The Last Great Mystic



Now where did I leave my car keys?



Sir Isaac Newton is universally revered as the greatest intellect of all time. Although the English logician/philosopher/mathematician, Bertrand Russell, reserves this spot for the German savant, Gottfried Leibniz, a contemporary of Newton’s. There is little doubt that Newton had a prodigious and profound impact on knowledge in the second half of the 17^th century. His contribution to science and mathematics is without peer and much of what he had to say remains relevant to the science of today. Indeed, it wasn’t until the coming of Einstein and his theory of relativity, at the beginning of the 20^th century, that we had cause to revise Newton’s worldview. And even then, Newton’s mechanics hold true for ‘real existence’. The effect of relativity only becomes important when we observe nature ‘in extremis’.

Newton is responsible for ‘inventing calculus'; a powerful analytical tool underlying much of modern mathematics. However, it is likely that Leibniz independently formulated calculus about the same time. Their rivalry over who was ‘first’ caused a bitter rift between these intellectual giants. Newton also made great strides in astronomy and invented the reflecting telescope. All large optical telescopes are of this type today. Thus Newton was a rare genius and his insight and vast intellect not only revolutionised the physical sciences but changed the way other men viewed the natural world- after Newton everything was possible and everything was explainable by the scientific, analytical method. Men of science revelled in their new found intellectual optimism and treated non-mechanistic, theological explanations of physical phenomena, with frank disdain.

Everyone remembers Newton, the great scientist. Not everyone is aware of Newton, the Alchemist. This is not particularly surprising as Newton did not publicise or publish his research into this obscure and arcane area of study even though he spent over two decades of his life and wrote over a million words on the topic. When his manuscripts were discovered after his death, ‘The Royal Society’ deemed the work not worthy of publication and even suppressed its content from a wider audience.

Alchemy became popular during the Middle-Ages: a strange amalgam between practical proto-chemistry and mysticism. The primary aim of many practitioners was to find a way of converting base metals, such as lead, into gold. With modern chemistry as our guide, we can look aghast at the naivety of an intellectual giant such as Newton. But he wasn't alone in his quest of the 'dark art' and Robert Boyle, he of 'gas law' fame, was also an adherent. Whilst Newton and his ilk never achieved their dream, their Alchemic dabbling did help to set the study of chemistry, as a science, on a sound footing. Most of the classic chemistry apparatus seen in today’s laboratories was designed by Alchemists.

Newton was a deeply religious man and scoured the bible for symbolism and hidden knowledge. From his biblical studies, Newton calculated that the end of the world would occur in 2060; seems like a shrewd guess to me. He also plundered ancient mythological texts looking for ‘enlightenment’. Strange, that the man who embodied the enlightenment should have been drawn to the esoteric and irrational. He used his ‘findings’ to help refine his alchemic studies, although to no one’s surprise Newton advanced irrational thought, not a jot. One wonders what further scientific discoveries awaited Newton if only he had concentrated all his efforts into science and mathematics.   

Newton was a complex man (aren’t we all- except if you are a woman: ask Bruce Jenner) and a man of immense contradiction. A compelling figure capable of intense logical analysis and penetrating thought. Contrast this with his ability to apply deep analytical analysis to things mystical. I can’t help but believe that Newton’s mystical and alchemic research was just as important to him as his works on light or gravity. Mayhap we should forgive Newton his foibles. He came as close to becoming a god as any man should be allowed. And judging from the extant literature, on gods, no one is perfect.         



Sir Isaac Newton, in repose 

Hooke Vs Newton

This is the first post of the Month. In truth, I have been preoccupied with my wife's health issues, although I have been working on several essays and assorted detritus that require the veneer of editing before I allow them to take root upon my blogging platform. I'm hoping that these works will reach fruition within the next couple of days, unless they don't.

The Two Protagonists- Spot the Spakka

The 17^th century was truly a time of scientific wonderment and where the polymath reigned supreme. The rise of men of profound intellect who had the audacity and drive to dabble and excel in numerous subjects of scientific, philosophical and mathematical interest. The intellectual 'Greats' of the time were true scientific pioneers. These men eschewed the cloying restrictions of Christian scholasticism, which had choked intellectual progress for over a millennium. The shackles were rent asunder, and scientific progress burst forth, unrestrained by ecclesiastic nonsense. No longer could a man of intellectual acuity lose his reputation or life for revealing nature's wonders, wonders that were arbitrarily deemed contrary to stolid Catholic dogma. And throughout this scientific wonderment strode Newton. A man whose intellect embraced all, a man of no limits, a man who is remembered by all. But what about Robert Hooke, Newton's slightly older contemporary? More about Hooke in a while.

For Context....

There is little doubt that Newton's achievements were prodigious. Indeed, it is worth mentioning these scientific achievements to gain a perspective of the man's true genius. Newton's breathtaking work in the realm of physics includes formulating the laws of motion. Although others had made important contributions in this regard, it was Newton who finally formalised the theories in a rigorous mathematical form. In his book 'Optics', Newton revealed his revelations concerning light and, due to his work involving reflection, developed a theory that light was made of tiny particles he called corpuscles. He also invented the reflecting telescope containing a concave mirror. Up to then, all telescopes were made with lenses and refracted light to achieve magnification- chromatic aberration akimbo! Not only did he 'invent' calculus (don't tell Leibnitz), but he also founded and contributed to other areas in mathematics, too many to list here. Of course, Newton is widely known for his formulation of 'Universal Gravity, ' a concept that would hold sway until Einstein came forth with 'Relativity'. By the way, Gravity is Latin for Weight. There is no doubt that Newton's book, 'Mathematical Principles of Natural Philosophy' is considered one of the most influential science tomes ever written.

Now, a word about Robert Hooke.

Although Robert Hooke was an undoubted polymath and genius, he is less well remembered today. Perhaps Newton's Greatness overshadowed all.    

Robert Hooke was born in 1635 on the Isle of Wight. He showed early mastery in a variety of subjects and, in 1653, secured a place at Oxford University, where he received his Master of Arts degree in 1662. He was a sickly child and man and not comely to the eye. His back was bent (scoliosis), and he was graced with a large head with bulging eyes. This is very reminiscent of Marty Feldman's portrayal of Igor (pronounced Eyegor) in the wonderful film, 'Young Frankenstein', made in 1974 and directed by Mel Brookes—go see. 

Here is a brief exposition of Hooke's achievements. He was the first to describe the law of elasticity using springs as his experimental medium (Hooke's Law). This had great practical applications as it paved the way for the production of a compact circular spring, an important step in the production of a portable timepiece. You can't take a pendulum clock on board a ship and accurate timekeeping was essential in determining longitude at sea. Hooke improved the primitive microscopes of the age and made important discoveries in biology, which he published in the beautifully self-illustrated book, 'Micrographia'.  It was he who discovered and coined the name 'Cell'.  Although Hooke was involved in elucidating the fundamentals of the 'Laws of Gravity', Newton pipped him at the post when it came to the primacy of the theory. Newton was able to provide a more rigorous and mathematical rendition of the phenomenon. On observing light refraction, Hooke determined that light must be propagated by a wave in contradiction to Newton's particle theory. Hooke's experiments involving air laid the groundwork for others to make seminal discoveries in this field and beyond. But Hooke was not only a scientist in the physical and biological sciences; he was also an architect, geologist and astronomer of note.    

Not only was the 17th century a time of 'Great Minds' twas also a time of great egos. I've discussed the controversy between Newton and Leibnitz concerning the 'discovery' of calculus elsewhere in this blog. Newton, in particular, it seems was a prickly, introspective and disputatious genius and locked intellects with others, including Hooke. Hooke was not a nice man if his diary is to be believed. It is said that he possessed an abrasive and unpleasant demeanour. The two men did not get along. Hooke felt that he did not receive the degree of recognition he deserved for his contribution to the theory of gravity. These prominent men could not avoid each other in the closed social circles that men of their class associated. Their mutual animosity was not only founded upon impersonal scientific matters it also extended to differences in personality and temperament.        

When discussing 17th-century science, Isaac Newton will always take precedence in any list of scientists who contributed to science's advances, achievements, and breakthroughs. Newton was a superlative genius in a century of profound geniuses (or is it genii?). That said, the addition of Hooke within this canon is not arbitrary; if Newton was king, then Hooke was undoubtedly the first in line to the throne. Although I'm sure that Hooke would have bristled at the thought that his intellect was surpassed by another.

We are apt to forget the singular and profound importance of the 17^th century as a modernising influence on the men of intellectual quality who subsequently changed the world. Most of our modern science is based on and follows upon 17^th discoveries. Perhaps of more importance is the change in the temper/timbre/tempo of mind that occurred. Nothing in the past could compare, and it remains with us today as a thoroughly modern scientific mindset. What a legacy! The importance of this intellectual revolution is worth stressing, especially because of its rapidity in societal terms: in the year of our Lord, 1600, the mindset of educated men was medieval; in 1700, the mindset was thoroughly modern. The England of 1600 witnessed witchcraft trials; this would have been unthinkable 99 years later. In addition, humankind had been humbled. No longer was our insular little bubble the centre of the universe. Everything had to be reevaluated in terms of our utter insignificance. Nuff said.

Newton + Leibnitz = Calculus

Who has the best mullet?

The great British philosopher, Bertrand Russell was of the opinion that the German savant, Gottfried Leibnitz was the ‘greatest known intellect to have existed’. This is a bold statement considering Leibnitz was a contemporary of Isaac Newton. And let us not forget that the middle of the 17^th century to the beginning of the 18^th was a prodigious period for scientific and mathematical invention led by continental and British intellectual giants.   

I will not become enmeshed, nay embroiled, in the debate to whom should be ascribed the accolade, ‘greatest genius’. From a purely scientific perspective, Newton appears to have been the more prolific and made great strides in physics and mathematics. Leibnitz was no slouch in the realm of physics/mathematics either and pontificated greatly on philosophy and is famously known for developing his theory of ‘monads’. In contrast, Newton devoted an inordinate amount of his intellect to esoteric and arcane theology. Refer to my post on Newton which delves into Newton’s profound obsession with ‘mystical studies’.

In this post, I would like to touch briefly upon the controversy which erupted between these savants concerning the primacy of developing the mathematics of calculus. Modern calculus is an extremely powerful tool for determining infinitesimals, integrals and rates of change. The application of calculus, over 350 years, has been influential in the development of many scientific discoveries. Unlike many abstract fields of mathematics, calculus has a plethora of practical applications and has insinuated its way into physics, chemistry, biology, and even economics.   

The consensus of modern scholarship is that Newton developed a form of calculus in 1665/1666 but was loathe to share his findings by publication. Leibnitz, independently formulated and published his version of calculus in 1675. Once Newton became aware of Leibnitz’s discovery, he let it be known that he had indeed made important strides in the development of infinitesimals a decade earlier. There followed a bitter debate and dispute, mostly between adherents of these famous men as to the primacy of the discovery. Both men are accredited with huge prickly egos that hindered any rational discourse. At the time, probably due to Newton’s almost ‘god-like’ reputation, Leibnitz was not ascribed the credit he was undoubtedly due, at least in the British Isles.    

As a digression: Of interest to me, is how great revolutionary ideas can be independently formulated at the same time. A parallel example can be seen with the expression of evolutionary theory in the middle of the 19^th century. Both Darwin and Wallace produced evolutionary theories within a short time of each other however, there was no bitter dispute between these measured and modest men. At the time, Wallace was given due credit but subsequent history has been unkind to Wallace’s memory and his contribution has all but been forgotten except by professional biologists. In contrast, although Leibnitz was castigated for plagiarism at the time, modern scholarship has acknowledged his independent contribution. Again, however, this is not a stance well known to the general mug punter. Original ideas are not formulated in an intellectual vacuum. Newton and Leibnitz were basing/basting and extending the work of those who had gone before. The dynamism of this intellectually fecund period cannot be overstated.  

 I think it wrong to consider either man as having ‘discovered’ calculus as such. Tis better to think that both men made highly significant contributions to the field and developed their analysis from earlier mathematicians. Thus, Archimedes was the first to find the tangent to a curve other than a circle, in a method akin to differential calculus. A gaggle of seventeenth-century mathematicians (see: Rene Descartes, Blaise Pascal, Pierre de Fermat, John Wallis, Cavalieri) made genuine advances in the field and laid the foundations for Newton’s and Leibnitz’s synthesis. And of course, Newton and Leibnitz’s contribution was not the endpoint. Both systems were plagued with problems allowing those who followed to refine/redefine differential and integral calculus to higher levels of sublimity. Importantly, Newton and Leibniz did not formulate the same calculus and came by their insights by different analytical roots/routes. Newton’s concepts were essentially empirical (he liked to draw lines, circles and tangents), while Leibnitz relied heavily on deep analytical contemplation. 

Today, the notation we use in modern calculus is derived from Leibnitz. Even though modern calculus has been revised, developed and 'perfected' from its original conception(s) this in no way distracts from the genius and astonishing contribution made by these truly, Great Men.

     

Gravity

Who is the greater, now that's a thought

Gravity, we take it for granted, we really do- but was is it, really? The concept was first given a sound rational and mathematical basis by Sir Isaac Newton in his Magnus Opus, ‘Principia’, 1687. But it was not always this way.

The ancient Greeks had their own ideas of why objects moved. The Greek/Macedonian philosopher, Aristotle of the 4th century BC, had worked out a system based on pure thought and a little empirical observation. Aristotle had some very strange ideas, many of which were not questioned for nearly two thousand years- such was the authority of this Great Man. Aristotle's concept of motion is very odd to the modern mind and follows naturally on from 'Aristotelian metaphysics'. To fully understand the concept of motion in Aristotelian terms requires a thorough drenching in Aristotelian metaphysics, a chore I have no intention of attempting here, so a brief summary concerning Aristotle's 'notions on motions' will have to do. According to Aristotle, motion on earth was due to the application of force- not an unreasonable and a correct supposition. Without an applied force there can be no motion. Why an object continued to move after the applied force was removed bothered the ancient Greeks. The concept of inertia did not occur to them. Aristotle believed that everything was composed of four basic elements: earth, water, air and fire. Amongst these elements like attracted like. Thus if you held out a rock and dropped it, the rock would fall because it was attracted to 'like', the bigger rock, the earth. His next class of explanation concerned the movement of the 'heavenly bodies.' Remember, Aristotle, like most ancients, thought the earth remained stationary and that the sun and other heavenly bodies moved around the earth in perfect circle. The movement of these objects was caused by the 'Prime Mover', the ultimate artificer, which we would equate with a deity. As the 'Prime Mover' was by definition, perfect, the motion was perfect and the perfect geometric conception for the Greeks was a circle. I will not delve into the ancient concept of motion any longer, except to say it was extraordinary wrong but extraordinary influential for many centuries.     

Isaac Newton worked out the laws and concept of motion which lay folk recognise as modern and it was he who proposed gravitational force to explain motion on earth and in the heavens. Newton's concepts did not arise from an intellectual vacuum and his work was influenced by eminent antecedents such as Kepler, Copernicus and Galileo. Simply stated, gravity is an attractive ‘force’ between two bodies dependant on relative mass and the distance between the two bodies. As mass increases so does the gravitational force of that mass. The attractive force between two bodies decreases as the distance between the bodies increases. Newton deduced that the decrease in attraction follows the inverse square rule. Or in other words, doubling the distance decreases the force by a factor of four. Gravity keeps us firmly planted and explains the motions of the moon, planets and even the sun with a high degree of predictability. Gravity is considered one of the four, fundamental physical forces in nature. We feel gravity on earth as a primary force because in relation to us feeble humans, the earth is very large.

Using his concept of gravity, Newton was able to provide an explanation for the motions of the planetary bodies which proved astonishingly accurate. But there was a problem which puzzled Newton and his learned contemporaries. How could two bodies separated by a great distance experience attraction? What was the mechanism involved? How could the sun 'detect' the earth and 'pull' it toward itself? Although Newton was able to describe the effects of gravity, he failed to understand it and never proposed a mechanism of action.

According to Newton, the laws governing motion and gravity were universal and applied to all bodies of mass regardless where they sat in the cosmos. The forces acting on an apple falling from a tree were essentially the same for the moon orbiting the earth. Newton was able to describe motion with the precision of a Swiss watch, or so he thought.

The Newtonian world view was shattered by an unassuming patent office clerk in the 1900s. Einstein's theory, of 'General Relativity' proposes that gravity is not a force at all but the consequence of mass warping space-time. Mass causes space to bend and the 'bent space' determines how mass moves. The greater the mass, the greater space is bent. This is not an intuitive concept, especially as most folk envisage space as not having any discernable  properties. Space is supposedly empty, isn't it? And to make things more interesting, mass also affects time as well. Thus mass, time and space are interrelated phenomena. Space consists of three dimensions and time simply adds a further, fourth dimension. Although, difficult to contemplate, Einstein's 'Theory of Relativity' has proven the best model we have to explain reality. The best analogy is represented in the 'rubber sheet' model represented below. As you can see, a large round object is placed in the centre of a tethered rubber sheet. This object causes the sheet to bend. Another object placed on the sheet will fall toward the dip in the sheet and therefore be 'attracted' to the large object.

a

Is this reality? Not really

Of course this simple illustration only utilises two dimensions. In the real situation we have to factor in at least two further dimensions and perhaps more. An explanation of why mass causes space-time to warp requires a consideration of the concept of 'stress-energy tensor'. A discussion of the physics and sadly, mathematics, is beyond the remit of a simple blog post. For those endowed with an adventurous intellectual spirit, I advise a Google search.

So there you have it, gravity is both subtle and weird, just like this blog.

    

Leibnitz I

Nice Hair Concealing a Massive Cranium

Just a note: I ain't no philosopher; I have received no formal training, and therefore I hold no qualifications in the subject. I am simply an educated individual with an enquiring mind that encompasses several acadaemic topics. I make no pretence of having deep knowledge and understanding of most of what I write in this blog. My particular field of expertise is cellular genetics and biochemistry. With all that said, I have a wandering/wondering intellect that restlessly and carelessly seeks to take part and learn of the marvels of the world. I invite criticism of my work. I will not take offence at contrary comments as long as they are respectful. My wife may call me a 'know-it-all', but we know better. 

According to the esteemed British philosopher and mathematician, Bertrand Russel, the German savant of the 17th century, Gottfried Leibnitz was, 'One of the supreme intellects of all time'. This is quite the accolade from a man who was no intellectual slouch himself. And indeed, the 17th century was a remarkable time, heralding in the 'Scientific Revolution'. Leibnitz's contemporaries included the acclaimed polymath, Isaac Newton- possibly the greatest scientist of all time (discuss). There are others too many to list here. The 17th century was an astonishing century for the production of great folk of intellectual genius. I'll leave it to my readers to seek out other remarkable individuals whose contributions to science, mathematics and philosophy simply boggle the mind. 

This brief post just scratches the surface when it comes to Leibnitz. It is a mere introduction to an introduction. The more I read about this man, the more I am in awe of his intellect. The sheer breadth and depth of his scholarship invite grandeur, and I can only gape in admiration of his achievements in metaphysics, science, mathematics, logic, linguistics, engineering, geology and even computer science. Therefore, this post is just the first in a series that will delve deeper into the wondrous insights of this Great Man. Sadly, Leibnitz is hardly remembered in Anglophone countries these days, except by specialists. Considering his vast contribution to scholarship and knowledge, the lack of awareness and interest in this man is criminal, and I declare that part of the UK curriculum should include obligatory introductory courses outlining his achievements. 

Leibnitz* was born in the German town of Leipzig in 1646 during the dying embers of the Thirty Years' War (another post mayhap?). His father was then a professor of philosophy. Young Gottfried studied law and, at the tender age of 20, obtained a doctorate at Altdorf. A good education of the time required the eager student to be thoroughly steeped in 'Scholastic Philosophy'. This philosophical system was based on the extensive teachings of St Thomas Aquinas (1225-1274). In turn, Aquinas relied heavily on the philosophy of Plato and Aristotle. By the mid-17th century, 'free-thinking' students were starting to rebel against these church-inspired teachings. Scholasticism was becoming to be seen as stodgy, dogmatic, and archaic, with little relevance to the developing ideas of the New Science. Liebnitz was of this ilk and became averse to the malign influence of the 'good doctor' on European universities. A little digression is required: at this time, the distinction between philosophy and science was a tad blurred.  What we would regard as 'true science' was often subsumed under the overarching concept of philosophy. With time, the subjects would part ways and science would achieve wonders, while true philosophy would continue to amass baseless concepts and commentary (a tad harsh and wrong, Flaxen!). Here endeth the discussion.  

Leibnitz was a true polymath, as was his arch-rival, Newton. The days of the polymath are no more. Ever-expanding scientific knowledge and the advent of micro-specialisation guarantee we will never see their kind again. Of course, when discussing Leibnitz, it is impossible not to compare him with Newton. Both men were rare geniuses of a high order. While Newton was an empiricist, Leibnitz placed greater emphasis on rational, logical deduction. Both men invented calculus independently. Leibnitz contribution involved integration, while Newton founded differentiation. A rift occurred between the two scholars concerning primacy. Newton could be exceedingly nasty and spiteful if he felt that his genius was to be challenged. At the time, it was determined, in Britain at least, that Newton was the first to unravel the mysteries of this powerful mathematical system. Modern historical investigation supports this view. Newton discovered calculus first, but was tardy in its widespread reveal.    

After this expansive introduction, tis time for a fleeting look at some of Leibnitz's achievements.

Monadology and Other Philosophies 

Leibnitz's concept of 'Monads' was his metaphysical attempt to apply a universal system to reality. He envisaged that everything was composed of an infinite number of entities Leibnitz labelled monads. Monads represent the fundamental state of everything. They are non-physical and represent a nondivisible unit of self-aware 'force'- ultimately energy. They occupy no space; however, each monad mirrors the entire universe from its own perspective. Leibnitz's Monadology is not as simple as it first appears, as it represents an ambitious attempt to unify everything and overcome a series of philosophical problems under a single concept. Several categories of monads exist, each with its own particular attributes. Thus, there are monads that represent matter, a second class concerns cognition, and ultimately, the supreme monad is a concept of god. As my regular readers are aware, I'm not a great fan of metaphysics. It belongs to a bygone age of intellectual development best left to Ancient Greek Thought and its subsequent expansion in the Middle Ages. Science conquers all. However, I have to make an exception with Leibnitz. His concept of Monadology is expansive, all-encompassing and extremely logical. The more I read about his metaphysics, the more I appreciate its innate beauty and harmony. Tis an impressive logical edifice. In a certain light, it anticipates quantum physics and panpsychism. It is certainly deserving of a deeper delve in a future post. I can't help but think that his ultimate reliance on the 'God Concept' is redundant. However, some free thinkers of the time were not yet ready to discard reliance on supernatural agencies. Educated men of the 17th century were generally pious, so perhaps I shouldn't be too harsh. True naturalistic development would coalesce later, resulting in the discarding of superannuated constructs. Enter the shade of Darwin, stage left.  

Leibnitz wrote extensively on metaphysics and published a treatise on Theodicy that argued that god created 'The best possible of all worlds.' He was heavily criticised and mocked by the French intellectual, Voltaire, for this misplaced optimism. All theodicies ultimately fail due to the inherent evil evident in this world. Why would a supposed all-powerful, all-loving god embed the horrors and unmitigated evils into existence? He also developed 'proofs' for god. His theodicy and extreme advocacy are obvious to the modern mind as sophistry run wild, and his arguments for 'letting god off the hook' are easily revealed as philosophic sycophancy better suited to the brutal Middle Ages. As said, he was a deeply religious man, like Newton, and his philosophy reflects his religious devotion. However, by the late 17th century, his extreme religious views were becoming misplaced and outdated.                 

Calculus and Mathematics Akimbo

I have already alluded to Leibnitz's work on the branch of mathematics known today as calculus. Sufficient to reiterate here that he was not the originator, although his contribution was independent of Newton, and today, we use Leibnitz's notation rather than Newton's. Also, Leibnitz invented a mechanical calculating machine (Stepped Reckoner) that implemented the four basic functions of calculation more efficiently than any preceding machine. This machine was used for centuries and anticipated the fundamentals of computing technology. And let us not forget that he also developed the Binary System, the basis of modern computing. And if this was not enough, Leibnitz made important contributions to the developing field of statistics. 

Engineering

Leibnitz worked on the design of a wind-powered water drainage pump for mines. Although the project ultimately failed, it was an early attempt to combine mechanical power systems and demonstrated his theoretical and intellectual reach, as well as his ability to apply theory to practice.  

Logic

Leibnitz worked tirelessly to systemise syllogistic reasoning by introducing a small number of axioms based on deduction. He introduced algebraic notation to represent logical connections, thereby heralding foundational concepts in Symbolic Logic.  

Final Comment

I will stop here, not because I have come to the limits of this man's formidable achievements and contributions to knowledge. There is more to be said, but that will have to wait for future post(s). Leibnitz was a voluminous writer, and much of what he wrote did not get published in his lifetime. Indeed, the final release of all his work was only completed in the latter half of the 20th century. Russell was of the opinion that much of his unpublished work was actually more profound than his published work. If possible, I will see if I can't tease out some of Leribnitz's more radical and deeply thoughtful musings.      

Gottfried Leibnitz/Leibniz* 

Usually, 'Leibnitz' is rendered 'Leibniz'. My spelling of the name is not incorrect; it is just uncommon. Nuff said.

CHAOS

Father of Chaos Theory

The human condition craves uniformity and certainty. Unpredictability is a gross insult and offence to our sensibilities. That said, we are surrounded by a morass of chaos. Some folk seek rational refuge, but we are a small island surrounded by the havoc of absurdity.

The 17th century was a wondrous time for the relentless march of science and rational thought. After a millennium of intellectual darkness, religion in the West was receding from secular dominance at long last. It was a time for intellectual giants to shine. And of all the bright stars in the rational firmament, none was so bright as Sir Isaac Newton.  Newton's tome, Mathematical Principles of Natural Philosophy (1687), represented a paradigm shift in Science and Mathematics. Newton's scholarship was so profound that the foremost scholars of the day could only gape in awe. Within this seminal work, Newton outlined his new mathematics, Calculus, and utilised this powerful and versatile mathematical discovery to complement and add new light to his laws of motion and gravity.    

Newton's unravelling of nature's laws pointed to a deterministic, clockwork universe controlled by equations that predicted everything. Perhaps the mind of God had become clear, and God was a mathematician.      

Newton used his new-fangled mathematics to calculate the motion of two celestial bodies, the Earth and the Sun. All well and good. However, when he tried to apply his equations to three celestial bodies, he confessed that the problem was beyond solution. His exact words: "...to define these motions by exact laws admitting of easy calculation exceeds, if not mistaken, the force of any human mind." I've discussed the intractable Three-Body Problem elsewhere on this esteemed blog- go seek and find.  

It is time to introduce  King Oscar of Sweden and Norway. The gracious king decided to mark his 60th birthday (1889) by offering a prize of 2,500 Crowns and a gold medallion to anyone who could solve a very difficult mathematical problem. Of the problems submitted, it was determined that the following question should be put forth: 'Is the solar system stable? Would the system remain, as if by clockwork, forevermore, or at some predetermined date, would collapse ensue? A very difficult question indeed. Solving this conundrum meant reevaluating the very equations that Newton considered unsolvable.

Enter our hero, the French mathematician Henri Poincare (b 1854), stage left. Poincare considered himself the man of the day and confidently set to work on the problem. First off, he had to solve the Three-Body Problem. He quickly realised the problem was too difficult and devised a shortcut. Firstly, he imagined two bodies interacting and introduced a speck of dust for his third body. He reasoned that the two bodies would be unaffected by the speck of dust, and thus, they would continue with ellipses around each other. The gravitational force of the two planets would attract the dust speck, and Poincare then attempted to work out the pathway the dust speck would take. The upshot of his analysis showed that the bodies under investigation would exhibit periodic paths, and periodic paths, by their very nature, are highly stable and repeatable. Obviously, the solution fell short of the rubric by a large margin. Newton's insight was vindicated, but Poincare's work set the stage for future contributions. Regardless of failing to come up with a definitive answer to the problem, the submitted paper was deemed impressive enough for Poincare to win the prize. 

A Little Oopsie With Big Consequences

Poincares' paper was about to be published in the Swedish journal Acta Mathematica when one of the editorial staff posed a point of clarification concerning the rounding out of data. Each step in a mathematical proof requires rigorous attention. Poincare had made an assumption that seemed justified in his chain of reasoning. He assumed that rounding out some of his data points by small amounts would not significantly change the overall predicted orbits. He reassured his detractor that his data and reasoning were sound, but just in case, he would double-check. To his horror, he found that even the slightest corrections in his data could result in huge changes in the outcome of orbits (O Bugger!). Unfortunately for Poincare, by then, copies of his paper were already cascading from the press. In a desperate bid to save Poincare's reputation, the next few weeks were spent scooping up copies of his paper to prevent wide readership and limit the damage. Poincare offered to pay for the print run, which ironically exceeded the money gained for the prize.   

In 1890, Poincare penned a second paper discussing the stark realisation that small deviations in the parameters defining stable systems could result in large deviations, culminating in unpredictable instability. His mathematical blunder led to the concept of Chaos Theory—a new and exciting branch of mathematical endeavour. However, it wasn't until meteorologist Edward Lorenz's rediscovery of chaotic dynamics in the 1960s that the concept became widely known. This story and others will have to await the second part of this saga. 

                                                

Gravity is a very naughty force......

The impossible dream?  

The quantum theory of matter, at the level of fundamental particles and energies, has been very successful in aiding our understanding of basic universal reality. Of course, there are many questions unanswered. Although much has been revealed, there still exists a raft of paradoxes (e.g. 'spooky' action at a distance), inconsistencies (e.g. double slit experiment), and enigmas ('spooky' action at a distance + double slit experiment). These notable conundrums should occupy the mind of humankind for many years to come. It is highly likely that our current conception of 'quantum theory' is but an approximation of reality and that a new or modified model will be required to advance that approximation to a new, refined and exalted status. But for the time being our current understanding of the quantum world will have to do.

Since the conception of quantum theory, it has been the dream of physicists to unify all the four basic forces into one coherent whole. These forces, in no particular/particle order, include: electromagnetism, gravity, and the strong, and weak nuclear force. In 1979 researchers working in the US and UK unified the force of electromagnetism with the weak nuclear force to form the concept of the electroweak force. For this seminal work, the three physicists involved won the Nobel prize. So far the union of the strong nuclear force remains elusive but there are sound theoretical considerations that suggest its integration to form the 'magic trio' is a sound practical proposition. To demonstrate the union experimentally will no doubt involve very high energies and physicists are currently working on this problem with apparent gusto. And when I say 'very high energies' I'm referring to the energies present immediately after the big bang. Gravity, is the weakest of all the forces, much weaker than the nuclear weak force, although it has the property to propagate over vast distances. Although the greatest scientific minds of the last century and this century (consider, Einstein and Hawking) have pondered deep and hard on how gravity might be part of this great quantum unity, however, and unfortunately, there has been little progress, apart from the development of untestable hypotheses.

The heart of the problem lies with the nature of gravity itself and our understanding of it. Until the 17th-century gravity was hardly a concept at all. It required the genius of Isaac Newton to formulate 'Gravitational Laws'. Newton's great insight was to recognise that gravity was a force dependant on mass and the equations he formulated accurately described the real world with uncanny accuracy. The greater the mass the greater the force. This force, derived from mass, decreases with distance according to the inverse square law. With regard to two interacting gravitational bodies, the greater their distance from each other, the less the gravitational attraction will be. Newton considered the force of gravity to extend unto infinity. This is a mathematical construct and gravity is unlikely to reach out that far in reality; as an analogy consider Zeno's paradox. I suspect that, in the real non-mathematical world, gravity has a finite spatial extent. This is a common mistake that folk make. When we look at the solution of a mathematical construct we often assume that it must absolutely relate to our physical reality, absolutely. This is not always the case. This does not mean the mathematics is incorrect, it means that the 'real world' is not always in tune with the underlying/ underpinning mathematics; think about it. 

Although Newton was able to describe the force of gravity mathematically, he was at a loss when it came to describing the force itself. He considered his inability to describe gravitational causality to be one of his greatest failures together with his inability to turn base metals into gold; this dual insanity would vex him until the end of his days. Newton's 'Law of Universal Gravitation' explained the movement of celestial bodies in his 17th-century world extremely well. It wasn't until the 19th century that Newtonian gravity was found to be amiss. New observable phenomena and better scientific techniques and instruments alerted physicists to the uncomfortable fact that 'Great Hallowed Newton' had been wrong. So great was Newton's reputation and intellectual standing, in posterity, that it took a while for physicists to fully comprehend that Newton's gravitational postulations had been in error.

The world, and mayhap the universe, would have to await the genius and serial insights of Einstein in the second decade of the 20th century to provide scientific solace and replacement. Thus, Newtonian gravity was replaced by 'General Relativity'. This did not just represent a change, in theory, it represented a paradigm shift- this is arguably a rare occurrence in science, indeed, especially in the modern world (All hail Einstein). General relativity stated that mass warped space and time. Therefore, space and time would be forever intertwined and dance together according to mass, and not just any old disco beat. Thus, our insight has been confirmed, after all: 'fat lassies' cause greater deformation of the wooden dance floor than their less endowed/empowered sisters- ain't dat the sad truth. Arse, big fat, arse= greater gravity.

General relativity explained anomalies that Newtonian physics could not. In fact, not only was general relativity a sound theoretical postulate, but it was also quickly found to be in accord with numerous practical observations. In the 1930s there was the real and exciting expectation that gravity was about to be integrated into the quantum world to produce a single unified quantum field theory, of everything. This, was the holy grail of physics, after all. The scientist(s) endowed with the intellectual clarity and perspicacity to quantify gravity would surely claim a Nobel prize, or two. But the macro effect of gravity remained steadfast and stubborn (nay, obdurate) and refused to join the quantum world of the very small; O bitter the cud! However, there have been several theoretical attempts to incorporate gravity unto the fold, the most interesting is based on string theory. The problem is that none of these postulations have any practical observational support.     

Physicists are optimistic by nature and love order and harmony in the universe of the very small and very large, so they will continue to seek and search for something which may ultimately prove to be a chimaera, albeit a beautiful delusion (ignis fatuus). Perhaps gravity is the 'rogue' force that cannot be tamed and that seeking unity is an untenable prospect. If only time will tell- but ultimately the telling of the time will depend on gravity.

    

Folks may have noticed that my posts have become rather sensible of late: blame it on the medication. It is certainly not due to the sunshine or the boogie. What would my readers like to see? I'm happy to knock out content on a variety of topics, within my ken, including, maths, physics, biology, history, theology, military stuff, and of course cosmology. Just let me know in the comments.  

The Scientific Method

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Scientific method is a body of techniques for investigating phenomena, acquiring new knowledge, or correcting and integrating previous knowledge. To be termed scientific, a method of inquiry must be based on empirical and measurable evidence subject to specific principles of reasoning. The Oxford English Dictionary says that scientific method is: “a method or procedure that has characterized natural science since the 17th century, consisting in systematic observation, measurement, and experiment, and the formulation, testing, and modification of hypotheses.”

http://en.wikipedia.org/wiki/Scientific_method

The scientific method is often misunderstood and frequently misrepresented sometimes by scientists who apply/belie their craft. Actually the 'Scientific Method' is fairly simple in conception. It is this 'simplicity' which understates its power in uncovering new knowledge. It is so simple that men of intellectual quality in times past considered the 'technique' too simple to provide any profound insight into the natural world. The ancient Greeks, a few notable exceptions aside, did not consider scientific induction worthy of contemplation. All useful knowledge, or so they thought, could be obtained by thinking very hard about a subject or by the dialectic. Now it is true that certain areas of knowledge are amenable to these techniques: logic and ethical considerations do well under these circumstances. But a great swathe of knowledge is denied if we rely on deductive reasoning alone.

The rise of the scientific method and thus science from the 17th century onward is responsible for the explosion in our technological advancement. Fascinatingly, Newton thought and wrote copiously about theology and alchemy but he is only remembered for his scientific and mathematical achievements; I wonder why? As an interlude, I will venture to say that all theology and the notion of faith is no way to obtain insight or knowledge about anything. While theology and religion(s) may be valid topics for the philosopher and psychologist, they play no part in science and no part in the revelation of knowledge by induction.

All science begins by an observation about the world in which we inhabit. The observer then posits an explanation, or hypothesis. This is the stage where the Ancient Greek philosopher would stop. He may have elaborated on his initial musings but he rarely tested it.

The true scientist challenges a hypothesis by experimentation. A single variable is changed and the chase begins anew. Is the subsequent result in accord with the hypothesis? If not the original hypothesis must be discarded in its entirety and a new hypothesis proposed or the original hypothesis is implored to undergo modification to fit impudent experimental results. In real science the initial experiment is repeated many times. New experiments are devised and the hypothesis is examined thoroughly and from many angles. If the hypothesis stands up to experimental rigor it may advance to the next stage and become a theory- a model for understanding a particular process. It may even enter the canon of existing knowledge (shit happens). But good science should not rest on its laurels. New and often ingenious, nay devious, experiments should be devised and so the work continues. A good theory should try and explain a phenomenon remarkably well. It does not have to be perfect. Any established explanation should be subject to change given new evidence. As an example, I'll consider Newton's laws of motions (good man, that Newton).

Actually, I've used this example elsewhere, but as it is such a good one I reckon its worth reiterating. When Newton described his theories in the mid 17th century they explained the natural world exceedingly well. All observations, of the time, pertaining to bodily motion conformed to Newton's will. Surely this was the last word on the matter? Twas destined that Newton's laws should be engrained into scientific certainly for an eternity (steady Flaxen, you are starting to wax lyrical).

Scientific theories should always be taken as fluid; open to change /challenge or frank abandonment. And indeed, by the early 20th century it became clear that the 'Newtonian Model' did not explain all aspects of stellar motion and small discrepancies had become apparent. However, so great was Newton's reputation that few researchers were willing to dispute Newtonian mechanics and most very happy to embrace observational error as a resolution to the problem. Furthermore, while Newtonian mechanics was able to describe the force of gravity, Newton freely admitted that he had no idea what that 'force' might entail.

Then along came Einstein. Einstein had the intellectual audacity to suggest that the 'Newtonian System' was not the last word. Not only did his theories of relativity explain the world better than the established system but he even had a mechanism which explained gravities' elusive force at a distance, at least to some folk's satisfaction. According to Einstein, gravity is a mere artefact of mass warping space-time- go figure. Relativity never appeals to common sense, intuition or even logic. And all this without a single practical experiment. Einstein got by with 'thought experiments'. Only a bona fide genius should subscribe to this methodology. Please don't try this at home.

 

In conclusion, science methodology not only produces the ever lasting light bulb it also gives us access to all knowledge that ain't math. If you think to the contrary I would challenge you to consider anew or at least challenge the author to comment, anew. To be honest I relish well thought out and intelligent debate. Arse.

The Triumph of Science in the 17th Century

 

Behold the countenance of two Great men

Following my much awaited previous post: ‘The Life and Times of Sir Thomas More: an Exposition in Sepia’, I thought it profitable to introduce a topic very dear to my heart- the rise of science in the West, during the 17^th century.

Our modern world owes much, and has been shaped by the rise of the scientific process in the 17^th century. The noted men of science, in the 17^th century, are of a different intellectual temperament than their predecessors in several, important and fundamental ways: they no longer demand the asceticism that the ancient and medieval scholars felt was of paramount importance. Previously, a hypothesis had to be ‘beautiful’ or ‘perfect’ according to prevailing notions. Thus, celestial motions had to be perfectly circular as a circle was deemed a perfect figure, according to ancient Greek philosophers. When Kepler, in the early 17^th century demonstrated that the planets followed elliptical orbits, contemporary savants were horrified (it was going to get a lot worse); scientists began to understand the importance of astute (and accurate) data gathering as an important prelude to formulating their theories. This was something that many found irksome but necessary for exactitude; the application of the scientific method. The scientific method is simplicity itself but had been sorely neglected, or undervalued, in preceding centuries due to the baleful intellectual influence of the great ancient Greek philosophers who favoured deduction over induction; the break with the philosophies of Plato and Aristotle. The works of these great ancient philosophers were held in great intellectual esteem even though these works had been formulated nearly 2,000 years ago. Men of intellectual quality, in the 17^th century, came to realise that Plato and Aristotle were in error on all areas of their ‘scientific’ endeavour.’ They began to realise that the reverence for these ancient Greek scholars had stymied scientific investigation for 2,000 years. This was a shock but also a goad to press on into exciting uncharted scientific territory, anew. There are other salient factors to be considered, however, these are of lesser importance and for brevity they will be omitted (arse, bucket akimbo, arse).

Clearly, the 17^th century was an amazingly fertile period for scientific investigation. The word ‘genius’ is banded about with sickeningy frequency in our modern world. Let me be clear: Newton was a genius and so was Tesla- John Lennon, for all his talents, was not. The list of individuals, of true genius, during this period is astonishing and without prior precedent. Let us ponder a few of the greatest scientists in history.

Galileo (1564-1662) kicked off and founded the scientific revolution although it is undoubted that he was influenced by notable and important, earlier savants: Copernicus; Tycho Brahe and Kepler. Galileo is remembered for his work/laws on motion- I don’t have space to write about them here. Galileo was also the first to use the new fangled (not a real word) telescope thingy to scour the heavens and made some very significant discoveries in the field of astronomy. His astronomical observations and his acceptance of the heliocentric model quickly aroused the ire of the Catholic church and poor old Galileo was forced to recant, thus destroying Italian scientific investigation for centuries to come.

Newton (1642-1727) is an extremely interesting topic for discussion. I wrote a a post about him several years ago: find it here. Newton was a genius’s genius, a man of profound intellectual gifts, but he was also exceedingly odd. Although scientific in the conventional sense, he performed a lot of work in the area of Alchemy in the misguided notion that he could turn lead into gold. He was extremely pious, secretive, disputatious, petty, peevish, timid and a life long virgin. For all his genius he would have been a rather dull dinner guest. Newton contributed to the science of optics, light, astronomy (invented the reflecting telescope), formulated the theory of ‘Universal Gravity’, formulated his famous three laws of motion and founded integral calculus. Quite an achievement for one man! In addition, Newton wrote voluminously on religious topics, multi-various (twat).

Gottfried Leibnitz ( 1646-1716), deserves a honourable mention. Although not primarily concerned with science, he made innovative contributions to mathematics, including being the co-founder of differential and integral calculus, with Newton, and created the modern binary system. As an aside, Newton and Leibnitz did not collaborate on the discovery of integral calculus (nuff said). Leibnitz was essentially a philosopher, and his contribution to philosophy was the introduction of Monads, go read, for it makes for an interesting story. I will say no more about Leibnitz as most of his work is outside the remit of this essay, except, that to my mind, he ranks as one of the greatest intellects to have ever lived, together with Newton, Pythagoras and Archimedes (prove me wrong in the comments- if you dare).

There is a litany of great men who made their indelible mark on science, in the 17^th century. Here is a list (not exhaustive, nor complete) of the prominent, great men of science, of the 17^th century. Each made admirable contributions to science and/or mathematics. Sadly there is no space to consider these men in detail, each require a separate post; keep tuned in: Blaise Pascal; Robert Hooke; Van Leeuwenhoek; Huygens; Halley; de Fermat and etc, and etc.

We are apt to forget the singular and profound importance of the 17^th century as a modernising influence on the men of intellectual quality who subsequently changed the world. Most of our modern science is based on, and follows upon 17^th discoveries. Perhaps of more importance is the change in the temper/timbre/tempo of mind that occurred. Nothing in the past could compare, and it remains with us today as a thoroughly modern scientific mindset. What a legacy! The importance of this intellectual revolution is worth stressing, especially because of its rapidity in societal terms: in the year of our Lord, 1600, the mind set of educated men was medieval; in 1700, the mind set was thoroughly modern. In England of 1600, witchcraft trials were still in vogue; this would have been unthinkable 99 years later. In addition, human kind had been humbled. No longer was our insular little bubble the centre of the universe. Everything had to be revaluated in terms of our utter insignificance. Church doctrine lagged behind, by degrees. The Catholic church outlook is essentially medieval to this day.

The Aether

"To deny the aether is ultimately to assume that empty space has no physical qualities whatsoever"   

Albert Einstein

Aether, the intractable and intangible aether: the substance that never was, perhaps. The concept of 'The Aether’ has a long and delectable history. Aristotle in the 4th century BC theorised that the aether was the 5th element and together with the four terrestrial elements, earth, air, fire, and water were essential components comprising the divine universe. However, the aether was altogether superior to its four lesser earthly elements as Aristotle considered the heavenly bodies solely formed from this mysterious substance. As the West began its ascent from the intellectual miasma and stagnation of the ‘Dark Ages’, sometime in the 13th century, the concept of ‘aether’ transmogrified into the quintessential element of alchemy. 

Like the ancients, medieval scholars considered the aether divine but it was not confined/consigned exclusively to the heavens. It was envisaged that all things on earth, even humble rocks, partook of the divine nature. The aether was bound and invisible and could only be perceived and let loose by God. The great polymath of the 17th century, Sir Isaac Newton, was a firm adherent of the aether. For Newton, the aether was an elastic medium permeating all space and its presence was essential for the propagation of vibrations. Most folk, if they consider him at all, think of Newton as a hard thinking rationalistic scientist, and there is some truth in this. However, Newton had a dark irrational side and was a fervent follower and practitioner of the pseudoscientific activity of alchemy. After Newton’s death, his ‘work’ in this area was actively suppressed by a scientific community fearing ridicule.

The Dutch scientist, Christian Huygens (d 1695) considered the presence of the aether essential for the propagation of light waves. By this time Newton’s conceptualisation of light as consisting of particles (corpuscles) had fallen into disfavour due to lights demonstratable wave-like characteristics. Of course, Newton’s corpuscular theory would reemerge when it was discovered that light could behave, depending on circumstances, as a particle or a wave (wave/particle duality).

By the 19th century, the aether was becoming rather troublesome. For here was a substance that was supposed to fill all space but it stubbornly remained invisible to scientists and it could not be measured or detected- a most perplexing phenomenon. In 1887, Michelson and Morley designed the ultimate experiment (at least to their mind) to determine once and for all whether the aether was real or whether it was a figment born of a phantasm spawned by a fancy....... Our intrepid scientists reasoned that light should travel at different speeds as it traversed the aether in different directions. As the earth rotated through space/aether, it should generate an ‘aetheric wind’ which would slow down light beams travelling contrary to the earth’s orbit. The experiment was set up in a basement and the apparatus was set upon a large pool of mercury for stability and accuracy. The experiment showed no evidence of ‘light drag’ and thus the concept of the aether was abandoned. Physicists had to face the strange conclusion that light travelled through the vacuum of space without a meddling, mediating, manifold, medium, manifest.

By the 20th century, and after 2,000 years as a cogent theory, ‘The Aether’ seemed well and truly discredited. There was still the problem that all known waves, except light, required a medium through which to travel. How can light waves be propagated in the vast vacuum of space without a propagating substrate? In our modern age, it has become clear, that the empty vacuum of space is not as empty as first thought. Space is imbued with a quantum field: atoms come into existence and disappear spontaneously and the fabric of space is capable of expansion, therefore, resulting in cosmic inflation. It was hoped that Einstein’s theories of relativity would one day provide a grand unifying theory of physics, but this has not been the case. While Einstein’s genius was able to explain the universe of the very large and very fast it has not been so successful at the quantum level. Leading physicists are contemplating the unthinkable: Einstein’s theories are not the answer and another theory awaits to fill the void- an overarching universal paradigm that will unite the quantum and cosmic worlds. It has become apparent that Einstein’s special and general relativity theories are at odds with the newly acquired and elusive concepts of dark energy and dark matter. Although we haven’t been able to observe this exotic non-baryonic matter and energy it is likely to be the driving force in the universe's expansion. Indeed, according to current cosmology, 68% of all energy in the universe is present in this occult (I mean 'occult' in the hidden sense with no reference to the supernatural) form. Mayhap dark energy is the force pervading all space and hence it may not be scientifically impudent to call it the fifth force of the universe or aether. Thus after a hiatus of 100 years, the concept of 'The Aether' is making a come back in serious scientific circles. If it does exist as a real quantum phenomena, then we should be able to detect its presence, eventually. If not, it will have to remain as a powerful, but theoretical concept. From this scientific darkness, we await enlightenment.