Learning and the Urge to Do It Over

Say you’re sitting under a tree being contemplative. What does that mean? I will argue that a large part of being contemplative entails noting what has happened so you can do it over again, or so to avoid it happening again. Or it might entail adding together many things that you can do over again to make a bigger more complex thing you can do over again.

Of course there are other forms of being meditative, such as artistic expression, or appreciating beauty, or just plain trying to appear to have some depth to you, for members of the opposite sex to notice. Perhaps you are even using formal syllogisms. But say that you are feeling expansively analytical while under that tree. What are you doing?

I have always viewed science as being the study of what we can do over again, but lately I have been considering how this urge can be applied to other knowledge, as well.

Is it key to learning itself?

First regarding science.


A common understanding of science (Popper has it, for instance) is that science is like deciding if a defendant at trial is guilty or innocent. There is an assertion—an assertion made about the true state of the world, about what is real—and then we look for evidence that the assertion is correct or false.

Let’s call that approach “evidence-based argument.” And I certainly agree that, when it comes to making a convincing argument, citing evidence is preferable to other methods (such as relying on authority, dogma, or emotion). But is science just about argumentation? No, even in this popular view (such as Popper’s) it is held that science is about testing. Science is a little different from just being a juror with an idea “on trial” because, in this view, science at least gets to look for new evidence. If an assertion is not capable of being submitted to this search for empirical evidence, then that assertion is not considered to be a scientific statement.

And what people like about this approach (science as the search for evidence that some statement correctly reflects the way that the world actually exists) is that it makes science seem to be about true or false, guilty or innocent, fact or fiction, yes or no.

But personally, I have never thought of science as working in this manner. Instead, I have always seen science as being about someone saying (in scientific papers and the like), “Hey, look what I can do over again. Here’s how you can do it over again, too.”

And being able to do something over again is different from arguing true or false.

Science is about making demonstrations. You create a certain setup of circumstances, and then nature rewards you by doing the same thing as the last time you set up those same circumstances. To get nature to do that is often quite an achievement. It can entail, for instance, figuring out the terms by which to measure things, as well as how to measure them and how to treat the results of those measurements such as with mathematics. Also, it is about tolerances or getting it to repeat within known standards of how much error to allow. But doing that is a different methodology from argumentation, and striving for repeatability is a different goal from simply testing out an idea by putting it into practice. Yet somehow, with all the talk of “falsification” these days, this emphasis on demonstration seems to have become drowned out. It has become possible to think of science as trying to prove or disprove the great eternal verities of the Universe, whereas the science itself is settling for just being able to do something over again. And the comparison of these two views of science is what I will start out talking about here.

The Zen Buddhists like to remind us that we might ultimately all be butterflies dreaming that we are humans, and the point is we cannot ever be absolutely certain of what is real. So where does that leave us, as we try to navigate our world without ever being sure of what is ultimately real?

Well, there is what we can do over again, even if that isn’t the same as having ultimate truth. We can see how science has been succeeding by using this more limited but also more achievable approach.

Argumentation is not as convincing as demonstration. That is because demonstration is about acquiring nature’s opinion, not just people’s.

Granted, it is possible to conflate that with other issues. For instance, it is possible to disagree as to which comes first, the theory or the evidence. But either way, in science it all still eventually comes down to what can be demonstrated. Science is about finding how a setup of circumstances enables us to do certain things over again. And that is different from claiming to know what is ultimately real, even if only tentatively.

Reproducibility (what science seeks) is its own different form of knowledge compared to seeking a priori truths. And having it provides a different source of satisfaction, the kind that scientists enjoy. Seeing the world in terms of what we can do over again is different from seeing the world in terms of true and false.

So I’ll further compare these two views of science.

Popper and all that

Popper fully adheres to the notion that science is about reproducibility. InThe Logic of Scientific Discovery, he writes, “…non-reproducible single occurrences are of no significance to science.” And later he adds, “We shall take it as falsified only if we discover a reproducibleeffect which refutes the theory” (his italics). So how does Popper get from science being in practice about doing things over again (reproducibility) to science being about discovering true or false?

He does it by adding an extra step. He says that science makes guesses (hypotheses), and it is then these guesses that are either true or false. And that is worth repeating. The way to go from science being about doing things over again, to science being about true or false, is to say that science works by making guesses which are then either true or false.

But is it really necessary to make guesses in order for science to be able to do things over again? Is it actually required that we talk of truth and falsity in order to have reproducibility? (It might be asked, “How can scientists know what to do over again without making guesses?” and I will answer that at the end of this post. But first, I want to look at what is misleading about science being about guesswork).

When Popper says that science is about truth and falsity, he is thereby sneaking in through the back door a lot of assumptions about the world. The world looks different when we say, “It is false,” instead of saying, “We couldn’t do it over again.”

Consider truth, for instance. Plato defined it as immutable. It lies unchanging in a static Platonic heaven. And indeed, a big trouble with Plato is that he has no way of describing change. But this changelessness is not a characteristic of doing things over again, since, indeed, what we can do over again is precisely some change. The truth (such as it is) lies in the transformation—it lies in whether or not we have described the change in a repeatable way—it is not about immutability.

Repeatability is not stasis.

Yet if we insist that science is about the search for eternal verities, we are conflating these two notions of truth.

So consider a butterfly pinned in a collector’s display to a background of cotton, in stasis. Do we know “for real” all about the butterfly with that static conception of what it is? Or do we need to know how a living butterfly moves—how it changes in repeatable ways as it flies—before we can fully know the butterfly?

Science is obviously about the latter.

My response to asking how science can work without making guesses at immutable truth is that, instead of making guesses—or even instead of induction—science makes models. And models, unlike either hypotheses or induction, are not attempts to describe what is real; they are attempts to emulate how nature changes reproducibly, even if the models incorporate assumptions that are known to be unreal. Indeed, models (or other methods of stating reproducibility, such as with a mathematical system) can be flat-out false and still successfully perform their tasks of telling us how things can happen over again. An example is Newton and how he wrote in a letter to the Rev Bentley, regarding Newton’s physics of planetary motion:

That one body may act upon another at a distance through a vacuum without the mediation of any thing else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity, that I believe no man, who has in philosophical matters a competent faculty of thinking, can ever fall into it

Yet for all the absurdity, it works in terms of reproducibility. A scientific theory—and Newton’s mechanics seems to be the great exemplar of a scientific theory—need not be true (ultimately or otherwise) in order to be a great scientific theory. In fact, it can be absurd.

However, taking this extra step, of saying that science is about making guesses as to what is ultimately true about the world, instead of seeing science as emulating how things change, has led to all kinds of unnecessary problems. Many people are already familiar with these problems. But to detail them, I will have to briefly go into some specifics, using Popper as my example.

Popper held that a guess “not yet justified in any way” is made via intuition, not induction, and that it is then used to make conclusions that are “…compared with one another and with other relevant statements…,” and then these conclusions are compared “…with the results of practical applications and experiment.” If the comparison proves “positive,” then the guess is temporarily accepted until such time that the result is “negative.” But a hypothesis is never taken as being “true,” only as being “not yet falsified.” It is said to be only “tentative,” in anticipation of future new theories that will better describe how the world ultimately is. Even so, if a theory fits well with other theories, then it can be said to be “corroborated.”

So Popper does not so much see the world in terms of true and false as he sees it in terms of just plain false. But what he gains from that is tentativeness or the recognition that science changes its mind as new theories come in. (He also avoids Hume’s problem of induction by saying that the entire process is deductive, rather than inductive, once a guess has been made).

In addition to Popper, we can also hear the story of the extra step in its original form (about true and false, not just false) by considering the so-called “scientific method.” It was invented by the “after Newton crowd” of philosophers in the generation after Newton, even after Newton had explicitly warned against it (see my post on the rats for details of this warning). In the so-called scientific method, science is portrayed as making a guess, or a hypothesis, that tests either right or wrong (there is nothing about reproducibility), and so it directly reinforces a Platonic view of the world.

But then, as to the resulting problems:

Kuhn and all that

The problem encountered with thinking that science is about making guesses about the nature of absolute reality is, of course, that science changes its mind as new theories come in. That was why Popper had insisted on tentativeness as one of the traits of science. It could be disheartening to discover that one’s favorite eternal verity was no longer eternally true.

But tentativeness also proved not to be a full solution. That was because Kuhn came along and pointed out that new ideas come in two types. Some new ideas are compatible with the old ones and so seem to be mere extensions of what science has been saying all along. But other new ideas are grossly incompatible with the old ones. And then that leads to all kinds of embarrassing troubles which go under the headings of discontinuity, incommensurability, paradigm shifts, and charges of realism versus anti-realism. People still argue today over what it means that science can sometimes reverse itself.

But notice that what science can do over again before a new theory can still be repeated after the new theory. In terms of reproducibility (what science actually does), there is no contradiction. It is only in terms of these guesses at absolute truth that the discontinuities and reversals appear, and that is because the contradictions are among the guesses taken in the extra steps. As for the science itself, a new theory merely means that now we can do over again more than we could do over again beforehand. There is no break in continuity.

If what constitutes knowledge is considered to be reproducibility, then there is no problem. But if what constitutes knowledge is held to be eternal verities, then we end up with the contradictions. That is because it is the extra steps—it is saying that science is about making guesses at eternal truths—that creates the furor.

It is when science’s descriptions of change get reinterpreted into being static eternal verities that one staticization ends up contradicting another staticization. And seeing science as about true-or-false (or just about falsification) is how reproducible change gets staticized.

Meanwhile, the scientists themselves are indignantly accused of “just calculating.” And why is that? Of course, it is because the scientists are only trying to describe the world in terms of reproducibility in the first place. They’ve known all along that it is not realistic to ever expect to know what is ultimately real.

What is it about science that makes scientists feel so comfortable with uncertainty?

How does science proceed without using true-or-false hypotheses?

operational truth

Science succeeds by making models. But models are not static guesses at ultimate truth. They are an assembly of assumptions and approximations with no pretense of getting things exactly right. But what they do accomplish is that they emulate how the world changes. With a model, we can do over again what the world does over again, even if our way doesn’t get it exactly right.

Students learn to grasp as much intuitively as they learn the derivations of the various models. The relaxed nature of the models becomes apparent once they, too, learn to say things such as, “Well, if we drop this term over here, and round off that one over there, and we ignore this issue, and we assume that this and that don’t come into play even though we know that they do, then we can do such-and-such over again.” To go through that process is to realize that the goal is not absolute truth but manageability.

But it works in terms of reproducibility. And we can be proud of how closely we can “emulate” with our models the way that the world changes, even as the models themselves are so full of blatantly false shortcomings. The kinetic theory of gases is a good example. It makes the stark assumptions that an air molecule, while colliding with the wall of its container, nevertheless does not touch that wall for purposes of our calculation, and that further we can treat the air molecule itself as a point having no volume. And yet with this theory we can make precise predictions of what we can do over again, and so we can visualize the world in terms of it.

Also, that illustrates how scientists can be so intuitively comfortable with uncertainty. We realize from the start that uncertainty is built in with what we are doing.

It isn’t about ultimate true and false.

Another example is the ideal gas laws, because of course no real gas acts in the ideal manner as is assumed in the laws. We know going in to using the laws that we’ll have to make corrections once we get the answer given to us by these laws.

So once again, it is not about making an ever more real representation of the world. Instead of that, we can have an operational sense of whether things are working or not. And that means: Can we do it over again, or not?

We sometimes hear it said that science can be understood in an “instrumentalist” manner, which may or may not be what I am talking about. The words “pragmatic” or “instrumental” do not in themselves connote reproducibility. Also, they usually imply a criterion of “usefulness,” which can be turned into the argument that it is useful to believe in such and such a static truth. But I am trying to get away from the notion of static outcomes and emphasize, instead, that science has a dynamic approach to knowledge. Science is about understanding things in terms of how they change—and how they change reproducibly—which means seeing them in motion. So I will call that an “operational” view. We see the butterfly in operation, not in stasis.

Further, in order to do things over again, the events have to be set up in a certain fashion (or else they won’t work reproducibly). The arrangement of the setup creates what can happen, so the model includes the way to set up a situation for reproducibility. (It’s in the assumptions that go into making the model). In order for the kinetic theory of gases to apply, the molecules have to be within a container. In order for Newton’s law of gravitation to apply, the bodies have to be about the same size. Relativity depends on defining reference frames.

Context counts. As a professor of mine used to say, “There is no such thing as A causes B. There is only A causes B under circumstances C.” Different circumstances create different outcomes. So the models keep track of all of that for us. It is not that the models work like a law or rule that applies under all circumstances but that the model tells us the necessary circumstances.

That creates an operational sense of truth. That means that the setup of circumstances is included with the descriptions of the motions and relationships that can accordingly happen. (Relativity exists part and parcel with reference frames). But since the setup is included in the models, it all works together. It operates. It is repeatable. Within certain tolerances, it is maybe even reliable.

But that is not just to say that it is “effective” rather than “true” to use an equation like a tool; it is to say that the circumstances must be included in how a change can occur in an overall operation.

When nature does it, it works because the Universe is made of energy, and one trait of energy is that it makes arrangements of itself, including how circumstances fit together. Thus we have a this-worldly way of understanding the relationships and actions expressed in equations–they are about how energy fits together–instead of otherworldly Platonic Forms and laws that supposedly preexist the physical world.

Perhaps a good way to see the difference with the static view is by comparing the words “real” and “really.” A Platonist might ask us, “But don’t you want to know what is real?” To which a scientist might answer, “I am not sure that it is possible to ever know what is ultimately real. Don’t you want to know what we can really do, and not just tentatively?”

With the models—with what we can do over again—we can build airplanes and medicines, and we can give explanations and make predictions. And no, that is not ultimate static truth. But look at what we can do, really.

I am not saying that scientists don’t have intuitions that they check out with experiment. I’m just saying that it doesn’t have to be in terms of truth or effectiveness, either one. There is a third option, which is to see the proposed change in terms of what is happening operationally. Success need not be about, “Is it true or false?” Or even, “Is it effective?” It is about, “Under what conditions can we do that over again?”


In part two of this post, I will look at how not everything in this world is repeatable. But far from being a problem, it turns out that that opens the door to applying this approach more generally to other areas of knowledge, outside of science. That includes applications to heuristics, common sense, AI, learning, and even to formal syllogisms.

We can learn to see even more of the world in terms of an operational sense of truth.

I will attempt to answer the question posed at the top of this essay. Is learning just the acquisition of static truths? Or is learning itself about what we can do over again?


IMAGE CREDIT: This is a picture of a Christmas tree ornament painted on wood by artist Bridget O’Leary.

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