If life is a vast space of possibilities, then mathematics can engage with biology. Statistics analyze biological data, and mathematical models improve biological theories and reveal hidden commonalties. But could the mathematics of biology touch fundamental realities?
“Power laws” are mathematical relationships expressed by exponents or logarithms—why are they so powerful in describing the world? Why are power laws found in diverse complex systems in biology and society? How could simple arithmetic have explanatory potency?
Consider three powers of probability: refining data, assessing theories, probing ultimate reality. Watch how these work in cosmology: confidence in precise measurements; assessing competing models; revealing how quantum fluctuations became galactic structures.
Call mathematics the purest form of knowledge, universal messaging anyone, anywhere, can understand. For math to advance, there must be breakthroughs, which may seem like magic. What are mathematical breakthroughs? How do they happen? How do they work?
The astonishing effectiveness of mathematics in the natural sciences, especially in physics, borders on the mysterious—and there seems no rational explanation. Our bafflement stimulates novel thinking. How to assess the meaning of math’s “unreasonable effectiveness”?
Does mathematics have two transcendent attributes: truth and beauty? What makes math true? What makes math beautiful? Are there different kinds of mathematical existence? How can math combine idealized perfection and explanatory simplicity?
How brain enhancements can correct disabilities are important questions. But not Closer To Truth questions. What happens to personal identity? Would “I” still be me? What about moral standing? Would it change? Could my mind be uploaded? Would “I” live on?
The pre-eminent power of music to affect human emotions exemplifies human-level experience. How can this happen? How does music alter mental states and what does this alteration reveal about mental states? Can music probe how the mind works?
How does the brain process sounds, transforming mechanical changes in air pressure into astonishing mental experiences we call music? The neuroscience of music – from enrapturing love songs to martial national anthems – is radically challenging.
What can we learn when people deceive? There are all kinds of deception: from lying, duplicity, and disguises, to propaganda, disinformation, and deep fakes. Self-deception, too, offers insight. Why would evolution select for deceiving ourselves?
Deception pervades all life, up and down the phylogenetic tree. Deceptions have a “purpose” – the well-being, often the survival, of the deceiver. But deceptions need not be done “on purpose”. In the tool-kit of evolution, what is the workload of deception?
Biologists work in different worlds than do physicists, separated by vast orders of magnitude, numbers of variables, and levels of complexity. Does the process of Breakthroughs by biologists differ from the process of Breakthroughs by physicists?