Thursday, January 19, 2012


The Euler Identity which is commonly expressed as e^(iπ) + 1 = 0 has long been recognised as perhaps the most beautiful formula (equation) in all of Mathematics.

Now the conventional explanation of this beauty is generally given with reference that the simple Identity combines five of the most important mathematical constants
i.e. e, i, π, 1 and 0 with the three mathematical operations addition, exponentiation and multiplication (which occur just once in the Identity).

All of this is of course true, but somehow it misses out on the true significance of the Euler Identity.

In other words as the conventional approach to Mathematics is merely of a (reduced) quantitative nature - in what I refer to as Type 1 Mathematics - it can only interpret the Identity in quantitative terms.

However its real significance is that it combines both quantitative and qualitative type interpretation in a truly remarkable manner.

Therefore to highlight this neglected qualitative aspect of interpretation we must employ Holistic i.e. Type 2, Mathematics.

Then finally in the blending of both quantitative and qualitative aspects of interpretation we finally move to - what I term - Radial i.e. Type 3, Mathematics.

In my own development - psychological and mathematical - the Euler Identity has proved of enormous significance.

Firstly it helped to resolve a long standing issue I had with the Number Spectrum.
So some 20 years ago I realised that the most scientific manner of interpreting the full spectrum of development was in terms of appropriate use of the holistic interpretation of the number types. This spectrum entailed pre-rational, rational, and post-rational (contemplative) type structures. Now for all the main stages (pre-rational, rational and post-rational) I was able to uniquely identify each stage with a number type (the holistic interpretation of which defined the key structural aspects of the stage). However the final most developed stages required incorporating the mature use of rational with contemplative type understanding (i.e. radial).
Putting it briefly the qualitative interpretation of the Euler Identity provided the essential link in explaining the move from contemplative to radial development.

More recently the Euler Identity has played a major role in enabling me to discover - what I consider - is the true meaning of the Riemann Hypothesis.

So just as the Euler Identity properly requires both quantitative and qualitative aspects of mathematical interpretation, the Riemann Hypothesis ultimately relates to the central condition necessary for the consistency of both aspects.

So the attempt to prove (or disprove) the Riemann Hypothesis through conventional (quantitative) means is thereby strictly futile.
In fact without acceptance of the Hypothesis (as the fundamental axiom) we would have no reason to trust all the accepted axioms of Conventional Mathematics.

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