08.03. Prediction and Truth: Lessons From Ptolemy



how is predictive power related to the truth of a theory or a model that's our topic for this video and the next video this is a question we've addressed a couple of times already in this course this time I want to use a couple of real examples from science that we can use to draw some specific lessons in this video we're going to look at the case of Ptolemy's the ancient astronomer and mathematician who developed a model of the cosmos that lasted for 1400 years now to start with I want to present a statement that I think most scientists and philosophers of science would agree with predictive power does offer us reasons to believe that a theory is capturing some feature of the structure of reality this is one of the most widely shared intuitions in science but I want you to notice just how vague and non-committal this statement actually is if a theory gives predictions that are confirmed that offers reasons to believe a theory but it doesn't say how strong those reasons are or whether it's a reason to accept a theory or just a reason to have slightly more confidence in the theory than you did before so offers reasons is pretty vague and offers reasons to believe a theory is capturing some feature of the structure of reality some feature is also vague for example does it only capture features a reality that bear directly on what is observable or measurable or does it capture deeper features that go beyond that it doesn't say just says some feature so I agree with the statement but agreeing with the statement really only amounts to a vague commitment to the notion that the success of science is best explained to some degree by the fact that it captures something about the structure of the world to say anything more specific you really need to be more specific about the theory about the nature of the predictions about how surprising or unsurprising they are about how they connect with other things that we may believe but how they fit in with the rest of our background knowledge and so on and when you do get specific and look at real historical case studies there are some examples of real successes where we do think that we've captured something about the structure of the world it's hard to imagine being wrong about the existence of atoms and molecules for example but there are also some historical examples that I think everyone should be familiar with because they serve as a cautionary tale that even what we take to be our best scientific knowledge is still fallible it's still open to revision and in particular predictive power alone isn't enough to guarantee that our models of the world are accurate consider for example the ancient and early modern theories of the cosmos on the left is a picture of the earth centered model formulated by Claudius Ptolemy in the second century AD on the right is the model of Nicholas Copernicus the first sun-centered model which was published the year of his death in 1543 ad we're gonna focus on Ptolemies model here ptolemies model had each of the five known planets at the time Mercury Venus Mars Jupiter and Saturn and the Sun and the moon attached to a circle that rotated around the Earth these are supposed to be perfect circles that rotate at constant rates because that was the belief at the time that the heavenly bodies are perfect in divine so they should move in a way that expresses that perfection now in order to capture some of the irregularities of the motions of the planets as seen from Earth Ptolemy mounted the planets on smaller circles called epicycles that rotated around a center point while that center point rotated with the big circle around the earth so by tweaking the rotation rates of the big circle and the epicycles he could generate irregular motions of the planets as seen from Earth even though they're true motions were uniform and regular and finally in this model outside the circle of Saturn there's the sphere of the fixed stars which were assumed to be all at the same distance from Earth and which rotates around the earth once every 24 hours now this model was actually pretty good as a predictive model what exactly was it used to predict it was used to predict the motions of the stars in the Sun and the moon and planets as seen from Earth when and where on the horizon do they rise and set how does their position change throughout the year how exactly did the planets move against the background of the fixed stars when will we see the moon in different bayes's when will we see lunar and solar eclipses these are the phenomena that this model was designed to explain and predict and as a tool for prediction taller EES model was quite successful it could generate many of the irregularities of the observed motions of the planets it fit pretty well with observational data and it could predict those motions into the future was not as widely appreciated in most depictions of the Ptolemaic model is how much tricky machinery Ptolemy used to fit his model to the data and preserve the core philosophical principles of perfect circular uniform motions for one he treated the orbit of each planet as a separate model so the calculations for the orbit of Mars they're based on a model that is designed just to capture the relationship between Earth and Mars he doesn't have an integrated model of the whole solar system and second in order to fit the motions of the planets to the data he added epicycles on top of epicycles to make fine corrections some estimates put the total number of circles in his solar system model as high as 80 but more commonly it may have used between 40 and 60 circles and third he didn't actually put the earth at the center of the orbit nor did he have the main circle rotate uniformly around the center he had a special point called a quant which was off-center and that was the point around which the main circle rotated uniformly and all of this was engineered to account for the orbits of the planets which we now understand are elliptical without breaking the rules that he had imposed on himself so Ptolemy is trying to fit a model based on uniform circular motions to account for motions that we now understand were not uniform and not circular as a mathematical challenge it's an absolute triumph frankly and there's some evidence so this is how Ptolemy actually viewed it when he developed the model at the time as more of a mathematical challenge than a literally accurate picture of reality but the predictive success of the model certainly was treated by many people as a reason to accept the literal truth of the earth-centered model in broad outline at least that the earth actually is motionless at the center of the cosmos so the planets are mounted on circles or spheres that rotate around the Earth during the medieval Christian period this schematically was the basic picture of the organization of the universe as a series of nested concentric rotating transparent crystalline spheres with a planet attached to the surface of its corresponding sphere like an encrusted jewel and the outer sphere was the sphere the fixed stars the standard view – in Christian Europe was that beyond the sphere the fixed stars was the realm of heaven where there was an additional hierarchical ordering of heavenly domains where heavenly beings lived the stars were conceived as literally pinholes in a celestial dome through which the light of the heavenly realms Shaun down to earth now notice in these artistic depictions that no one's rise to represent the epicycles that are in ptolemies working model it's this simpler picture of the cosmos that dominates religious art and medieval encyclopedias in fact the epicycles would be a real problem if you tried to integrate them into the medieval crystal spheres view because then you would need rotating spheres attached to rotating spheres and the material of these spheres would have to pass through each other and what exactly are they supposed to be made of if they would allow for this in many ways it's a lot easier if you're working astronomer to just treat Ptolemies model as an instrumental tool for prediction rather than a realistic model of the world there's a long tradition of ancient and medieval astronomy that does treat it this way so what lessons about the nature of science can be extract from this example well the first is obvious the predictive success of a model does not guarantee the truth of the model or perhaps we should be more clear the predictive success of a model doesn't guarantee the truth of the assumptions of the model interpreted realistically as claims about what exists in reality now this really isn't a surprising claim because guarantee is such a strong word but what's interesting about the ptolemy case isn't simply that the model is wrong in some aspects it's how wrong the model is systematically from top to bottom the model is very effective at predicting the locations and motions of the planets as seen from Earth but it's radically wrong as a picture of the cosmos the planets don't move in perfect uniform circles there are no epicycles the earth is not the center of the cosmos the earth is not motionless there is no sphere of the fixed stars all of that is false so what we have here is actually a stronger claim the predictive success of a model doesn't guarantee even the approximate truth of the model now I don't want to overstate the point this isn't by itself an argument for skepticism about science or that we should never try to interpret theories realistically I can accept this lesson and still have good reasons to believe that science can and does give us at least approximately true descriptions of the world some of the time but cases like these in the history of science generally show that it's possible to be systematically wrong about one's conception of the world even in the face of seemingly very strong evidence for it and that's a valuable lesson to remember it helps to foster a certain kind of humility an openness to the possibility of being wrong which is an important scientific value and an important critical thinking value and finally examples like this illustrate some of the points I was trying to make in the previous video about the challenges of interpreting scientific theories now in the next video we'll look at a somewhat more contemporary example

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