I read Dave’s comment with great interest! It is fascinating to consider why we believe things to be the case as opposed to not being the case. At risk of being a bore as usual, I am fond of pointing out that the origin of the phrase “to prove” is in the sense of “to test” – as in “the proof of the pudding is in the eating”.

The potential asymmetries or differences in the proving analogy between music and mathematics do not trouble me much – mainly because I believe that in the ultimate explanation of the universe, time is an illusion. Consequently, the only thing that is “real” is that the composition, its derivation, and its multiple performances are related to one another by the laws of physics, and are consequently much more likely to be experienced. Cause and effect emerge only from the “arrow of time”, which arises (for some as yet unexplained reason) in our human brain.

I believe that the relationship between the encoding and the rendering, is the test, and the only reason we perhaps cannot easily perceive its mechanism is that our human memory of the “future” is so hazy and multi-faceted when compared to our memory of the “past” which is perceived as singular and sharp (even though it actually isn’t) by virtue of being constantly redefined and reinforced in the specious present.

Just as with traditional prescriptive music, all of the potential and actual renderings (performances) are in fact already encoded within the piece, and just as a gene is expressed (or not) in its ecological niche, then an n-p meme is expressed in its informational niche, giving rise to a rich variety of outcomes.

( A wonderful explanation of a timeless understanding of the universe is presented in physicist Dr. Julian Barbour’s book “The End Of Time”.

http://www.amazon.co.uk/dp/0753810204 )

I think your analogy to mathematical theory is quite apt in that there is so much synergy between maths and music on so many levels.

My background is in maths both at school and university leading on to a long career in computing and I still, to this day, marvel about some of the “proofs of theorem” that are so simple in execution yet so difficult to grasp in concept. As a simple example, take for instance, the proving of a factorial theorem where you generate a formula to add up the product of all the numbers between 1 and ‘n’. The solution of summing a divergent series was well know to the Pythagoreans in the 6th century BC and the numbers are known as triangular numbers:

See:

https://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E2%8B%AF

for a more visual representation.

The answer is (n*(n+1))/2 which almost any schoolboy will give you as an answer but how many know that there are many, many ways to come to the end result, just as there are many, many ways to come to the end performance in music.

How magical that the solution to the problem becomes instantly obvious once the numbers to be added together in the sequence are shown in a different form i.e instead of depicting 5! as 5*4*3*2*1 we realise that factorial (n+1) is simply factorial (n)* (n+1) where n is greater than 0 and factorial 1 ALWAYS equals 1.

See:

https://en.wikipedia.org/wiki/Factorial

We can now redefine the problem as a triangle for each group of numbers (1+2+3+4) increasing in height, just like a pyramid in fact and similar in some ways to musical notation!! Music and maths definitely do have a special synergy in that the saying “simple is beautiful” was never so true. I leave it to the reader to work out the derivation of the end equation, just as the performer will do with a musical piece.

One other solution used to prove a theorem is using what is known as mathematical induction by which we:

1. Show something works the first time.

2. Assume it works for this time.

3. Show it will work for the next time.

4. Conclude that it works all the time (within certain pre-defined constraints).

Once the mathematical equations are established, there are a multitude of methods that can be used to confirm a formula by looking at the problem from different perspectives, similar to the musician interpreting a work. Many solutions, but one end result – once again as in musical composition.

Maybe you should incorporate these steps to your musical thinking/strategy a little more as I do believe that the concept fits in with your overall objectives, especially any future short pieces.

We always think of beauty in maths as being the simplicity and simplification of difficult concepts. The initial proof of the theorem (musical composition) is invariably difficult whereas the replication of further proofs (musical performance) once the goal has been well defined normally tends to be somewhat easier as well as providing a voyage of discovery to the listener. Composition or “Getting to the initial result” – is hard graft allied to a modicum of luck sometimes as you have no doubt discovered over the years.

There is however, in my humble opinion, one major difference between mathematics and music in that the mathematics always lead back to a common ground i.e the existence of the formula as opposed to the music which simply evolves as it is subject to outside forces (emotions, feelings, surroundings etc.). However, thinking in a different way about a problem often leads to miraculous discoveries – for the musical equivalent read “performances”. Maybe that is the dividing line between the elevation of music from a science to an art form.

Your own personal “base formula” (Eric’s formula) is undoubedly in your own head and consciousness, leaving the various “proofs” to both the player as well as the listener. The two are not so far adrift and appreciation of the end result can often not be quantified easily in words as I am finding out here, so less of my babble!

Meanwhile, I have now listened to the whole collection a number of times, sometimes enjoying certain compositions on differing levels depending on the listening environment and also my own level of concentration, just as i would do when analysing a good mathematical proof!

Keep up the great work and I look forward to more “proof by induction”.

ðŸ˜‰

Dave

]]>A fascinating post that I read with great interest! You asked if I would glance over what you had written, and check it from a science perspective. I found just a few points worth discussing. (Please understand that I am not an expert, and I am being pedantic in the points identified – none of what follows fundamentally affects what you are saying!)

Here are the points:

(1) “Everything quantum appears to be in an indeterminate state where everything is possible. Classical physics becomes flawed, turned upon its scientific head.”

I think you may be alluding to states like quantum superposition, which occur and can even be maintained in certain situations – but its not true to say that everything is indeterminate – some things in the quantum world can be very accurately determined. Also, I think you meant to say “where every outcome is possible” – clearly some things remain impossible. It might be more accurate to say that the quantum world, it appears, is governed by probabilities. The certainty that accompanied classical physics is no longer a given.

(2) “..theoretical science rarely provides answers or solutions that can be experimentally validated, corroborated.”

Actually no, this is not the case – for example, Quantum Electrodynamics is the most precisely tested theory that has ever existed. The theory provides accurate predictions for certain non-probabalistic properties, and the theory matches actual real world measurements to an accuracy of better than one part in a billion. It is true to say that the latest theories involving strings and membranes in a multidimensional universe admit of no experimental testing that is within the current capabilities of human technology – although some commentators suggest that experiments which indirectly lend supporting evidence may not be far off.

(3) “A quantum is the minimum amount of matter involved in an interaction between two particles.”

Being picky again – quanta apply not just to matter, and not just to particles – its perhaps better to leave it more open. I quite like the Wikipedia offering: “A quantum is is the minimum amount of any physical entity involved in an interaction.”

(4) “With both QE and NP any outcome can be possible.”

Many outcomes are actually impossible. Pedantically, any outcome that is physically possible is assigned some level of probability, however small. I’m not quite sure of how best to word this, but perhaps “With both QE and NP any possible outcome is probable.”?

(5) “Now they gather in a cloud the position of which can never be determined.”

Ultra-picky again! Perhaps one should say: “Now they exist in a cloud, the position of which can in practice only be determined at the expense of causing a huge disturbance to the experiment, and consequently obfuscating other properties.” (For example, we cannot simultaneously know a particle’s location and momentum with infinite precision.)

(6) “It seems that they are quantum excitations.”

Er, no. Quantum excitation is a process. I’m guessing you have picked up on the fact that scientists have claimed to find some excitation processes which display behaviour that seems “particle-like” – but the converse is not the case – not all things that behave like particles are excitations.

All this pedantry does not take away from your interesting viewpoint. Physicists have always referenced music – from Pythagoras’ music of the spheres, right up to modern theories which view the constituents of the universe as tiny vibrating strings. I’m sure that you are quite entitled to make metaphors in the opposite direction!

Cheers, Pete.

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