Scott Douglas Jacobsen
Jun 16 · 4 min read

By Scott Douglas Jacobsen

Herb Silverman is the Founder of the Secular Coalition of America, the Founder of the Secular Humanists of the Lowcountry, and the Founder of the Atheist/Humanist Alliance student group at the College of Charleston. Here we talk about science, math, and limits (maybe, or maybe not).

Scott Douglas Jacobsen: In one view, the limitations of the human mind set boundaries on possible human science. Human empirical methods with the inclusion of artificially constructed structures can extend the reach of the human mind, whether computational constructs, e.g., algorithms or data collection systems, or tools to manifest the world with greater precision to the senses, e.g., telescopes and microscopes. However, these translate the information back into the range of experience and processing of human beings.

In another perspective, the discoveries about the world reflect the tendencies in thought, and so the limitations, of the human mind, whether individuals or groups. What we know to various degrees, seem to know, and think we know, these reflect the form of information processing of human beings at large. Hills and valleys of fidelity and complexity reflecting the internal mechanics of the mind.

Pure mathematics seems to reflect this the most exquisitely. Some discoveries would, probably, remain impossible without the aid of technology. In particular, the world of large data sets, powerful computational systems, and to-the-task algorithms to help teams of professional mathematicians.

As technology advances, and as a practical philosophical inquiry, how will science advance? Where will possible human science hit a wall? Will machines launch independent scientific enquiries in the future to make discoveries barely comprehensible to most human beings?

Professor Herb Silverman: Aristotle pioneered the scientific method in ancient Greece alongside his empirical biology and work on logic, rejecting a purely deductive framework in favor of generalizations made from observations of nature. Modern science began to develop in the scientific revolution of 16th- and 17th-century Europe when the scientific method was formalized.

At this point in 2019, I’m not too worried about the possibility of human scientific discoveries hitting a wall. Based on the progress of the history of science and technology, it is not unreasonable to expect that means will be found to circumvent what appear to us now to be absolute limitations.

Look at all the scientific progress we’ve made in just the last century. People once said that we would never fly, before the Wright brothers did. People said we would never make it into space, until we did. And then that we would never make it to the moon, but we did.

Interstellar travel is one of those future innovations that many people believe will never happen. It won’t happen tomorrow or in the next year, but eventually, if we last long enough, I think we will get to Alpha Centauri, the closest star and closest planetary system to our solar system. It is 4.37 light-years from the sun. Using current spacecraft technologies, crossing the distance between our Sun and Alpha Centauri would take several millennia, which would require generations of people in spaceships. But scientists are now investigating nuclear pulse propulsion and laser light sail technology, which might reduce the journey time between our sun and Alpha Centauri to decades.

Some scientists think there will be an end to physics if a “Theory of Everything” (TOE) is discovered. This would entail an all-encompassing, coherent theoretical framework that fully explains and links all physical aspects of the universe. In particular, such a theory would reconcile general relativity and quantum field theory. General relativity only focuses on gravity for understanding the universe in regions of both large scale and high mass: stars, galaxies, clusters of galaxies, etc. Quantum field theory only focuses on three non-gravitational forces, (strong, weak, and electromagnetic force) for understanding the universe in regions of both small scale and low mass: sub-atomic particles, atoms, molecules, etc. At present, there is no candidate for a TOE that includes the standard model of particle physics and general relativity.

A number of scholars claim that Gödel’s incompleteness theorem suggests that any attempt to construct a TOE is bound to fail. Gödel’s theorem, informally stated, asserts that any formal theory sufficient to express elementary arithmetical facts and strong enough for them to be proved is either inconsistent or incomplete. Stephen Hawking, originally a believer in a TOE, after investigating Gödel’s theorem, concluded that a TOE was not attainable.

In fact, Gödel’s theorem seems to imply that pure mathematics is inexhaustible. No matter how many problems we solve, there will always be other problems that cannot be solved within the existing rules. So, because of Gödel’s theorem, physics is inexhaustible too. The laws of physics are a finite set of rules, and include the rules for doing mathematics, so that Gödel’s theorem applies to them.

Also, just about any problem solved in mathematics or science seems to raise additional questions that we would like to solve. So I expect there are infinitely many questions that we would like answers to, which won’t be found in a finite amount of time. There might even be infinitely many possible theories, not all of which humans can ponder. With or without machines, even now the majority of scientific discoveries are barely comprehensible (or incomprehensible) to most human beings.

The limitations on human scientific and mathematical discoveries, I expect, will be based on the limits to human life — which might end from climate change, an asteroid, nuclear war, or for some reason we don’t yet know about. Now that’s what should probably be a priority for us to address.

Jacobsen: Thank you for the opportunity and your time, Professor Silverman.

Photo by Roman Mager on Unsplash

Question Time

A journal with educational content via subject matter expert interviews.

Scott Douglas Jacobsen

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Scott Douglas Jacobsen is the Founder of In-Sight: Independent Interview-Based Journal and In-Sight Publishing. Jacobsen supports science and human rights.

Question Time

A journal with educational content via subject matter expert interviews.

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