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What evidence exists to suggest that computational science produces more information than studying real phenomena as they are?

I think about this topic often, because I think synthetic knowledge is a fascinating topic, but once I begin to observe how empirical things really behave, then I recall that "all models are wrong" seems to be the case. But I am not also entirely sure about "usefulness" of wrong models.

Then I ask, is studying the real world is fundamentally more important than studying models of it? Why do we think that computational science is useful?

Possible answers include:

  • a study where costs are reduced due to using models, but a similar product is achieved.
  • a study where lack of empirical data is replaced with simulated data.
  • a paper where it's demonstrated that a model does not really replace an empirical test. Supporting the idea that the real world is more important than the models.

Related:

Computational Science Demands a New Paradigm

https://physicstoday.scitation.org/doi/10.1063/1.1881898

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    $\begingroup$ The only question that I see is on your title, but I wouldn't know how to address it. $\endgroup$
    – nicoguaro
    Commented Sep 3, 2022 at 12:48
  • $\begingroup$ A pertinent question if it were better focused. $\endgroup$ Commented Sep 8, 2022 at 3:36

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This is the nature of science, at least the more physical ones.

You have a hypothesis about some object. You devise some experiment that would highlight this hypothesis the clearest, with the least unrelated influences. You make a prediction of the experiment based on the hypothesis. You compare the prediction with the outcome of the experiment.

It should be clear where numerical computation enters in making the prediction. If the hypothesis is part of a well-established field, then also devising the experiment, like optimizing the shape of the apparatus, or the placement, times and kinds of measurements, can profit from scientific computation.

Doing such optimized experiments can avoid doing many more less optimized experiments. Computing numerical models can also show where indirect or weak effects are (or should be) the sharpest.

No numerical simulation can replace reality. The mathematical models are (sometimes drastically) simplified reflections of reality. The numerical solution of large models is always inexact to some degree, of "fast", "cheap" and "exact" you can have at most two.

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  • $\begingroup$ "No numerical simulation can replace reality.". Perhaps, but this is anti-thetical to one philosophical stance: en.wikipedia.org/wiki/Computational_theory_of_mind $\endgroup$
    – mavavilj
    Commented Sep 4, 2022 at 18:18
  • $\begingroup$ Yes, point taken. But what has that topic to do with scientific computation on digital computers? The brain is more like an analog computer, imprecise in its elementary components, but error-correcting by being massively parallel. $\endgroup$ Commented Sep 4, 2022 at 18:32
  • $\begingroup$ en.wikipedia.org/wiki/Simulation_hypothesis ~ If all we think is computation, then all we observe also is, and what is "really real" is meaningless. I actually like this idea a lot, because a lot of what we interpret in science is in fact just distributions. Or, in other words, why can't we make all science "computational", if that's the observational layer? $\endgroup$
    – mavavilj
    Commented Sep 4, 2022 at 20:28
  • $\begingroup$ There's also a paradigm somewhere that attempts to replace experiments with computational experiments. $\endgroup$
    – mavavilj
    Commented Sep 10, 2022 at 16:49
  • $\begingroup$ Yes, there really is no bound for delusion and hubris. Solipsism is a valid weltanschauung, but practically ascribes god-like powers to the proponent. There was this one author of philosophic science-fiction that wrote extensively and amusingly about this mental boundedness of us meatsacks, a Stanislaw Lem, esp. in the stories about GOLEM XIV and Ion Tichy. $\endgroup$ Commented Sep 10, 2022 at 19:17
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There is one simple yet important case: your experimental data has not happened yet!

You can not compare the value of weather forecasts against experimental data, as the data you would have to compare has not manifested yet. The same holds true for models of our ecosystem and climate. We very much like to know what is going to happen to our planet before it happens, and computational science is the way to go.

Now, this does not mean that these models are not compared against historical data, but the reason we do these simulations is essentially to predict the (near) future.

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Another important case: computational tests allow for more and cheaper experiments than the real phenomena.

For instance, to find out the best position for a support beam on a bridge, without finite-element modelling you'd have to build 100 bridges, put load onto them until they collapse, and keep the design that can hold the maximum load. Not very practical, you'll agree.

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