There is a Mind-Only school of Buddhism with koans, but I never paid much attention. What I know is that the way people think determines their physical reality. Wander around San Diego, California, then go to Tijuana, Mexico. Different cultures, different reality. Another instance is the rigid belief in private property that allows a neighbor to cut down an old oak tree so he has a better view out his kitchen window. Now that is a strange idea!
I would point out that the Calculus has far more uses than just figuring out financial rates of return. The same process can calculate any physical process that is exponential or in motion. For the final exam in my Calculus 1 class, we were presented the dimension of a complex tank with a drain. Given the flow rate of the drain, we calculated the time to empty the tank. Probably in Calculs 2, we would have variable flow rates depending on the volume of water at any instance. This is also calculable. The Calculus is great!
You said it, Tedder; calculus is beautiful! Plato was obsessed with the faces and angle of polyhedra because he believed that certain mathematical patterns therein revealed a hidden realm. I think his mind would have been blown by calculus, which reveals dimensions invisible to our human senses.
Regarding the part about Aristotle pioneering empiricism: he did move science away from Plato's realm of the forms a bit, but he certainly did not always practice empiricism. For instance, he claimed that heavier objects fall faster than lighter objects. So it was respected as fact until Galileo proved Aristotle's theory to be incorrect. Galileo dropped two unevenly weighted cannon balls from the Tower of Pizza and found that they landed at the same time. Moreover, Aristotle claimed that the earth was the center of what was then thought of as the universe (or cosmos), rather than the sun. Why did he think this? Because it made sense to him. And because he was so respected (and that was the worst part), 100 years or so later when Aristarchus claimed it was the sun that was at the center rather than the earth, he was ignored. It was not until about 1700 with work done by Copernicus, Kepler, Galileo and finally Newton that Aristotle's theory was proven to be wrong. In my opinion, his book "The Poetics" is his best. And, yes, that is a minority opinion.
Jason, what a great note! I hesitated to use term "empiricism" to describe Aristotelian philosophy, because that term was actually coined during the Enlightenment by Immanuel Kant. But Kant also wrote that logic hadn't needed to take a single step forward since Aristotle, who is sometimes called the "grandfather of empiricism." This double-click of yours is a higher-resolution look at the interesting relationship between Aristotle and empiricism, which I over-simplified!
Nathan, I didn't mean to imply that what you wrote was not grounded in "philosophical fact." But I personally find no harm in questioning the facts. In my opinion, you have been doing a great job with these posts you have been writing during the past few years. Not only are they factual, but they are interesting and often cover areas that are underreported. By the way, I did not intend to contradict your claim that Aristotle was a pioneer of empiricism. I merely intended to stress that he didn't always practice it.
I suspect that between the time depicted in the first painting of Newton by Robert Hannah and the last, William Blake's, that Newton's work in calculus involved a lot of lifting and dropping various weights. His physique has improved considerably.
All good here Nathan, thanks. Rainy season again and everything is growing madly. After this last summer I've promised myself never to complain about the rain again, regardless of how much comes bucketing down
Very cool, I knew about Newton's literally deadly pursuit of counterfeiters but had no idea about his role in setting the gold standard. If only all bureaucrats took their jobs so seriously!
There is a Mind-Only school of Buddhism with koans, but I never paid much attention. What I know is that the way people think determines their physical reality. Wander around San Diego, California, then go to Tijuana, Mexico. Different cultures, different reality. Another instance is the rigid belief in private property that allows a neighbor to cut down an old oak tree so he has a better view out his kitchen window. Now that is a strange idea!
I would point out that the Calculus has far more uses than just figuring out financial rates of return. The same process can calculate any physical process that is exponential or in motion. For the final exam in my Calculus 1 class, we were presented the dimension of a complex tank with a drain. Given the flow rate of the drain, we calculated the time to empty the tank. Probably in Calculs 2, we would have variable flow rates depending on the volume of water at any instance. This is also calculable. The Calculus is great!
You said it, Tedder; calculus is beautiful! Plato was obsessed with the faces and angle of polyhedra because he believed that certain mathematical patterns therein revealed a hidden realm. I think his mind would have been blown by calculus, which reveals dimensions invisible to our human senses.
Regarding the part about Aristotle pioneering empiricism: he did move science away from Plato's realm of the forms a bit, but he certainly did not always practice empiricism. For instance, he claimed that heavier objects fall faster than lighter objects. So it was respected as fact until Galileo proved Aristotle's theory to be incorrect. Galileo dropped two unevenly weighted cannon balls from the Tower of Pizza and found that they landed at the same time. Moreover, Aristotle claimed that the earth was the center of what was then thought of as the universe (or cosmos), rather than the sun. Why did he think this? Because it made sense to him. And because he was so respected (and that was the worst part), 100 years or so later when Aristarchus claimed it was the sun that was at the center rather than the earth, he was ignored. It was not until about 1700 with work done by Copernicus, Kepler, Galileo and finally Newton that Aristotle's theory was proven to be wrong. In my opinion, his book "The Poetics" is his best. And, yes, that is a minority opinion.
Jason, what a great note! I hesitated to use term "empiricism" to describe Aristotelian philosophy, because that term was actually coined during the Enlightenment by Immanuel Kant. But Kant also wrote that logic hadn't needed to take a single step forward since Aristotle, who is sometimes called the "grandfather of empiricism." This double-click of yours is a higher-resolution look at the interesting relationship between Aristotle and empiricism, which I over-simplified!
Nathan, I didn't mean to imply that what you wrote was not grounded in "philosophical fact." But I personally find no harm in questioning the facts. In my opinion, you have been doing a great job with these posts you have been writing during the past few years. Not only are they factual, but they are interesting and often cover areas that are underreported. By the way, I did not intend to contradict your claim that Aristotle was a pioneer of empiricism. I merely intended to stress that he didn't always practice it.
Aw, thanks Jason. Thanks for reading over the years; it's meant a lot.
I suspect that between the time depicted in the first painting of Newton by Robert Hannah and the last, William Blake's, that Newton's work in calculus involved a lot of lifting and dropping various weights. His physique has improved considerably.
Haha very funny, Leon! Hope you and the girls are well
All good here Nathan, thanks. Rainy season again and everything is growing madly. After this last summer I've promised myself never to complain about the rain again, regardless of how much comes bucketing down
Hope you are well !
Very cool, I knew about Newton's literally deadly pursuit of counterfeiters but had no idea about his role in setting the gold standard. If only all bureaucrats took their jobs so seriously!
"If only all bureaucrats took their jobs so seriously!"
Very funny, Dennis!