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A lot of people in science talks about science as a discipline to find the fundamental laws or rules of the nature. They consider these laws to be the underlying mechanism that is making the nature as it is. Usually they will use mathematics equations to describe these so called fundamental laws.

Now if you say that a particular mathematical equation describe the trajectory of a ball and this law is the underlying mechanism then who in the nature is actually computing the equation? Is it the ball, the particles, the earth, the air? Well the answer is nobody and that's what makes the whole argument of "underlying laws" or "how nature works" wrong.

I guess the proper way to address all the scientific knowledge (or any knowledge for that matter) about nature would be that it is about coming up with "generalized representations" of the observations i.e it just "describe" the observations and it doesn't mean to find how nature actually works.

  • 1) note that these representations are idealized approximations, that is, they do not describe nature exactly; and that 2) they sometimes turn out to have unexpected and incredible scope - for example, the laws of gravitation originally gave a unified description for the motions of objects in the solar system and on earth, but they turned out to explain the motions of cosmological objects 13 billion light years away, and ago; 40,000 billion times farther than the objects in our solar system, objects still seem to follow the amazingly simple f = m1*m2*G/r^2 with the same constant. – nir May 1 '15 at 7:56
  • I would point out that, just because an equation describes a relationship doesn't imply that someone is computing anything. For instance, it has been observed that certain objects in nature, like pine cones, exhibit patterns that follow the Fibonacci sequence. That doesn't mean that the pine tree was calculating the Fibonacci numbers. It is just that our mathematical system nicely describes nature. – Addem May 1 '15 at 8:06
  • @Addem: That's exactly my point. The mathematical models we use are description of reality and not the underlying laws – Ankur May 1 '15 at 8:07
  • @nir Would you say that f = m1*m2*G/r^2 is the cause of the way objects behave or is it an effect due to some unknown cause? – Ankur May 1 '15 at 8:10
  • I would say the laws describe nature - I did not imply otherwise; what I wrote was a comment, not an answer. – nir May 1 '15 at 8:23
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The traditional philosophy answer to this question is that what scientists are looking for is a relation of causation. When we collect observations that are collected from experiments to test well-formed hypotheses, we are hoping to capture some kind of essential relationship between the latter and the former; that whenever A happens, B happens. We say that the world has natural laws to explain the regularity of these consequences, which in turn lets us predictably interact with the world with an assumption that it will react in a regular manner. Thereby does invention and technology arise.

Now for Scottish philosopher David Hume, this view was problematic for reasons very similar to the ones you raised. If we think that the world is governed by a relation of causation but that our observations reveal this because of the connection between our observations and the facts of the matter, what kind of connection is that, and why should we think our observations connect to how things should be? Our observations are connected intrinsically with our concepts and ideas, and there's no reasonable guarantee that the world operates on rules coincidental with how our brain (or any abstract realm of "ideas") works.

The most reasonable account we can give, concludes Hume, is that when we talk about laws of nature, we're just making reference to our own past experiences of the world and making habitual judgements about the similarity of the present and future with the past that we've experienced. And although other philosophers (notably e.g. Kant) have disagreed with Hume about the search for regularity principles, his point still, I think, stands the test of time.

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I would say that there do appear to be laws of nature and we have mathematical formulations that describe (properties of) those laws.

I'm not aware of many scientists who would conflate the 2 things (the law and its description) other than by loose language. It's a bit like seeing a photo of David Beckham and stating that that's David Beckham. Clearly it isn't, it's a piece of photographic paper, but most people would know what you meant.

It is true that some formulations can be reasonably described as a generalisations of observations. We tend to call that Phenomenology in physics. A good scientific theory will have the extra property that it will be able to predict observations that no-one has seen yet. That's how we can do thing like go to the moon and have MRI scanners.

I'd argue that it's the fact that we've found a number of theories that have this remarkable, predictive capability that leads scientists to believe that there are laws of nature and that we have some reasonably good descriptions of some of them.

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When discussing the issue with a layperson, it is not uncommon to hear things like "F=ma" being called "natural laws." However, in the strictest of philosophical senses, the scientific argument is that there are natural laws -- that the universe does follow rules. This would be in opposition to any argument that the universe is out to intentionally confuse us (scientists don't like the argument that Loki controls the universe). From this argument, they derive worth in the attempt to pair these natural laws to mathematical equations like "F=ma".

If, indeed, the world was consciously trying to mess with science, this attempt to assign mathematical equations could go drastically wrong. Accordingly, it is a fundamental tenant of science that natural laws exist, and it's science's job to figure them out to the best of our ability.

The pattern of generalizing data into theories is simply part of science's process which seeks to uncover these natural laws, but in the strictest philosophical sense, it is not the natural laws themselves.

My favorite example of this was the Lorentz transformation. Science had produced Maxwell's equations, but they had a funny catch. Light was supposed to have "a velocity," which is strange because velocities are usually relative to a frame (You may be sitting still in the ECF coordinate system, which rotates with the earth, but hurtling along at 1000km/hr in ECI, which is an inertial coordinate system used for satellites). It was theorized that there may be a "lumiferous ether" within which light flowed defining the frame of reference for "the speed of light."

When they actually tested this, they found that it did not matter which frame of reference they used, light always appeared to travel at the same velocity. This was highly expected for some scientists. However, there was no attempt to argue that the universe was failing to follow their natural laws properly. They simply accepted that there was something missing from their laws. Lorentz's transform accounted for this mathematically, until Einstein came along and suggested the transform was more easily modeled if both space and time could be warped. The model moved to better approximate science's search for the "natural laws," not the other way around.

  • Would you call gravity a law of nature OR a generalization of the observation that there is attraction between objects? – Ankur May 1 '15 at 6:24
  • @Ankur that is a very hard question to answer because the word "gravity" has so many meanings. If someone pinned me in a corner, I would say "gravity" is a law of nature, but newtonian F=GmM/r^2 is a generalization of observations, as is "mass distorts spacetime." Interestingly, if I was pushed further, I would argue gravity is not a generalization, but a specialization of the observation of motion. As an example, science separates the attractive forces of electrostatics from gravity. – Cort Ammon May 1 '15 at 14:41
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Actually, it is the ball, earth, air, etc. that is doing the computation! It's doing a really messy computation involving octillions (or more) of elastic collisions and all sorts of changing rotational, vibrational, electronic, and other energy states. Fortunately, these messy stochastic calculations are approximated well by simpler calculations that we can do on a computer.

And, what do you mean by "actually works"? If your mathematical model is indistinguishable from what "actually happens", in what sense do you not know how it "actually works"?

That's much of the point of searching for natural laws--to find regularities that we can express with such precision that we can treat the actual universe as an instantiation of our model (or with differences small enough to not matter to us).

  • Isn't the mathematical model (the variables, the operations etc) clearly distinguishable (actually completely different thing altogether) from the phenomena until you knows the mapping (representational knowledge) of those mathematical objects to the components of the observed phenomena? – Ankur May 1 '15 at 7:45
  • @Ankur - Of course, but that's part of the content of the theory that includes the natural law (i.e. it must tell you how to apply it). – Rex Kerr May 1 '15 at 17:37
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The question actually boils down to the question of whether or not there is a single underlying reality. Science assumes that there is, and recognizes that what we observe is merely a shadow of a slice of that underlying reality, since we can only hope to observe a very small part of the whole world, and our observations will not be a perfect representation of the real thing. The laws of nature then refer to the rules governing the underlying reality, not what we observe or the scientific hypotheses that we make.

The problem with discarding the assumption that there is an underlying reality is that there is then no consistent worldview. You would have to grant that it is absolutely true that something exists, even if there is nothing you can say about what kind of thing exists. Since the negation (that nothing exists at all) is absolutely false, you can see that the fact that something exists is indeed one aspect of the underlying reality.

Since it is rather evident from Science (even if not absolutely provable) that the underlying reality is governed by laws, your question of what enforces the rules themselves is a very astute one. Clearly something must, otherwise there is nothing to bring about the governance in the first place. We must conclude then that the totality of all the laws governing reality must both govern and enforce itself, since anything that governs that totality must be included in it by definition. Note that this totality includes even laws that govern other laws.

From this point, the atheist concludes that the world explains or creates itself. In contrast, the theist concludes that there is a conscious lawmaker called God that made and enforces all the laws for certain purposes, who is self-explanatory (such as being called "I will be what I will be" in Abrahamic religions). The only difference is essentially whether the self-explanatory core is conscious (whatever that means). And the agnostic thinks it cannot be known. Note that all have to accept that it is perfectly consistent to have absolutely nothing at all exist, but it is simply a fact that our world does exist.

Whichever viewpoint you choose, it would be difficult to imagine just how the laws are enforced, but certainly it is not by computation in the sense that we are familiar with, and so your reason of rejecting the existence of underlying laws is flawed because you assume that something must compute that way. To give an (imperfect) analogy, a machine works in a specific way because its parts and programming forces it to work that way. If you did not see those constituents, it does not change the fact that it is governed by them, and in fact you can often infer not only the existence but the nature of those constituents to a certain extent just by observing the way the machine works. This is science. The difference is that there is some fundamental part of reality which governs itself, which science may never reach, and that is part of the next point.

The observations that we can make in our world may not be able to probe much of reality. This is almost certainly true if we use only scientific experiments, because experiments are incapable of distinguishing between many different hypotheses that are consistent with all the observations but contradict each other. This problem cannot be eliminated because there are infinitely many hypotheses that can 'explain' everything we have observed but differ in places we have not or cannot observe. For example, you could have been constructed by some laws just one second ago and implanted with memories that make it seem as if you have existed for much longer. It is consistent, but no experiment can refute it. This is where we need logic and philosophy to guide our hypotheses and so we choose the simplest ones that explain all our current knowledge.

It is highly likely (and history has repeatedly confirmed) that the underlying reality will always be more complicated than the simplest model we construct for our current knowledge, but that does not mean that we give up and do not construct any model at all just because we will never get it. We make models of the world with the main purpose of being able to predict roughly how the world will behave in the future, so that we can take appropriate actions now. For instance, we give food and water to people who depend on us because we predict that they require food and water to live. And so far, at least this necessity of nourishment seems to coincide with the underlying reality!

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who in the nature is actually computing the equation

I think this makes the mistake of assuming that equations cannot describe reality, unless reality is an equation.

By the same logic, I (or indeed any sentence) cannot describe a fish - unless I (or my sentence) is a fish. Which of course, is absurd.

My apologies if I mistook your reasoning, it is a little unclear; but really I don't see how else you suppose that because reality is described with equations, that means equations have to be "computed" - for what is described to make reality (nature) go.

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Science is about trying to describe reality, as it relates to us, using math. What such findings reveal about the nature of reality, as well as the assumptions that are used in the genesis of such descriptions are not always as definitive and obvious as science sometimes seems to indicate.

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