Okay, here's the most mind-boggling ChatGPT response I've gotten. Someone recently posted an HN article on mathematical proof techniques which included a statement about how we shouldn't confuse the mathematical concept of induction with the electromagnetic concept of induction. After a bit of querying ChatGPT about this, here's what it came up with:
> "One of the Maxwell equations, Faraday's law, relates changes in the magnetic field to the induction of an electric field. It states that a time-varying magnetic field induces an electric field, which is analogous to the concept of induction in electromagnetism. This induction process occurs as the changing magnetic field "propagates" through space, giving rise to an electric field that is perpendicular to both the magnetic field and the direction of propagation."
> "Mathematically, this phenomenon can be likened to the inductive step in mathematical induction. Just as mathematical induction builds upon previous steps to establish a result for the next value, the induction of an electric field in electromagnetic waves relies on the changing magnetic field at a particular point to induce the electric field at the next point in space."
> "Moreover, the wave-like nature of electromagnetic waves, including light, can be understood in terms of a progressive "domino effect." Each point in space influences the neighboring points, as changes in electric and magnetic fields induce one another. This propagation of the electromagnetic wave throughout space mirrors the idea of the sequential propagation of statements or properties in mathematical induction."
That's kind of impressive, isn't it? Cross-domain interconnections and all that?
It's extremely underwhelming. The _only_ thing in common between induction of an electric field and induction in math is the spelling of the word "induction". The meaning in each context is vastly different. I stopped reading there; can't comment on the rest of it.
Oh come on, the whole Maxwell idea is that the changing electric field induces a changing magnetic field which induces a changing electric field and so light propagates through space. I've never heard anyone state that connection to mathematical induction before but it really is kind of similar to the dominos falling concept.
> "One of the Maxwell equations, Faraday's law, relates changes in the magnetic field to the induction of an electric field. It states that a time-varying magnetic field induces an electric field, which is analogous to the concept of induction in electromagnetism. This induction process occurs as the changing magnetic field "propagates" through space, giving rise to an electric field that is perpendicular to both the magnetic field and the direction of propagation."
> "Mathematically, this phenomenon can be likened to the inductive step in mathematical induction. Just as mathematical induction builds upon previous steps to establish a result for the next value, the induction of an electric field in electromagnetic waves relies on the changing magnetic field at a particular point to induce the electric field at the next point in space."
> "Moreover, the wave-like nature of electromagnetic waves, including light, can be understood in terms of a progressive "domino effect." Each point in space influences the neighboring points, as changes in electric and magnetic fields induce one another. This propagation of the electromagnetic wave throughout space mirrors the idea of the sequential propagation of statements or properties in mathematical induction."
That's kind of impressive, isn't it? Cross-domain interconnections and all that?