Philosophical Speculations on the Meaning of Spirals

May 29th, 2017


According to Emmanuel Swedenborg, the form of a spiral lies at the heart of the created world.   While this idea faded into obscurity as the mechanistic worldview of Newtonian physics came to dominate our sensibilities, it is finding resurgence in the science and mathematics of complexity.


Living in a Post-Truth World – The Challenge to both Science and Spirituality

November 27th, 2016


On November 16, the Oxford Dictionary announced it had chosen “post-truth” as the 2016 Word of the Year. After Brexit, the recent US election and the increasingly isolated and polarized nature of online communities where fake news stories get equal play or better than the real ones (see: Buzzfeed Facebook Probe), the choice seems entirely appropriate. This forum has posted 13 articles on the difficulty of knowing what is true and an extended series on the challenges of being rational. So perhaps being “post-truth” is no big deal? Nothing could be further from the truth! We ignore true facts of our experience, our science, and our spiritual teachings at our peril. The fate of the world, and the fate of our souls, hangs in the balance.

640px-philly_thinker-225x300 (more…)

Why Big Data Can’t Be Trusted (Part One) – and What to Do About It!

October 31st, 2016

Imagine 100 monkeys typing (presumably randomly) on 100 typewriters for a limitless period of time: Eventually, hidden somewhere in the seemingly endless streams of nonsense, they would produce all of the works of Shakespeare. This popular thought experiment has been around for more than a century (longer than typewriters!) and demonstrates interesting features of both randomness and infinity. It is a useful starting point for discussing unique problems now being encountered with large data sets.



My Big TOE – a Personal Lens to Knowledge Acquisition

March 3rd, 2016

My nephew Cody and his wife Natalie began a food blog called the Gantzery about a year ago focused on healthy and nutritious recipes, but with a strong personal flavor. It often contains interesting philosophical remarks. This week, these remarks asked about one’s “personal lens” in how we approach the world in the search for knowledge and understanding, and it inspired some deep personal reflection.  What is my lens? My Big TOE!


Photo courtesy of The Gantzery. (more…)

The Curious Mathematics of Nothing – and Why It Is So Important.

July 28th, 2015

Abstract:  We usually think of mathematics as something kids have to learn in school – we rarely or only dimly comprehend that it provides the foundation for virtually all of modern science and the ubiquitous technological infrastructure that nurtures us. Mathematics is a marvel, and the greatest minds have not been able to explain why it works as well as it does in explaining the way the world works. Curiously, one of the more incomprehensible features of modern mathematics is – nothing.

zero (more…)

Insights into Infinity – Is the World Finite?

November 20th, 2013

Recently I happened across two very different pieces about infinity.  The first was a blog post by Mario Livio, and the second a short video by Curtis Childs on Infinity.  In his post, Livio poses the question as to whether there are any infinities in nature or whether they are just mathematical concepts.  (more…)

Does Knowing = Having Justified True Beliefs?

October 23rd, 2013

Justified True Belief is the Holy Grail (to borrow a religious allegory) of epistemology – “knowing” is to believe something, on the basis of rational evidence and thought, that is in fact true.  While this concept has taken a beating over the past forty years, starting with some paradoxical thought experiments by Edmund Gettier, it generally describes the model for knowledge that philosophers have applied for more than 2,000 years.  But is it helpful?  Is there a better way to define “knowing”? (more…)

Uncertainty – More Data is Not Enough!

August 15th, 2013

Today I read two articles in the online journal Nautilus:  Michael Tuts’ “Discovering the Expected”, which discusses the process physicists have used to validate the discovery of the Higgs Boson, and Amir D. Aczel’s “Chasing Coincidences”, which highlights our tendency to remember the unexpected.  The first article highlights the need to throw out the data that does not suit our purpose, and the second highlights how our unconscious attention throws out experience that does not contain meaning.  In each case, it is the patterns and relationships that are important.  But uncertainty is also significant from a metaphysical perspective.


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…)

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.


Cognitive Bias – The Difficulty of Judging What is True

July 27th, 2011

I recently heard an economist talking about the problem of cognitive bias in the economics profession, and it occurred to me that this is a key issue in the science and spirituality discussion. A quick survey of the topic (link here) demonstrates the hugely fallible quality of human rationality. How can we get past the problem? Honest and humble introspection – and respect for those holding contrary positions. (more…)

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 Skeptic’s Dilemma – Solipsism

March 17th, 2011

When I was a kid, my older brother used to tease me with questions that were beyond my understanding. One line of questioning I recall went like this – How do you know other people exist? Maybe you are dreaming. Maybe it’s all a movie in your brain and there is nobody there? How do you really know? (more…)