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Hyperian History Of The World (20th Century, Part 4)
Hyperian History Of The World (20th Century, Part 4)
The academic fracture of the 20th century also applied to the arts, particularly music. The romantic era of the 19th century drew to its end at the beginning of the 20th century with the mighty symphonies of Gustav Mahler. Like Wagner before him, Mahler utilised huge orchestral forces and crafted symphonies of epic length and huge scope. The final part of his eighth symphony sets the text of the final scene of Goethe’s Faust to music resulting in an intensely dramatic experience. Finally, in his ninth symphony, Mahler composed one of the most deeply profound works in music history, the best reflection of Mahler’s own statement that, ‘a symphony must be like the world. It must contain everything.’
Mahler died in 1911, and at around that time, other composers had begun to do something strange. For centuries composers had made use of traditional diatonic harmony which had become the standard musical language. There is some evidence for the breakdown of traditional harmony in the symphonies of Mahler, and even further back in the operas of Wagner, yet this was nothing like what was to come. Rather than build on and develop the systems of the past, composers began to just completely create their own systems of harmony from scratch.
The most famous composer to invent a new system of harmony was Arnold Schoenberg. Schoenberg noticed that, in traditional diatonic harmony, certain notes (depending on which key one was in) were more privileged than others (out of the twelve in the scale). The main note of a key (known as the tonic) and the note a fifth above it (known as the dominant) were far more privileged than the others in the scale, and occurred more often in a piece of music. Schoenberg decided, for what ever reason, to create a new system of composition in which no note is more privileged than any other and each of the twelve notes has just as much chance of occurring than any of the others. Originally called twelve-tone composition, this system came to be known as serialism, and it produced very odd, unusual sounding music without any sense of harmony. It did, however prove very influential in the 20th century, inspiring composers to move away from traditional harmony and explore ever more unusual and avant-garde ideas.
However, most of this music alienates average audiences. Classical music in the 20th century became increasingly intellectual, often in an overly pretentious way. Perhaps this was the reason for the rise in the artistic merits of popular music in the 20th Century, with firstly Jazz and then Rock music becoming the music of choice for ordinary people.
As an intellectual endeavour, 20th century classical music has produced an incredible array of ingenious ideas. In a very short time music has progressed to a state where, literally, anything is possible. There are no rules anymore, a composer can literally do anything he or she wants (even as far as sitting and doing nothing) and it can be called music. But now, there is huge polarisation. Ordinary people dismiss this all as nonsense, “this is not music!” they say, they view it as overly intellectual, pretentious and even arrogant. But, the highbrow musical intellectuals, those ‘in the know’ dismiss the views of the ‘ignorant’ masses, and insist that they and they alone have what it takes to appreciate this art.
Armed with the right knowledge, and the right mindset, one can find appreciation in the bizarre soundscapes of Stockhausen, Boulez, Carter, Penderecki, Ligeti, etc. But, if one is being honest, something is lacking. This music doesn’t contain any of the magic, any of the majesty of a Beethoven symphony, a Wagner opera, a Mozart concerto or a Bach oratorio. Mozart and Beethoven certainly did not compose for a highbrow intellectual elite. They were men of the people and their music was for the people. Beethoven frankly despised the elite, and his music speaks regularly of a universal brotherhood. Perhaps, then, this is because his music was making use of a more ‘natural’ system of harmony. Once again, to understand this, we must go all the way back to Pythagoras.
Pythagoras realised the connection between mathematics and music. He noticed that musical notes that sounded pleasing together had simple mathematical relations. A bell exactly half the size of another bell gives a note exactly an octave higher and so forth. For Pythagoras, mathematics was the very basis of all existence, it was something that existed naturally and was discovered by humans, not invented by them. Therefore, pleasing musical sounds were ones most in line with this natural order. Musicians, when composing pleasing music, are simply tapping into the natural mathematics of the universe, and discovering the harmony therein, this universal harmony that Pythagoras called ‘The Music Of The Spheres’.
Over the centuries following this discovery, musical theory developed, and was always based on these fundamental elements found in nature. When a note is played by an instrument, it actually generates many notes at once. The primary note that is played generates other notes, or overtones, and these all combine to produce the final sound. The overtones are always based on the original note in the same mathematical way, therefore the fundamental note plus its overtones constitute what is known as the ‘Harmonic Series’.
Say the fundamental note has a frequency of 100 Hz. The first overtone will be a tone with frequency 200Hz. This being double the original tone (a ratio of 2:1), it will sound exactly an octave higher than the first tone (just as Pythagoras said). The second overtone will have a frequency of 300 Hz. This is not double the first overtone, so won’t be another octave higher, but it does relate to the first overtone with a ratio of 3:2, a ratio which Pythagoras had noted produces the interval we call a fifth. While not quite as harmonious as an octave, the fifth still sounds very pleasing, very harmonious. The next, third overtone has a frequency of 400Hz. This is double the frequency of the first overtone, so will sound exactly an octave higher than that tone (and therefore two octaves higher than the original). But it also relates to the second overtone with a ratio of 4:3. This produces the interval known as a fourth. Slightly less pleasing that the fifth, but still quite nice. As we continue on with the harmonic series we get more and more overtones that have more and more complex mathematical relations. The more complex the ratio, the less pleasing the interval. Pleasing, harmonious music is that which is based on the simpler ratios, the more harmonious intervals.
Why are there twelve notes in the conventional octave? Traditional, diatonic music is based, primarily on the relations between notes that are a fifth apart. Other than the octave (which is the same note but higher, or lower), the fifth is the first interval produced by the harmonic series. If we start with the lowest A on a piano and play the note a fifth up from it, we play E. Then, continuing to add fifths, we get B, F#, C#, G#, D# (or Eb), Bb, F, C, G, D and then back to A (the very highest A on the piano). By going up in fifths until we get back to A, we have passed through twelve different notes, and these are the twelve notes that make up the conventional chromatic scale.
These chromatics notes, when played side by side, can often sound jarring, due to the more complex mathematical relations between them. But when anchored by notes with more simple relations (octaves, fifths and fourths) we can attain a more pleasing harmony. This is what was discovered over time by musicians, and culminated in the glorious harmony of the Baroque era, which itself culminated in the harmonic genius of Johann Sebastian Bach. Bach was easily the most mathematical composer of all time, and he fully and completely established a harmony that was able to cleverly use chromaticism but maintained harmony by anchoring it all down with fifths and other more basic intervals. Bach’s harmony ushered in the glorious era of classical music giving us Mozart and Beethoven before the romantics reached dizzying artistic heights in the 19th century.
Then, as has been said, everything got weird. Bach’s diatonic harmony was based on natural mathematical relations. Composers were still, as per Pythagoras, tapping in to the natural order when they composed their music. But, into the 20th century, composers started to get too big for their boots, trying to establish their own systems of harmony, of composition that bore less relation to the natural mathematical order, and became something far more ‘man-made’.
Beethoven had been tapping in to the pre-existing realm of mathematical perfection when he composed, rather than constraining himself with an artificial, man-made system like Schoenberg and others were now doing. Interestingly, Schoenberg thought he was freeing himself from the ‘dogmatism’ of diatonic harmony, yet he had done this with one fundamental misunderstanding. He had failed to realise that traditional harmony is the way that it is because it all comes from the natural order of mathematics, the one that Pythagoras discovered 2,500 years ago.
Schoenberg’s ‘man-made’ system of composition is just like the man-made systems of logic which mathematical philosophers were attempting to formalise at the same time before Gödel’s incompleteness theorems destroyed the idea. Just as these mathematicians failed to understand that mathematics was the arche of existence, Schoenberg and many other 20th century composers failed to understand that traditional musical harmony was a direct subjective experience of true mathematics, the arche of existence.
Going back to music, we can see the connections here. Diatonic harmony is the music that derives from natural mathematics. 20th century composers abandoned this in favour of artificial, man-made systems. This music, though it produced its masterpieces, has simply run its course. All the radical ideas have been explored, everything has been done. When, in 1952, John Cage composed his infamous 4:33, in which the performer sits in silence and that’s it, the musical world should have known that this era of avant-garde experimentalism was over. With Cage this music reached an abominable terminal point.
Being based on natural mathematics, diatonic harmony is not constraining at all, in fact, it is the gateway to infinite possibilities, as opposed to much 20th century music, which ran its course quite quickly and now produces nothing but the same old pseudo-intellectual nonsense over and over again.
Yet there were still some composers who kept clear of these man-made systems. Igor Stravinsky did in fact abandon traditional harmony in his epic ballet ‘The Rite of Spring’, yet he didn’t constrain himself with a man-made system like Schoenberg, and the music of this ballet, although lacking traditional harmonic elegance, ends up sounding very ‘natural’, an almost archetypal expression of primordial humanity. The other great Russian composer of the 20th century was Dmitri Shostakovich, who continued the older traditions of musical forms such as symphonies and string quartets composed mostly with diatonic harmony, yet his music towers above most other 20th century classical music in artistic majesty, whilst chronicling much of the horror of 20th century history.
Other art forms suffered in similar ways in the 20th century, descending into the chaos of avant-garde experimentalism, perhaps in response to the horror of much of the world events of the time, but also due to the general fracture of humanity after centuries of irrationalism and old world power. As part of the Hyperian revolution, art must be returned to the people, reflecting the natural order of existence, the archetypes of the collective unconscious which all can relate to.
Just imagine Beethoven, profoundly deaf, yet still managing to compose the most wondrous music, some of the greatest artistic achievements of all time. Where did this music come from? How was Beethoven able to hear it? It came from the infinite content of his own mind, which, like the whole universe, is merely an expression of the natural, mathematical order, just as Pythagoras said 2,500 years ago.
Tags: Music
Hyperian History Of The World (20th Century, Part 5)
Hyperian History Of The World (20th Century, Part 5)
The fracture of humanity was greatly affecting both the arts and the academic world in the 20th century, but it was far more evident in the tumultuous political events of the time. The 19th century had seen a rise in nationalism in the nations of Europe. At the beginning of that century, both Germany and Italy were, as they had been for centuries, collections of smaller city states. By the end of the 19th century, both Italy and Germany had become single, unified nations.
Nationalism in Europe at the time led to each nation taking great pride in their history and culture, but also to each nation trying to outdo the others in terms of industry, economics, technology and, more ominously, weaponry. New weapons technology led to each nation attempting to make for itself the strongest, most powerful armed force that it could. Inevitably, this arms race would lead to war.
European nations had been perennially at war for centuries, but in the 20th century, partly due to these new weapons, warfare would become greater and more terrible than ever before, involving enough nations so as become known as ‘World Wars’.
The first world war began in 1914 when the tensions which had been building between the nations of Europe finally broke. Driven by national pride and eager to serve and defend their country, hundreds of thousands of soldiers were sent off to fight, yet this was the first major war to make use of the new weapons technologies, the effects of which would be terrible. Fighting in the trenches was simply a slaughterhouse, and the insignificance of the initial causes of the war only made the horror all the more senseless.
In 1917 Russia left the war in order to take care of events back home. The Russian Revolution of 1917 was really two revolutions. The first one, in February, saw the people rise up against the ruling Romanov dynasty, one of the old powers of Europe, leading to a confused state of affairs in which numerous factions tried to take control. This led to the second revolution, in October, which was more of a coup by the Bolshevik party led by Lenin. Eventually, inspired by the communism of Karl Marx, Russia and other countries became the Union of Soviet Socialist Republics firstly under Lenin and, after Lenin’s death, under Josef Stalin.
Meanwhile the first world war had ended and Germany, having lost, entered a period of almost poverty. The nationalistic spirit was still very much alive however, particularly in the younger nations of Germany and Italy. This led to the rise of fascism in both of these nations, firstly in Italy under Benito Mussolini, and secondly in Germany with the rise of National Socialism and Adolf Hitler.
Whilst the USSR had become a communist tyranny under Stalin (far from the utopian equality which Marx had imagined), Germany, under the Nazis, took nationalism to the extreme, with Hitler’s ideology being that the German people were the master race and all others were inferior, with particular attention being given to the Jews.
Hitler’s thirst for power (like that of Napoleon over a century earlier) eventually led to the second world war, which began in 1939. As Hitler attempted to control all of Europe and bring it under his control, he was resisted by the Soviet Union and the allied powers, whilst his allies, Japan, after attacking Pearl Harbour in 1941, launched a war in the pacific against the USA. Across the world, violence erupted, but the main war was between the conflicting ideologies of Hitler and Stalin and the fight between Germany and the Soviet Union took violence and horror to another level. The battle of Stalingrad, for example, lasted over five months and more than two million were killed.
Whilst all this was going on, Hitler was also taking his program of racial superiority to its horrifying conclusion. In the course of the war, some twelve million people, half of them Jews, were taken to concentration camps and slaughtered, in what is known as the Holocaust.
In 1945 the Soviets entered Berlin. Knowing that the game was up, Hitler committed suicide and the Nazi regime crumbled. The concentration camps were liberated and the war in Europe ended. Unfortunately, the war in the pacific continued, with the Japanese refusing to surrender. This caused the USA to take drastic action. The major advances in science, particularly in physics, hadn’t failed to be noticed by military forces, and the new science had led to the creation of the most terrible weapon of all, the atomic bomb. Knowing that the Nazis were working on something similar, leading scientists, including Einstein himself who, being Jewish, had fled Germany to the USA, convinced the US government to develop the weapon themselves before the Nazis did. Eventually, as the Japanese refused to stop fighting, President Harry S. Truman ordered the atomic bomb to be dropped on the Japanese city of Hiroshima, although not before dropping thousands of leaflets on the city from the sky informing the people what was about to happen. Nonetheless the city was destroyed and hundreds of thousands killed. Amazingly, the Japanese government still refused to surrender and the US dropped a second atomic bomb on Nagasaki. Finally the Japanese surrendered and the war came to a horrifying end.
Whilst Hitler had killed twelve million in the holocaust and millions more had died in the war, Stalin, who had won the war, wasn’t doing any better at home. His communist regime had become so extreme that any resistance was snuffed out immediately. It is not known exactly how many millions were killed by Stalin and something similar would happen in China, which also adopted communism under Mao. The theme of the century seemed to be mass slaughter.
The conflict of ideologies now led to the ‘Cold War’ between the USA and the USSR. Whilst the Soviets had communism, the USA had capitalism and democracy. No actual war was fought between these two powers, yet the whole world now lived under the constant threat of Nuclear War, with more and more nations developing these terrible weapons.
However, a better result of the cold war was the quest for both of these nations to outdo each other technologically. This was best represented by the ‘Space Race’. Despite the horror of the century’s events, humanity still achieved some wondrous things. In 1961, Soviet astronaut Yuri Gagarin became the first human being to travel into space. After this, US President Kennedy vowed to outdo the Soviets and land a man on the moon. Kennedy was assassinated in 1963, yet the program continued and, in 1969, Neil Armstrong walked upon the moon. This was a truly staggering achievement, one of the greatest human endeavours in history.
The USA had begun as a new power, yet had soon fallen under the sway of all the old powers. Both the USSR and the Nazis had been new powers, but the wrong people had ended up in charge. The success of the moon landing was the result of the right people being put in charge of it and the best, most intelligent and skilled individuals being utilised and their potential unleashed. Imagine a government that was entirely run in such a manner. What couldn’t we achieve?
The political turmoil of the 20th Century showed that humanity was growing tired of the old powers, yet they are still not gone. They have clung to power relentlessly and no new system has been the right one to overthrow them and heal the fracture of the world. But that new system is now here. Neil Armstrong walked on the moon, but we shall go further…
…to the stars.
Brice Merci – Hyperian
“From Arche to Omega Point: An Introduction to Illuminism”
Tags: Illuminism
Hyperian History Of The World (20th Century, Part 3)
Hyperian History Of The World (20th Century, Part 3)
It wasn’t just science that suffered in the 20th century by being sundered from mathematics and philosophy, but those other two disciplines suffered also. Nietzsche had basically destroyed grand philosophy at the end of the 19th century and 20th century philosophy could barely be called philosophy at all. Rather than construct grand systems to explain reality, as had once been the game of philosophers, many 20th century philosophers wasted their time obsessing over pointless little details such as linguistics, as in the philosophy of Ludwig Wittgenstein, activities which would have baffled the great ancient Greek philosophers.
Some philosophers did however turn their attention to mathematics, but in entirely the wrong way. Rather than use mathematics to explain their philosophy, which would have led them to the truth of reality as Pythagoras had asserted twenty five centuries earlier, instead they tried to use philosophy to explain mathematics.
The idea actually originated with mathematicians who, due to their general philosophical illiteracy, were attempting to explain mathematics in terms of a system of axiomatic logic. The idea was to reduce all of mathematics to a set of simple axioms to which basic rules would apply in order to produce the whole of mathematics. This idea was known as Mathematical Formalism, and its most prominent advocate was mathematician David Hilbert, who set mathematicians the task of reducing all of mathematics to a set of axioms, thus reducing mathematics to a system of man-made logic.
A similar idea was taken up by mathematical philosophers Alfred North Whitehead and Bertrand Russell, who also attempted to reduce mathematics to symbolic logic. Their ‘Principia Mathematica’ of 1913 famously featured hundreds of pages of logical symbols just to prove that 1+1=2.
All of these attempts to reduce mathematics to logic were destroyed in 1931 by logical genius Kurt Gödel with his Incompleteness Theorems. Using strict logic, Gödel proved that any axiomatic system could never produce a system that was both complete and consistent. A system derived from multiple axioms will always involve statements that are true, but that cannot be proven to be so by the system itself.
Gödel’s logic was undeniable, and his work showed definitively that Hilbert’s task could never be accomplished, to the dismay of those mathematical philosophers who had been working on it. However, Gödel’s theorems were drastically misinterpreted, such was the chaotic state of academia. For even mathematicians and philosophers had been infected by the epidemic of empiricism which had taken over the academic world since the takeover of science from religion. As such, these mathematical philosophers were unable to view mathematics in its purest rationalist form, the way Leibniz had viewed it, the way Descartes had viewed it, the way Plato and Pythagoras had viewed it. Instead, they insisted on viewing mathematics as some kind of man-made abstraction, hence their attempts to reduce it to man-made logic. After Gödel showed this could not be done, they concluded that mathematics itself was therefore incomplete and inconsistent.
Yet Gödel’s theorems only applied to the false man-made idea of mathematics which these academics had been using. Ironically, it was the philosopher Wittgenstein, who mainly obsessed with linguistic philosophy, who had a better idea about mathematics when he said that mathematics was only ever tautology. For example, to say that 1+1=2 was to say that 1+1=1+1 or that 2=2, i.e. mathematical statements were only ever stating that a certain thing was indeed that certain thing. Wittgenstein concluded therefore that mathematics was nothing other than empty tautology and could never say anything about reality.
Wittgenstein was correct to reduce mathematics to tautology but was wrong to say that this meant it was ‘empty’. The problem with axiomatic systems, which Gödel had shown to be always incomplete or inconsistent, was that they were based on multiple axioms. It is the very fact of there being more than one axiom which causes these systems to fail. As ever, a lack of pure rationalism was the problem. Leibniz would have immediately invoked the Principle of Sufficient Reason and asked questions such as, why should there be multiple axioms? Why would a consistent, logical system be based on a particular, arbitrary number of axioms?
If we take Wittgenstein’s idea of mathematics being nothing but tautology, we realise that all mathematical statements essentially boil down to the most basic tautology, 0=0. If all of mathematics can be reduced to a single statement, we thus realise the mistake that was made by the mathematical formalists. Their mistake was to insist on multiple axioms. Gödel’s Incompleteness Theorems only apply to systems with more than one axiom. If a system has just one axiom, from which everything else derives, then it can be both complete and consistent.
As ever, the ancient Greek philosophers had been right all along, when they had realised that all of reality had to derive from one single substance, or one single idea, the arche, which Pythagoras had declared to be none other than mathematics itself. Thus we can see the extent to which humanity had severely lost its way. These mathematical formalists had completely the wrong idea about mathematics and even when Gödel showed the absurdity of what they were doing, they still got it wrong by interpreting Gödel’s theorems as showing that mathematics could never be complete or consistent, when in fact it is only their idea of man-made systems of axiomatic logic which had been shown to be this way.
True mathematics must be complete and consistent. An isolated logical system is only ever a subset of true mathematics and, if isolated from the whole, will always contain self-referential statements which are the source of its incompleteness or inconsistency. Metaphysically, these ideas have interesting consequences. As individuals, we are like these subsets isolated from the whole. As such, in isolation, we contain ideas of self-reference and this causes inconsistency, incompleteness, errors or gaps in the system and it is these very errors, or gaps, which allow an individual to have free will in a universe which otherwise seems deterministic or machine-like.
We are all part of the whole, which is complete and consistent. Yet, as individuals, we fall foul of Gödel’s incompleteness theorems, which allow us the free will to explore reality. As we do so, we eventually realise that we are both individuals and the collective and, when we realise this, we become complete and consistent.
To understand this requires a unification of science, mathematics, philosophy, metaphysics, psychology and many other subjects into one single system. Unfortunately, the fracture of mainstream 20th century academia was instead leading to absurdities far removed from the truth of reality. But behind the scenes, others were working on the truth, in the tradition of the great ancient Greek philosophers and rational geniuses such as Descartes and Leibniz. Hope was not lost.
Brice Merci ‘ hyperian
The Principle of Sufficient Reason (PSR)
The Principle of Sufficient Reason (PSR)
PSR= „For everything that exist, there is a sufficient reason for why it is thus and not otherwise”
It simply states that everything happens according to Reason and never randomly. In its simplicity is the profoundest thing of all.
We can say that the Principle of Sufficient Reason is the First Cause, or the Prime Mover. It is the origin of all mathematical motion and hence of all motion. A point move through the unit circle ad infinitum and give rise to eternal sine and cosine waves because the PSR mandate it.
So the PSR is pretty much the God Equation stated in words, or a synonymous to ontological math, mind, life and light.
The PSR *seems* simple at first glance – it is “simply” Leibniz’ principle that everything has a sufficient reason (must have a proper, rational explanation). But the *implications* are massive. The PSR is “God” (not in the conventional sense). The entire universe (all of ontological mathematics) can be derived from the PSR, and from its mathematical equivalent, Euler’s Formula.
A corollary of the PSR is Occam’s Razor (the universe takes the shortest, simplest, most economical path – beauty, simplicity, symmetry, order and reason are all indissolubly linked). Leibniz’s principles: The Sameness of Indiscernibles (no two things are identical) and the Law of Continuity (nature makes no leaps) are also necessary consequences of the PSR.
In fact all laws in the universe, all mathematical equations, all ‘scientific’ equations as well (when they haven’t been butchered and misinterpreted by materialism / empiricism) come from the PSR. Some of the most notable logical principles though?
0. PSR = Euler’s Formula
“Nothing exists, or can exist, without a sufficient reason for its existence. For every fact there is a reason why it is so and not otherwise. Nothing comes about arbitrarily. If you can’t state the sufficient reason for a phenomenon then you do not understand it. If something does not have a sufficient reason for its existence then it does not exist.”
1. Occam’s Razor (corollary)
“Occam’s razor is the English equivalent of the Latin lex parsimoniae — the law of parsimony, economy or succinctness. It is a principle urging one to select among competing hypotheses that which makes the fewest assumptions and thereby offers the simplest explanation of the effect.” — Wikipedia
That is, if there is no sufficient reason to complicate things, keep it as simple as possible. The sufficient reason for something will also usually be the simplest reason.”
Ultimate simplicity is the tautology 0 = 0.
2. The Sameness of Indiscernibles
3. Law of Continuity
4. Infinity Multiplier
“Existentially, if one of something is possible then there’s no sufficient reason why an infinite number should not be possible: the conditions that were sufficient for one must also be sufficient for an infinite number. If one is forbidden, all are forbidden. If one is possible, an infinite number is possible because there’s no sufficient reason why any arbitrary limit should apply.”
5. Principle of Least Time
“Fermat’s Principle: ‘Light travels between two given points along the path of shortest time.'”
6. Principle of Least Action
“If something can be done with a minimal effort, what sufficient reason could there be for taking more effort than required i.e. sufficient reason always stands on the side of least action since there’s never any sufficient reason for superfluous action.”
7. The Plenitude Principle
“Everything that can happen will happen eventually. (Existence “begins” as perfect potential and evolves to perfect actualisation, and in doing so it creates God. God does not create existence.
God in fact IS existence in some sense, but requires an evolutionary process in order to actualise himself i.e. to turn all of his potential into actuality.”
8. The Perpetual Motion Principle
“Everything that exists is always in motion. A genuinely stationary state is impossible.”
Monads aren’t static, they’re dynamic – and therefore infinite monads can create spacetime / extension.
It’s impossible for you to be stationary. Even if you think right now you’re ‘sitting down’, you may be moving at 0 speed through space but at *maximum* speed through time.
9. The Plenum Principle
“Everything is filled. There are no gaps. Existence is not limited in any way. There are no boundaries between existence and something else called non-existence. Existence is all there is. Any system that leaves any possibility of any gaps (such as in any materialistic theory) is false. There can be no gaps and no leaps, except in specific mathematical situations.”
10. Principle of Monadic Spacetime
“With his monads, Leibniz considered that he had unambiguously defined existence. The fact is that there is no other entity that can do so. The Plenum Principle states that there can be no gaps in existence and the Perpetual Motion Principle states that everything that exists is always in motion. So, in the light of these principles, the question of existence becomes radically simple and one of pure mathematics. With what shape of “particle” can you unarguably and unambiguously fill all of existence, and keep it filled no matter how the particles move with respect to each other?” (Dimensionless monads.)
God Series book 3 ‘The Last Man Who Knew Everything’ by Mike Hockney goes into more detail on Leibniz, and the logical consequences of the PSR.
by Alessio Cappelli and Thomas Foster – hyperians