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Suppose I have a theory A that can predict all experimental outcomes, E, in a particular domain of interest almost exactly.

Now suppose later a second theory is developed B that cannot predict experimental outcomes precisely, but instead can make a prediction within a certain range of E.

Now let us suppose that no one can understand how theory A produces the right answer. Theory A just involves doing certain arithmetical sums and happens to work.

But let us suppose B is built up from more fundamental scientific ideas, and allows one to clearly conceptualise how the theory works (despite not being as accurate as A).

So my question is, does theory B have a place in science, given that A can already predict all experimental results in the domain of interest?

Put another way, is science done when it can predict the world, or is there still science in understanding it (even at the cost of accuracy)?

  • Well, newtonian physics is still a part of science, although it is weaker than relativity. – rus9384 Aug 14 '18 at 10:18
  • @rus9384, yes but suppose relativity was discovered first. Would there be any need to discover Newtonian physics post relativity, and would this be in the realm of science? – Kenshin Aug 14 '18 at 10:19
  • After relativity newtonian model is an approximation. As approximation it'd be useful, but it does not reveal anything new from theoretical point. – rus9384 Aug 14 '18 at 10:25
  • @rus9384, that's right, so the newtonian/relativity example you gave initially doesn't quite match my scenario, where theory B comes second, and explains less. – Kenshin Aug 14 '18 at 10:26
  • The problem is that understanding better means greater accuracy. Or else I don't get what you mean by "understanding". Typically it is linked with predictions. There are many relativity simplifications, as well as quantum theories which were developed later. But they don't and can't give better understanding because they are weaker. – rus9384 Aug 14 '18 at 10:59
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If we've got a largely opaque computation (perhaps an artificial neural net) that can provide answers, we've got something of a dead end. We can't extend it, and if it has slight inaccuracies we don't know how to adjust the model.

If we have a theory that the results come from these scientific principles, then we can probably extend it to other fields. If there's discrepancies between the model and observations, we can investigate them, and see what other factors might be in play, or whether our original principles were slightly wrong. (Example: applying Newton's law of gravity to orbital mechanics resulted in the discoveries of Uranus and Neptune, but didn't handle Mercury. It turned out that Newtonian mechanics are slightly wrong, and applying relativity makes Mercury's orbit work.)

One purpose of scientific theories is to summarize information, and an opaque calculation can't be summarized or simplified. (For example, consider objects moving and colliding with each other. In a frictionless vacuum, all we need to know to figure out how to calculate the results is a couple of conservation laws.)

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does theory B have a place in science

As described, it's completely reasonable for theory B to have a place in science. It's even likely if it has properties such that it makes it easier to make useful predictions.

In fact, it's very common to make use of theories where we know that there are more accurate and more complete theories available. Newtonian mechanics, for example.

Now, you added two extra properties to your theories that deserve some discussion. You said

Now suppose later a second theory is developed

The ordering of the discover of theories doesn't really matter in science. In practice, it may affect how prevalent the usage is and will likely affect the prestige of the theory (precedence is important to scientists if not to science) but utility usually trumps most other considerations.

built up from more fundamental scientific ideas

This is probably the most philosophically interesting statement. It is often very useful to have a mental model of a theory that helps to intuit what is going on. Whether or not that mental model actually represents something fundamental is, however, often questionable.

This has shown to be particularly true for theories that probe beyond the limits of our senses. It does appear that we struggle to develop intuitive mental models at those extremes and scientists who probe those reaches tend to rely heavily on the mathematics as it's proven to be more reliable in practice.

Whether this is a inherent trait in humans or we just haven't developed the right mental models is, I believe, an open question.

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