Windfall Films, part of the Argonon Group, has produced an hour long special, *Inside Einstein’s Mind,* for the renowned stateside PBS science series, *NOVA. *UK viewers will be able to see the special next month on BBC Four.

“Einstein’s general theory of relativity was one of history’s most creative and dramatic revisions of our concepts about the universe. The centennial provided the perfect opportunity to celebrate the theory that changed modern thinking”. – Jamie Lochhead, writer and director at Windfall Films

Showcasing a visual journey through the most powerful idea in science, General Relativity. *NOVA*, a production of WGBH Boston, aired the show on PBS in America earlier this week (25th November). The documentary will air in the UK on BBC Four in December under the title *Inside Einstein’s Mind: The Enigma of Space and Time.*

At 36, Einstein was able to theorise the malleable nature of space and time, providing a whole new way of regarding reality. This one off show takes viewers on an engaging and visual exploration through the Einstein’s masterpiece. The production, which premieres in the US on the 100th Anniversary of Albert Einstein’s greatest work, the general theory of relativity, takes viewers on a journey from the theorists’ young mind to the extremes of modern cosmology.

Windfall Films is an award winning producer of factual content having created a portfolio of internationally acclaimed programming from* Inside Nature’s Giants* to *D Day As It Happens* and *Your Inner Fish* to *Making North America* for broadcasters across the globe. *Inside Einstein’s Mind* joins a captivating roster of programming from the BAFTA and Emmy award winning production company who continue to go from strength to strength.

Actually it turns out there is a problem in the elementary geometry underlying the general theory of relativity. Einstein said that “in the presence of a gravitational field, the geometry is not Euclidean.” At that time Euclidean geometry and non-Euclidean were seen as both logically consistent (just not logically consistent with each other). When Hilbert added the coordinate line to geometry, virtually everyone in the twentieth century took Hilbert’s system as a correct foundation, including Einstein.Yet there was a flaw that resulted from adding a coordinate system. The non-Euclidean geometry then becomes self-contradicting!

When Hilbert added the features to comprise the real number line and coordinates, the very earliest axioms required subtle modifications. From Euclid’s to draw a line from one point to any other, and extend it in a straight line, Hilbert first produced, two points determine a line and determine it completely. But this eventually became every pair of points is in some line (Axiom I. 1) and two different lines cannot contain the same pair of points (Axiom I. 2) (paraphrased). This ‘line’ is what became a coordinate line. Yet Axiom I. 2 is incompatible with one of the two types of non-Euclidean geometry (geometry with no parallels), and this is not the only problem. Then there was a problem with the remaining type. Apparently virtually no one had thoroughly and correctly reexamined the implications indicated by the subtle modifications of those elementary axioms.

Math with coordinates or angles, was based on Hilbert’s Theorem 8 [5 in earlier editions of his book] about a line dividing a plane in two, and on the SAS triangle congruency theorem (12). Hilbert said that based on Theorem 8, Theorem 10, which expanded the structure to three dimensions, expressed “the most important facts about the ordering of the elements of space.”

Hilbert proved Theorem 8 based on his Axiom I. 2, one of the modified axioms, and on Pasch’s triangle axiom, which Hilbert believed was an independent foundational axiom, common to Euclidean and non-Euclidean geometry, including that remaining type. Theorem 12 (SAS) presupposed Theorem 8. However, contrary to what Hilbert believed, the triangle axiom was not an independent foundational axiom. It was a proposition that combined a more elementary triangle axiom and Hilbert’s Axiom of Parallels which Hilbert called “Euclid’s Axiom.” This Axiom of Parallels, “Euclid’s Axiom,” was a logical equivalent of the original Playfair’s axiom, which was the logical substitute for Euclid’s famous fifth postulate added by Playfair to Euclid’s geometry in 1795.

Why the non-Euclidean geometry is self-contradicting is explained in short order in a brief Facebook Note, that explains how general relativity lost its coordinate system. Part II of the Note explains how this was overlooked throughout the twentieth century: https://www.facebook.com/notes/reid-barnes/when-is-an-assertion-about-coordinates-merely-an-assertionan-unsupported-asserti/789731027746140

This show was so inspirational and out of this world. I love Einstein. I hope this show gives young kids alot to think about.