Archive for the ‘Pythagorean geometry’ tag

Oct 28, 2012

The Kline Directive: Theoretical-Empirical Relationship (Part 5a)

Posted by in categories: education, ethics, physics, policy, scientific freedom, space


I was not intending to write Part 5, but judging from the responses I thought it was necessary to explain how to read a journal paper – and a good read cannot be done without a pen and paper. If you are writing a paper, when you have completed it, I would suggest you set it aside for at least a week. Don’t think about your paper or the topic during this shmita period. Then come back to your paper with a pen & paper and read it afresh. You’d be surprised by the number of changes you make, which means you have to start well before your deadline.

Note, you can find articles on how to review or write papers and here is one, by IOP (Institute of Physics, UK) titled Introduction to refereeing, and is a good guide to read before reading or writing a paper. This is especially true for physics but applies to all the sciences and engineering disciplines.

Note, for those who have been following the comments on my blog posts, IOP explicitly states “Do not just say ‘This result is wrong’ but say why it is wrong…” and “be professional and polite in your report”. So I hope, we as commentators, will be more professional in both our comments and the focus of our comments. Thanks.

In this post I will address what is not taught in colleges. There are three things to look out for when reading or writing a paper, Explicit and Implicit Axioms, Mathematical Construction versus Mathematical Conjecture, and finally, Concepts and Logical Flow. In this first part I discuss Explicit and Implicit Axioms.

This may sound silly but 1+1 = 2 is not an axiom. Alfred North Whitehead and Bertrand Russell proved that 1+1 adds to 2. Therefore, we see, that the immense success of the modern civilization compared to all other previous civilizations, is due to the encroachment of the imperceptible mathematical rigor in our daily lives by nameless, faceless scientist, engineers and technicians. Now that is something to ponder about. If we lose that rigor we lose our society. We can discuss economic and political theory but without this mathematical rigor, nothing else works.

Any theoretical work is based on axioms. For example in Pythagorean geometry, one assumes that surfaces are flat in such a manner the sum of the angles of a triangle adds to 180º. In Riemann geometry this is not the case. Explicit axioms are those stated in the paper.

Implicit axioms are axioms that are taken for granted to be true and therefore not stated, or considered too trivial to be mentioned. More often than not, the author is not aware he or she is using or stating an implicit axiom.

For example, mass causes a gravitational field is an implicit axiom, as we cannot with our current theoretical foundations nor with our current technologies prove either way that mass is or is not the source of a gravitational field. This axiom is also considered trivial because what else could?

But wait, didn’t Einstein … ? Yes correct, he did .…

Mass is a carryover from Newton. It shows how difficult it is to break from tradition even when we are breaking from tradition! Since Newton figured out that mass was an excellent means (i.e. “proxy” to be technically rigorous) to determining gravitational acceleration in mathematical form, therefore mass had to be the source. All tests pertaining to Einstein’s relativity test the field characteristics, not how the source creates the gravitational field.

But our understanding of the world has changed substantially since both Newton and Einstein. We know that quarks are at the center of matter and exist in the same ‘amount’ as mass. So how does one tell the difference between quark interaction and mass as the gravitational source?

The importance of implicit axioms in particular and axioms in general, is that when we recognize them we can change them and drive fundamental changes in theory and technologies. I asked the questions, what is gravity modification and how can we do it? These questions are at best vague, but they were as good a starting point as any? But life happens backwards. We get the answer and then only do we recognize the precise question we were attempting to ask!

When I started researching gravity modification in 1999, I just had this sense that gravity modification should be possible in our lifetimes, but I did not know what the question was. It was all vague and unclear at that time, but I was very strict about the scope of my investigation. I would only deal with velocity and acceleration.

I spent 8 years searching, examining, discarding, testing and theorizing anomalies, trying to get a handle on what gravity modification could be. Finally in 2007 I started building numerical models of how gravitational acceleration could work in spacetime. In February 2008 I discovered g=τc2 and at that moment I knew the question: Can gravitational acceleration be described mathematically without knowing the mass of the planet or star?

So the implicit axiom, mass is required for gravitational acceleration, is no longer valid, and because of that we now have propulsion physics.

If, in the spirit of the Kline Directive, you want to explore what others have not, and seek what others will not, my advice is that when you read a paper ask yourself, what are the implicit and explicit axioms in the paper?

Previous post in the Kline Directive series.

Next post in the Kline Directive series.


