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Essay: Was Einstein data-driven?

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  • Published: 29 January 2023*
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Modern ideal of Science attempts to specify a procedure an individual must follow to come up with a credible idea or theory. However, recently I’ve caught myself thinking that scientific method with its sequence of action wherein a hypothesis is followed by experimental verification can’t possibly describe all the advances in the history of science. Sometimes scientists must call upon their powers of individual rationality to decide what ideas to test, in advance of the sort of definite experiments and observations of phenomena that Science demands to bless an idea as confirmed.

Let’s start with a readily understandable, non-disturbing example. A scientist identifies a strong regularity in the cumulative data of previous experiments.  But the corresponding hypothesis has not yet made and confirmed a novel experimental prediction—which his academic field demands. Thus, the individual scientist has readily understandable, rational reasons to believe something not yet blessed by Science as public knowledge. Noticing a regularity in a huge mass of experimental data before a hypothesis is made doesn’t seem all that contrary to scientific method.  You’re still data-driven, right?

But that’s because I deliberately chose a non-disturbing example.  When Einstein invented General Relativity, he had almost no experimental data to go on or a phenomenon to explain, except the precession of Mercury’s perihelion.  And Einstein did not use that data, except at the end.

Einstein came up with the theory of Special Relativity using the following principle: You begin by saying, “It doesn’t seem reasonable to me that you can tell, in an enclosed box, how fast you and the box are going.  Since this number shouldn’t be observable, it shouldn’t exist in any sense.”  You then observe that Maxwell’s Equations invoke a seemingly absolute speed of wave propagation, c, commonly referred to as “the speed of light”.  So, you reformulate your physics in such fashion that the absolute speed of a single object no longer meaningfully exists, and only relative speeds exist.  I am skipping over quite a bit here, obviously, but the point still remains.

Einstein, having successfully done away with the notion of your absolute speed inside an enclosed room, then set out to do away with the notion of your absolute acceleration inside an enclosed box.  It seemed to Einstein that there shouldn’t be a way to differentiate, in an enclosed room, between the room accelerating eastward while the rest of the universe stays still, versus the rest of the universe accelerating westward while the room stays still. And because inertial mass and gravitational masses are exactly equivalent gravity can be viewed as a kind of inertia.  The Earth should then go around the Sun in some equivalent of a “straight line”.  This requires space-time in the vicinity of the Sun to be curved. And of course, the new theory had to obey Special Relativity, and conserve energy, and conserve momentum, etc.

Einstein spent several years grasping the necessary mathematics to describe curved space-time.  Then he wrote down the simplest theory that had the properties Einstein thought it should have—including properties no one had ever observed, but that Einstein thought fit in well with the character of other physical laws.

How impressive was that?

Well, let’s put it this way.  In some fraction of alternate Earths proceeding from 1800, perhaps a sizeable fraction, relativistic physics could have developed in an entirely different way. We can imagine that Newton’s original “interpretation” of the motion as relative to an absolute ether prevailed.  We can imagine that various corrective factors, themselves unexplained, were added on to Newtonian gravitational mechanics to explain the precession of Mercury—attributed, perhaps, to distortions of the ether.  Through the decades, further corrective factors would be added to account for other astronomical observations.  Sufficiently precise atomic clocks in airplanes would reveal that time ran a little faster than expected at higher altitudes and more corrective factors would be invented.

Until, finally, various different empirically determined “corrective factors” were unified into the simple equations of General Relativity.

And the people in that alternate Earth could say, “Even though the final equation was simple, there was no way you could possibly know to arrive at that answer from just the perihelion precession of Mercury.  It takes many, many additional experiments.  You must have measured time running slower in a stronger gravitational field; you must have measured light bending around stars.  Only then could you imagine our unified theory of gravitation.  No, not even a perfect intelligence could know it in advance for there would be many ad-hoc theories consistent with the perihelion precession alone.”

In our world, Einstein didn’t even use the perihelion precession of Mercury, except for verification of his answer.  Einstein sat down in his armchair and thought about how he would have designed the universe, and how he thought a universe should look—for example, that you shouldn’t ought to be able to distinguish yourself accelerating in one direction, from the rest of the universe accelerating in the other direction.

And Einstein executed the whole long (multi-year) chain of armchair reasoning, without making any mistakes that would have required further experimental evidence to pull him back on track.

Rather than observe the planets, and infer what laws might cover their gravitation, Einstein was observing the other laws of physics, and inferring what new law might follow the same pattern.  Einstein wasn’t finding an equation that covered the motion of gravitational bodies.  Einstein was finding a character-of-physical-law that covered previously observed equations, and that he could crank to predict the next equation that would be observed.

It is true that nobody knows where the laws of physics come from, but Einstein’s success with General Relativity shows that their common character is strong enough to predict the correct form of one law from having observed other laws, without necessarily needing to observe the precise effects of the law.

So, from a perspective of scientific method, what Einstein did is still induction from evidence.  It’s just that the evidence was the possible characters of physical laws. This let Einstein update his model of the character of physical law, which he then used to predict a particular law of gravitation.

If you didn’t have the concept of a “character of physical law”, what Einstein did would look like magic—plucking the correct model of gravitation out of the space of all possible equations, with vastly insufficient evidence.  But Einstein, by looking at other laws, cut down the space of possibilities for the next law.  He learned the alphabet in which physics was written, constraints to govern his answer.  Not magic, but reasoning on a higher level and across a wider domain allowed him to find the equation for his theory.

So, from an epistemological standpoint, Einstein was still data-driven—he just used the data he already had, more effectively, compared to any alternate Earths that demanded huge quantities of additional data from astronomical observations and clocks on airplanes to make discovery of General relativity inescapable.

I use Einstein as my example, because Einstein was also unusual in that he openly admitted to knowing things that Science hadn’t confirmed.  Asked what he would have done if observations had failed to confirm General Relativity, Einstein replied:  “Then I would feel sorry for the good Lord.  The theory is correct.”

We should not criticize Einstein for this as we should not criticize people when they turn out to be right.  Wait for an occasion where they are wrong.  Otherwise we are missing the chance to see when someone is thinking smarter than us—for we criticize them whenever they depart from a preferred course of cognition (which in this case is the scientific method).

If we take off our Worship goggles, and look at Einstein in terms of what he actually did all day, then the guy was sitting around studying math and thinking about how he would design the universe, rather than running out and looking at things to gather more data.  What Einstein did, successfully, is exactly the sort of high-minded feat of sheer intellect that Aristotle and other rationalists thought they could do, but couldn’t.

Science does not trust scientists to do this, which is why General Relativity was not blessed as the public knowledge of humanity until after it had made and verified a novel experimental prediction. However, just because Science does not trust scientists to do something, does not mean it is impossible.

As of now, at least, reasoning based on scanty evidence is something that modern-day science cannot reliably train modern-day scientists to do at all.  As for the possibility that only Einstein could do what Einstein did… that it took superpowers beyond the reach of ordinary mortals…  Let me put it this way:  It is possible, perhaps, that only a genius could have done Einstein’s actual historical work.  But potential geniuses, in terms of raw intellect, are probably far more common than historical superachievers like Einstein and Newton.  To put a number on it, I doubt that anything more than one-in-a-million probability is required to be a potential world-class genius, implying at least seven thousand potential Einsteins running around today.  And as for everyone else, I see no reason why they should not aspire to use efficiently the evidence that they have.

But my final moral is that the frontier where the individual scientist rationally knows something that Science has not yet confirmed, is not always some innocently data-driven matter of spotting a phenomenon and generating a hypothesis in line with strong regularity in a mountain of experiments.  Sometimes the scientist gets there by thinking great high-minded thoughts that Science does not trust you to think.

Originally published 15.10.2019

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