William M. Briggs

Statistician to the Stars!

The Difference Between Essential And Empirical Models

One, two, ...

One, two, …

I was having a back-and-forth with a colleague on modeling types (see this post for a modeling hierarchy) and falsifiability. It’s crucial we distinguish essential and empirical models, but first a word why falsifiability is not especially interesting. Regular readers know that I have no great love for falsifiability.

If a probability model says a thing has any positive probability, no matter how small, and the thing happens, the model has not been falsified. How could it have been? The model said the thing could happen: it did: the model was right. Saying the model has been “practically falsified” is like saying “She’s practically a virgin.”

For large, complex models, say of the climate or behavior, even if a model says a thing has zero probability for a thing which happens, all are reluctant to toss out the actually falsified model and instead say, “Close enough.”

There’s lots more to say, which I’ll skip. The crucial element is that we must never confuse probability and decision. They are not the same. This is why all hypothesis testing methods, p-values or Bayes factors, are wrong-headed. They all conflate probability and decision. See Uncertainty for a book-length discussion (I have not said all there is to the topic in three paragraphs).

Quick: how many legs do dogs have?

Even a Loyola graduate fresh from her safe space knows the answer is four. Dogs have four legs. Why? Who knows? They just do. It is in the nature of dogs to have four legs. The essence of a dog, partly, is to have four legs. Not three, not five: four.

Here is our essential model, which says, “Dogs have four legs”. Everybody understands what you mean by this. Nobody is confused. Everybody knows you mean to address the essence of dogginess. Essence or nature is easy! It is the universal quality of dogs to have four legs.

Notice that our model is incomplete. It doesn’t tell us all about dogs; it only mentions one essential feature. There is more to dogs than four legs, which everybody also knows. Our model also doesn’t tell us why. Why do dogs have four legs? Maybe you know, maybe you don’t. It doesn’t matter. Our model is silent on this important question. Our model is still correct and even obvious, though. It doesn’t have to say why to be useful, just like you don’t have to understand how a diesel engine works to drive a truck and know you are driving.

Now the big twist! “Dogs have four legs” can be taken in a strictly empirical sense, as a model that predicts every dog you see will have four legs. That a good model? No: my number-two son has a three-legged dog, for instance. The empirical model “Dogs have four legs” has failed; it has been falsified. It is not true.

The falsification of the empirical model does not—of course it does not!—falsify the essential model. Everybody knows that something has caused this particular three-legged dog to fail in its essence. You don’t have to know what this cause is to know that it must exist (or must have existed). There could be any number of causes. Indeed, I know I was told, but I forgot, why Ramona (the pooch) lost its leg. Or if it ever had it. Whichever, I know that it should have the fourth leg to be a “complete” dog.

I know, and you know, that something is wrong with the mutt, where “wrong” is used in the essential and not empirical sense. Nothing can ever be “wrong” in the empirical sense. Things are the way they are, and aren’t the way they aren’t, a tautology and a truth. But things can be askew essentially. Take a side away from a triangle and you’re left, empirically, with two lines, and there’s nothing wrong with two lines, unless you mean it to be a triangle, and then something essentially has gone wrong. The word “wrong” is not “judgmental”, but a plain statement of fact.

You can see the difficulty, since the model “Dogs have four legs” can be take essentially or empirically, mistakes can be made. The wings of equivocation beat the air. All models aspire to be essential, but most are empirical. The problem is too many empirical models are claimed to be essential.

“Objection!” some bright student will say, “It is possible, and people have been known, to make mistakes in identifying the essence of a thing, therefore all that is left to us is empiricism.” False, student, for many more have made empirical mistakes. Are we to deny the weatherman his profession because he occasionally calls a sunny day rainy? And are we thus to abandon all empirical measurement?

No, that our ultimate goal is always essence (or nature), and that we sometimes fail is no dissuasion.

More on this most important subject in Uncertainty: The Soul of Modeling, Probability & Statistics.

36 Comments

  1. Dogs have four legs versus ALL dogs have four legs. Important difference.

    Occasionally calls a sunny day rainy??? Try 25% failure rate in most forecasts. If we’re only talking rain, it may be lower. Wait, isn’t than an example of saying “close enough” and ignoring the actual accuracy? (Denying the weatherman his profession is different, of course. They can be amusing if not taken seriously. Some here make the cutest errors, like the low being higher than the high.) Weathermen would be empirical after the fact, I think.

  2. Best model of the dog is a dog, I often said in my junior years. Was me a prophet? Alas, no. Just a tauto-mer.

    Seriously, even an imperfect experiment may have more to say than most unfounded theories. Moreover experiment do have errors to be estimated, and perhaps taken into account in interpretations. Perhaps.

  3. The Stanford Encyclopedia of Philosphy has a helpful discussion on Aristotelian ‘essence’:

    “‘Essence’ is the standard English translation of Aristotle’s curious phrase ‘to ti ên einai’, literally “the what it was to be” for a thing. This phrase so boggled his Roman translators that they coined the word essentia to render the entire phrase, and it is from this Latin word that ours derives. Aristotle also sometimes uses the shorter phrase ‘to ti esti’, literally “the what it is,” for approximately the same idea.”

    Of course, Aristotle disagreed, radically, with Plato, perhaps not on the idea of essences, but about our knowledge of them. Plato opined that we can never, under any circumstances, have real knowledge of “the what it was to be” of a thing, no matter what that thing is; instead, for Plato, we can only have ‘likely accounts’. One does well to remember that Aristotle did not so much refute the Platonic project, as disavow it.

  4. RE: “…crucial we distinguish essential and empirical models…..”

    By ‘essential model’ are we to assume that means a model that assumes that correlation =’s causation? (this seems to be the meaning of the jargon here based on the content in the earlier post incorporated by reference, but probably not the meaning intended here)…

    Or (this seems most likely), that by ‘essential model’ an ‘essential model’ is a model about the a thing’s attributes — some key “essence” of the thing modeled? If that’s the case … why the awkward jargon (and why not define uncommon jargon clearly?)? If that’s not the case, then what??

    All models (with rare exception) are built based on a sample(s) of a population(s). Sample size [especially ensuring a size is adequate, or, recognizing it isn’t] is the facet everybody learns about … however, understanding the attributes of the thing being sampled (what its “essence” seems to mean today, here), including the environment in which it operates and the interplay between, are part of the model-building exercise. Intrinsic to this is recognizing when one does, or doesn’t, or that one might not have all relevant into about the comprehensiveness of the sample dataset(s) from which a model is generated and that the resulting model is limited accordingly. That, and understanding & representing the real-world physics (or biology, as applicable) correctly.

  5. So this ‘essence’ – it really boils down to definition and classification, correct? So much of biology is simply the identification of the essences of animals, plants, microbes, etc?

    Is the ‘essence’ of a person encoded in DNA, or is the fact that a ‘person’ has DNA that’s similar to other ‘persons’ in certain ways part of their essence (thus a person with “damaged” DNA).

    The biggest question, I have, is what are the dividing lines.

    When does the Wolf stop being a Wolf and start being a Dog?

  6. “Even a Loyola graduate fresh from her safe space knows the answer is four. Dogs have four legs. Why? Who knows? They just do. It is in the nature of dogs to have four legs. The essence of a dog, partly, is to have four legs. Not three, not five: four.”

    I can’t see where this leads to “when does a wolf stop being a wolf”? A wolf has four legs and that is the essence of a wolf, in part. The last two words are important. The model is only of a wolf in part. Why it’s a wolf is not covered, so far as I can see. That’s a separate issue, it seems to me.

  7. I love falsifiability. Even though I love it, that doesn’t mean I am so in love with it that I blindly follow it. I do try to say that “Science is a means of figuring out what isn’t part of the model. Science is not about figuring out what is part of the model!”

    Except sometimes, we sort of do figure out that something is part of the model.

    I told my son, “I seeded the black berries”. I then handed him a jar of seeded jam…

    “Does this have the seeds in it or doesn’t it!” was his aggravated response.

    Language sucks… It will become easier for him after he seeds a couple of batches of blackberries….

  8. It’s the argument that always comes from the left, that is to say the intellectual heirs of the nominalists. The epistomological edges are fuzzy; therefore there’s no ontology. Or: to define a dog is problematic; therefore there is no dog; therefore there can be no essential model of a dog.

  9. Gee, now I am more confused. I have never understood what “essence” really means, and now I am more confused than ever. We don’t know, a priori, that all dogs have four legs. We observe many dogs and they all (with some particular exceptions, as noted in the post) have four legs. So that type of observation for ourselves and as relayed to us by others. All dogs (with some exceptions) have a tail, two ears, a wet nose, etc. We can’t classify by breeding because dogs and wolves can interbreed. What is the essence of an animal that is bred from a wolf and a dog? Biologists have done a good job of hierarchal classification species, ….., kingdom.. Do those classifications indicate essences? I am really confused and would like to be enlightened.

  10. Bob, I agree with you. I am a bit uncomfortable with Briggs’s notion of “essential” versus “empirical” models. Also with the notion of model definition, at least in the dog example given here.

    I usually come at these issues from the perspective of physical science, and typically physics. My concern with the notion of “essential” versus “empirical” is that it seems the notion of essential immediately takes the thought process into areas that are difficult to tie down so that all observers/thinkers are discussing the same concept and can replicate the observation/thought, i.e. into the philosophical or metaphysical and away from the physical. Empirical to me implies that the model or hypothesis has been defined explicitly enough so that the method of measurement is clearly part of the model and usually the model is not compared to some abstract notion of essence but to some other candidate model. “Essence” seems to imply a universal, unchanging “truth” which is not the experience from the physical sciences.

    In the dogs have 4 legs example, for example, the statement does not contain an explicit prescription for classifying a candidate object as a dog. We could say that “All dogs registered with the AKC have been born with 4 legs” but that would still not give an alternative we wished to rule out. Perhaps better would be “Dogs registered with the AKC are more likely to be born with 4 legs than any other number of legs.” Then we could either sample, or better yet exhaustively canvass the dogs listed with the AKC. Or we could define dogs by some genetic sequence and say “Animals with a certain specified genetic component unique to dogs are more likely to be born with 4 legs than any other number of legs.” This would make clear a few things. First, how do we select objects to include in the class “dogs.” Second, at what time in life do we observe the number of legs. Third, what are the alternatives that we wish to obtain evidence for or against. It helps in this case that the alternatives are not continuous. From a model so phrased and observations based on them, we could come to a conclusion what the most likely number of legs was that we observed and adopt as a working empirical model that we expect dogs to have 4 legs. Departures from that model could then be examined individually.

    Another example is the issue of how fast objects with mass fall toward the earth. One model that was believed at one time was that “Objects with greater mass fall to the earth faster than objects with less mass and the rate of the more massive objects fall is proportional to the mass.” Based on Galileo’s observations another candidate model became “Objects of any mass fall to the earth with the same speed.” But there is still some slack in these statements, we have not specified the details of the measurements enough. If instead we say “Objects with mass falling from a given height above the surface (or center) of the earth and either massive enough that air resistance is negligible, or allowed to fall in a vacuum will fall with the same speed and reach a given lower height at the same time.” Now we could do experiments over as wide a range of masses as possible, perhaps over a range of heights, and by carefully reducing our experimental errors find that the second model is not wrong within the experimental errors that we have characterized. We could also say that the first model is wrong unless the differences in fall rates between masses is smaller than our experimental errors. We could then accept as a working model that the fall rate is independent of mass, given the other conditions. Then we could (and historical workers did) use that working model to compute the consequences of other observations, such as the orbits of planets, trajectories of artillery shells and bullets, etc. We might find that computing the consequences with the first model did not agree with observations (unless the dependence on mass was smaller than the errors of any experiment/observation so far done) and feel even better about using our second model as a working model. We could then compare the effects obtained in fluids such as air or water and perhaps get to other working models about fluid resistance. But the point is that the second model would not be taken as “essential” but simply a working model that is to be continually checked against predicted consequences, and if found to be wrong somewhere, both the observations and the model are examined to figure out why.

    The key points here are 1) whatever models we form and seek to use are only considered temporary models that seem to work, and not a representation of “essence.” 2) The models must be stated in a non-arbitrary fashion such that anyone who checks out the consequences will predict and measure the same quantities. 3) The model is never considered an absolute truth or essence, but simply the current best guess, always to be compared with experiments like the ones we originally did as well as with other experiments for which it should be relevant, and it should be continually compared with alternative models.

    There are many other cases of physical models that have been successful at predicting consequences for long times until they were found inaccurate compared to a different model. Neither the old or new model had the “essence” they just agreed more or less with experiments.

    If a model ever captured the “essence” would that mean no other model would ever be possible by definition?

  11. Ye Olde Statistician

    August 15, 2016 at 4:19 pm

    Among the many attributes a thing may have, some are essential to its being what it is, others are necessary consequences of this, and others are simply accidental. There is something in dogs by which even a child upon apprehending one (and possessing the necessary vocabulary) will cry out “doggy!” Of course, a breeder knows a dog in a different, perhaps more detailed manner than a child. (Somehow or other, you cannot slip a wolf into the annual American Kennel Club show.) A biologist knows a dog in still a third way. A hunter or a shepherd in another, a chef (in certain cuisines) in still another, and so on. Who can say that a dog is known in only one way?

    Now the statistical way does not work. You cannot gather up a bunch of dogs, make measurements, count legs, or whatever, take pictures of their DNA and determine what characterizes doggedness. On what basis did you gather up the dogs in the first place? Why not gather up a few dogs, a cat, two petunias and a banana? That is, there must something in virtue of which we can recognize these critters up front in order to call them “dogs” at all.

    Those who insist on firm distinctions grow upset at the thought of three-legged dogs. How can a dog be essentially four-legged and yet have only three legs? The human response is to note that three-leggedness in this context is not a different essence of a different critter. Rather, we immediately recognize it as a defect in its doggishness. (In the same manner, a car with a flat tire is still a car and not a different kind of artifact.)

    OTOH the wolf can be recognized as distinct from a dog from the fact the the dog is naturally domesticated (“Natural” meaning “by birth.”) whereas the wolf is naturally a wild animal. Notice that different kinds of things need not be different biological species. (Nor even biological: we can recognize a bean-bag chair as a species of chair even though it looks not at all like an Adirondack chair.)

    The essence (or nature) of a thing is not simple or one-dimensional. A dog is not only naturally four-legged and domesticated but includes other elements of shape and behavior. And given that we do not normally confuse Chihuahuas with St. Bernards, it is evident that there is an irreducible hierarchy of forms as well. So part of the essence of dog is the essence of canine in general (hello, wolf!) of mammal in more general and so on; and in the other direction, the essence of Spot is more specific than the essence of dog and differs from the essence of Rover.

  12. “The essence of a dog, partly, is to have four legs. Not three, not five: four.”

    PARTLY.

    The essence of a wolf can be, partly, to have four legs. That does make the wolf a dog. That’s not what this saying. Essence is not like fingerprints and no two are alike when referring to a partial essence of a creature.

  13. Empirical errors are easily fixed. Essential errors are much harder to root out. Remember “the ether?” That’s because the former is objective while that latter is just BS. Often it is just not possible to gather all the empirical evidence to have a sure grasp of complex systems, but that doesn’t mean you throw it out what you do have. That would be dumb and lazy (or profitable, if say you worked for Exxon).

    JMJ

  14. Essentially, how does a dog differ from a wolf? Since I cannot tell the difference unless there’s a label on each, they are empirically the same. Google research tells me that grey wolves and dogs are genetically identical. I might be able to tell the difference if one wants to eat me for dinner, and the other wants to lick me to death. Historically it is obvious even to a caveman that there is a difference.

    It appears that the difference between dogs and wolves is the differences their relationship with humans, and this has to be caused by something. Dogs love us, and wolves fear us.

    I am not sure how this fits into the essence Briggs talks about, because all the things I talks about are measurable, empirical things.

  15. The “partly” is to address Bob’s dog traits of wet nose, two ears, etc. … The dog will have four legs plus a wet nose plus two ears plus other traits associated with doggieness. If the example were “Wolves have four legs” there would be a list of other traits that are more associated with wolves than dogs.

    If you are interested in the differences between dogs and wolves (which admittedly is not the topic of this post), there is this: http://missionwolf.org/page/wolf-dog-difference/

  16. 1. Ah yes, the “essence” of a thing.

    It seems “essence” simply “must” be comprised of several components: the “crux” of the thing, the “substance” of it, the “core” of its “nature”, and of course its basic “actuality.” Now we can distinguish each of these things by what we feel they mean to us. A casual observer may think that the “essence” of a thing contains its “crux” and its “nature.” Or is it the other way around? Or perhaps its “actuality” is more important and encompassing than its “essence?” It must be directly related to the property of “being.”

    I submit the previous paragraph to be empty dialectical gibberish. Unless someone can and chooses to precisely define what “essence” is in the context of a model, preferably a physical model, and preferably by defining how it is measured so that it is recognized by any observer, in any relevant situation and preferably quantifiable, then discussion relating to the “essence” of anything becomes only personalized dialectics with meaning only to the individuals saying the words at the time, and with unknowably different meanings to each. It seems to me this is part of the reason so many arguments ensue here about such things, because no speaker has a definitive grasp of what the other speakers mean by the vague terms, and each argues against a phantom: a mistaken idea of the what the other means. The conversation then focuses on the psychological attributes of the participants and how they personally choose to view the meaning of such things as “essence.”

    Statements that begin “The essence of a thing is……” or “The essence of the thing is not…..” are fine as statements of personal belief, or they may, depending on the word being used, relate to the personal belief of some author of past works. They should be prefaced by the words “To me, …. ” as in “To me, the essence of a thing is…..” Regardless, unless the concept (in this case “essence”) can be defined such that any reader can observe elements of the universe and come to the same conclusion with respect to “essence” in the same physical entities, then the concept seems to have little utility in dealing with the observable world and more utility in exploring the workings of the minds of the users of the concept.

    2. Re:JMcJ and the “ether”

    Assuming the reference is to the “luminiferous ether” which was proposed in the late 1800s, the proposal was decidedly empirical and was in fact ruled out on the basis of experiments. The ether model grew out of the work earlier that century deciding whether a model of light transmission by particles or by waves was more empirically justified. It turned out that Maxwell was able to synthesize the behavior of light and electromagnetism in one set of equations, named after him, and the model (Maxwell’s equations) was wildly successful in predicting experimental outcomes ranging from lab measurements of current in wires, electromagnets, and the like. A prediction of the model was that the equations had a wave solution comprised of transverse waves which explained the experimental results for light pertaining to diffraction, certain astronomical observations, etc. The model had a problem with the rest of physics, however. All previous wave equations required a medium in which to propagate and which was closely related to the speed of the wave in the medium. The medium is needed to provide a restorative force for the wave oscillations. A great deal of success had been had with this approach for waves in fluids such as water and air. To accord with the apparent need for a medium, a model was proposed that space was filled with an ether, which was at rest in the universe (coinciding with Newton’s universal coordinate frame) and which light used as its medium for propagation. As is done with all models in physics, the consequences of the model were computed and it was found that if the model was not wrong, then the speed of light in a specific direction should be measurably different depending on the time of year due to the speed of the earth in its orbit about the sun, with respect to the ether. The experiment was done (the Michelson-Morley experiment) and the result was that the ether model was found to be wrong. In particular, the speed of light was found to be constant, regardless of relative motion in the universe or relative motion between the source and the observer. The combination of no ether and constant speed of light created a great deal of theoretical tension, only resolved when Einstein (on the shoulders of Lorentz) proposed his special theory of relativity. Lorentz and others continued to push modified forms of theories with ether, but eventually experiments showed they were clearly wrong. The ether was and empirical solution to a model problem and was ruled out empirically. Special relativity has so far been found not wrong for every experiment testing it, but time will tell. It will be interesting when it is found wrong.

  17. Ye Olde Statistician

    August 15, 2016 at 6:21 pm

    “Essence” seems to imply a universal, unchanging “truth” which is not the experience from the physical sciences.

    The essence of a proton is that it possesses a positive charge. I believe this is universal and unchanging and from the physical sciences.

    One model that was believed at one time was that “Objects with greater mass fall to the earth faster than objects with less mass and the rate of the more massive objects fall is proportional to the mass.”

    If you drop two such objects in a pool of water to slow their fall to easily observable rates, you will find that this is still true. (http://arxiv.org/abs/1312.4057) For that matter, the gravitational force between two bodies does depend on their respective masses F=GMm/d^2. (Of course, they talked about weight, which was empirically measurable, not mass which was a theoretical abstraction.)

    But essences apply to things, not to doings, so there is no essence of falling; although it is the essence of ponderable matter to fall, i.e., to move toward the point of lowest gravitational potential. How fast it moves there is an accident depending on the local gravitational field and the resistance of the plenum.

  18. Well, darn. The essence of a proton is that it possesses positive charge. That settles that…

    And I always thought the essence of a proton was that it has spin 1/2. This distinguishes it from photons and gravitons (spins 1 and 2).

    Or was it that the essence of the proton was that it has mass 1.67e-27 kg?

    Oh wait, the essence of the proton was that it participates in the strong nuclear force, which distinguishes it from leptons like the electron.

    Oh no, now I remember, the essence of a proton is that it is a Fermion and obeys Fermi-Dirac statistics, with states regulated by the Pauli exclusion principle. Right, right.

    It seems this dog-gone essence thing is a slippery mutt.

  19. If you drop two objects in a pool of water of equal masses, the rate at which they will fall will in general be different and will depend on the shape of the objects (a narrow rod will fall faster than a ball of the same mass), the surfaces of the objects (dimples or ridges will affect the rate of fall), etc.

    Aristotle established a number of very interesting works. I have read and appreciated his works on rhetoric and some other works, but his approach to science kept the practice of science back for hundreds of years. His insistence on logic as a test of a physical principle instead of experiment kept a clear understanding of acceleration and inertia from occurring until Galileo (and some others) introduced the notion of empirical observations being the test of physical theories, not logic.

    The principle has to do with acceleration, not force. The acceleration on a mass m in the gravitational field of the earth is given by

    F = m*a = -MmG/d^2

    as you point out. This means of course that for any object of mass m, the acceleration is

    F/m = a = MG/d^2

    which says the acceleration is independent of the mass of the falling object.

  20. Right now my dog, an Alaskan Malamute, has about four and a half legs and won’t give any of them up without a fight.

    (of course the bony one came from a steer)

  21. Anon: The difference between dogs and wolves—no annoying do-gooder environmentalist insisted on the reintroduction of dogs to the Yellowstone ecosystem. We could discuss the essence of that “model” (enviros) but it would be too lengthy. I can think of a couple of parts of it……

    JMJ: Lack of understanding of complex systems is also profitable if you’re a conniving greedy woman who thinks she has the right to be president whether or not anyone else agrees.

  22. Ye Olde Statistician

    August 15, 2016 at 8:58 pm

    [Aristotle’s] insistence on logic as a test of a physical principle instead of experiment kept a clear understanding of acceleration and inertia from occurring until Galileo (and some others) introduced the notion of empirical observations being the test of physical theories, not logic.

    But it was Aristotle who insisted on empiricism: “Nothing is in the mind unless it is first in the senses,” and this was kept up by the Aristotelians of the middle ages. There was some suspicion that contrived experiences might tell us only what things did under artificial conditions rather than under natural conditions — an inordinate fear of the observer effect — but, as Albertus Magnus put it: “Experimentum solum certificat in talibus.” (“Only experiment verifies in such cases.”) Peter of Maricourt, who discovered the laws of magnetism by experimenting, wrote that an investigator “diligent in the use of his own hands… will in a short time correct an error which he would never do in eternity by his knowledge of natural philosophy and mathematics alone.” And Roger Bacon contended that “We learn more through artful vexation of nature than we do through patient observation.” Theodoric of Freiburg determined the correct explanation of the rainbow by experiments with glass spheres filled with water. Jean Buridan de Bethune wrote that “One might assume that there are many more separate substances than there are even celestial spheres and celestial motions, and invoke whole legions of angels to move them; but this cannot be demonstrated by arguments originating from the senses, and the philosophy of nature demands always that our arguments be sensible.” The examples multiply. The idea that Aristotle and the Aristotelians who expanded on his system restricted themselves to pure logic is a Modern myth.

    The real hold-up was the lack of any instrumentation to measure most properties with the necessary precision. They could do weights and lengths, but time was only coarsely measurable until the invention of the mechanical escapement. The Greeks did not even possess words for “velocity” and “acceleration.” Those were medieval inventions. Bradwardine showed that uniform acceleration was equivalent to uniform velocity at the mean velocity and Oresme devised a geometric proof that Galileo used without attribution a couple centuries later.

    But the whole Aristotelian notion of “motion” is equivalent to acceleration. Kinesis is a change to a property that a body already possesses. So that if a body possesses a velocity to begin with, then the kinesis is an acceleration and the contention that anything that is in kinesis is being moved by another is actually Newton’s first law, and was more or less expressed by Buridan in the 14th century when he said that “when a mover sets a body in motion he implants into it a certain impetus, that is, a certain force enabling a body to move in the direction in which the mover starts it.” This motion would continue until diminished or corrupted by gravity, resistance or friction. In the celestial realm, where there is no resistance, the motion would continue forever. Impetus, he said, was the product of weight times speed. In this, we recognize the egg from which both inertia and momentum hatched.

  23. There is an often misquoted line from the Bible which people misquote as “Money is the root of all evil.” It is often taken by misquoters as having a meaning that money itself is evil. As we all know, the actual quote is “The love of money is the root of all evil.”

    So it is with Aristotle. I was too harsh on him. As you say he advanced a great many ideas about the physical world. And he did indeed try to use observations as a guide. However, his approach lacked two important aspects. 1) His approach was intrinsically qualitative, not quantitative. He simply was not a mathematician and did not couch his observations with the precision allowed by math. 2) Perhaps because of this, while he made observations, he did not make quantitative observations, nor did he construct and perform quantitatively characterized experiments, repeatable by others. Nevertheless, what he achieved was no small feat for his time. It is in this sense that, compared to modern physics, he relied more heavily on qualitative logic from observation, than quantitative comparison with controlled experiment.

    The problem was the love of Aristotle (about 350 BC) in the more than thousand years afterwards. Partly out of regard for Aristotle and the presumption that he was correct in all things, experimental, quantitative approaches to physics were not pursued until the time of Copernicus and Galileo (around 1500 almost 2 thousand years after Aristotle), presaged by some original thinkers as you note in the cases of Maricourt and Buridan (around 1300). Once the leap to quantitative comparison to experiments was made, progress was much more rapid, leading to improved techniques and equipment, which in turn led to more sophisticated experiments. A major difficulty is that without quantitative expression and experiment, the interpretation of the qualitative statements is necessarily poorly articulated and only relates to modern physics by sympathetic interpretation attempting to read concepts into his words that he may or may not have meant but certainly never demonstrated quantitatively. Thus to continue to try to interpret current physical reasoning in terms of what Aristotle wrote does not take advantage of the several thousand years of dramatic progress that has been made.

    For example, apparently his definition of motion was “Change (motion) is the actuality of that which potentially is, qua such.” His concept of kinesis was simply “change” and vaguely defined.

    From YOS: “But the whole Aristotelian notion of “motion” is equivalent to acceleration. Kinesis is a change to a property that a body already possesses. So that if a body possesses a velocity to begin with then the kinesis is an acceleration…”

    Aristotle’s stated concept was change, any change. As you say the Greeks did not even have words for velocity and acceleration This interpretation that it is “equivalent to acceleration” is a charitable stretch based on modern knowledge of how one might interpret this notion. The words “a change to a property that a body possesses” could equally well be alleged to describe (or presage) change in position, change in velocity, change in acceleration, change in higher derivatives of position, change in thermal energy, change in mass, change in molecular composition, change in nuclear composition, etc. etc. However, the words as stated are so arbitrary that nothing specific (certainly nothing quantitative) about any of these particular physical quantities can be claimed from the words. It is simply a charitable interpretation. If one wants to read things in one could find fingerprints of relativity, or quarks, or dark matter, information theory, or DNA, or virtually anything one chose. But that is simply a result of the vagueness with which the concepts were described and the ingenuity to read meaning into words that likely did not intend it.

    It is fine to have a fondness and appreciation for ancient thinkers, and an interest in historical writings, but trying to apply the often vague and ill-defined qualities with which they dealt to current questions of physics is deliberately handicapping one’s thought processes and leads to outright errors. The example of “essence” is one such notion that is not helpful in a quantitative approach to physics. Other examples were raised before, such as “actuality” “potentiality” etc. etc.

    A very good collection of the works in the conceptual trajectory leading to our current understanding of physics is a book edited by Hawking and titled “On the Shoulders of Giants.” He reproduces what he considers the pivotal works for the history of physics, with discussions of the history and impact of each. He starts with Copernicus, then goes through the works of Galileo, Kepler, Newton, and Einstein. It is a large volume and contains the actual writings of the scientists considered. He has a similar volume titled “God Created the Integers” on what he considers the linchpins of modern mathematics. Again reproducing the original writings with explanatory commentary. He starts with Euclid, Archimedes, and Diophantus, then leaps to Descartes, Newton, Euler, and more familiar modern mathematical groundbreakers. They are worth reading and directly relate to our current concepts. Later editions may include more works, my copies are a bit old.

  24. Unfortunately, the departure of this conversation from the point, namely the relative utility of the concept of “essence” versus the application of empirical models to making progress understanding the physical world as represented by physical sciences such as physics. The conversation has strayed to discussions of words such as “actuality” or “nature” or historical uses of words such as “change” or “impetus” all of which contribute nothing toward clarifying whatever might be the meaning of something called “essence” in the physical world as we know it today.

    The thrust of modern physics is that understanding proceeds by comparing mental models quantitatively by computing the predictions of well characterized guesses (or models) for experiments and comparing to the physical outcomes. This process has the benefit of clarity to all observers and performers of experiments, lack of arbitrary meanings, ability of anyone to replicate the understanding, and assurance that the concepts discussed are understood in precisely the same way by all such observers and experimenters. With respect to Briggs’s notion of essence there is no such clarity, no ability to assure that the concept is understood in the same way by all, and no way to decide in a non-arbitrary way what is or is not “essence” of a physical entity. At least not until the concept is more precisely defined.

    A very good example was posed earlier in the question: what is the essence of a proton? Or an electron? How is it defined and measured, and compared to other notions of “essence?” Models of the proton or electron as used in modern physics suffer no such lack of clarity or utility. Without such clarity discussions involving the concept of “essence” will never generate utility in understanding physical reality to the same extent that the empirical modeling approach of modern physics achieves.

  25. “If a probability model says a thing has any positive probability, no matter how small, and the thing happens, the model has not been falsified.”

    I disagree.

    During one of the spectacular financial crises of recent decades, quant modelers were saying things like “We are seeing twenty-five sigma events occur every day now.” (Paraphrasing.)

    To me, this is falsification. When your model tells you that what you see is twenty-five sigmas away from the mean, the infinitely more likely explanation of reality is that said model is garbage.

  26. Bob Kurland,
    Essences are grasped by the intellect in a non-formal way–this process can never be captured in an algorithm.
    The definition given as the essence can change. We define man as rational animal. But supposing one discovers intelligent aliens then we would need to revise our definition of man–we may say man is rational animal from the planet Earth or maybe man is rational animal descended from Adam and Eve.

  27. And yet you all seemed to miss the point – to classify models, so we can judge their merit as a useful tool.
    THIS model is an essential model because it is derived from something the constructor of the model assumes is (part of) the essence of the thing being modeled.
    THAT model is empirical because it is derived from measurements made of the thing(s) being modeled.
    These two types of models require differing ways to judge their merit.
    That is all.

  28. Ye Olde Statistician

    August 16, 2016 at 8:17 am

    @fah
    Mathematical approaches were being developed in the Middle Ages, esp. by the Calculators of Merton at Oxford. But it is difficult to devise a mathematical descripription of stuff when you have no good way of measuring the stuff. Enter the Instrument Makers of St. Albans. But even so, there were no ways to measure pressure, temperature, color, etc. Even time was imprecise. The medievals develped ideas like “numerator” and “denominator,” solved the problem of motion on an inclined plane (Jordanus de Nemours), began to apply the scribal shorthand for “and” (formalized letter T from “et” — it looked like +) to arithmetic. And began to use a symbol for a generic ratio using dots for the numerator and denominator: ÷ to mean division. Aristotle was suspicious of applying mathematics to problems of the physics, because physical matter was in continual motion (indeed, it was virtually defined that way) and mathematics — which meant arithmetic and geometry — was static. Not until Newton was a calculus devised for mobile being. Even so, the medievals made a stab at it; but remember they were laying the foundations, not capping the rooftop.

    Things would have really gotten rolling in the 14th century except for the Black Death, which dropped the population density of Europe below critical mass. It did not reach 14th century levels again until the 16th century. And this time they had the printing press. So not only was the number of verbal neutrons impacting other minds back up to level, but they were coming faster and with few copyist errors. Besically, we had a Scientific Revolution about as soon as it was possible to do so.

    It was more of a Scientific Evolution, really; although the Dead Zone of the Renaissance confuses matters. There is more continuity than there is discontinuity. The real discontinuity is the one often overlooked: the change in purpose from understanding nature to exploiting nature. F. Bacon wrote in the most misogynistic terms about man dominating and enslaving nature and Descartes wrote of man’s conquest of the universe. Science was henceforth to be the handmaid of engineering and industry rather than of philosophy. The goal was no longer understanding, but knowledge.

    Nowadays, we have empirical models picked out from Big Data in which the variables of the resulting equations do not represent any real-world quantities. That is, a bunch of inputs — X1, X2, …, Xn — are put into the black box, a bit of orthogonal factor analyses are performed to reduce multicollinearity, and — hey, presto! — out comes one or more formulae: Yi = g(F1, F2, …, Fk). But a factor Fj might not represent any of the various X1, X2, …, Xn. The equations “work,” just like old rules of thumb, but provide no understanding of the process. Then new data comes along and new equations with new Factors and coefficients must be generated. Remember: with 7+ variables you can fit just about any set of data, provided you can jiggle the coefficients to force the issue.

    Some discussion here:
    http://tofspot.blogspot.com/2012/01/autumn-of-modern-science.html
    +++

    Models of the proton or electron as used in modern physics suffer no such lack of clarity or utility.

    Unless these models actually are the essential nature of the thing. This is almost always easier with inanimate things than with the animate. We might wonder only whether any of the grab bag of features is derivative or emergent of more fundamental forms. That is, what is it in virtue of which a thing is a proton in the first place. In order to measure the mass of a proton, for example, you must already know it is a proton. How do we know this?

    No one said philosophy was easy.

    We define man as rational animal. But supposing one discovers intelligent aliens then we would need to revise our definition of man

    Or we could do as Augustine did in City of God and include these aliens as men. The metaphysical species “man” need not be identical with a biological species. Not everything is natural science.

    Copernicus
    Interestingly, Copernicus’ model was purely theoretical and not based on observation. He was not a scientist as we understand it. An astronomer in those days was a mathematician specializing in the motions of the stars across the sky. He made virtually no observations, but simply did new calculations on the Alphonsine Tables using his new theory and pure Platonic circles (largely for mystical woo-woo reasons). He wound up with more epicycles than Ptolemy. There is a diagram of his system here:
    http://tofspot.blogspot.com/2013/06/if-only-tool-you-allow-yourself-is.html

    An empirical model was developed later by Tycho Brahe, who was dissatisfied with both Ptolemy and Copernicus. His geo-helio model is often ridiculed today, but it not only made the same predictions as Copernicus’ (often with greater accuracy) but accounted for the physical data as well: it explained why no visible parallax could be found among the stars and why no Coriolis effects were seen. By the standards being touted here, Tycho was a much better scientist than Copernicus. He was just wrong.

  29. BoyNamedSioux: I think that if the thing happens once, that does not falsify the theory. However, if the event is predicted to be 25 sigma away from the mean, and it’s happening over and over and over, that could be taken as strong evidence that the model is need of tuning. 🙂 Technically, it may not be falsified, since it still says the event is “possible”, but it lacks predictability and usefulness. In probability models, utility is often the goal, not an actual proof of anything. A model can be wrong and still be useful if it predicts accurately.

    Kneel: Agreed. It’s two types of models and their merit is based on different measures. It is that simple.

  30. All of the discussion is interesting but irrelevant.

    For empirical models as used in physics today, the quantities compared have non-arbitrary definitions such that anyone who wishes to replicate or improve on the experiment comparing the model to an outcome can do so. Two observers have a non-arbitrary process for assessing whether their respective outcomes are the same.

    No such definitions have been given for any attempt to compare one observer’s assessment of the “essence” of something versus another observer’s assessment. Essence as discussed in this thread has been a concept for which every statement that “The essence is…..” should be stated “To me, the essence is..” As Kneel maintains, a model is an essential model if the constructor assumes is part of the “essence” of the thing being modeled. Unless that “essence” is defined so that another person can do the same comparison the “essential” model is nothing more than one person’s personal, not necessarily rational, view of an aspect of reality.

    For the proponents of “essence” the question is simple, describe the process for measuring “essence” or for comparing one observer’s assessment of “essence” to another observer’s. Unless assessments can be compared across observers, then the concept is useless as a general method for objectively assessing reality.

  31. On reflection, I now think Briggs is right and that all of us commenting here, myself included, have misunderstood what he is saying. In particular we have misunderstood what he means by an essential model versus an empirical model.

    First, the assumption is wrong that I have been making, as well as others, that what he means by an empirical model means it is quantitative and what he means by an essential model is only qualitative, not quantitative. Second, the notion is wrong that he is proposing some other plane of reality in which something ethereal called “essence” is considered, which has a purview other than that which is normally used in a scientific discipline. In particular, an essential model can and should be used to compute consequences and compare to experimental outcomes. The word “empirical model” has a very common use in science and engineering and I think that is the meaning Briggs intends here. Further, the process I extrapolated from Feynman’s view of the progress of science is exactly the process I think Briggs means when he talks about seeking an “essential” model. Let me use an example.

    We could carefully construct an experiment in which we measured the position and time of a massive object falling toward the earth at some specific location on the earth. We could do it in a vacuum with carefully calibrated masses and precisely monitored time. We could then record the position and time of the object as it fell. If the mass was any specific value, then if we started at x = 0, we would measure for t = [ 0,1,2,3,…,10] seconds the values x = [0, -4.9, -19.6, – 44.1, …,-490] meters. We could then plot those values and find an empirical (meaning unmotivated by anything other than mathematical convenience) quadratic fit to the data which would give us an “empirical” model x = -4.9*t^2, where 4.9 has units meters per seconds squared. We could run hypothesis tests and find some measure of the goodness of fit and p values, etc. and convince ourselves that the model was “good.” We might also measure the velocity of the object as it falls and find an empirical model that the velocity v = -9.8*t meters per second, where again 9.8 has units meters per second squared. Now, based on these empirical models we could do a pretty good job predicting how to point artillery to hit something, how to zero the sights of rifles at some distance, etc.

    Now as we shot things higher and higher and did experiments on tops of mountains we would find our empirical models did not compare quite as well with measurements, but they might still be statistically “good” empirical models, we just needed to account for possible errors. We might even develop more detailed empirical models that accounted for the differences in different situations, all of which would be determined to be statistically “good.” If we started to shoot things very high, so that they went into orbit, and we tried to apply our empirical models, we would be perplexed because we would not be able to predict the speeds attained, the heights of orbits as functions of launch speed, etc. This would be because our models were empirical, not essential, as I think Briggs means it. And while they might be statistically “good,” that assessment is at least misleading if not flat wrong.

    Now someone comes along and gets hit on the head with an apple and makes a guess. He has previously guessed that the (instantaneous) force on an object can be defined to be equal to the mass of the object times the (instantaneous) acceleration the object experiences as a result of the force, i.e. F = m*a. He has previously also defined acceleration as a specific mathematical limit as the time involved goes to zero (i.e. instantaneously). So he makes a guess about how the apple falls, in particular, that the force on the apple is proportional to the mass of the apple, the mass of the earth, and distance of the apple from the center of the earth, i.e. F = m*a = -M*mG/r^2 where M is the mass of the earth, G is a constant of proportionality, and r is the distance from the apple to the center of the earth. Now with this guess, he is able to compute the consequences of our previous falling object experiments and finds he gets the same behavior of time and position. But now he is also able to predict how the force varies with different heights from the center of the earth and he is able to predict the orbits of objects launched with different velocities. He also finds he is able to compute the outcomes of observations of orbits of bodies in the solar system and gets consistent estimates of the positions and even masses of those objects (at least in terms of ratios of masses of one of them). This new guess, or model, is what I think Briggs means by an essential model, as opposed to an empirical model. The distinction is not that it is addressing some different, universal quality called “essence” but that if its outcomes are computed it is capable of predicting not only the specific data taken, but also the outcomes of experiments on phenomena not yet measured or measured under much wider circumstances.

    There are many other examples in modern physics and astronomy. The early attempts to explain the spectral lines observed from elements tried to find empirical mathematical series that matched the observations and some of these were fairly successful for specific elements. The observation that the red shifts measured for distant objects seemed to be proportional to the distance gave an empirical constant which then became something for guesses at how the universe might be evolving to match, which then led to predictions of a big bang, which eventually allowed a comparison to the observation of the cosmic microwave background.

    So what I think Briggs means by essential versus empirical models is not that the models necessarily address different qualities, nor that one is quantitative and the other is not. The difference is that one model agrees with a restricted set of experiments and if it is used to compare to a wider range of experiments, it produces outcomes that are wrong. This is just the process that Feynman described in the process of science, although in this context he could have been referring to continuous refinements of essential models.

    This view leads to a practical distinction between empirical models versus essential. In this light, I can reverse my opinion and state that I agree with Briggs on this point.

  32. Ye Olde Statistician

    August 16, 2016 at 3:54 pm

    On reflection, I now think Briggs is right and that all of us commenting here, myself included, have misunderstood what he is saying.

    By George, I believe you’re right. See my comment regarding Big Data.

  33. Briggs

    August 16, 2016 at 6:38 pm

    fah, YOS,

    Amen and amen.

  34. Briggs was obviously right and Fah wa also right in his description of the comment threads with his original comment.

  35. TOF,
    “we could do as Augustine did in City of God and include these aliens as men. The metaphysical species “man” need not be identical with a biological species. Not everything is natural science.”

    But is it common sense? Or you are putting neat definitions higher than reality?
    We know what man is and what an alien would be. An alien is not a man.
    What do I care about “metaphysical” species, whatever it means?

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