never actually realised.

If you could set up exactly the same circumstances twice, the outcome ought to be exact. But because you can't, you can only get arbitrarily close to making history repeat.