This is an extract from the OPIP book. Previously, (B)obby and (A)lice discussed the characteristics of top physicists.
A: Let’s talk about creativity. If I gave you the job to come up with new ideas, what would you do exactly?
B: When confronted with work, my first thought is always the same: how can I delegate it?
A: That coming from you doesn’t surprise me, but it’s not very helpful.
B: Hear me out. Let me rephrase what I just said: I’d first think about asking someone else.
A: I’m glad Einstein didn’t think that way.
B: Oh, he did. When he came up with relativity theory, it wasn’t conceived from scratch. The theoretical groundwork was already in place. Hendrik Lorentz and George Francis FitzGerald independently proposed the concept of length contraction and time dilation, which are important aspects of Einstein’s theory of special relativity. Henri Poincaré proposed the principle of relativity, which suggests that the fundamental laws of physics hold true no matter what constant velocity you are moving at or where you are in space. And even the formula E = mc², so inextricably linked with Einstein in our minds, doesn’t appear as new anymore if we consider that several physicists before him stated both very similar formulas (such as Fritz Hasenöhrl’s E = 3/8mc2 and others[1]) as well as the concept of equivalence of mass and energy.
A: You’re making Einstein’s work sound like plagiarism. You’re an iconoclast. Don’t take our gods from us.
B: That wasn’t my intention. While the key ideas were already on the table, it was Einstein who fully grasped their significance. He synthesized and expanded upon them, forming a comprehensive framework for relativity. That’s mostly the main challenge: connecting the dots.[2] The dots themselves are important too of course, but the real task lies in painting the complete picture using them. Moreover, Einstein made many other significant contributions, so full creds to him. Although, he did admit, “The secret to creativity is knowing how to hide your sources.”
A: Stop it now. Your point is: look around what’s already there?
B: Exactly. Part of the creative process may be to know when you don’t have to be creative. It reminds me of good fiction writing which is often not so much fiction at all, in the sense that it’s all made up. Talented writers don’t invent so much, but they find so much. This makes their work ring true on a deeper level that fabricated stories cannot achieve. Most good fiction writing is autobiographical, at least to some degree (Flaubert: “Madame Bovary, c’est moi!”).
A: Any other ways we could “ask someone else”?
B: Being guided by mathematics is another example. This can be hard work, as mathematics is complicated. But it also falls into the “asking someone else”-category because the creative engine isn’t us. We just do our calculations, and mathematics then gives us new insights into the world.
A: Does that work?
B: Sometimes it does. In 1928, Paul Dirac developed a mathematical equation to describe the behavior of electrons. However, the equation also predicted something new: the existence of “antimatter,” particles with the same mass as electrons but opposite charge (first called anti-electrons, later positrons). This prediction stemmed from the realization that Dirac’s equation could have two possible solutions, similar to how the equation x2=4 has two solutions (x=2 or x=-2).[3] The existence of such positrons was experimentally confirmed by Carl Anderson in 1932.
A: Can we always rely on mathematics to tell us the truth?
B: Unfortunately not. There have been many cases where mathematical equations successfully explained the phenomena they were intended to, but they also made new predictions that turned out to be utter baloney.[4]
A: Are there indications when equations predict new things correctly or are just going nuts?
B: From what I’ve read, it’s not properly understood when they make correct or incorrect predictions. The practical implication of this is that we should listen to what mathematics predicts, but regard it very skeptically. As Einstein said, “As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.”
A: Maybe Einstein only said that because he was more a physicist than a mathematician.[5]
B: That could be true, other statements from him point to that as well, for example, “Since the mathematicians have invaded the theory of relativity, I don’t understand it myself anymore.” In any case, we should be quick with proving or refuting what mathematics suggests to not lose time. An extra level of skepticism should be applied if the predictions are very hard to test, or worse, if they cannot even be tested in principle.
A: Any other ways we can ask someone else to get ideas for new theories?
B: Artificial intelligence (AI) might be a way. The recent developments in that area are impressive. I’m making heavy use of it for this conversation.
A: Okay, that explains why occasionally there are quite insightful comments coming from you. In any case, what’s the path to creativity for AI?
B: One approach would be to feed AI with as much data as we can, and hope that AI’s neural networks will do the magic and come up with new things. We wouldn’t know exactly what’s happening in that “black box,” but it may work. After all, that’s how it works in our brains too. Or, we guide AI a little by making the creative process more transparent and “conscious,” so that AI would only need to follow certain rules to get to new discoveries. Such transparency could also bolster human creativity.
The book continues by discussing the essence of creativity and how physicists (and other problem solvers) can become more creative. Get it now.
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[1] Physics World (2011): “Did Einstein discover E = mc2?”.
[2] That reminds me of Steve Jobs’ “You can’t connect the dots looking forward; you can only connect them looking backwards” from his famous commencement address at Stanford University in 2005. Opip.lol/smart-jobs
[3] See Opip.lol/antimatter.
[4] One example is the “ultraviolet catastrophe” where the equations predicted that a black body would radiate infinite energy at ultraviolet frequencies. This discrepancy was solved by Max Planck’s introduction of quantized energy levels in 1900, leading to the birth of quantum mechanics.
[5] A related anecdote: Friends of John von Neumann wanted to find out whether he was more of a mathematician or a physicist. So they posed him the following problem: Two trains, 20 miles apart, are heading toward each other at 10 miles per hour. At the same time, a bee flying at 20 miles per hour heads off from train A, and once it reaches train B, flies back to train A and so forth. When the trains collide, what is the total distance the bee has flown? A mathematician might take a while to calculate those “infinite series,” while a physicist may take a step back and realize that the trains collide after an hour, and during that time the bee must have flown 20 miles. So when von Neumann quickly responded with the answer, his friends concluded, “Okay, he is a physicist!” However, von Neumann then revealed he had quickly calculated it all in his head—or so the legend has it. See Opip.lol/bee
