P versus NP – a Confounding Issue in Mathematical Complexity

October 2nd, 2012

A simple problem – what is the shortest route for visiting a number of different cities – is extraordinarily difficult and may become impossible as the number of cities rises.  If you can show that any “NP Complete” problem can be solved in a reasonable amount of time (“P”) you can win $1Million, as this is one of the seven “Millennium Problems” in mathematics that the Clay Foundation has offered a cash prize for solving. Personally, I doubt the NP Complete problems can be solved in P time – and I believe that their intractability demonstrates a hard stop to what we can “figure out”. (more…)

Do The Puzzles of Mathematics Prove God?

September 20th, 2012

Mario Livio’s book “Is God a Mathematician?” (2009) provides a delightful history of mathematics and its many heroes, but fails to answer the question posed in the title. Dr. Livio does address directly the slightly different question of whether mathematics is a human creation, or a human discovery. In other words, is mathematics absolute, and therefore potentially a “creation of God”, or is it invented, a kind of technology resulting from human endeavor. While mathematics and the physical world are very different things, I think it’s clear they are both a “creation of God.” (more…)

Explaining the Puzzles of Physics

May 9th, 2012

Explaining the Puzzles of Physics – a response to Michael Shermer (Scientific American, May 2012, p.86)

The field of Physics has been confounded for nearly a century with intractable puzzles.  It is also rife with contention between religious and atheist points of view, with both sides claiming proofs, or more precisely, un-proofs, for their points of view.   A recent example is Michael Shermer’s “Skeptic” column in the May 2012 Scientific American, titled “Much Ado about Nothing”.  Mr. Shermer borrows his title from Shakespeare’s romantic farce, a remarkably apt context for his article, but he is apparently oblivious to the irony. (more…)

Mathematical Predictability – Hard Limits in Economics

September 27th, 2011

This week the EconTalk podcast featured a discussion on whether economics, with its limited predictive capabilities, can be classified as “science”.  I found the exchange (between Alex Rosenberg and Russ Roberts) to be wide-ranging, interesting and very perceptive, but I was disappointed that both missed the mathematical dimension to the issue of predictability.

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May 2, 2011. Synopsis – What is Truth?

May 3rd, 2011

On May 2, 2011, about 20 participants joined a lively discussion on the difficult question of how we determine that something is “true”. This included an exploration of gaps in the ability of science and math to prove beyond doubt that something is true, and reflections on whether science and religion are distinct areas of inquiry or whether there are ways these spheres of understanding can inform and support each other. Many topics for potential future consideration were identified. (more…)

Blind Spots – Reflection and Recursion

April 6th, 2011

In the previous discussion of solipsism, we avoided the abyss of pure skepticism by being willing to accept evidence that other people exist, even without an “absolute” proof. Where do we derive our awareness of others and the distinction between “self” and “other” – and what are the implications of this self-reflection? This is a really big question with implications for sentience, consciousness, and even the foundations of logic. (more…)

The Nature of Truth

March 14th, 2011

Dealing with truth can be tricky. Some interesting resources are listed below, all of which provide important insights. (more…)

ISAS – Session #1 – May 2, 2011

March 14th, 2011

May 2 – What is Truth? – On May 2, about 20 participants joined a lively discussion on the difficult question of how we determine that something is “true”. This included an exploration of gaps in the ability of science and math to prove beyond doubt that something is true, and reflections on whether science and religion are distinct areas of inquiry or whether there are ways these spheres of understanding can inform and support each other. Many topics for potential future consideration were identified.

The presentation and discussion was led by George Gantz, the series Director.  A Synopsis is posted in the Forum Discussions under The Nature of Truth. The session was recorded and is available on New Church audio at this link.

This ISAS live discussion session was held at the Harvey Wheeler Community Center at 1276 Main St., Concord, Massachusetts, from 7:30 to 9:00 PM.