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The amazing applicability of mathematics to the real world has caused many mathematicians, philosophers, and physicists to pause throughout history. How can something as abstract and ideal as mathematics apply to the real world?
In 1960, Nobel physicist Eugene Wigner (1902-1995) (right) wrote an essay, “The Unreasonable Effectiveness of Mathematics in the Natural Sciences.” It meanders widely through a multitude of observations. But he touches on several essential, surprising observations about the relationship between physics and mathematics:
1. That humans can engage in the process of mathematics and develop extensive mathematical ideas which are free from contradiction
2. That the same mathematics applies to physical theories
3. That the human mind can extract mathematical relationships from such a small sampling of data which correctly model the data
4. That when the same mathematics tells us something we did not expect about physics, we can often run an experiment and find that the mathematics was correct in its description of the physics
Observations 1 & 3 are actually more about the surprising abilities of humans than about mathematics. In fact, 1 & 3 are major reasons why most contributors to Mind Matters News do not consider humans to be mere machines. It’s not that humans are quantitatively better than machines (they often outperform us on specific tasks), but rather that we are qualitatively different from machines (there is an entire set of tasks that humans can do that machines are incapable of performing).
Observations 2 & 4 are about the relationship between mathematics and reality. It is best expressed by the conclusion of Wigner’s essay, which states, “The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning.”...
According to Mullings, the reason for the association between mathematics and physics is not that the mathematics is causative but rather that mathematics studies the logical structure of possibility and constraint. As a result, if the mathematics successfully captures the possibilities and constraints in the real world, it will provide a tool for further analysis of potential possibilities.
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Source: Walter Bradley Center for Natural and Artificial Intelligence
