Raymond Levine
The Sleepwalkers: The Story of Mankind’s Vision of the Universe and Mankind’s Own Place in it

Raymond Levine | The Sleepwalkers: The Story of Mankind’s Vision of the Universe and Mankind’s Own Place in it | 05.20.24

Visuals displayed throughout the presentation.

- Well, good evening or morning or afternoon depending where you are. This talk is entitled, “The Sleepwalkers,” and as the caption shows it’s a story of mankind’s vision of the universe and mankind’s own place in it. It’s a story through space and time of motion and inertia, knowledge gained then lost or forgotten and later rediscovered, a journey through philosophy, theology, a priori thinking and empirical experimentation, astrology and mysticism, and above all creative thinking stumbled upon just like a sleepwalker. And before I start the story, I must just show you, I hope you can see it on your screens, the book, which is the main inspiration for this talk. It’s called “The Sleepwalks” like this talk and it was written by Arthur Koestler in the late 1950s. I read it 20 years later and it’s been on my bookshelf ever since. And it’s one of the more influential books in my own journey through life.

So I am hugely indebted to Koestler for a lot of this material and I hope some of you may think the book is worth buying and reading. I certainly believe it is. So our journey starts with the unknown stargazers in the towers of Babylon. Next slide, please. And here they are in a somewhat stylized form and before them there were the Chaldean priests in the cities of and elsewhere who believed the planets and stars they could see with the naked eye were in fact gods whose wishes must be divine by close observation. Next slide, please. Again, pretty stylized, but they didn’t have good portrait painters in those days. Now, so close that some of their observations are surprisingly accurate when set against modern ones with the most sophisticated of telescopes. This was not just an academic or theological pursuit, it affected the society’s very existence.

For example, the creation of accurate calendars to predict seasons so crops were sewn and harvested at the optimum times. Now the rulers of these cities had different priorities, although feeding the people was important to their survival, they believed that the gods were more important and had a greater role to play hence their interest in astrology or divining the god’s wishes unlike the actions, this was a matter of states. Let’s now move to Greece, specifically the Greek islands of the and the adjoining shores of what is now Turkey. The earliest Greek writers have various views of the universe, but the coherent system didn’t appear until the insights of Pythagoras of Samos in the sixth century BCE. Pythagoras is said to have influenced the ideas and destiny of humanity to a greater extent than any other single person before all . Next slide, please.

And again, still very stylized, but you can see him holding an astronomical instrument, probably a very primitive astralaide but I don’t think that was invented till much later. Now, Pythagoras was much more than a mathematician, he was also a philosopher, a musician, a medical practitioner, and an astronomer, a true polymath. His greatest achievements was perhaps his theory of the harmony of the spheres in which he combined his musicology discoveries with his astronomical observations to create an insight into the divine organisation of the universe. To Pythagoras numbers were sacred.

Now he was convinced that the planets were spherical and free floating in space and that according to his , they moved, no flat earthers for sure. Though he did believe that the earth is at the centre of the universe, which is a major part of this story. It was not until several centuries later that one of his followers, Aristarchus also of Samos born in 310 BCE, placed the sun at the centre of the universe. This was a giant step forward. It was not seen again, at least in Europe for another 1700 years. Next slide, please. Again, somewhat stylized, but you can see the image of the sun right at the centre of what will in due course become called the solar system. Now this is indeed a paradox. We think of science and for that matter all of human endeavour as a steady progression in the sense that once known or discovered the advancing knowledge is never lost, that becomes the building block on which the next advance is made. That is a conceit not supported by the evidence.

Why did this happen? Did thinkers just forget the work of Aristarchus or was it no longer considered relevance and worthy of preservation? These questions have long been argued over. Perhaps the most useful explanation is that the rise of Christianity in the Greek speaking world in the first four centuries of the common era led to an emphasis on theology and introspection at the expense of what we know as science but what earlier generations called natural philosophy. Charles Freeman wrote a brilliant book on this called, “The Closing of the Western Mind.” Again, I will, for those who could see it, I hope you can, I’ll display it on my screen. It was written some years ago now and he explains how the church and the Roman emperor came together to impose a single view of orthodox Christianity. This was all in fact taking place not in Rome but in Constantinople to where the empire had moved under Constantine and which was really the centre of the early Christianity.

So they came together in a council. The intention was to impose a single view of orthodox Christianity with all other views declared heresies driving their leaders out of the empire and in some cases, as far as China, can we see the next slide please? And do you see that the council of Constantinople? There is the Emperor Theodosius on his throne with his crown. The guys to his left as we look at the picture are the church fathers and bishops and you can see at the fronts that there’s the picture of what looks like a devil, no doubt, helping to identify the heresies or perhaps embodying them. Now from this, the empire gained a social unity, making it easier to govern. The church moved closer to power. Some might call it an unholy alliance. This was devastating for three thinkers. The results was self-censorship in aid of a safe life, something which has echoes in our own age. In time the philosophical schools were closed, the libraries destroyed or dispersed, and the knowledge was lost, at least in Europe.

It was not that there were no thinkers capable of developing the Greek learning rather that most of them were just not interested or less charitably saw no useful career progression in it. There were a few important exceptions, William of Ockham, Abelard in Paris, and Nicholas of Cusa and of course and Thomas Aquinas who contributed to what survived of the ideas of Aristotle. In fact, so far as cosmology and other sciences are concerned, Aristotle’s adherence delayed some major discoveries. For example, because Aristotle taught that the only possible natural motion of celestial or terrestrial bodies was in a circle or a straight line. Cosmology went into decline after Aristarchus or more accurately into a dead end. From the first century CE until the 16th and beyond, it was dominated by the thoughts of Claudia’s Ptolemy, a Greek working in Alexandria. Next slide, please. There he is with an allegorical figure of astronomy standing behind him. Now following Aristotle, which he largely did, Ptolemy adhered to a geocentric view of the universe with the planets and the sun moving in concentric circles around the earth, which he thought didn’t move. So far so good or so he thought.

However, he then found that this model didn’t account for the motion of the southern planets as actually observed by himself and by others. He therefore resorted to an assumption of motion involving circles within circles in order to achieve conformity with observed data. This was a highly theoretical system which could be seen to bear no relationship to anything in the real world. It was purely a mathematical device to and I quote, “Save the appearances or the phenomena,” as it was called. Now it is hard to imagine a more compelling destruction of the idea that progress is inevitable and it is ever onwards and upwards on the road to knowledge. It took some 1500 years to even start to undo the damage caused by the system. Food for thought. The discover of the heliocentric system is as every school child knows, under Nicholas better known as Copernicus. Let’s see him. Next slide, please.

He lived and died in East Prussia near the Baltic Sea then as now an outpost of civilised Europe. Except he wasn’t the discoverer as we’ve already seen that accolade goes to Aristarchus. No doubt he wasn’t the first and certainly wasn’t the last to get credit for someone else’s work. Not that he sought the accolades, he was known to some as the timid canon. You look at this depiction of him on your screen, you’ll see he does indeed look fairly timid, but the main reason is because having written 30 years earlier, his great work on the heliocentric system called on the revolutions of the heavenly spheres, he insisted, excuse me, he insisted that it should not be published until after his death, a wish honoured after his passing in 1543. That’s around 70 years of age. Was he the first great astronomer of the European scientific revolution as it came to be called? Not really.

He was a man of the middle ages and apart from abandoning the model, he got most other things wrong and was by no stretch of the imagination, a champion of free thinking. He preferred to adhere closely to the rules of the church. He followed Aristotle in believing that the planets moved in concentric circles but he did understand that this view was not consistent with observed data. He also believed that the planets moved at constant speed, no doubt, again following Aristotle. And so again in error. His reluctance to publish with the benefits of hindsight is said to be because he feared retribution from the church for teaching a doctrine contrary to scripture, however, his writings were only placed on the index of prohibited books some 70 years after his death and were never prescribed as heretical. It seems more likely his reluctance to publish was based on the fact he knew his writings contained errors and was afraid of ridicule amongst the educated elites of Europe.

So how come such an intellectually conservative man discovered a world view unknown in Europe in his time. He was not in the same league as the other mediaeval philosophers and think has already mentioned in passing. He left no writings outlining his thought processes and precious little on his methods. His book on the revolutions of the heavenly spheres did not refer to Aristarchus in the published edition though Copernicus’s own manuscript did with the name then crossed out in ink. Although speculative, one possibility is that he borrowed the idea from elsewhere. It was probably not Aristarchus’ directly as there’s no record of Aristarchus’ work surviving in Europe in the late mediaeval period. What gives the thoughts credibility is that his work did survive elsewhere along with other works of Greek philosophy and science and that place was Central Asia in the area now comprised in Eastern Iran or Uzbekistan, Turkmenistan and Afghanistan.

They were all parts of greater Iran during the period of roughly the 9th to 13th century CE. We might ask why Greek was known in this region that stems from his conquest by Alexander the Greater, the 320s BCE and the subsequent foundation of a Greek state called centred on present day Afghanistan. It had an important role in preserving the Greek language and culture, including of course its scientific and philosophical achievements. The key link is a man called, Nasir al-Din Tusi who flourished in the 13th century. An Iranian polymath who was influential in many fields of learning. In this context, however, he’s known for his work as an astronomer in a purpose built observatory and there would be nothing comparable to that in Europe for another three centuries. Al Tusi was concerned to iron out faults in the system rather than overthrow it but he is credited with the view that spheres which rotate on their axis are more compatible with own observations than Ptolemy’s own view that the earth is stationary. That was a position later adopted by Copernicus and it’s widely accepted that Copernicus made use of Al Tusi’s work.

Copernicus couldn’t read Arabic, the main language of learned writings in Iran at that time, but he could have found someone who did perhaps a Jewish scholar from , Abner of Burgos is a possible candidate. Alternatively, the knowledge could have come through the Byzantine Greek scholar Gregory Gennadius. Others claim that Copernicus could have arrived at these conclusions independently, perhaps influenced by work and his known dissatisfaction with Ptolemaic theory, we may never know. Al Tusi made very accurate tables of planetary movements for calculating the positions of the planets and in which he gives the names of the stars. His model for the planetary system is believed to be the most advanced of its time and was used extensively until the developments of the heliocentric model following Copernicus, which brings us neatly to the next major European astronomer, Tycho Brahe. Born into a wealthy aristocratic family, he built the first well-equipped observatory in Europe on the isle of , I apologise for my pronunciation of the Danish.

It was a gift from the king of Denmark who also funded the cost of the observatory as part of his support for humanist learning. Next slide, please. And as you can see from his picture, Tycho was also famous for his silver nose following an injury in a duel. He was in every other way quite unlike the timid canon Copernicus. The latter is said to have made only 27 astronomical observations of his own, whereas Tycho devoted his life to it. He was passionate to the point of obsessiveness about precision in his measurements. In both the ancients and mediaeval world he was without equal except perhaps for Al Tusi. But his obsession did not mean he lacked ambition far from it, he was appointed by the Holy Roman Emperor, Rudolph II as the imperial mathematical, an office whose main roles seemed to cast horoscopes and took up residence in Rudolph’s glorious and enlightened capital city, Prague to show once again that science does not move ever onwards and upwards.

Tycho did not support Copernicus’s heliocentric system and continued to believe the earth was the centre of the universe. His own vision based on Ptolemy never gained much foothold in academic circles and there is no theory of the universe associated with his legacy. That said, his observations meticulously recorded were the stepping stones to the next great discovery. Could we have the next slide, please? Now his salvation was his good fortune to be alive and working at the same time as the younger Johan Kepler, displayed on your screen. In time, Kepler became the first giant of European astronomy and succeeded Tycho as the imperial mathematics. He came from a modest background and enjoyed none of the early advantages of Tycho. Nevertheless, after both had achieved some renowned for their work, they developed a kind of codependency in that Tycho recognised in Kepler, a man, perhaps the only man who was capable of fashioning a new vision of the cosmos from his Tycho’s observations. Kepler for his part knew that he could spend a lifetime making his own observations and still not even approach the body of work already recorded by Tycho.

Like Pythagoras, Kepler first understood the cosmos as an analogy with music. He intuitively felt that the laws governing the planets were harmonies. This astronomy was the study of the music of the spheres. Like Isaac Newton after him, Kepler was heavily influenced by mystic faith straining to fathom the mysteries of heaven. Though he also had a modern mechanistic understanding of the world, therefore strode the watershed and it was that approach which led to his groundbreaking work in establishing the laws of , which today bear his name. Mathematics was at the core and by suggesting that the act of creation involved God applying a preexisting geometric model, did he make God redundant? Recognising his inner conflict in these matters, Kepler shared his thoughts with his academic circle and kept his head down in public. A wise course of action for a philosopher about to change how mankind saw its relationships of the universe.

It is worth noting that in the words of Arthur Koestler “After an immense detour, Kepler, a tortured genius who shared all the contradictions of his age, became enamoured with the Pythagorean Dream and on this foundation of fantasy by methods of reasoning, equally unsound built the solid edifice of modern astronomy. It is one of the most astonishing episodes in the history of thoughts and an antidote to the pious belief that the progress of science is governed by logic.” So firstly, Kepler demolished the notion that the planet’s orbited in a perfect circle. Through meticulous observation and use of Tycho’s data, he was able to demonstrate that the orbits were ellipses, not circles. Can we see next slide, please. You see, ignore the bottom diagram. The one at the top is a circle and you can see that it has a centre by the blue dots. The one below it is like a flattened circle, that’s an ellipse. It also has a centre with the black dots, but you can see that it’s shown as having two focal points, F1 and F2, whereas the circle also has two focal points, but they’re in fact in the same place at the centre.

So F2 equals F1 on the top diagram. Now it follows from the fact that, Keplar saw the earth’s motion as an ellipse that the sun is not really in the centre of the orbits. It would’ve been if had it been a circle, but in an ellipse he believed and showed that the centre was aligned with one of the two focal points. A further consequence was that the earth and the other planets varied in their distance from the sun. You can see looking again at the middle diagram, if the sun is at F2, it gets very… The earth gets very close at its orbit when it nears F2 but is very far away when it’s at the F1 end of the orbits. In fact, the real ellipses are not quite as flattened as they’re shown on the diagram, but in the case of the earth, this difference is measured at about 3 million miles out of an average of 93 million earth to sun. And this, the elliptical orbits, was the first law of planetary motion. His second law is that, a radius joining any planet to the sun sweeps out equal areas and equal lengths of time.

This simple law, well, simple to a mathematician anyway, destroyed the belief in planets having a constant or uniform motion as Aristotle and Copernicus had believed. The effect of the second law is that the nearer a planet is to the sun the faster it moves and conversely it’s slowest when it’s furthest from the sun. Next slide, please. Here you see the planet’s moving. The red circle is moving at uniform motion because it’s a circle. The others being ellipses are moving at differing motions depending where they are on their orbits. If you look at the purple one on the extreme right, you see how it speeds up as it gets near the sun and then really slows down and starts to get overtaken by others inside us and then as it comes round towards the sun, again, speeds up and shoots past them. And that illustrates the second law of motion. Kepler also described the heavenly motions in geometrical terms positing that the outer planets took longer to complete one orbit of the sun, not only because they were further away, but also because they travelled on average more slowly. This was his third law of planetary motion.

Now, Kepler also assigned a physical course which in itself was revolutionary, namely a force emanating from the sun, but it needed Isaac Newton to correctly explain this as the force of gravity pulling the planets in towards the sun. That of course if that is all that there was, they would fall into the sun and cease to exist. So that force was balanced by a centrifugal force of the orbits, which pushed them away from the sun. But what Kepler’s theory did was mark a transition to a worldview which was explained in terms of forces rather than spirit turning mythology and religiosity into mathematical imagery. Now, although Kepler was a man who had left the mediaeval world behind, he’d not yet completely entered the modern mechanistic world. He was like Pythagoras strongly influenced by mystic belief and arrived at many of his insights by a process of intuition and not all of his theories stood the test of time. He himself abandoned some for lack of proof when he found his calculations of the orbits of Mars differed from Tycho by just eight minutes of arc.

That is by less than one eighth of one degree, he completely revised his theory, which had taken him years of work to construct rather than do what others had done and ignore the discrepancy as just a sort of rounding error. In this, he underlined his status in the modern scientific world. Kepler instinctively knew that Ptolemy and Copernicus were wrong, but at first he wasn’t sure why there was something going on in his mind which enabled him to intuit where the answer lay, even if it took a long time to find it, at least he was asking the right questions. So those who object that his discoveries could only have been made by using logic, the repost would be yes, but you must first know what you are looking for that comes from somewhere else, which we call intuition. And intuitive thinking is more common than is usually acknowledged. When presented with a problem we often intuit the answer or in other words, we know or think we know instinctively what it is.

We then go on to find a logical justification for that answer. The logic comes after the events not before. Unlike Copernicus, Kepler’s correspondence and writing left copious amounts of detail are both of his vacillations and self-doubts and are fascinating insight into the creative scientific process. This prompts the title of this talk, The Sleepwalkers, indicating the half waking, stumbling around whilst somehow keeping one’s orientation and not crashing into objects barely perceptible to a sleepwalker. If Kepler’s laws are more strictly their value to scientific endeavour and the wider world of commerce, navigation and everyday life, were not always clear to Kepler, it should not surprise us when others didn’t appreciate his work. One such was Galileo Galilei, contemporary of Kepler working in Padua and later in Tuscany. Luckily he was more appreciated in England where Isaac Newton effectively rounded out and completed Kepler’s work with his laws of motion and mechanics involving the explanation of the force of gravity, which Kepler himself had come close to discovery. Excuse me.

But never quite made it. Our view of the world is no Newtonian to this day. Relativity and quantum mechanics have not yet changed that though they might, at least for the few who can understand them. The reason could be that the newer physics set the limits of Newtonian mechanics, but those limits are so far beyond our lived experience as to be virtually meaningless in everyday life. But back to Galileo. Next slide, please. Yes, looks a little grumpy. Doesn’t see. He’s possibly the greatest enigma in European history. He’s famous today, he is the inventor of the telescope and a great astronomer who is persecuted for his modern scientific beliefs by a cruel and ignorant church. This is a partisan view is stowing greatness on him where it is undeserved whilst submitting the more justifiable reasons to praise him. Again, to quote Koestler, “Galileo did not invent the telescope nor the microscope, nor the thermometer, nor the pendulum clock. He did not discover the law of inertia nor the sunspots. He made no contribution to theoretical astronomy. He did not throw down weights from the leading tower of Pisa and did not prove the truth of the Copernican system.

He was not tortured by the inquisition, didn’t language in its dungeons did not say, and yet it moves and he was not a martyr of science. What he did was to found the modern science of dynamics which ranks him among the men who shaped human destiny. It provided the indispensable compliment to Kepler’s laws for Newton’s universe. As Newton himself said, "If I’ve been able to see further, it was because I stood on the shoulders of giants and those giants were chiefly Kepler, Galileo and Descartes.” Others are a little kinder to Galileo. Einstein describes him as the father of modern science. He justified this by saying that pure logical thinking can give us no knowledge whatsoever of the world of experience. All knowledge of our reality begins with experience and terminates in it. There was a man who also said he doesn’t believe that God plays dice with the universe. He was perhaps closer in spirit to Kepler.

Apart from discovering the moons of Jupiter by observations through a telescope made by Galileo, but based on a prototype invented by a Fleming, he contributed little to astronomy. He developed no new theory of the universe, although he was a strong defender and advocate of the Copernican system. If he had any knowledge of Kepler’s laws, he did not appear to use them. The legends which surround him are in part due to his supreme confidence in his own abilities and in past his disdain for those of others, he also had a way with words which made his work widely accessible but did not always endear him to those who might otherwise have been sympathetic. One such was Matteo Barbini, an early friend and supporter of Galileo. But after being as a simpleton, Galileo created a character called simplicity, widely thought to be Barbini. He became less supportive and perhaps this was also because Barbini had by then been elected as and had wider considerations of the purely scientific.

These included the authority of the church as the sole interpreter of scripture, as the Word of God. Although this role was already in serious, perhaps terminal decline, it still had some importance in the 17th century. Some thought that the Copernican system supported by Galileo was inconsistent with scripture, but of course this wasn’t really the issue. What was at stake was the church’s authority and everyone knew it. The church’s solution was a pragmatic one. By all means teach Copernicus as a theory, a mathematical exercise according to mathematical principles, but don’t assert, it is true, truth belongs only to scripture and its interpretation belongs only to the church. The face saving formula whilst leaving scientists a considerable amount of freedom to pursue scientific matters. Galileo was ambivalent on this. At certain times he humbly accepted the doctrine and renounced his belief in Copernicus that others the indignantly asserted his right as he saw it, to speak the truth again as he saw it.

Now to our modern ears it goes without saying that he should speak out for what we might refer to as his truth, but that was not how it was done in his day. His defiance, arrogance as it was seen at the time, lost him sympathy amongst his friends and supporters inside and outside the church and led to his censure an eventual trial. Although convicted, he was not harshly punished being sent to a very comfortable type of house arrest. His reputation, however, was badly damaged and he was said to be a broken man. But only a few decades earlier, a philosopher had been burnt at the stake in The Campo de'Fiori in Rome for daring to doubt, a literal interpretation of the Bible and showing support for a heliocentric world. Perhaps today the star burns more brightly than Galileo’s. In an insightful comparison, Koestler says, “Galileo was utterly devoid of any mystical contemplated leanings in which the bit of passions could from time to time be resolved. He was unable to transcend himself and find refuge as Kepler did in his darkest hours in the cosmic mystery.

He did not stand aside the watershed. Galileo is holy and frighteningly modern.” In a sense, this brings our story to an end. The final building blocks were provided by Isaac Newton, the most famous English scientist of his day and ours. It is sometimes said that his greatest achievements was in finding Kepler’s laws hidden as they were in dense, rambling works virtually unreadable. And at times it seemed that even Kepler himself couldn’t make head nor tail of his thoughts. Not only did Newton find them, but he also saw their significance and crucially what was missing in order to connect them to one another. In doing so, he had the benefits which Kepler did not, but more advanced mathematical tools such as differential or infinitesimal calculus, which he was the first to use despite the claims of and analytical geometry, the credit for which is generally ascribed to Descartes.

By explaining gravity as a force acting between bodies at a distance coupled with the effect of a centrifugal force caused by the rotation of the body, Newton supplied the missing link in Kepler’s mechanistic worldview. It all became beautifully self-evidence. It was as if the roof had been provided to four disjointed walls. It was also the final nail in the coffin of Aristotelian physics. The crucial achievement was to demonstrate that theory fitted the observed behaviour of the cosmos, and to express this in precise mathematical terms, namely the force of attraction is proportionate to the attracting masses and diminishes with the square of the distance. The so-called inverse square law, which explains why bodies are weightless in space where the force of gravity has diminished to almost nothing. Next slide please. And you can see the orbit of the moon around the earth with the earth and the moon pulling on each other, but because the earth is the greater mass, the gravity keeps the moon in its orbit around the earth. Applying the force to all bodies from the largest to the smallest was revolutionary.

And without the proof, would no doubt have appeared just a mystic stream. In arriving at this conclusion, Newton made use of Galileo’s work of the orbit of the projectile on earth as well as capitalists on the orbits of the moon. This can be seen as under underlying the importance of synthesis as the final insight following analysis and breaking up of what has gone before. Like every creative act, which is a process of disintegration preceding a new synthesis comparable to the dark night of the soul through which the mystic must pass and past, he must. We’ve seen in this brief summary our mystical wisdom was never far from scientific advancements. The modern idea that they are completely separate and have nothing of any use to say to one another is at least a sub as blinkered as it is naive, both a part of the way in which the exceedingly complex human brain makes sense of the world in which we live, the only one we can truly hope to know. And this is no accident that the author of The Zohar placed wisdom and understanding is the highest emanations from the Godhead.

It seems to me that Albert Einstein fits this image. He said, “I’m not an atheist and I don’t think I can call myself a pantheist. I believe in Spinoza’s God who reveals himself in the orderly harmony of what exists not in a God who concerns himself with fates and actions of human beings.” A simple declaration of faith combining Spinoza and Pythagoras. We’ve already touched upon the way in which mankind sees its relationship to the cosmos. To review this quickly by way of a postscript, the earliest civilizations in the Nile Valley in Mesopotamia and the Indus Valley perceived the universe as finite in both time and space. In Egypt, the sky was portrayed as a woman or a cow kneeling over to cover the earth. In Iran, it was given a finite time of just 12,000 years. The Hebrews, like all the ancient peoples of the near East, believed the sky was a solid dome with the sun, moon, planets and stars embedded in it. In biblical cosmology, the firmament is the vast, solid dough created by God during his creation of the world to divide the primal sea into upper and lower portions so that the dry land could appear. It was a very finite world and although mankind was small in this, he was not insignificant or so he thought.

By the time of the Greeks, this model was known to be too limiting. Reasonably accurate calculations were made of the distance from the earth to the moon and of the earth’s diameter. The Greeks realised that previous views of the size of the universe were hugely understated. Similar developments in India describe time as cyclical with a new universe created by Brahma every 8.64 billion years. In both cultures, some were speaking of multiple universes coexist. Mankind was now vanishingly small and to preserve his importance in his own eyes, religious thought developed as an alarming place to fill the gap. Geocentric views also progressed long after their sell by data as we’ve seen. This had helped to anchor mankind in the centre of the universe. Just as his conception of its size was dawning, it is hard for the human mind to grasp the concepts of infinity and space or time much less the modern understanding that the universe is expanding at an alarmingly fast rate. Its size is now said to be 46 billion light years.

And bear in mind, this is just the observable universe who knows what, if anything lies beyond. Most of us do not even try to grapple with this. Whilst the concepts could be understood in a mathematical sense, it’s much harder to do so in terms of physical reality. It’s doubtful that even sophisticated computer programming could illustrate the reality of the cosmos in a way that’s accessible to the human brain. Perhaps I’m wrong, but it seems more likely that we are still mentally stuck in a Newtonian cosmos, which is self shows, how small and insignificant we are in cosmic terms. Just possibly this humbling is good for us as a species. It grounds us and allows us to understand our limitations. We are not Gods. Next slide, please. And remember what happened to Icarus when he flew too close to the sun. Next slide please.

Q&A and Comments

And thank you for all for listening. Now I see that there are a number of questions and Thomas Oche is telling me that he read the book many years ago and it strongly influenced his career as a mathematics educator. Well done. Kepler remains his hero and humbly mine too. Yes, he talks about… Yes, indeed it’s… He wasn’t alone Koestler, that is in holding that view of Galileo. I have read similar things elsewhere, rather than just relying on Koestler who can at times be known for his slightly outlandish views, his theory about the czars is slightly off beam in my judgments. But who am I to criticise Koestler?

The next question I’m asked if any of the early writers consider what came before the universe they saw. I don’t really know the answer to that. I suspect that some of the later writers did because we have had in the 20th century much academic discussion and scientific discussion between the theories of steady state and Big Bang as a scientific explanation of the universe. I do remember when I was younger, steady state seemed to be gaining the upper hand, but the consensus now seems to be around the Big Bang as the theory. As for the early writers, as I’ve said, I really don’t know the answer to that. Yes, it’s a highly contentious question for writers who are struggling to understand what they can see and to say what could have been there before they couldn’t see. So, sorry, I can’t answer the question specifically.

And I’m told here that I do my audience a disservice by referring to a centrifugal force. Newton knew as such a thing didn’t exist. Well, that is actually true, but there is a centrifugal force which for rotating bodies tends to throw them out. So whatever name you give to it, such a force does seem to me to exist is the reason why a motorcyclist will lean into a turn and why a windsurfer will lean into a jibe in order to stay balanced on their motorbike or windsurfer. So we may be just talking about a difference of terminology here and I’m told on a further comment from the same commentator. It’s a persistent relic of early renaissance orthodoxy. I can’t express a view on that. I’ve no doubt, sir, that it’s true.

And I’m then asked to repeat the title of the book you showed. I actually showed two. The first is called ‘The Sleepwalkers’ like this talk. And the second, which may be the one you are referring to is called ‘The Closing of the Western Mind’ and the author is Charles Freeman. And centrifugal force comes again. This comment says, of course there is a centrifugal force defined in physics described already before Newton. You can find the formula on the internet. Well, as I’ve said, I would agree with that because having been a wind surfer for 25 years, I know there’s a centrifugal force, it kept me upright. So I do think we are probably talking about a difference of terminology rather than and anything more detail than that.

So I think I have dealt with all the questions that I’ve seen on my screen and I think we are also about out of time. So just remains to thank you all for listening and thank you for the questions which I have done. Wait a minute. There comes the formula for centrifugal force. F equals M over omega equals R. Hard to read on my screen but as I haven’t studied mathematics since I was 18 years old, I’m not in a position to say whether it’s right or wrong but I feel confident that it is. So there we go.

So thank you all very much indeed and both for listening and most of all for your questions and I hope I answered them sufficiently. Thank you so much indeed, goodbye.