Engineering scientific discovery

I was recently listening to archived Radiolab episodes, and came across this story about Eureqa, a computer algorithm that looks for patterns in data sets.

The amazing thing about this story is that the algorithm finds correlations and relationships between datasets that are incredibly accurate and even predictive. These finds have all the hallmarks of scientific breakthroughs – the program could by rights be listed as a coauthor on this scientific paper and it has even recreated seminal discoveries (like Newton’s Second Law!) – however, humans may be beyond our capacities to understand the “laws” Eureqa finds.

But, that is for you to decide! You can enter data into this algorithm from the comfort of your own laptop and see what relationships pop out. Perhaps you (with the help of Eureqa) will identify the meaning behind a new relationship and will make the next great discovery.

Try it out here! This is a great way to develop relationships for your own datasets.

Plotting walkingbaron’s temperature as a function of his room’s x – y coordinates we get the following:

Screen shot 2013-03-30 at 1.09.51 AM

Eureqa finds the following best fit relationship:

T = 12.6008 + 1.18541y + 0.591413x + 0.00272746xy^2 + 0.00170691y^3 - 0.0132424x^2 - 0.0701875xy - 0.0784782y^2

With the fit:

Screen shot 2013-03-30 at 1.10.01 AM

Not bad! Although I would feel a bit anxious about extrapolating this fit in many directions, and there is no clear physical significance (beyond the fact that they represent the partial derivatives of the temperature surface and therefore the coefficients in a two dimensional Taylor series expansion of the temperature profile in the neighborhood of the point (0,0,12.6)) for the necessity of the many parameters in the model. However, I am new to the program and am impressed!

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I am a math and science teacher at a boarding school in Delaware.

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Posted in Advanced Chemistry, Multivariable Calculus, Steven Strogatz

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