Saturday Class - Kepler’s New Astronomy: What Every Citizen Must Know - May 9, 2026

Added: 2026-05-12

[00:00:00]Okay, thank you Tony. Thank you to everybody who's listening.

[00:00:05]Um, as Tony indicated and as I indicated in the blur that I sent out by email that this is part of an ongoing series of classes which I'm going to be doing and others will join me in this um, which is to vive an understanding of classical science as a general policy that is beneficial not just to specialists or people interested in science but to the population as a whole, the general citizenry.

[00:00:39]Uh we we put a lot of emphasis in the popular culture on the need for STEM uh re uh training in secondary schools and in universities and that's very good and necessary to train a technical workforce. But what I'm focused on and what Linda Larouche also always emphasized and was clearly necessary is that the general citizenry have a familiarity maybe not with all the specific uh technicalities of science, scientific discoveries, but a real experience and familiarity with the way scientific discoveries are actually made. That is what it does to the mind. what kind of mental activity, what kind of creative uh processes uh one experiences when either making an original discovery or reliving one of the fundamental discoveries uh that brought us to where we are today because this really is the history of mankind. And I I used in the uh blurb that we sent out the you know the example of having trying to figure out what's going on in the political world uh based on you know the flood of information most of it completely unreliable a lot of it generated by AI uh to actually figure out what's what's really going on. And the more information you get flooded with, the more you scroll X, the more you look, you know, at Google and all these things, the less you're able to figure out what what what the actual underlying dynamic is. And part of that can be corrected if you have a familiarity and an experience of making creative discoveries. Because what scientific discoveries are as also great art, literature, uh theology, everything is getting beyond the information, getting beyond the the impressions of the senses to understand the uh principles that are governing these processes in such a way that you you can then master these processes for the benefit uh of future development.

[00:03:20]And um if you have an experience either as a student and I recommend that we uh advocate for this kind of education all the way down to elementary schools through secondary schools, high schools, but also in universities, but also as a lifelong popular uh avocation if nothing else. uh because not only does it really help your mind, but it's a lot of fun. It it it will contribute to your uh ability to make sense of the world in all kinds of other areas, not just scientific ones. So tonight I've chosen to discuss something which I think is very re very easily to see the comparison which is Kepler's discovery of the laws of planetary motion.

[00:04:21]Now most people are not too aware of Kepler. Those who have studied a little bit of science might know of Kepler's laws and they're given an algebraic uh expression of them that the first law is the law that planets move at ellipses and the second law is that they sweep out equal areas in equal times. And the third law is that the square of the of the distance to the sun time is equal to the cube of the periodic of the time of the total orbit. Those don't mean much.

[00:04:57]They're just algebraic expressions.

[00:05:00]But what does mean a lot is how Kepler discovered it. because he discovered it first and foremost from a standpoint of an understanding of what the nature of man is and man's relationship to God as a creator who created a creative universe and made man as his image as creative beings and uh if you start from that perspective which is not anything you you find in an algebra chart or through some logic ical reasoning, but something that you can know to be true based on your own experience of what it means to be a human being and how the universe works.

[00:05:45]Um you can see that the mind, the human mind has the capability of ascending beyond the domain of sense perception and in this case untangling very very complex visual cues. Uh to be able to grasp in your mind something which is completely impossible ever to visualize.

[00:06:14]We can never see the actual orbits of the planets uh certainly from the Earth, but we'll never be able to see them from any vantage point in space. I can show you more of that, but it's just it's just impossible to visually understand this. But yet is possible with your mind to actually grasp it and make it not just something you know but something once you know it. You can use that capability to make further discoveries about not just about the stars but about man, God and nature itself.

[00:06:52]So let me begin uh with this uh discussion and and I will just say u one more thing which is that this is just the one example of what I'm talking about in terms of the pedagogical approach to science.

[00:07:11]uh there's literally thousands and thousands and thousands of discoveries that uh are important to work through and we're going to work through as many of them as we as we're able to produce. As Tony mentioning, we we've been I've been doing this for a long time. So, this is just the one step. Um but I think it's a good one to start with. Uh and I and I hope you'll feel the same once we go through it.

[00:07:41]So, um, let me just begin. Uh, Tony, why don't you put up the first slide? Uh, and this is a something Kepler wrote, um, in his, um, first book. Kepler lived, by the way, from uh, 1571 to 1630.

[00:08:04]in his first major book he was in Germany in the uh area that's today known as uh Benberg um southwestern Germany which was then part of the AustroHungarian Empire and he went to he was his he he he came from a a very poor family his father was a mercenary soldier who would go off and fight in these religious wars that were dominating Europe at the time come back for a file and then go out and fight another war. And at one time he just never came back again. And uh his mother was a loving mother, but she was attacked largely because of Kepler when he became famous. Um I won't go into that story too much but uh he w to the university of tubing where he studied theology, astronomy, philosophy and he became a uh a follower of the writings of Nicholas of Kuza who I will refer to in a minute and this was his uh un uh characterization of the situ situation uh in in the AC in the academic in themies in the educational system uh that that he was exposed to and you'll see that even in the 1580s it was very similar to what we have today. As regards themies, they are established in order to regulate the studies of the pupils and are concerned not to have the program of teaching change very often.

[00:09:46]In such places, because it is a question of the progress of the students, it frequently happens that things which have to be chosen are not those which are most true, but those which are the most easy.

[00:10:02]And I think that characterizes our situation today. So before going uh on to his actual discovery, I want to review what I did in the last uh class that I did where I discussed the uh Socratic idea and I also refer to Kooza uh of the concept of potential and I will review that very quickly. So why don't you go to the slide number two Tony?

[00:10:32]So this is uh there you go. So this is the diagram of the subject of a dialogue uh that Plato wrote called the Mino dialogue. And I would encourage everybody to uh read that dialogue. And it is a subject of a much more ancient discovery which is the uh relationship between a a line and a square, a area and a linear magnitude. This is an old discovery. We know it comes from the Pythagoreans. We know it was in ancient Egypt. we we have you know some circumstantial evidence that it it goes back in ancient history. I think it's one of the most fundamental discoveries.

[00:11:20]Uh and this was a uh the subject of the dialogue to just indicate how the relationship between science and politics and society is the dialogue is between Mino who's kind of an oligarch Plato Socrates and u a slave boy and they're talking about knowledge. Socrates and Mino and Socrates says that everybody has inherent capabilities sometimes is falsely translated as we just remember things. We don't learn things, we just remember them. But he played really saying we every human being has creative discoveries, creative capabilities. And so he goes through a process where he asks the slave boy to solve the problem of how to double a square by uh just asking him questions.

[00:12:16]And you know the the the simple uh obvious first attempt to double the square is to double the side. But you can see from this diagram that if you were to double the side of the square, you would get a square whose area is four times as big, not twice as big. So through a bunch of discussions he he the slave boy discovers the answer which is that you the magnitude which doubles area of the square is the diagonal of the first square and uh that this is extremely interesting because it was late it was shown and this is not in the dialogue but it was a a a discovery of the Pythagoreans that the you cannot measure the length of the diagonal of the square by the side of the square and um that these are incommenurable.

[00:13:17]Today they they in in mathematics sometimes they refer to this as irrational magnitudes as if you know they're crazy or something but they're irrational because they're not susceptible of making a whole number ratio. Okay. And in in uh other dialogues like the theotus dialogue um Plato takes uh makes another point about the importance of these kinds of magnitudes and refers to them with the Greek word dunamis which means power and power in English we use the word power but it's also could mean potential or it's it refers not to the physical characteristics of of the line, but to the substance of it, the essence, the the the immaterial power that creates the line that that makes it exist. So here you have in this simple diagram you have a a square which is an area bounded by line segments and you have a diagonal which is also a line segment and it looks the same as the others. is just a little bit longer in length and it is the side of a square whose area is uh double and yet the two side the diagonal and the side are incommensurable with each other. And so the term that Plato uses and he in the theotus dialogue and elsewhere uh which to describe this is that the diagonal of the square is the magnitude which has the power to produce a square whose area is double. Okay? So it's not that it's a line, it's a line which has a power.

[00:15:11]Where's the power? It's not in the visible characteristic of the line. It's nothing you see, but it's something you know in your mind because you've shown you've created in your mind a a process by which you're able to accomplish something that is true but is goes out but but cannot be discovered through the domain of sense perception.

[00:15:38]So this idea of dunamies of powers is very essential discovery in Greek uh in platonic and Socratic philosophy but it also as Kuza Nicholas of Kuza later showed and livenets and and many others that it's an essential characteristic of the universe as I discussed in the last class with reference to Kuza's last work called um uh summon a vision that this idea of power or as is translated by my friend Will Worth possibility uh it's is the essence of all knowledge and that the question is everything exists because it is possible to exist and what makes it possible that's what's important to know that to know what makes this possible and Kuza says that the but the deeper question is what makes possibility possible? What makes anything possible? And that he says is the summit of vision and the poss what makes possibility possible he uh says is an attribute of God. So um now this is just one example. This is the power to double a square. What about if you want to triple the area of the square or or quadruple the area of the square or whatever whatever magnitude you want. So go to the next slide.

[00:17:12]So this is u a generalization of that principle and you have here um a right triangle a right ang a right triangle inscribed in a semicircle and that's of course a very simple uh theorem of Uklid easy easy well-known and so you end up with two similar triangles this triangle OQP and triangle OPA and by the the uh law of similar triangles you have the proportion OQ is to QP as uh QP is to PA. So if whatever length whatever the relationship of OQ is to O A then QP is the length which has the power to produce a square which is in whose areas are in that ratio.

[00:18:13]Okay. So this is a generalization and it's very interesting as you'll see later that this is a circle that this is has a circular capability. So here you have lines but you have a relationship between the lines and the circles. If you go to the next one, Tony, there's an animation which I made which illustrates this a little bit.

[00:18:37]Okay. So you can see we have a circle and you have a little triangle in there and as the triangle moves around the uh altitude line there PB changes and the ratio OB to OA changes and all those proportions are creating the all the possible magnitudes that have the power to increase an area of a square by whatever magnitude you want.

[00:19:07]So you get you get the particular discovery of the uh magnet of the doubling of the square but then you have the generalization of that expresses itself in this relationship with the circle. Now there's another very important uh principle that's illustrated here which you have to keep in mind and you'll find that is pervasive in all of science which is that these magnitudes are not knowable by each other. As I mentioned the the side of the square of the one is not is the the diagonal is not commenable cannot be measured by the uh side. So this raises a very important question which is that it's you'll you have to be able to discover and live with something which you cannot necessarily know precisely but you know precisely what it h what its power is.

[00:20:10]And so if you're trying to look for pre precise uh information, precise data, you'll you'll be on a fool's errand. And nevertheless, it's the dis it's the the knowledge proceeds by discovering that which you cannot know precisely, but what you can know the power of.

[00:20:34]That's a very important philosophical general philosophical principle and it's exhibited in these mathematical these geometrical ex discussions. So I think just already you can begin to see that the significance of studying science in this way because it opens the mind and opens the door to very deep principles through these kinds of mathematical expressions if it's taught this way. But I know when you're sitting there in a elementary geometry class and you're given all these things and trying not to fall asleep or get bored or so forth, none of this will would come to mind.

[00:21:16]But see how profound it is that there's a general principle here and we can go through, you know, all of Greek geometry and you'll see it's full of this and and this is pervasive all the way up through the 19th and 20th century. we'll be going into some of the more advanced ones. Okay, so now let's keep going. Uh go to the next slide. So the next problem is okay, let's double a Q. Uh and this is uh very famous. It was known as the Delian problem because it was referred to by Eratosineses uh who wrote it down. But it was referred to at the time that this was um a problem of how to double the cube was a very difficult geometrical problem because as you can see here if you double the side of the cube you'll get a cube whose volume is three times the size or uh eight times. uh if you but you you if you double the volume you want two but two is to four as four is to 8. So you want what's called the uh the two you need to find two means between two extremes. In the previous example of the square you had to find one mean between two extremes one and two. Now you have to find two in order to be able to find the magnitude which has the power to double the Q.

[00:22:51]So this was a very difficult problem to solve. Can be the same problem that that you used before. Uh and this was uh known as a delium problem because the myth was that uh the people of Delos had a cubic altar and the gods asked them to uh make an altar which was twice the volume.

[00:23:17]And Plato said that the gods posed this problem to the people of Delos, not because they cared about an altar, but because they thought that the people of Delos would not have befallen all the troubles that befell them. uh they were in the middle of a plague and all kinds of economic problems. If they had spent more time studying geometry uh and developing their minds than all the immoral and irrational things they were doing. So that's this problem of doubling the queue became known as a delion problem. And I give you that history because it'll be relevant in a few minutes. Now how do you solve this problem is uh is very interesting and it was ultimately solved by uh a man named Aritus who was a collaborator of Plato.

[00:24:14]In fact in in uh one point Plato went to Syracuse to try and organize politically there and he got thrown in jail and Aritus helped get him out. Aritus was a very prominent figure in um Syracuse uh in that time but Architis was also a philosopher and a scientist. So go to the next slide and you'll see why this problem is more difficult. So here you see that you can find this magnitude by inscribing a new circle around the uh uh smaller of the two triangles in that first image that we saw and then draw the altitude. And now you have a relationship that OB is to OQ as OQ is to OP as OP is to O A. So you have two means between two extremes. So that if um uh if OB is 12 OQ then uh OQ and OB is the side of the square whose area is volume is one. OQ will be the side of the square that has the p the side of the Q which has the power to double the volume. Okay. So you're dealing with now from what we would today call two dimensions to three dimensions and the relationships all change. You can't use the same principles. You have to come up with a new discovery, a completely new one. If you go to the next one, Tony, you'll see I made a little animation to show you how difficult this is to solve by ordinary means because um you if you you see we got we have the two triangles and it'll start going here in a second.

[00:26:20]And you see that if you um the difficulty is that since all those relationships are all moving together and they all depend on one another, you don't have an exact way to determine the 1:2 ratio. You know that in principle you can determine any it's somewhere in there. The magnitude which has the power to double the volume of a cube is somewhere in there. But where it is, you can't find it because if you try and measure one, the others won't be in the right proportion. So now you have to find something that is unknowable from the standpoint of your existing u knowledge. So, Architis came up with a brilliant discovery which if you go to the next slide, you can uh I made an animation to illustrate this and we might have to run this a couple of times because it's pretty complex. Okay, so the way Architeis did this is if you take that orange line and make that 1/2 the length of the green diameter and you rotate it around it that diameter it makes a cone. And then if you rotate make a triangle in that circle and you rotate it around the cone, it sweeps out a Taurus which is the orange surface and the yellow surface is a cylinder. And where their three points inter intersect is the uh proper proportions to find the magnitude that doubles the volume of the cube.

[00:28:12]Why don't you run it again just so people can see it because it's it it's kind of it's very beautiful and it's a very complex thing to watch because there's a lot of lot of moving parts here but it's really quite amazing and this was done like in 300 BC long before you had computer animations and uh Aritus thought this up in his head and uh explained it and solve the problem of how to find the magnitude which has the power to double the volume of the cube.

[00:28:51]And this is this is quite fascinating and it tells you something else which is that these circles that we saw with the doubling of the square is actually just a one view of uh just one view without the um of the circle when it's these are actually embedded in higher geometrical figures.

[00:29:30]In this case, the cylinder, the cone, and the um Taurus.

[00:29:38]And you'll see later in another other classes when we get into more advanced geometry that these figures although they were known to the Greeks um were very uh uh show up in advanced geometry around uh Remon Gaus and so forth and uh open up doors to even more profound thoughts.

[00:30:10]Okay, now let's go now on to Kepler.

[00:30:18]So keep that in mind. Okay, now before we get to Kepler, we want to go to his uh inspiration or one of his inspirations which was Nicholas Obusa.

[00:30:29]Now Nicholas Abuza really was the founder of the Renaissance. He was a cardinal of the Catholic Church. He came from Germany but he lived in Italy most of the time. He spent some time in prison. He wrote a lot of very important works. He lived from 1401 to 1464.

[00:30:48]And um his most one of his most important works was called learn it ignorance. This is how Kuza described this principle which I illustrated with respect to the squares and other magnitudes.

[00:31:03]Um the idea that you don't have to know something precisely.

[00:31:10]What you want what your what science seeks is to know is to make your ignorance um more learned or to make your your uh ignorance your knowledge less imperfect.

[00:31:25]So this is a very important thing to keep in mind that that's how discoveries and progress always proceeds it. It's not from what you know and as you'll see with Kepler. It's the little gaps that don't quite fit that give you a a signal that there's something that you don't know and you have to make your ignorance more learned. And when you make that discovery, you'll find there's something new that you had no idea even was a existence and there's another gap and another gap and another gap and it never ends. And that's how human progress uh occurs. So Kooza in order to try and explain this um concept he made a a game called the bowling game. in Latin is called ludog globy. And in this game, he made a ball, but he cut out part of the ball so it wouldn't roll uh straight. And then he uh the the game was played by having a um on the floor a series of concentric circles. and you stand on the outside of the biggest circle and you roll the ball and try and aim it in such a way that it's very spiralally irregular path gets as close to the center as possible.

[00:33:02]Okay. So he made that game which you know I guess he did also for fun but for him it also illustrated a fundamental universal principle. And here's a quote from the book he wrote about it called on the bowling game. And he says here analogously that is to the game the rational soul intends to produce its own operation with its steadfast intention persisting. The soul knows the hands and instruments when a sculptor chisels on a stone. Intention is seen to persist immutably in the soul and is seen to move the body and the instruments. In a similar way, nature to which certain men give the name world soul moves all things while there persist its unchanging and permanent intention to execute the command of the creator. And the creator with his eternal unchanging and immutable intention persisting creates all things. Now what is an intention except a conception or a rational word in which all the respective exemplars of things are present.

[00:34:15]Now keep that in mind. It's very beautiful in itself. But this captures the essence of how Kepler discovered what nobody else could discover which is the principles of planetary motion. So now Tony go to the next one and I want to also introduce Kusen's thought from with a quote from uh his um seinal work called learned ignorance and um on uh this book I I Tony will put in the chat there there's a translation online by Jasper Hopkins and also the link to the book that my friend Will W I I I think gave the last class um on uh uh translated when he was in prison the works of many works of Nicholas of Kuza and you can get his book of translations on the uh Amazon and uh you can also buy Kuzza's works on Amazon too but there's an a PDF version online Tony has the link so let me uh you want to put up There we go. Okay. So, this is from Learned Ignorance. Now, Learned Ignorance is in three books, three sections. It's actually not that big a book. Here's a here's the paperback version of it. It's pretty thin, but it has three sections which are called books, and this includes the translator's introduction. So, it's not that long, but it's very deep. And I really recommend everybody study it.

[00:35:52]It's just very beautiful. And in the um the first book, Cuz uses mathematical expressions, geometrical expressions and so forth to describe uh how one develops this concept of learned ignorance to better understand man's relationship to God. The second book is about how this expresses itself in the physical world, in the actual created world itself. And the third book is about man's relationship to God through Christianity.

[00:36:26]Okay. Now, let me just this is a this is from the second book where he's talking about its relationship to uh the the natural world, the created world. And and I I I picked this out because it is the underlying philosophy of basically all modern science or all great discoveries in modern science, even though most people might not be familiar with it. and it definitely was a key element of Kepler's work. So let me read it. I maintained at the outset of my remarks that with regard to things which are comparatively greater and lesser, we do not come to a maximum in being and in possibility.

[00:37:08]Hence in my earlier remarks, I indicated that precise equality befits only God.

[00:37:14]Now think about that from the standpoint of these incommenurable magnitudes.

[00:37:19]They're not precisely. They cannot be made precisely. Wherefore, it follows that except for God, all positable things differ. Therefore, one motion cannot be equal to another, nor can one motion be the measure of another, since necessarily the measure and the things measured differ. Although these points will be of use to you regarding an infinite number of things, nevertheless, if you transfer them to astronomy, you will recognize that the art of calculating lacks precision since it presupposes that the motion of all the other planets can be measured by reference to the motion of the sun. Even the ordering of the heavens with respect to whatever kind of place or with respect to the risings and settings of the constellations or to the elevation of a pole and to things having to do with these is not precisely knowable.

[00:38:17]And since no two places agree precisely in time and setting, it is evident that judgments about the stars are in their specificity far from precise. I'll go to the next one which is a continuation of this same passage.

[00:38:33]Um and Kuza says uh and we are surprised when we do not find that the stars are in the right positions according to the rules of measurement of the ancients. For we suppose that the ancients rightly conceived of centers and poles and measures. From these foregoing considerations, it is evident that the earth is moved.

[00:38:59]So this is the first uh post first in in 1500 years that anybody had challenged the tomic ep system of epis of geocentric earth. Now before moving on to Kepler, let me just explain that um what I mean by that. uh the the um first of all we have the story that uh it wasn't until Capernacus that mankind discovered that the earth was moved and and the sun was at the center of the solar system. This is not true. There's there's lots of evidence that the Greeks, ancient Egyptians, other cultures had a concept of a heliocentric solar system or universe as they called it because beyond the solar system was not known.

[00:39:56]Um but this idea of the geocentric solar un solar system or a geocentric universe was a myth that was propagated by the by empires by imperial systems from Babylon through Rome and Greece and so forth as a political and philosophical idea because under a geocentric system the earth is at the center and Kuz makes a big point about this argument. The earth is at the center and the fixed stars which are the least moved thing um is at the circumference at the surface. And so the earth where everything is changing and moving is the least uh similar to heaven which is not moving. And so therefore God is out there not moving, unmoved. you're here stuck and you have to depend on an oligarchy or an imperial system to maintain control and that the planets the moon moves a little bit more little bit less than the earth but more than the planets the planets the Greek word planeta means wanderer or stars which wander around the background of the fixed stars move a little bit more and the um fixed stars don't move relative to each other. So the other thing about this is it conforms to sense perception.

[00:41:31]It's what you see when you go out on the night sky. So the evidence for the truthfulness of the geocentric uh solar system is not something in the mind. It's purely in the in the um domain of sense perception. So you can see how that fits into an oligarchical idea. Don't ask any questions about what the cause of these motions are or what's really going on. You only need to account for this description because this is what you see. Go out and look at the night sky. You can see it for yourself. Trust your eyes. Don't use your mind. Okay. So now let's go to now we come into Kepler. And Kepler had a completely different approach to this uh idea. And his first book was the uh called the mysterium cosmographicum or the uh mysteries of the universe. And uh this uh beautiful quote sums up his philosophy uh that um of uh why you have to overthrow the system the geocentric uh fixed idea system. So um uh he says God like one of our own architects approached the task of constructing the universe with order and pattern and laid out the individual parts accordingly as if it were not art which imitated nature. But God himself had looked to the mode of building of man who was to be.

[00:43:15]So that captures I think Kepler's philosophy in very in brief that I'm not looking to account for what I see. I want to know what God knows. I want to know how I could get my mind to rise to that level.

[00:43:38]So this was his first book. uh in 1596.

[00:43:43]In6009 he uh began to um uh work with um the observations, the new observations of the planetary motion that had been discovered by Tiko Bryant who was a Danish astronomer who did some the most precise observations of the motions of the planets. Um, and then uh and and that that allowed him to produce his discovery of the planetary motion, which I'll get to in a minute. But after he did all that, he republished his book, The Mysterium Cosmographicum, um, like 30 years after after his first publication, which was his first book.

[00:44:36]And uh this was at a time I get I think it was like 16 uh well it was right on the eve of the outbreak of what became known as the 30 years war. And here's where he references again the Delian problem going back to the Greeks that it's the lack of interest in philosophy, in science, in discovery which is characteristic of societies which are falling apart and descending into uh genocidal wars and going nowhere. So he says this after looking back at it after 30 or 40 years. Yet alas, of what great goods do miserable mortals despoil one another by their shameful itching for quarance? How profound and ignorance of their fate overwhelms them as they have deserved? With what deplorable perseverance do we rush into the midst of the flames in fleeing from the fire?

[00:45:41]Go to the next one. Oh no, that's the same. Um yeah. Um that go there you go. Would that even now indeed there may still after the reversal of Austrian affairs which followed be a place for Plato's saying for when Greece was on fire on all sides with a long civil war and was troubled with all the evils which usually accompany civil war.

[00:46:12]He was consulted about a Delian riddle, that's the doubling of the cube, and was seeking a pretext for suggesting salutoy advice to the peoples. At length he replied that according to Apollo's opinion, Greece would be peaceful if the Greeks turned to geometry and other philosophical studies as these studies would lead their spirits from ambition and other forms of greed out of which wars and other evils arise to the love of peace and in moderation of all things.

[00:46:45]So you can see the continuity uh hearkening back to the same relationship of the mind nature and God uh from the from Plato's time to uh Kepler's. Now the problem um in that Kepler was trying to solve was how do I actually know what the motions of the planets are? Now this is a very complex thing but I'm going to just raise two simple elements. When you go out and you look at the night sky and this is something I think every child should learn to do and it's very difficult in modern society because our cities have light pollution and it's very hard to see the planets and the fixed stars but you can you can get around that by doing field trips with children. And also you can um maybe have planetaria available so that the children get an experience of what they're actually observing and then combine that with with field trips.

[00:47:45]Uh but what you see is that the planets have uh two characteristic motions.

[00:47:52]First of all, they do not move uniformly that sometimes they appear to be speeding up and sometimes they appear to be slowing down as they move over the course of their orbits. Now, you don't see the whole orbit. You just see the motion of the planets against the fixed stars, but sometimes they're moving faster. And the when I say faster, you you only can measure this by measuring it night to night to night to night to night and over a period of a month or so, you begin to see the distance it's traveled and you can compute the speed.

[00:48:23]um and other times in their orbits they appear to stop and move backwards and then begin to move forward again. So the first thing is called that's called retrograde motion and the other is non-uniform motion. Okay. So how do you account for this? If you take the geocentric um orbit uh concept that the planets would be moving in perfect circles and this is the other element uh that Kuzza was objecting to but was standard in all mathematics and physics uh since the time of the death of Archimedes onward that the physical universe only moved in perfect circles because the circle is the most perfect of all curves and therefore that's the only thing the physical world can um move in. So you had to assume that all motion in the universe occurred according to either straight lines or perfect circles. Now this is in my view very similar to the argument that the materialists make today that all development in the universe has to occur by a stochcastic process that is a process which is fundamentally random and only takes on some kind of order over a long period of time. The that randomness is fundamental. Today we don't say perfect circles and straight lines are fundamental. We say randomness is fundamental. and nothing can happen in the universe that isn't a result in the physical universe that isn't a result of some ultimately random action. That's the same kind of assumption.

[00:50:13]So the the particulars are different but the mentality is the same. And I think that's very important to keep in mind as to why it's important to discover these kinds of these kinds of uh new um discoveries because you learn how new discoveries are made by breaking out of the fundamental assumptions not not the observed uh and superficial ones but the fundamental ones. So now go to the next one um Tony and this is from Kepler's book the new astronomy. He spent about 10 15 years painstakingly working through these new observations of the planet's motion of the motion of Mars um in uh of Taikobra. He was appointed at one time the u imperial mathematician by the emperor and he did this work when he was living in Prague and he wrote this in6009 and this is the introduction to the book. He says the testimony of the ages confirms that the motions of the planets are orbicular. Okay, that means that everybody up till now has believed that the motions of the planets are in perfect circles.

[00:51:31]It is an immediate presumption of reason reflected in experience that their girrations are perfect circles. I'm sorry, oricular means that they come back to where they started. For among figures it is circles and among bodies the heavens that are considered the most perfect. However, when experience is seen to teach something different to those who pay careful attention, namely that the planets deviate from a simple circular path. It gives rise to a powerful sense of wonder which at length drives men to look into causes. So it's the deviation from the assumption of simple circular action. It's what you don't know. It's the fact that the world is not behaving according to this simple assumption that cause it gives a powerful sense of wonder that causes men to look drives men.

[00:52:28]Passion.

[00:52:30]It's not something that you do coolly and coldly without emotion. It's a passion to look into causes and uh that's what Kepler did and we're very blessed because Kepler wrote down his whole uh experience here. It's a very lengthy book called the new astronomy and uh I think you you it should be the basis for probably early secondary school educa math and science education. you can master all the basics with it and really get to know a creative mind but that's another we talk about that more so so go ahead Tony why don't you go to the next one it is just this from which astronomy arose among men that powerful sense of wonder astronomy's aim is considered to be to show why the stars motions appear to be irregular on earth despite there being exceedingly wellordered in heaven and to investigate the circles wherein and the stars may be moved that their positions and appearances at any given time may thereby be predicted. But where Capernicus did so through mathematical arguments, mine were physical or rather metaphysical. Now uh before Kepler of course you had the famous uh work by Capernicus who said that the uh sun was at the center and the earth moved around the sun and this explained the retrograde motion. So by Kepler's time you had three competing uh views of the solar system. One was a capernic view that the sun was at the center and the earth and the planets moved around the sun in perfect circles.

[00:54:25]The other was the tomic view was that the earth was at the center and the planets moved about the earth and the sun moved about the earth in perfect circles and you had the view of Taiko Bry which was sort of a mixture of the two that the sun moved about the earth and all the planets moved around the sun. Now I've done some animations to illustrate this but let me just preface before I show those that what Kepler points here these are all mathematical arguments and you'll see from the uh animations that all three systems give you exactly the same results from the standpoint of the observations.

[00:55:11]So there's no way to determine from these systems what is true. They all give you the exact same result with wildly different information.

[00:55:27]Okay, let's go. Let's let's go through these animations and try and make this clear. So go to the next one.

[00:55:35]This is the tic system. Okay, the earth is at the center. You have a circle. Now you put the planet on an epicycle, another circle and the center of that circle goes around the earth and you see that when the planet comes close to the earth or uh it would appear to go backwards.

[00:55:58]So you get these large loops. Why don't you run that again just so people can see it. So the way Tommy calculated this was to create a system of epicycles that accounted for the retrograde motion by uh creating a second circle that would go around the planet at go around the earth at uniform speed. And when the planet moved uh in that direction, it would uh appear to be going backwards. And this conformed to much of the observed data, but never made a claim that it was true. Just that it works.

[00:56:41]Okay. Now, this doesn't account for the non-uniform motion. So, to account for the non-uniform motion, Tommy had to keep the Earth at the center. He put um something called an equant in there which was a point that was not at the center. It had the planet move around that so that it would appear to be moving slower and faster even though it was not moving slower or faster because remember everything had to move in perfect circles in uniform motion according to the aristoilian doctrine.

[00:57:15]So go to the next one.

[00:57:23]So there's the Earth. It's not at the center. There's the center of the orbit.

[00:57:29]And then you have an equant which is on the other side of the center from the Earth. So if you have the equant being the center of motion, they make it the sun, but it's not the sun. And then that's Mars. So that's on it. And if you watch the center of that circle, you'll see that as it gets closer to the Earth, it moves faster. And as it gets further away, it moves slower.

[00:57:58]Why don't you run it again so people could see it?

[00:58:09]Again, Tommy didn't say this was true.

[00:58:12]Well, he just said it it works out according to the calculations.

[00:58:17]And and again the two um the two uh axioms here are that the universe would move in perfect circles and in uniform motion.

[00:58:37]And so you can make a calculation with those two axioms that appear to account for the um observed motions. Okay, go to the next one.

[00:58:55]And this is an illustration of how that solar system would look if you put in all the visible planets at the time. You see it looks pretty chaotic, right? But and there were uh mathematicians that made mechanical uh objects called ories which simulated this. You can see if you look at Jupiter and Saturn um you can see how they sort of move around and you can begin to see the epicycle. But that's what the whole thing looks like. All right. Now let's go to the next one.

[00:59:40]I think we just did that one, didn't we?

[00:59:42]Or did I have it in there twice?

[00:59:51]Okay, this is Tao's Bry system which has the sun moving around the Earth and the planets moving around the sun.

[01:00:01]So there you go. Mars is moving around the sun and earth is moving around the the sun is moving around the earth. And you see this gets a very complex path that it traces that Mars would trace. But if you were a observer on Earth, this would um appear to account for the retrograde motion.

[01:00:26]And these little dots that appear here are the uh periods of equal time. So where they're closer together is when they're when it's moving slower and when it's further apart, you can see it's they're moving uh faster.

[01:00:44]So that just gives you a little taste of how that this system works. You go to the next one now.

[01:00:58]I think we just did that one, didn't we?

[01:01:01]Yeah.

[01:01:07]This one, I think, is Yeah, this one compares the tomeic system and the tyonic system. And you can see two completely different mathematical models and they give you very different results but you could not distinguish one from the other mathematically.

[01:01:29]So they give you exactly the same result.

[01:01:40]That's what Kepler said. These are mathematical systems. they give me. So which one is true?

[01:01:45]Well, the answer that they would give is doesn't matter. We're not trying to tell you what's true. We're just saying this is what this is what we observe. Okay.

[01:01:56]Now the final one. Let's let's throw in the capernic system in here.

[01:02:13]Okay, this is the Capernac system has the Earth at the as a planet and the sun moving around and you see where the Earth passes Mars like right here, Mars would appear to be going backwards.

[01:02:29]So this accounted for the retrograde motion but Capernicus could not account for the non-uniform motion because he was stuck with the circles and the idea that the universe had to move only in uniform motion.

[01:02:48]Um so here's what he did to go to the next to the non-un motion. Why don't you do the next one?

[01:03:19]So that's equal time, equal speed going around an planetary orbit. But that wouldn't work because it was those are uniform motion.

[01:03:28]So he puts an epicycle capernicus does.

[01:03:32]And so you get this epicycle which then makes accounts for the non-uniform motion of Mars. So the dogma here and you see the farther apart uh dots on the left there show that that's where the planet appeared to be moving uh faster when it was closer to Earth and slower when it was further away from Earth.

[01:03:57]So the dogma here there's two things. One is the perfect circles and let me just give you a physical illustration of a of another one of a perfect circle. If you put a blindfold on and tried to walk in a perfect circle, you could do it if you had a rope that attached to a post, say, and you kept the rope tight and you u walked at a 90° angle to the rope, you would trace a perfect circle even with your eyes closed.

[01:04:33]So the idea was that dumb matter could only move in perfect circles because there was some connection to some center some center like that. The non-uniform motion then throws a a a um wrench into the matter because in non-uniform motion the planet is always speeding up or always slowing down. At every moment it's doing something different than what it did before.

[01:05:00]So that's why the apparent non-uniform motion had to be um accounted for by uniform motion and it only appeared to be non-uniform. Now Kepler being a follower of Kuis said that's not true. It's probably there's a physical reason for this and the physical reason is that the uh universe is as Kepler said it's not based on uniform motion in perfect circles. It's based on change because he adhered to Kuza's idea that God did not make the universe statically perfect but made it self-perfectable and therefore change. It had to be able to change. Now this caused a problem because uh the concept was that how could dull matter planets move and know how to speed up and slow down.

[01:06:07]And I'll get to Kepler's solution for that when I show you the how he solved the problem. So go to the next one, Tony. So his first effort was what he called the vicarious hypothesis. He said, "Okay, I'm going to take Taiko's brahi's observations and I'm going to try and come up with the best uh expression with the sun at the center, the um equant that is the the center of motion being on the other side of the center of the orbit's cir orbit center and have that be the center of motion and that um the planet then would speed up and slow down because it was moving around an equant, not the sun. And the eco1's just an empty point in space.

[01:07:11]And therefore you had equal time markers and the would be spread out equally around the circle and the only um the apparent the non-uniform motion was only apparent.

[01:07:29]Now in this hypothesis he worked as hard as he could on making it correct and uh compared it to the results of uh Taiko's observations and there was always a gap of 8 minutes of an arc which is really small. Think about, you know, a protractor where you measure angles and think about one degree and think about 8 minutes of that one degree, which is 160th of that degree. So you can see it's pretty small magnitude, but this was within the error of observation. a little bit greater than the error of observation but enough that you could ignore it and say this this vicarious hypothesis is the most accurate under estimate of the orbit to date and he could have mathematician just said okay I give up I you know I've done it I've made a breakthrough I've solved the problem but he did not believe that the universe was constructed according to this way he said there had to be a cause and so he made a physical hypothesis. He said what what's actually happening is that the planet is being moved by a power just like the powers that we discussed with doubling the square and doubling the cube. The power, the possibility, the potential, he called it an idea. He used the Latin word species.

[01:09:06]And the idea was an intention like like he spoke like Kuza spoke in the in the bowling game. The in there was an intention that the planet should speed up and slow down and that this power which he called gravity uh diminished its strength according to the distance from the sun. And he knew very well about the inverse square law because that was known with respect to light. And this also contradicted a arisatilian dogma which is that um a physical body could only be moved by a non-physical by a phys by another physical body. So Talamy and all the others believed that the planets were actually embedded in crystallin spheres, see-through spheres, and that they were moving in this physical body, and that there was some kind of demigod or something that that controlled their motion. But Kepler said, "No, that that doesn't make sense.

[01:10:18]that doesn't fit with the idea of God as a creator. So he said what would how would this physically be created?

[01:10:26]And so he came up with this physical hypothesis that the planet was moving around the sun in a non-uniform orbit that took it made its distance from the sun uh greater and lesser as it moved about the sun. and that this uh transformation um occurred physically and therefore I'm going to discover actual what not how do I make something that looks like what the planets do but how do I actually understand what they actually do according to my conviction that God created the universe so that man would be able to understand it. So go to the next the next one. This is his physical hypothesis.

[01:11:16]No, the next one. This is the vicarious.

[01:11:23]Okay. This is his physical hypothesis.

[01:11:26]So he had the um no equant. The planet was moving about the sun physically. the sun had a power that was moving the planet physically around the sun and that uh it would speed up and slow down. You see how it slows down when it gets further from the sun and speeds up as it gets closer to the sun. So at every moment it's doing something different.

[01:11:56]and that the measure of equality was equal areas are swept out.

[01:12:02]And that's Kepler's so-called second law that the planet sweeps out equal areas in equal times.

[01:12:12]This is a comparison to the vicarious hypothesis. And you can see the gap is 8 minutes of an arc.

[01:12:25]There's a gap.

[01:12:28]Um so that 8 minutes of an arc that Kepler's vicarious hypothesis um the discrepancy between the between what the observations and this mathematical approach of the vicarious hypothesis was small but it was still an indication that that small error was the door through which you could come to a more perfect a less a a more learned ignorant knowledge of the actual motions of the planets. But the key breakthrough here was to dare to conceive of an actual physical hypothesis and that an immaterial power like gravity could move a material object. And this, of course, was another break with the arisatilian system and with our modern-day materialists.

[01:13:30]So, let's go to the next one.

[01:13:40]No, that's the same one we just watched.

[01:13:51]Now this is what Kepler's first law it's called which is after after he discovered that the planet moves non-uniformly and sweeps out in equal areas in equal times he found that there was still an error and he ultimately came to the conclusion that the actual shape of the orbit was elliptical and ellipses have been discovered by the Greeks, but there was no physical reason known physical process that went according to elliptical orbits. And there you see that the orbits where the planet moved slower are long and thin and the orbits where the plan run it again, Tony. And the orbits where the planet moved uh faster are shorter and fatter.

[01:14:48]So this is Kepler's so-called first law, which is actually his second law. But that's what I mean about how mathematicians and academics change the order of things.

[01:15:04]Can you run it again or There we go.

[01:15:50]Okay. Now, there's one more thing to bring up and then we can open it up to questions. So, go to the next one, Tony.

[01:16:03]And this will the next slide. It's not a it's not an animation. It's a still.

[01:16:13]There we go. Okay. So, this this takes us again back to the Greeks.

[01:16:22]Um, and you see that this is the area. This is a this blue area is a representative of an area that was swept out. Okay. How do you measure that?

[01:16:37]Well, you measure that from this section of the circle, which is uh well, I guess you can't see my cursor, but the section of the circle that goes from C along the diameter to the uh circumference and then along the arc to P and then back to C. So, that's a little pi uh cut. And that's proportional to the angle the angle that the line CP makes to the um with the uh diameter now but that's only that's the whole area but only part of it is swept out by the planet because it's the the motion is around the sun.

[01:17:22]So you have to subtract from that area the triangle from the sun to C to P.

[01:17:29]That that rectalinear triangle.

[01:17:33]See that? And that rectal linear triangle as you probably remember from your elementary school geometry. The area is 1/2 the base times the height.

[01:17:42]And the height is that dotted line. And that is the sign of that angle. So now you have an expression of what Kuza uh raised as an issue which is the discrepancy between the curved and the straight because the area the triangular area is is uh bounded by straight lines and the area swept out is actual curve.

[01:18:15]uh go to the next animation and you'll see what the problem is here.

[01:18:23]Okay. Now this is a animation of the relationship between the sign and the arc. The sign is the orange line. And if you carefully watch the relationship between the angle and the length of that orange line, you'll see that that orange line is moving nonuniformly.

[01:18:43]Run it again. to the ark.

[01:18:58]So now you have a new wrinkle that was put in here, which is that to measure the area swept out, which Kepler had shown was an actual physical characteristic of planetary motion, you had to rely on a new type of incommensurable magnitude, a what today we would call transcendental function. and that this incommenability was of an still higher power than the power to double a square or double a cube or anything similar.

[01:19:33]And so this introduced something completely new not just into mathematics but that's something very um very uh puzzling in mathematics was actually expressed as a physical principle by the planetary motion.

[01:19:53]And this meant that the universe was conformed to the to the uh kind of uh creative nonlinearity that we can understand with our minds and prove as an expression of the principles that were laid out by Kua and Kepler. And this created the revolution in science. that that we were not stuck with the mathematics of Aristotle and the universe did not move according to perfect circles, linear motion and things that were simple mathematical expressions, but that it was the more it was the higher ones, the the the less easily knowable ones that actually governed the the physical universe. And that confirmed Kepler's uh idea that God created the universe uh as if nature art was imitating art and God looked to man who was yet to be.

[01:21:02]So I think I'll stop there. I probably did, you know, maybe a semester of uh physics and mathematics and less little bit over an hour. So, I'm sure I left a lot of questions, but I I hope I at least gave you a little bit of excitement about what can be discovered about your own mind by delving into the actual method of discovery that got us to where we are Today.