“To say that human beings “invented numbers”—or invented the structure implicit in numbers—seems like claiming that Neil Armstrong hand-crafted the Moon. The universe existed before there were any sentient beings to observe it, which implies that physics preceded physicists.”
No, there’s a conflation of two things here.
Have you ever really looked at a penny? I’m looking at a 1990 penny now. I know that if you look at the front and you see the bas-relief of Lincoln, and the date 1990, and it’s a penny, then you can be sure that the back side will have a picture of the Lincoln memorial. It works! And you can find all sorts of connections. Like, there’s a single “O” on the front, in the name GOD in the phrase IN GOD WE TRUST. And there’s a single “O” on the back, in the phrase ONE CENT. One O on the front, one O on the back. A connection! You could make lots and lots of these interconnections between the front and the back of the penny, and draw conclusions about what it means. You could invent a discipline of Pennyology if only somebody would fund it.
Is it true that Pennyology is implicit in pennies? In a way. Certainly the pennies should exist before the Pennyology. But the pennies are only whatever they are. The existence of pennies doesn’t tell us much about what the practitioners of the discipline of Pennyology will actually notice. They might never pay attention to the pair of O’s. There could be a fold in Lincoln’s coat that after the proper analysis provides a solution to the whole world crisis, and they may never pick up on it. While it’s predictable that different independent attempts at Pennyology would have a whole lot in common since after all they all need to be compatible with the same pennies, still they might be very different in some respects. You can’t necessarily predict the Pennyology from looking at the penny. And you can’t predict what mathematics people will invent from observing reality.
You can predict some things. A mathematics that invents the same 2D plane we use and that proves a 3-color theorem has something wrong with it. But you can’t predict which things will be found first or, to some extent, which things will be found at all.
If there’s a reality that mathematics must conform to, still each individual version of human mathematics is invented by humans.
Similarly with physics. Our physics is invented. The reality the physics describes is real. We can imagine a platonic-ideal physics that fit the reality completely, but we don’t have an example of that to point at. So for example before Townsend invented the laser, a number of great physicists claimed it was impossible. Townsend got the idea because lasers could be described using Maxwell’s equations. But people thought that quantum mechanics provided no way to get that result. it turned out they were wrong.
Actual physics is invented. Certainly incorrect physics must be invented. There’s nothing in reality that shows you how to do physics wrong.
“To say that human beings “invented numbers”—or invented the structure implicit in numbers—seems like claiming that Neil Armstrong hand-crafted the Moon. The universe existed before there were any sentient beings to observe it, which implies that physics preceded physicists.”
No, there’s a conflation of two things here.
Have you ever really looked at a penny? I’m looking at a 1990 penny now. I know that if you look at the front and you see the bas-relief of Lincoln, and the date 1990, and it’s a penny, then you can be sure that the back side will have a picture of the Lincoln memorial. It works! And you can find all sorts of connections. Like, there’s a single “O” on the front, in the name GOD in the phrase IN GOD WE TRUST. And there’s a single “O” on the back, in the phrase ONE CENT. One O on the front, one O on the back. A connection! You could make lots and lots of these interconnections between the front and the back of the penny, and draw conclusions about what it means. You could invent a discipline of Pennyology if only somebody would fund it.
Is it true that Pennyology is implicit in pennies? In a way. Certainly the pennies should exist before the Pennyology. But the pennies are only whatever they are. The existence of pennies doesn’t tell us much about what the practitioners of the discipline of Pennyology will actually notice. They might never pay attention to the pair of O’s. There could be a fold in Lincoln’s coat that after the proper analysis provides a solution to the whole world crisis, and they may never pick up on it. While it’s predictable that different independent attempts at Pennyology would have a whole lot in common since after all they all need to be compatible with the same pennies, still they might be very different in some respects. You can’t necessarily predict the Pennyology from looking at the penny. And you can’t predict what mathematics people will invent from observing reality.
You can predict some things. A mathematics that invents the same 2D plane we use and that proves a 3-color theorem has something wrong with it. But you can’t predict which things will be found first or, to some extent, which things will be found at all.
If there’s a reality that mathematics must conform to, still each individual version of human mathematics is invented by humans.
Similarly with physics. Our physics is invented. The reality the physics describes is real. We can imagine a platonic-ideal physics that fit the reality completely, but we don’t have an example of that to point at. So for example before Townsend invented the laser, a number of great physicists claimed it was impossible. Townsend got the idea because lasers could be described using Maxwell’s equations. But people thought that quantum mechanics provided no way to get that result. it turned out they were wrong.
Actual physics is invented. Certainly incorrect physics must be invented. There’s nothing in reality that shows you how to do physics wrong.