Comment by krupan | Hacker News Reader

Comment by krupan | Hacker News Reader

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I agree that this was a great little essay. I like your illustration, but I think your point at the end of your comment disagrees a little with the essay, and I have to disagree with you a little as well. A computational model, such as Maxwell's Equations, is a theory. Creating a simulation of two balls falling would also be formulating a theory. It may be an incorrect theory though, as you point out, and that's where the other leg of science, experimentation (what you refer to as tying back in to the physical world), is necessary.

Taking more from your example, I would agree that scientists today are trying to answer questions by diving right into computational models (theory) without experimentation, but I believe it's because they are tackling questions that are very difficult to experiment with. I don't think that's altogether unprecedented though. There are instances of scientists producing theories without the means to test them throughout history, only to have them proven or disproven by experimentation at much later times.

A computational model [...] is a theory

I guess that's where we disagree. I respect your point, and of course I accept we are in a regime where computational models are the only options in some cases (we can't start a whole new universe off to see how it worked). That has no bearing on their limitations, though.

I think a computational model is not a theory, it is a theoretical construct. I concede this may seem like splitting hairs to everyone except me.

I'm confused on the difference between a theoretical construct and a theory.

when you have good reason to believe something about model-entities, you don't thereby have good reason to believe it about actual-entities, unless you also have good reason to believe that model-entities are relevantly similar to actual-entities. So the model itself is just a piece of a theory.

isn't a model a functional representation of a theory? I don't see how it is only a piece of a theory if the whole theory is represented in the model and is functional.

Can you represent the whole theory in the model? The model would need to represent evidence that its representations of the world are accurate. If that evidence is a mathematical proof, a program could probably encode it. But if it's experimental evidence, I don't know how it could.

That seems backwards to me. Theories don't "represent" evidence, experimental or otherwise (I'm not even sure what that's supposed to mean, it doesn't make sense to me). You formulate your theory - which is a model of cause and effect - from one set of observations, and test it with another set of observations. The model - the theory - may include facts from experimental evidence, eg G the gravitational constant, but that doesn't seem problematic for theory representation in program form.

Theories make predictions about the world. I'd argue they're useless without this. As such, they are function of a prior state, returning the new state.

Certainly you can't validate your theory without doing physical experiments, or at least having lots of data that the theory was not based on, to check it. But validation of a theory is distinct from its representation.

"Theories should pay rent in anticipated experimental data."

say i have a theory that says, changes in temperature depend on changes in pressure in some specified way. And you say, oh I have a similar theory, it's a computational model. In my model of the universe, when my model of temperature changes, then so does my model of pressure, and it changes in exactly the same way your theory describes.

I'd say ok, that's a great theory about your model of pressure and your model of temperature in your model of the universe.

And you say, no no, this is a theory about actual pressure and temperature in the actual universe, just like your theory.

In that case your model is not enough. I also need reason to believe that your models of temperature and pressure are relevantly similar to actual temperature and pressure such that relational properties that hold of the entities of your model also hold of the entities they're supposed to represent. If it turns out you modeled temperature as a jpeg representing a picture of a cat, then how is that a theory about the temperature?

Whereas my theory is a theory about temperature simply because my theory says: temperature, that real thing in the world, will do such-and-such.

Both the theory and the model depend on the definitions of their constituents. If you don't have a theory of temperature or pressure, your theory is similarly useless, because you will have no way to interpret the words "temperature" and "pressure".

Your theory assumes these things, but you want to say that the model is invalid because it also assumes these things.

But the more important misconception you appear to have is that you are not considering the human element; no representation of the theory has meaning unless a human interprets it. Programs manipulate symbols; but it is the human who chooses what the symbols mean, and that includes incorporating theories / models implied or assumed about those meanings. It's no different for a theory written down in a book.

I don't think there is any difference between believing something about "model-entities" and believing something that a theory predicts will be the case. You haven't justified your implied assertion that predictions according to theories are not only different, but more trustworthy, than predictions according to models (theories in computational form).

Unless we believe that the universe is actually made of math, then Maxwell's Equations are also just a model.

I think the argument being made isn't that "theories in computational form" are inferior, but rather something more pedantic - that there's no such thing as a "theory in computational form". Theories are about nature. A computer program that performs some simulation isn't itself a theory. The theory is "such and such natural phenomenon behaves like this here computer program."

Well, theories must be stored in some representation, whether it's a configuration of neuron state, ink markings in a book, verbal descriptions in sound, etc. My position is that programs are just another representation.

Programming languages generally don't have semantics that include claims about the physical world.

Ink scratches on wood pulp don't have semantics either; it's the interpreter - i.e. the reader - that imbues them with semantics.

Similarly, programs manipulate symbols. It's up to the person who runs the program to imbue those symbols with meaning.

F=ma; that's some coloured pixels on your screen. It's also an expression of one of the laws of Newtonian mechanics. It can be used to calculate the approximate acceleration of a mass after a particular force has been applied to it. But the coloured pixels on your screen isn't doing that; you need to apply your mind.

Similarly, here's a function:

  function calc_a(m, F) { return F / m; }

That might be part of a program which calculates the acceleration due to a force. It's also just a series of bytes, which, when interpreted by a translator, will ultimately shuffle bits of electrical state around a very complex circuit. You still need to apply your mind to give it meaning.

It sounds like we agree - programs aren't theories. Something else is required that relates the program to the real world. Note: you could have a programming language whose semantics specify a proposed relationship to reality, just as we posit such relationships in natural language. But most programming languages don't allow such things.

A scientific theory is a self-contained description of a natural phenomena starting from first principles. My interpretation of a theoretical construct is something which is predicted to exist but has not been observed (or cannot be observed due to physical limitations). It can also be a set of results derived from thought experiments but not yet observed experimentally.

I apologize if anyone else has mentioned this, but I think most working scientists are uncomfortable with purely computational work and "theories" because they don't appear to be falsifiable within the framework developed by Popper. Current global climate models (GCM) are only subject to verifiability and this relegates them to a lower status then, say, Maxwell's equations. Maxwell's equations are capable of being used to explain almost all macroscopic electrodynamic phenomena, at least within the confines of classical physics. OTOH, there is no proper theory of the climate than can be treated with equal footing. There are only computational models and input data. There is a large amount of parameterization and data treatment (cynics would say massaging) that need to be done to get the models to converge.

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