John and I spend this, our penultimate episode in the series, discussing Hobbes—his anthropology, his physics, his politics—and the nature of modernity’s “new science.”
This has been a great series, I wish I had time to read the sources. I have a suggestion about nature of Mathematics. I think it's similar to the way I think about science: is it independently discoverable? E.g. if you're Shakespeare and write Hamlet, you never have to worry about somebody else writing Hamlet. But you do have to worry about being plagiarised. Scientists have to worry about plagiarism, but they also have to worry about being scooped.
Isn't this true for at least some mathematics? If we destroy all knowledge of calculus, are we sure it can never be discovered again? Are we certain that aliens don't know calculus? Think of even something abstruse like Fermat's last theorem. Apparently Andrew Wiles hid what he was doing by trickling out other work he'd already finished to make himself look busy. Would he have done that if he didn't think someone else could beat him?
I'm also curious whether either of you followed the "Beyond Belief" series in the early 2000s, and what do you think of David Brin's account of the Enlightenment as a collection of tools for reciprocal accountability?: https://www.youtube.com/watch?v=jHyFREAKQec (for something more light-hearted I recommend Robert Winter's following talk on Beethoven and how he wrote the 9th)
Thanks for the reply. I admit to falling mostly within the math is discovered camp. I think many inventions are discovered too. I'm not sure about needing divinity in the form of a deity that current humans worship. I feel that introduces yet more of what we're trying to explain.
These series also have me thinking again about interesting grey areas between discovery and invention, and what Stuart Kauffman calls the "adjacent possible". Especially large combinatorial spaces that can never be fully explored. Like protein sequence space or complex structures in organic chemistry (also literature, music and art).
Looking forward to the rest. If you get a chance take a listen to the video I linked with David Brin. The Beyond Belief series exhibits many of the assumptions you're discussing. But I like his approach of framing the Enlightenment through the Fermi Paradox.
Of course calculus would be discovered again! If something is related to the rate of change of something else, it needs differential calculus to describe it and it would be rediscovered in its own way again. Likewise if something is related to the total amount of something over time, then integral calculus would be needed to describe it.
Of course the symbology may be different, but the concepts would be the same. Given how much of mathematics has historically been developed to describe physical phenomenon (or used in the service of that goal) I am pretty confident that any alien species would have to understand it even if they never had contact with us.
Thank you for taking the time and effort to do this wonderfully educational podcast. I'm a 73-year-old grandmother who struggled with understanding Plato/Aristotle in Pholosophy 101 fifty-four years ago and never got past that. I really appreciate the insights you bring in this episode and I want to go back to the first episode in this series to catch up.
This has been a great series, I wish I had time to read the sources. I have a suggestion about nature of Mathematics. I think it's similar to the way I think about science: is it independently discoverable? E.g. if you're Shakespeare and write Hamlet, you never have to worry about somebody else writing Hamlet. But you do have to worry about being plagiarised. Scientists have to worry about plagiarism, but they also have to worry about being scooped.
Isn't this true for at least some mathematics? If we destroy all knowledge of calculus, are we sure it can never be discovered again? Are we certain that aliens don't know calculus? Think of even something abstruse like Fermat's last theorem. Apparently Andrew Wiles hid what he was doing by trickling out other work he'd already finished to make himself look busy. Would he have done that if he didn't think someone else could beat him?
I'm also curious whether either of you followed the "Beyond Belief" series in the early 2000s, and what do you think of David Brin's account of the Enlightenment as a collection of tools for reciprocal accountability?: https://www.youtube.com/watch?v=jHyFREAKQec (for something more light-hearted I recommend Robert Winter's following talk on Beethoven and how he wrote the 9th)
Thanks for your question!
John and I already recorded the last ep, but we'll respond to you at the top of our next episode.
Thanks for the reply. I admit to falling mostly within the math is discovered camp. I think many inventions are discovered too. I'm not sure about needing divinity in the form of a deity that current humans worship. I feel that introduces yet more of what we're trying to explain.
These series also have me thinking again about interesting grey areas between discovery and invention, and what Stuart Kauffman calls the "adjacent possible". Especially large combinatorial spaces that can never be fully explored. Like protein sequence space or complex structures in organic chemistry (also literature, music and art).
Looking forward to the rest. If you get a chance take a listen to the video I linked with David Brin. The Beyond Belief series exhibits many of the assumptions you're discussing. But I like his approach of framing the Enlightenment through the Fermi Paradox.
Of course calculus would be discovered again! If something is related to the rate of change of something else, it needs differential calculus to describe it and it would be rediscovered in its own way again. Likewise if something is related to the total amount of something over time, then integral calculus would be needed to describe it.
Of course the symbology may be different, but the concepts would be the same. Given how much of mathematics has historically been developed to describe physical phenomenon (or used in the service of that goal) I am pretty confident that any alien species would have to understand it even if they never had contact with us.
Thank you for taking the time and effort to do this wonderfully educational podcast. I'm a 73-year-old grandmother who struggled with understanding Plato/Aristotle in Pholosophy 101 fifty-four years ago and never got past that. I really appreciate the insights you bring in this episode and I want to go back to the first episode in this series to catch up.
Thank you Cathy! It means so much to hear that.
Please get any questions you might have by Thursday around, say, 3pm central time so we can (hopefully) answer them.