 Okay, so it is my honor and privilege to receive Martin van Dijk for this Alfa seminar. The title of this presentation will be The Coordination of Time in Galileo's experiments. So you will talk around one hour maximum. After that we'll take a short break and there will be a comments of Kevin Chavez to start the general discussion. Thank you, the floor is yours. Thank you very much. Merci pour l'invitation. Je parlerai en anglais. C'est plus facile pour moi. Peut-être aussi plus facile pour vous de me comprendre comme il faut. So The Coordination of Time in Galileo's experiments. That's the topic of the talk. It will be partly historical, partly more philosophical. But to really properly set the stage I want to start out with a rather long quote by Galileo describing his most famous experiment so that you know the kind of things that we're talking about. So here it goes. In a wooden beam about 12 brassia long, half a brassia wide and three inches thick. So let's assume one has six meters long, so very long wooden beam. A channel was cut along the narrow dimension. A little over an inch wide and made very straight so that this would be clear and smooth. There was glued within it a piece of vellum as much smoothed and cleaned as possible. In this there was made to descend a very hard bronze ball, well rounded and polished. The beam having been tilted by elevating one end of it above the horizontal plane from one to two brassia at will. As I said, the ball was allowed to descend along the said groove and we noted in a manner I shall presently tell you the time that it consumed in running all the way. Repeating the same process many times in order to be quite sure as to the amount of time in which we never found the difference of even the 10th part of a pulse beat. This operation being precisely established, we made the same ball descend only one quarter the length of this channel and the time of its descent being measured, this was found always to be precisely one half the other. Next making the experiment for other lengths by experiments repeated a full hundred times the spaces were always found to be to one another as the squares of the times. As to the measure of time, we had a large container filled with water and fastened from above which had a slender tube affixed to its bottom through which a narrow threat of water ran. This was received in a little beaker during the entire time that the ball descended along the channel or parts of it. The little amounts of water collected in this way were weighed from time to time on a delicate balance. The differences and ratios of the weights giving us the differences and ratios of the times. And with such precision that as I have said these operations repeated time and again never differed by any notable amount. End of quote. So a famous quote, and let me immediately round it up with a famous commentary on that specific quote. A bronze ball in a smooth polished wooden groove, a vessel of water with a small hole through which it runs out and which one collects in a small glass in order to wait afterwards and thus measure the times of descent. The Roman water clock that of Stasebius had been already a much better instrument. What an accumulation of sources of error and inexactitudes. It is obvious that the Galilean experiments are completely worthless. The very perfection of their results is a rigorous proof of their incorrection. So of course, Alexandre Coiré doubting the epistemic value of the experiment and let me add the last senses of the paper from which I've taken this quote. Not only are good experiments based upon theory but even the means to perform them are nothing else than theory incarnate. So of course, Coiré is making his point of skepticism or is expressing his skepticism with respect to the value of Galileo's experiment because he wants to make a very specific point about what it takes to set up good experiments. And you can only get good experiments if you already have good theory. So theory cannot start by experiments that's having things the other way around. So that's the main message that Coiré wants to drive home. Now, I think there are actually two points hidden in Coiré's criticism. The one is the one that's most often focused on that has to do with the problem of idealization where he's stressing, well, smoothly polished, yeah, yeah, all well, but the results will never be as perfect as Galileo claims them to be. So Galileo is clearly exaggerating for rhetorical reasons but apart from the problem of idealization there is also the problem of coordination in the specific sense, what reasons does Galileo actually have to think that he's measuring something like time? So even if the situations where as ideal as you would like them to be, is he actually measuring the time of descent using this apparatus, this water clock? To what extent does Galileo have good reasons to think that he's actually measuring time in the absence of course of a theory that would tell him that indeed he is measuring time in certain circumstances. So that's where the problem of coordination comes in. So what I will do in my talk, I will first go a bit further giving some background on this philosophical idea of the problem of coordination, which of course has a rather well-known history within the philosophy of science of the 20th century. I'll use that to then go back to Galileo's research program to have a look at some of the temporal developments within Galileo's research. I will then pay attention to one very specific experiment that he carried out and that we have the manuscript notes where Galileo noted down his results. It's not the experiment that we started out with but it's one related to it. I'll then introduce Huygens' work on the pendulum and this is actually also something that's put at central stage by Cuare in his paper on Galileo. So I'm actually following Cuare there and I will then end with some concluding remarks if time permits. So let me first go to this problem of coordination and I think at least in it's not the general ID but calling it an issue of coordination is most commonly related to Hans Reichenbach who spent quite some time in his work on the theory of relativity and a priori knowledge, one of the key texts in Reichenbach's own development from Neo-Kanchin view on science to what then will become his logical empiricist analysis of science where he introduces the problem in the following terms. The physical object cannot be determined by axioms and definitions. It is a thing of the real world, not an object of the logical world of mathematics. Offhand it looks as if the method of representing physical events by mathematical equations is the same as that of mathematics. Physics has developed a method of defining one magnitude in terms of others by relating them to more and more general magnitudes and by ultimately arriving at axioms, that is the fundamental equations of physics. Yet what is obtained in this fashion is just a system of mathematical relations. What is lacking in such a system is a statement regarding the significance of physics, the assertion that the system of equations is true for reality and it's of course the latter part that must be somehow given by something like a coordination. But the basic problem there, the basic problem that exercised Reichenbach is that you cannot assume that this reality already has mathematical structure but if it does not yet have mathematical structure how are you gonna relate a mathematical structure to something that is not mathematically structured? That is the basic problem that Reichenbach was dealing with. Now in these general terms probably or possibly not something that can be easily solved because it's really set up as a dilemma either mathematical or not mathematical and if it's already mathematical the coordination has already happened and if not mathematical how are you gonna ever do a coordination? So that's the basic form of the problem. Now in the way that Reichenbach sets up the problem and the way that he's gonna think about ways of solving it there's a lot in the background but one philosopher that's clearly very important is Poincare. And Poincare is analysis specifically of space and time and the questions that are raised once you start thinking about exactly these kinds of questions. So let us first go back to this paper by Poincare from originally 1898 and let's see how Poincare introduces this for the issue of time. Time on the one hand as a mathematical parameter as it is present in physical theories and on the other hand time as a physical thing or a process something that we are somehow trying to measure. Now the first basic point that Poincare makes in the paper can be summarized with the following sentence. We have no direct intuition of the legality of two intervals of time. We, so the basic problem is gonna be how are we ever gonna know that two temporal intervals have the same length? Because of course you can have an experience of time passing and that's the kind of experience we have of time passing but you cannot as it were keep the time that has already passed present and then compare it with the time that is passing now. So there is no direct access in our kind of experience for the experience that we have we don't have access to equality of temporal intervals. So that's the basic form of the problem. Now Poincare goes on by telling a little story of how physicists nonetheless have tried to deal with temporal processes and the basic starting point is okay you cannot have a direct intuition or direct experience of this legality but you can define things as being equal. And so it starts by choice and there were of course heading the direction for some kind of conventionalism. What physicists do is that they freely choose a certain kind of physical process as exhibiting equality of time. Not because you know that they are equal not because you can experience that they can be equal but because you have to start somewhere and you define them to be equal and what better choice than to use a pendulum for this? Why a good choice? Well because it is a repeating process so that's one thing that's of course interesting it repeats itself so it is kind of plausible to them call two subsequent patterns as being equal in time and the second thing is of course that you can take different pendulums and compare them with each other and at least you can say if the two pendulums are of the same length that they do this for each swing they keep their synchronous with each other. So there are a few reasons why it is a good choice it makes sense to pick this as your definition for equal time. It makes sense but there are a number of problems the number of problems having to do with the fact that you will start realizing that the behavior of this pendulum is also dependent on factors such as temperature and friction and so if you are start to take into account that there are a number of disturbances that will also determine how a pendulum behaves then you will start wondering whether the choice was actually a good choice and this drives you towards a second phenomenon in Poincaré's retelling and this is astronomical phenomena. You're gonna define equal time by another periodic phenomenon you can notice in nature the day-night pattern as it is caused by the rotation of the earth. But again similar worries will arise if this is really a rotating system and if you have the sea on it and the sea is not strictly following the rotation then there will be causes that will again intervene and make this phenomenon probably not strictly isochronous and so on and so on. This brings Poincaré then to the second main point of the first half of the paper. So what physicists in the end will actually do is turn this around and say le temps doit être défini de telle façon que la loi de Newton et des forces vives soient vérifiées. So what you're gonna say and what you're actually already implicitly doing so let's go back to what I said oh there will be other causes and because of these other causes the motion will not be strictly uniform. Well how do you know that there are other causes and that they will have this effect? Well basically because you have these laws of Newton that tell you something like this and this means that you're already actually using time as it is present in the formulation as a theoretical parameter in the formulation of the laws of Newton as your implicit criterion for equality of time in physical phenomena. So the definition of time is not so much so in the first step you want to define time by picking a random not a random by smartly picking cleverly picking a phenomenon that can define equality of time. In the second step you're gonna say oh let's not define it by a specific phenomenon let's define it by these general laws and then let's look at which phenomena according to these laws take equal time. Again Poincaré corrects himself by noticing well wait a second if this is the case then of course if we would do a mathematical transformation on this parameter of time. Newton's laws are empirical laws they would remain true but they would only get a more complicated formula. So the final conclusion is how is time being defined by physicists well the time must be defined in such a way that the equations of the mechanics are as simple as possible. So how are physicists defining time? Again you cannot experience it so you have to define it well the proper definition is however whatever it is it must be such that the laws that we will come up with are the simplest laws that we can formulate. So that's Poincaré's analysis in this famous paper which of course is particularly famous because the second half of the paper that really goes into problems having to do with simultaneity and leads into the kind of considerations that are also behind Einstein's work a few years later. Now I want to, before going back to the Galileo case let's look how Galileo was actually making these kinds of choices because that's more or less the agenda for the talk let's see actually how historically physicists have been dealing with this problem how they have been picking the right kinds of phenomena to instantiate something like uniform time before doing that I want to add one philosophical commentary taking it from Basvan Flaasen's book on scientific representation which has one chapter devoted to the problem of coordination where he starts with Reichenberg goes to Poincaré so in a sense I've been just summarizing also what he is doing there but he's doing it to make a specific point and the specific point is the following Poincaré oversimplified by suggesting that it's mainly a matter of submitting definitions in such a way as to keep theory as simple as possible and this is a point that in a way is also already made by Einstein as Flaasen himself points out that Poincaré's story is a bit too simple and on the one hand you have theory on the other hand you have the definitions and the definitions are freely chosen such as and the main reason why this is too simple according to van Flaasen is that measurement, practice and theory evolve together in a thoroughly entangled way so Poincaré is singling out and that's of course what Einstein is doing saying oh but Poincaré is pretending that we need to keep Newton's axioms fixed and then we define such that but Einstein's point is why keep these fixed you can make the choice at other points as well and van Flaasen is agreeing but turning this again in a historical point measurement, practice and theory evolve together in a thoroughly entangled way somewhat hesitantly one might say that the measured parameter or at least its concept is constituted in the course of its historical development choices are made and ones made may encounter resistance whether in experiment or in theory writing or more usually in combination of the two or else be vindicated by smooth progress on both fronts so it's the measurement and practice measurement, practice and theory evolve together in a thoroughly entangled way that I'm going to use as my red thread in the rest of my talk by trying to lay bare this kind of historical process where questions about how to measure and questions about what theoretical ideas to hold through were thoroughly entangled you cannot just say oh here's the choice and there's a theory, no the two were developing at the same time so that's the perspective I'm going to take and I'm going to look at the development of Galileo's research program and I think it makes sense to call it a research program in the sense that there is a rather systematic sets of questions that Galileo is tackling and is coming back to and is rethinking based on new experimental findings, new theoretical explorations and the first step in this systematic program takes place somewhere in the years between 1589-1592 at the moment that Galileo is a young professor of mathematics at the University of Pisa and he sets out to develop something like what he calls a mathematical natural philosophy so he's going to ask the questions that natural philosophers are asking but he's going to answer them in a different way and the different way is basing himself on mathematics, after all he's a professor of mathematics and the first and the main idea of the treaties as he writes it and we only have the manuscript so he is dissatisfied with the result himself, there are a number of reasons why he never decides to publish it he rewrites it and then at a certain point drops the work but the main probably the most central idea is where he sets the speed of falling bodies proportional to the difference in specific weights on the one hand the body and on the other hand the medium so Aristotelian natural philosophers have been debating questions about what's the cause behind the speed of a falling body and what are the factors that we should take into account and Galileo's main idea is to look at this as basically a problem in Archimedean hydrostatics and Archimedean hydrostatics gives you a criterion whether a body will go down in a medium, will stay in equilibrium or will move up, that's basically what it tells you and it tells you to find out which of these three measure the weight of the body and measure the equal volume of the medium its weight and depending which is the greatest that determines the direction of the motion Galileo adds this extra hypothesis that is difference in this weight actually also gives you a measure for the speed of the falling bodies second idea that he treats in the treaties is the speed of bodies descending on an inclined plane and there is gonna set it again proportional to effective weight so he's seeing a similarity between the problem of descent in a medium part of the weight of the body is taken away by the medium and the problem of descent on an inclined plane, again part of the weight of the body is actually taken away by the inclined plane and this is the kind of diagram he has, the details don't matter but so he can mathematically determine the effective weight of the body on the inclined plane and then set the speed proportional to this effective weight and third central conceptual idea is the idea that impressed forces expand out of themselves, so they die out so and this is on the one hand related to the problem of the trajectory of a projectile so again this is the kind of picture he draws so if you throw a ball the first part of the trajectory is being determined by the fact that you have impressed a force in a certain direction on the ball but gradually this force will start extinguishing, it will decay and at the moment that it's decaying the weight of the body comes in as a second factor and it starts out more or less rectilinear and then it will start going on this more or less circular part until this impressed force is completely extinguished and then the weight of the body takes over and you again have something like a free fall now this idea of the impressed force and its decay is important for a number of both historical and conceptual reasons but it is particularly important because Galileo can appeal to this to justify the fact that he treats free falling bodies as having a uniform speed because of course experience suggests that if a body falls and if you let it drop from a high tower you will start noticing this that this body is actually accelerating throughout its fall whereas his mathematics of free fall suggests it should be uniform but the answer he has to this observation is that yes that's true but you must ask yourself before the body was falling it was not falling because you were holding it up and the fact that you were holding it up means that you were impressing a force on it to keep it up once you let it go the impressed force is still present but it's slowly slowly decaying and it is because it's decaying that you observe an acceleration that's actually the body that's going towards its actual speed and it reaches this speed as given by the formula at the moment that the impressed force has completely expanded itself so that's the kind of overall coherence of how these different ideas hang together now we talked about the treaties and the concepts he uses but the main point that's important for my story is that time itself is never mathematicalised it's not treated as being something like a mathematical parameter Galileo hardly talks about time he does but it's not the topic of his treaties he's talking about speeds and speeds have to do with times but there is no point where he's attempting a mathematician of time itself and you can even to some extent see him doing the opposite so you're talking about speeds Galileo how are you going to measure speeds isn't that a question you would want to ask be a mathematician how are you going to measure speeds well he has an answer measure the specific weights and that gives you the speeds so the only way he is implicitly mathematicalising time is by doing the weight with time so that's I think important about his early stage in his research program okay let's now go to the second step and this is dated 1592 more or less the moment he drops work on the demo to treaties maybe because that's what we will see now probably also because a number of other reasons and it's linked to the move from Pisa to Padua so Galileo gets a better position again as professor of mathematics at University of Padua and on the way to Padua he drops by his friends Guido Baldo del Monte a mathematician as himself but more experienced who was actually instrumental in getting Galileo the position in Padua and they carry out an experiment together and this is from Guido Baldo's notebook and you see here the setup of the experiment they basically take you can see this as a roof and you take a ball you ink it so you have ink and then you throw it over the inclined plane of the roof and you look at the trajectory that it leaves trying to answer this question that was already there what is the shape of the projectile motion now I'm here basing myself on the paper from 2002 I think by Jurgen Ren, Peter Damerhoff and Simon Rieger really go into quite a lot of circumstantial evidence that really nails the case up till then people sometimes mentioned this manuscript by Guido Baldo but they really showed that we really should see this as joint work by Guido Baldo and Galileo and they also stressed that initially the main thing that Guido Baldo and also Galileo take away from this experiment is that the curve of the projectile is symmetric remember again the kind of explanation I gave in the demo to first is more or less rectilinear because of the impressed force is dominating then it becomes more or less circular because you have a mixture of impressed force that is decaying and the weight and then the weight is taking over and that suggests if you talk about it in this way this suggests an asymmetric curve that allows it. Here they have observational evidence with this very smart experiment with the inked ball that shows that the curve is more or less symmetric and that's the main point that Galileo takes away if we want to understand how this decaying force etc is intermingling with the weight of the body there is a symmetry involved and therefore they note that the curve looks like a parabola the nodes don't say it is a parabola but it says it very much looks like a parabola which for our from our perspective is of course very suggestive because once you see the projectile motion as parabolic you basically have Galileo's law of fall because law of fall states that the distances are as times squared and that's exactly the kind of form that a parabolic curve will give you but again nowhere in the early nodes does Galileo draw this conclusion and this I think is related to the fact that again at this point he has not linked this mathematical curve to time as a mathematical parameter you're only going to read the law of fall in the parabolic curve if you're able to read the other, the horizontal components as being a uniform time and because only then of course the x and the y ordinates give you distances as squares of times so for us it's very easy to read it into it but you can only read it into it if you have identified one of the two ordinates as being a time parameter and there is no evidence at all that Galileo initially is looking at it in that way so we have something that looking back will become important in linking time as a mathematical parameter to empirical phenomena because here you have something that allows you to coordinate this inked trajectory is an instance of a coordination of time as a mathematical parameter with an empirical phenomenon but only of course once you have defined time as being this mathematical parameter and that Galileo has not done yet at this point this brings us to a third stage that can be again rather confidently dated to the year 1602 so 10 years later Galileo is still professor in mathematics at Padua and here I'm gonna base myself mainly on this book that came out a few years ago swinging and rolling and feeling Galileo's unorthodox path from a challenging problem to a new science by Jochen Wütter, actually PhD student of Jürgen Ren who really for the first time has given a well-grounded assessment of all the manuscript material that Galileo left so there is a huge codex of folios with experimental notes taken by Galileo but it's really disparate notes, a note on this, a note on that a calculation, a diagram and over the years people have given interpretations of isolated notes and if you just take one manuscript note in isolation you can give it almost any interpretation you like and what Butner has done is really bottom up starting from all the folios and putting them all next to each other and seeing where do things recur etc he has bottomed up I think made the best case possible for okay this is what the manuscript evidence actually teaches us about Galileo's work what he was doing in mainly 1602 and a few years after that and how these what were the developments that these manuscript notes bear trace to and basing so looking at Butner's findings in 1602 Galileo assumes a new phenomenon that the pendulum has a property of isochronity so that if I take one pendulum with a certain length and I release it from a certain height it will start swinging if I take a second pendulum of the same length but I release it from a different height at the same time they will keep on swinging together even if the one is doing this and the other is doing this they will keep on doing this together so that's the basic property of the isochronity the pendulum that Galileo is now suddenly interested in he assumes a second thing he assumes that motion on inclined planes inscribed in a circle also show this property of isochronity so if you take a circle and you will describe a chord and you describe a second chord in the same circle and you release the ball on the first chord at the same moment they will reach the lowest point at the same time, second property assumed by Galileo and the third one is the law of fall so what Butner's analysis shows is that this is the starting point for these manuscript notes so the notes are not going to show us how Galileo came to this but once he has these ideas suddenly he starts doing something now we can say a few things on how Galileo probably would have come to these properties the first the pendulum so this remember was the diagram I showed you that Galileo used to determine the effective weight of bodies on inclined planes but it's of course very suggestive the circle is here purely for mathematical reasons initially the circle has no physical interpretation it's just mathematically there but what he's looking at is actually a balance with a bent arm but if you do this for a few different positions mathematically the circle will show up as kind of a useful diagrammatic feature but in around 1600 probably just before starting these sets of notes Galileo writes a treatise on mechanics mechanics as in the old idea as being the theory of simple machines where he again includes this treatment of the effective weight of bodies on inclined planes and there he adds well it doesn't actually matter if the ball is here on an inclined plane or if it would be in a circle so it's here the effective weight of the body going down on this inclined plane or if you would consider a body going down in a circular hoop at this point it would have the same effective weight so here he starts wondering or he starts suggesting that this circle also can be giving a physical interpretation that's of course the point where you're actually thinking about a pendulum so here we have at least one point where the pendulum comes in as a possible object of interest in its own right and this then can be connected with the second fact the isochronity of motion on inclined planes inscribed in a circle because these inclined planes here are outside a circle so the circle they are actually tangent to the circle but again geometrically you can also put this inclined plane in the circle as a chord and geometrically there is a relation between what he has for the speeds on the inclined planes and the speeds inscribed on the chords inscribed in the circle so on the one hand diagrams suggest that the pendulum might be an interesting object in its own right and at the same time they suggest that there might be a relation between this specific property of the pendulum that then shows up once you start looking at the pendulum this is something you will rather easily start noticing well that the motion on inclined planes do in themselves show a related property and this is what really is the challenge that sets off Galileo's work in these manuscripts because then you can start trying to construct the motion on the circular arc such as the motion of a pendulum by these inclined planes so you're going to try to see whether you can actually demonstrate and that's really the challenge that Galileo sets himself where you can demonstrate the isochronity of the pendulum based on motion on inclined planes and this is where the law of fall comes in because then you need to know how bodies behave on inclined planes on the one hand and on the other hand you know that they must have an accelerated motion if the isochrony can be demonstrated from motion on inclined planes you must assume this motion on inclined planes to be accelerated you can no longer assume them to be uniform and it's again rather easy to see why this must be the case so imagine we have a ball going down like this we have the second ball going down like this and whatever their speaks there must be something about it because you could also take the third one going down from here there must be something in how they accelerate that is responsible for this isochronity so the acceleration cannot be something extra no it must be essential actually to the phenomenon and this is where he in this context that he most probably set up the experiment with the inclined plane that I started with to find out empirically is there something mathematically but the important point here is he has a reason to think there must be a mathematical regularity in the acceleration because of the isochronity of the pendulum and because he thinks that his isochronity of the pendulum has something to do with acceleration on the inclined planes so you have reason to assume that there must be something mathematical you set up the experiment and you pick the best possible approximation of a mathematical law being the law of fall now again as butner works shows this is the challenge that Galileo tries to solve can I demonstrate the isochronity of the pendulum based on the behavior on the inclined planes and this is actually a failed research program Galileo doesn't achieve his goal he could not have achieved his goal for two reasons one the pendulum is not isochronous so it's only approximately isochronous if you take small swings but if you really take bigger swings it's not isochronous even if Galileo believed they should be isochronous and secondly a rolling ball and a swinging ball physically they behave differently so there are good reasons why Galileo could not have found what he tried but it's failed but fruitful because actually everything that is in the discursive that Galileo published in 1638 is coming out of this research path so this is again what butner's book shows that everything that is in the discursive is actually coming out of the attempt to demonstrate the isochronity of the pendulum based on this motion on inclined planes okay there is one further development and that is taking place again as far as the documentary evidence we have after 1602 and that has to do with this projectile trajectory because now Galileo is already convinced that the law of all holds true if you now go back to this parabola and look at the parabola well then you're gonna say ah so this parabolic trajectory is the composition of the one anti-accelerated downward motion and thus the horizontal motion must be a uniform motion because you know have reasons to assume that this is an SS times squared okay then mathematically this must be a time parameter so at this point he's taking this step and actually interpreting it as the composition as this uniform neutral motion well basically a forerunner of Newton's inertial principle actually and then the second accelerated downward motion so taking all this together we see Galileo experimenting with inclined planes with pendulums with projectiles and he is now really explicitly thinking of time as a mathematical parameter even more specifically time is a mathematical parameter that is relating this different phenomena to each other it is only because time is here so again time is here in the pendulum time is here and time is here it's time as a mathematical parameter that is relating this empirically different phenomena to each other so going back to Coiré's quote good experiments are based upon theory well we can say that yes in a way Coiré was right but Galileo had more theory than Coiré could see behind his experiment in itself the experiment with the water clock is indeed not a very good experiment it's not very convincing most of a lot of Galileo's contemporaries were not convinced more or less approximately but why would we think that this is actually the right mathematical interpretation of your empirical findings and Coiré is taking up on this suspicion and for good reasons but Galileo himself had more theory but failed theory in the sense that Galileo could not theoretically link all these together but he knew that there were reasons to assume that this might be possible he had some partial successes in relating these to each other and it's these partial successes that give him let's say a partial theory that Coiré was asking for now the second aspect of Coiré's claim so good experiments are based upon theory and the means to perform them are nothing else in theory incarnate we can see illustrated I think very beautifully in another of these experimental notes taken by Galileo and this is an experiment on one of these folio 116 Verso and this is the folio and I'm here basing myself again on very beautiful analysis that has been given of this specific experiment by mathematician Alexander Hahn in 2002 this is the basic setup so Galileo has an inclined plane that's put on a table and he releases a ball from different heights so first from this point then from this point and each time depending on the height it's going to go down a certain length over the inclined plane it comes at the bottom and with the speed that it has achieved during a descent on the inclined plane it will then be projected from the table and it will then describe a trajectory if Galileo's right a parabolic trajectory and hit the ground at a certain distance r now what can we learn from putting the height against the distances because that's what Galileo is experimentally going to do is going to let the ball go from different heights and is then going to look at the distance at which it reaches the ground well first for purely geometrical reasons the height is proportional to the length of the descent on the inclined plane then if Galileo's law of fall holds true these lengths will be as the squares of the times taken for this motion now if as Galileo also believes uniform acceleration is due to the fact that speeds grow as times and this is again what he put central in his discursive then the squares of the times will be as the squares of these speeds and then if Galileo is right that this parabolic trajectory is the composition of a uniform horizontal motion and the downwards motion well then how far it will go this will be better mined by the speed it has because the horizontal speed will be conserved and so the square of the speed will be as the square of this distance and what Galileo is thus testing is whether all these assumptions taken together hold true because he's putting the heights against these distances now this is as Han points out in his analysis a much better test a much more precise test than the test with the water clock for two reasons one the water clock is not strictly uniform and secondly with the water clock one of the major source of imprecision in Galileo's experiment is well on the one hand you have to start and stop the water clock and on the other hand the ball so you have to release the ball as closely together as possible and then close the water clock at the moment that the ball hits so that's quite imprecise well both these problems are dissolved in this setup because Galileo again is not measuring time he's measuring distances but the distances can be put together because time is here the central parameter in this link of proportions so he has made the measurement of time internal to the setup he doesn't need to measure time in itself the phenomena against each other can do this you can actually look at it in two ways either you say Galileo is using the fact that this motion is uniform as his definition of time he's saying so he's actually saying these distances will be as the speeds and the speeds by definition will be as the times and now let us test whether the distances of the along the inclined planes are as the squares of times so either he's using this as his clock to test the law of fall or you can look at it in the other way he's using his law of fall as the definition of time to test whether this motion is indeed uniform you can look at it in both ways there are as it were two clocks within the experiment and what I would suggest is that we can see what's happening here is that indeed you can choose to define time either in the one way or the other but the fact that you can do both is here the interesting thing and this introduces a severe empirical coherence condition the time in the one and the time in the other it's the same time it's the same parameter small t that is showing up again so this is where I think you can really see this entangled history of the measurement practice and the development of the theory really taking place so again choices are made and once made may encounter resistance whether in experiment or in theory writing or else vindicated and this is where it is being vindicated it needed not be the case of course that this distances where as the heights it turns out to be the case so the chosen definition of time is a coherent one it works out it can be vindicated it is sensible to stay with this definition and use it to start analyzing further empirical phenomena and of course one empirical phenomenon that is at this point still an open problem for Galileo is the pendulum but this is what he did not achieve he did not achieve so here you see how the projectile motion and inclined plane are really tightly mathematically coupled to each other but it's still an open question whether that is the same time as the time that shows up or that seems to show up in the motion of the pendulum and this is the thing that and finally solves because Ergens in 72 73 I am not sure publishes his horology oscillatorium where he presents a demonstration that he actually first found out in 1659 where he does what Galileo set out to do but failed to do Ergens gives a demonstration that indeed from the law of all basing himself on Galileo's law of all Ergens demonstrates that this implies isochronity but it does not imply it for a circular pendulum Ergens is able to prove two things and this is really the big success on the one hand he proves that a circular pendulum is only approximately isochronous for small swings which is empirically the case so Galileo extrapolated from this isochronity for small swings towards isochronity in general and for this reason was criticized by a lot of his contemporaries Ergens shows that Galileo's own law of all indeed implies that it is only isochronous for small swings and he shows for which curve it is isochronous the pendulum is not swinging according to a circular arc but according to a cycloid and this is of course the point where we really reach Cuare's conclusion and this is why Cuare is pointing to Ergens as the end of the story the means to perform good experiments are nothing else than theory incarnate from now on is this pendulum not just a practical timekeeper in the sense that as already pointed out by Frank Arena's analysis it makes sense for practical purposes to use this as a timekeeper but Ergens has now shown that it is a good timekeeper for theoretical reasons that it is indeed that if you assume Galileo's mathematical proportions then the time the mathematical parameter in s is proportional to times squared that this time will indeed be periodically kept by the pendulum ok so I more or less an hour gone let me just add one concluding remark so concluding remarks but let me just give one because it really then closes the circle and lets us go to Newton so what Ergens has shown is that from now on the motion of the inclined plane the projectile the pendulum are all mathematically related they all belong to the same mathematical framework and allow you then to to have a good to see this physical instrument this physical thing the pendulum as being a timekeeper as being a very good as being almost perfect timekeeper one thing that's interesting about pendulum and already Galileo was doing this is that you can synchronize it with astronomical time you can start counting how often the pendulum goes up and down up and down during 24 hours defined astronomically so at least again practically you can synchronize the pendulum with the astronomical clock this of course suggests that the time this astronomical time must be somehow also related to this time as a mathematical parameter and that's of course what Newton then sets out to prove Newton really takes the step of adding further phenomenon and showing that the same time small t mathematical parameter is actually the time as measured astronomically and what's really interesting and interesting for deep deep reasons is that Newton can only do this by basing himself on the measurements with the pendulum of constant of acceleration so what Newton really what allows him to demonstrate a law of universal gravity and thus to show that this astronomical phenomena are again due to the fact that they are the same kind of mechanical system is because he can compare the acceleration of a body on the earth with the acceleration of the moon and that's the famous moon test which was only possible because this pendulum had indeed become theory incarnate and allowed this highly successful coordination of mathematical time and empirical phenomena so that's where I will end so let's take five and after that break the general discussion before the general discussion let's now do the comments so can you share us when a brief comment to open the discussion comment or question thank you very much for the talk very emulating it's always hard to get back from the contemporary physics settings to the historical ones but one thing that I found very interesting is how this is different from the medieval malfunction of motion that's happened just before Gaido's times and how before Gaido's motions were mathematics and time was always part of motion it was never done as this mathematical parameter so we should quite quite well how we are getting away from medieval physics and ice and physics one of the question I had was it seemed to me that the way that Gaido described motions it doesn't seem to be that far away from the idea of natural motions so my sense of natural motions does he actually say something about that does he explicitly say that he's going away from the idea of natural against non-natural motions or is it still in this kind of high student settings it's one of the question I would have you want to be first to go into the answer or as you wish do the first the other questions as always if you have a question the questions are also for Anne Frausen's passage as you said because I'm always surprised and I read this Anne Frausen's book that as of change there may be a reference once in the footnotes because this idea of time-setting and mathematical devices being set with iterative processes seems to be very similar to the thing as of change has been described in the event intro to temperature and if your analogy holds I wonder if you can have the same ontological results and the consequences of time being maybe not something that is actually very out of the world that we have to be creative and maybe if it is the case maybe we should revise our metaphysics of time in a more rational way or less natural way do you think that analogy holds that's why we rise to one question ok thank you and the first question on the relation let's say to the Aristotelian and medieval analysis of motion is a good one I wonder I consciously stayed away from here because if you read the initial treatise that Galileo writes in between 1589 and 1592 that's really in conversation with these debates so on the one hand he's saying ok let's treat motion as not being caused by the kind of causal factors that the Aristotelian think but caused by weight and weight understood as Artemidas understands it something that can be measured on a balance in relation to volume gives rise to something like specific weight so let's change the causal infrastructure but let's then see what kind of physics arises from this and initially and so I said Galileo rewrites it and the interesting thing it's really fascinating to go through how Galileo rewrites his own treatise is exactly to do with his questions of natural motion so initially he tries to speak as much Aristotelian as possible so in the sense oh you have natural motion, you have violent motion and lightness and heaviness so he tries to keep as much as possible of the Aristotelian vocabularly at least but gives it a different flavour and he comes to some problems there it doesn't really work out so well because on the one hand he keeps on talking about natural motion upwards and lightness but now it's actually not just it's not really light it just means that the medium is denser than the body so he's trying out but there you really see him struggling with this framework of natural motion or forced motion what's already there the possibility of an intermediary horizontal motion so I said so after 1602 when he goes back to the parabola he analyses it as a neutral uniform motion well in the demotu he's already talking about horizontal motion as something that's neither violent nor natural but he doesn't see it as uniform yet then time it's not asking it cannot really say much more about it so but he's clearly struggling with how to do how to square his orchimedean causal structure with this conceptual structure of motion on a cosmic scale let's say afterwards after the developments he decides that the natural fall is accelerated etc he keeps on calling this natural motion and when he writes the dialogue and the discorsi he keeps on using the terminology of natural motion but the link with the Aristotelian meaning has become very tenuous so there I think you see him drifting away more and more from what his concept meant but still for Galileo a physics must use these terms of natural motion and so it's it's not just motion as a state no there is something like natural motion but what actually is meant by calling it natural is becoming rather ambiguous or more and more ambiguous I would say because the cosmic the relation between the mechanical and the cosmic has become more a problem than something that he can assume so I think that's that's for the first and the second yeah so the the relation between Van Vraasen and Haasok Shang that's a very good something I think a lot of people have the same experience when they read that chapter and Galileo Van Vraasen talking a lot on the problem of temperature actually as an example of this kind of slowly going back to the Van Vraasen quote that there is the question like why doesn't he I think for Van Vraasen so he has this one footnote and I think Van Vraasen would say yeah yeah Shang does this much better than I do in the sense historically much much more I think the reason why Van Vraasen likes to go back to Mach is that Van Vraasen really wants to put all these ideas in a strongly empiricist tradition so what Van Vraasen rhetorically I think wants to do is say yeah Haasok Shang that's good that's convincing but in a way that's just an update of Mach and so he really wants to push so he really wants to put this in a very specific kind of tradition I think it's a nice provocation but I do think that it's more or less everything that Haasok Shang does with the iterative procedure is this is the measurement practice and theory evolve together in a thoroughly entangled way and I also think that yes indeed this has implications for how we understand the status of the thing being measured in the sense that we cannot be naive realists about it this is why Van Vraasen again here goes on with somewhat hesitantly one might say that the measured parameter is constituted so he's not committing himself to this kind of neo-cantian vocabulary but he's saying well probably if you want to make sense of the status of this kind of thing this is constituted but it's constituted in a historical so I would say it's Kassir so I have another claim that Van Vraasen in scientific representation is reinventing Kassir actually but with again an empiricist band so yes and I do believe that this indeed has this kind of implications for the possible metaphysics of time for example that you cannot think of so the only way that we know that we are measuring time when we are measuring time is because it's coming out of this kind of historical process and there is we cannot step out of this we cannot step out of the practices of on the one hand measuring on the other and theorizing that we've actually measured this time with a big T or something like this there's no room for that so I hope see that as the indication the door is open thanks Van Vraasen that was great so I'm wondering about the notion of fury here so at some point you said something that made me think twice about this something like he had a partial theory in the back of his mind so this means that theory has to be taken as something very far from mathematical theory or something like that with axioms that are well specified and so on it's almost implicit like where is the like if we say that measurement and theory go together we try to get that time is it just like in a very evolved way almost like an axiomatic theory or do we also have to take into account implicit concepts I don't know even storytelling maybe that has been around these concepts before and is more syntactic than about reference or whatever so where are the boundaries and does it make a difference for our concept of time and how do you see this notion of theory and how does van Fraassen see it that he writes something like this so van Fraassen to start with him makes the distinction in this chapter so you can always look at this kind of entangled history in two ways you can look at it from within the history so when you're struggling trying to come up with ways to actually make something measurable and at the same time develop the theory about the thing that you're trying to make measurable and you can look backwards from the vantage point where this has been successfully stabilized where questions about measurement you don't need to ask them anymore you know how to measure so you you know how to measure time you have these instruments they're measuring time for you and based on these measurements you're going to do other interesting stuff and looking back from that vantage point you have the concept, the thing that you're talking about has become this thing in the theory the theory tells you what it is and then you can look back at the process that has led towards this being the theory that more or less mathematically defines and of course if we here take Newton's as the example that's clearly a mathematical theory it is not an axiomatic system as we would think of an axiomatic system in modern mathematics but it's clearly a mathematical theory that where time is a parameter within the theory and that's what time now is but of course why I talk then about a partial theory is because Galileo is convinced that there must be a theory but he hasn't found it so that's what I expressed a bit clumsily with a partial theory he has as proportional to times squared he can do some mathematical manipulations on it using theory of proportions he can say oh if it's on this inclined plane, that inclined plane he can do he has a theory there and he believes he strongly believes that this theory must be extendable such that it would also demonstrate things about the pendulum motion it's a conviction it's a strong conviction that this must be possible because it's based I think basically on the fact that isochronity shows up both so the isochronity of the quartz and of the pendulum that's for him too striking to ignore and even when he doesn't achieve the goal even when he's not able to demonstrate one from the other he keeps on suggesting that there is a relation so there I think we're really in the midst of things where Galileo thinks there must be somewhere out there a theory that will do this and I have some of the building blocks but cannot put them together yet right sorry no this makes me think a bit it's maybe too far beyond Galileo but I asked this question like is this belief and you said this conviction but it makes me very much think of just like the practice of developing a theory as we all do it to some extent researchers we have this hunches and we actually if we really are trying to be rational about it and talk to colleagues and so on be presented as hunches like all conjectures or hypotheses but deep down we feel that it has to be true if we can invest in it maybe months I mean I have this obsessive tendency to months in a row like there has to be something there and then work hard and try to prove it even though maybe it was wrong so it was never a belief at all it was a hunch I'm on the right track there has to be something and it felt a little bit like that I would never call that a belief not even a conviction and definitely not a theory so I don't know about Galileo I don't know almost anything about that idea but could you see it in this way too and could such hunches and intuitions maybe have an impact on how we interpret quite complicated notions like time and our experiments and so on even though we have no real epistemic hard commitments there it remains so I think psychologically the distinction is a vague one and I think what I have been describing in Galileo could very well be described in these terms as well but I think it's a very deeply held hunch so even if after months and years it does not come to the result he does not drop the idea and so he can never prove the isochronity he thinks he can prove something else there is something else that he can prove he can prove that if you take this chord and if you take these two chords that motion this motion is going to be quicker than that motion he can prove that based on his law of thought and he knows experimentally that the pendulum is even quicker is always quicker than this this is for him I think the strongest reason to stay committed to the idea so this is isochronous this is faster than that and this is faster than that so taking that together it's for him too striking to give up on the idea so it is a hunch but one that has slightly more commitment built into it I would say but and then Galileo is a rhetorician so he tries to hide where he is but he knows and I think again with the description of the so Quare is right that just the experiment that Galileo describes is a rather weak epistemic reason to hold on to the law of thought I think Quare is completely right and Galileo tries to hide this behind his rhetoric of more than a hundred times and always come out very much true etc etc so he's overselling the point there but at the same time he did have something to back up his rhetorical overselling all these other experiments the pendulum etc but that's not something you could present in these terms that would not have been convincing for the readers as he imagined them and maybe for himself even but I think we can make sense of the fact that there is more going on that's good though that gets me to a question that I wanted to ask because there is sort of something hanging in the air still that like so you mentioned and this is actually something that I know a little bit less about that Galileo's contemporaries actually did many of them his competitors really didn't see this as a particularly convincing empirical argument so in that sense I guess where I'm trying to get to is his motivation then right for presenting things in the way that he does maybe the answer is just the answer that you just gave it really is in the end today largely rhetorical in that sense though maybe a bit paradoxically or a bit against the grain of how it's often presented when it's used as one of these cardinal examples in the history of science it's perhaps a lot less successful as filling the function that Galileo hoped that this kind of experimental intervention would fulfill maybe it's a lot less successful than we often give it credit for being I don't know maybe you have said what you have to say if you don't repeat yourself I think I can fill in some of the historical detail that is in itself interesting because I think a lot of his contemporaries were convinced and also partly because of the rhetoric and there, but there I think one example and I'm basing myself on the literature here that's very interesting is Mara and Mersen so it's really key figure in the network of philosophers and mathematicians and natural philosophers the first half of the 17th century is a correspondent of Descartes but also of the Italians and Mersen when he first reads Galileo, he's convinced and he sets up the experiment and it's pretty good, it's pretty convincing and then he's communicating with other people like Descartes and other some Jesuits and they are all pointing out but I have a different law and it's also plausible so they're really confronting Mersen with underdetermination in practice so you have these approximate results and you can interpret them as being evidence for Galileo's law of law yes but you can also interpret them as evidence for alternative laws that are being presented or you can interpret them as Descartes Descartes says there is no law of law there is no mathematical law of law because Descartes metaphysical reasons to hold this because weight is due to all these collisions of the subtle matter and it's never going to translate in a smooth function it's probably if you hear at circumstances at our earth it's a good curve fit to put it in terminology that Descartes of course didn't have he's suggesting to Mersen it's a good curve fit but it's not because there is an underlying law and Mersen comes away convinced saying yeah, the experiment by Galileo and I think that's really a very interesting little story but at the end Galileo was of course proven right and not by accident this is why I think he was proven right because these hunches he had they're going in a direction that's in Van Vraasen's terms indeed were vindicated in the end but their vindication is the good term in the end they were vindicated but Mersen was perfectly right to be doubtful privilege of privilege I have a long question I'm sorry Galileo has been a problem for me for a long time and now I have a specialist so my difficulty is to understand what we understand as time in Galileo because he's passing from the Aristotle position to be the first after that so in Aristotle time is the quantitative properties of change and one of the problems is coordination in Aristotle is biological change just saying that and at the end there's some fuzzy part of Aristotle saying you only have all the spheres you are constant everything coordinates to that sphere we don't know how about anything and with Newton we have time why all clocks are coordinates because they all measure something external the real time and Galileo seems to be in between so yeah the pendulum in time plane same time but you know plants growing isn't the same because he's not yet in the Newton to my knowledge he never said that time existed the penalty of stuff who does he I'm wondering it's a good question Galileo is of course less a metaphission than Newton is consciously and also by temperament I guess Galileo is really a mathematician stepping in the domain of natural philosophy and only doing something like metaphysics when forced to by his interlocutors whereas Newton or of course not in the or in the pre-Kipya only in this general school in a few places but we know Newton had more developed ontological ideas for example on time but also space I was a bit like hesitating because with respect to space Galileo is a bit more explicit and there he does seem to more or less naively assume an absolute space so there is kind of a tension in Galileo between on the one hand the way he's developing relativistic ideas to say well maybe the earth is moving and we just don't notice because motion has all these relativistic features but at the same time he assumes that there is like a privileged framework from which to say ah and the sun is at rest and the earth is moving but he doesn't have any criteria in it I'm calling it a more or less naive realist position on space whereas Newton as a sophisticated he not only posits that there is something like absolute space but he also shows how to empirically make sense of this or determine it at least up till translation so there it doesn't work out in the end but Newton is more sophisticated on this whereas Galileo just naively assumes that there is in the end an ultimate frame of reference that they find space with respect to time I'm wondering whether there are any points it's a good question I should go back to the text where he is coming close to even asking the question of the status of time but I'm assuming that if he would he would again make some kind of this naive realist move and saying in the end there is this real time and what I'm doing is showing the mathematics of it without really coming to terms with how the mathematics allows you to really get to this one thing but this one more thing that I can say and this is tying in closer to my story is that this is of course the importance that I mentioned that the pendulum can be synchronized with time as we experience it in the day-night pattern so you can on the one end we have this general notion of time as we experience it and as it is present in all these other phenomena growth etc and which basically shows up in day-night and seasons and there the pendulum allows you to connect the thing that Galileo is doing with this time because on the one end this pendulum is supposed to incarnate the mathematical time and on the other hand you can really Galileo never did it for 24 hours but not long after Galileo the Jesuits are gonna do it they're really setting up a pendulum and keep it swinging for 24 hours in count how many beats it takes such that you can determine the length of a second pendulum but the second is now being defined astronomically so you can link up this mathematical time with this broader time even if this broader time in itself is not yet mathematically in the same way that's what's gonna happen with Newton so that's I see your point but here if we buy what you're saying that in fact is not a metaphysicist which I agree but he's driven by mathematics so the division of movement between vertical and horizontal it's a mathematical division but at the end it's a physical tune you claim that you fall in right line even if the earth is turning so independent of two there's such a combination so time is also related to these mathematical division that will have later some kind of metaphysical integration it's a mix so I'm confused but Galileo was confused and this is going back to the issue of natural violent motion so Galileo I always see Galileo as someone who on the one hand knew what he didn't know and then tried to hide it so he he knew that he didn't in the end have a coherent framework to think about natural motion etc that he on the one hand had very interesting insights in his local phenomena and again something like a conviction that the global cosmic system should be built up from these elements but that he couldn't do it but then he tried to write as if he knew how to do it anyway and this is so where a lot of these questions are a hand way we put under the surface of the text by Galileo I would say and he's always trying to oversell everything but you can see this as some lack of humility which there was and Galileo probably was quite an arrogant man and disliked by many for this reason on the other hand there is a good research strategy there he's pushing things and setting an agenda for people after him and again he's semi-consciously doing this setting the agenda like this is what you people coming after me should also be trying to expand on and I think the contrast with Descartes is very interesting because Descartes has his famous letter to Mersenne where he says about Galileo he philosophizes better than most because he's doing this mathematical thing but of course a big but and the problem is that Galileo is no metaphysician that he's doing all these small local things that he's having this bottom-up strategy but in the end of course the bottom-up strategy was the winning strategy so this is where I think there is something right in Galileo's overselling it's really pointing the way towards a bottom-up strategy like let's do this and let's push it and see how far it gets us rather than doing the top-down cartesian approach so what is then does he have real commitment to what he's selling or is he just merely selling it because it's practically and pragmatically because I remember a paper we discussed conflict between Galileo and the church and the church is basically saying you're selling all these stuff but can there be a comprehension system it's based on your ontological results but obviously your explanations don't undermine your ontological reasons and at the end of this course according to what Mersenne says this course will go to the world he seems to be less confident explaining what he's explaining with his ontological data so is he really having a commitment so it's getting us back to is it a hunch or something stronger and I do think there so in the controversy with the church on the status of Copernicus you see indeed the same thing cropping up in the sense that Galileo is pushing the point for Copernicus up till it's breaking point in the sense that he's trying to present it as possibly demonstrated whereas he very well knew that he could not rule out Tichobrai's system and you see his texts again some of the tension surfacing but there again I do think that there is something interesting going on something more interesting than oh he had this conviction I just wanted to hold on and hide the fact that that Galileo introduces an implicit criterion in his letter to Christina which is I'm making progress so first we didn't have evidence to choose between the world systems then my telescope came along and now we know that Ptolemy cannot be right and he's right there but of course there is still Tichobrai versus Galileo versus Copernicus and there he is ok but we cannot rule out that further empirical evidence will be found and there he then gets on the tides wrongly in the sense that he tried to push the point that they were really empirical evidence of the motion of the Earth that could not be squared with Earth at rest but I think the more interesting point is that he is making it again into a question of progressing research programs and in the end he's forced in an uncomfortable position by the dialectics of the debate he he feels that he needs to make a stronger point so on the one hand he only wants to make the point let us continue the research and see where it leads us and on the other hand he is driven by some of the constraints of the debate to try to make the point stronger than just that but there again I do think that there is a rather conscious heuristic motivation having to do with how to develop research through this kind of historical process you're fine I would like to push you on the idea that it's bottom up top down that you use for the captain because for example this is not just bottom up it's also this clearly getting the captain principle of philosophy you start from principle you get to physics of course you do experiments from time to time to check so it's not completely but it's in the same style but okay maybe a bottom up was in vogue the founding of the royal site you cannot say Newton is bottom up this guy is just a mess going in all direction metaphysical theological experiments too but it's a mix and he seems to see as you well know in the two first book of especially in the first book of Prequipia that mathematics is a way to explore physical possibilities it's the world can be explored modally by mathematics which I see Galileo going in that direction but it's more clear you're maybe not there and the cap would say you're crazy except you know the mind of God hmm yeah so what way it's bottom up and what way it's top down yeah so saying it's bottom up need not imply that it is a purely inductive approach to physics or to science what I mean with the contrast between then the top down metaphysical approach and the bottom up approach is that you're only gonna once you have the right principles the good theory the theory is gonna get you all kinds of new stuff that you couldn't get without theory that you could not get inductively purely empirically or whatever but the question is how do you find out what the right the proper principles are and there I see Galileo as doing this kind of oh I have this thing pendulum inclined plane hmm projectile and let's see if we see these as related to each other according to which which would be the principles that would allow us to see these as related to each other and that is the way to find out the right principles and I see Newton as coming out of that tradition what he's doing is saying ah so you have indeed if these are all the phenomena that must be related that this is where the three laws come from they're really Newton's interpretation of all this work done by Galileo and Hergens on all these isolated phenomena what Newton is doing is saying oh so you have the free fall you have the inclined plane you have the projectile you have the pendulum and you have collision what are the common principles to from which perspective we can see the mathematics that's in all these phenomena is related that the three laws so you're coming to the insight in the proper principles by looking at the specific phenomena and going up from there once you have the right principles you have something much more powerful at your disposal as you point out where you can then explore where this will lead you so I understand better and it's why Newton does not call them laws they use axioms it's too sophisticated to use axioms not for nothing because he believes that at that point if you get to them they cannot be changed they will not be ruled out because he has done for mechanics but Euclid has done for spatial measurement so again there you see it's something else the same thing so we can I can measure this and then doing some kind of operations but I can also systematize this I can see all measurement operations can be systematized in this way let's assume these as axioms these as postulates and then check and that's what Newton sees himself as having done for mechanics