"Zeno’s Paradox deals with the ultra-small structure of space and time. In its essence, the paradox notes that if a moving body is in a specific place at every instant, then there is no instant when it is in transition from one place to another; and therefore motion is impossible. Since this contradicts everyday experience, it is called a paradox."
This is an interesting paradox for a number of reasons. Can we indeed have an 'instant in time'? Can time be disected into packets? Is time even linear? We make many lofty assumptions about Time but it is an artificial construct that we don't actually understand.
Time (t) is definitely in our "thinking apparatus"; it's not "out there", it's "in here". It can't be a physical dimension, like x, y, or z are positions.
We see "changes" but cannot discern, on any scale, the resolution limit for the "process" of change. We therefore invent "clocks" of ultra-fine precision, but they're just our change-measuring tools. They don't create what we are trying to measure with them. They limit our concept of "time" to "intervals", but ignore the "duration" aspect, which is (obviously?) continuous, or "analogue", not "digital".
@thinking-turtle, you are correct in stating that the principles from which Huygens and Van Flandern were working from were completely different.
Huygens started off with results known for centuries about reflection and refraction. He then took a mechanical model he had already developed for the collision of solid bodies, which was quite successful, and made a miniaturized version of it for light, explaining those aforementioned known results. In the two chapters that follow in his Traité de la lumière, he studies refraction in the air and in Iceland crystal using his model, and the model seems to stand up.
Van Flandern, on the other hand, was an astronomer who was tired about all sorts of concepts in currently accepted cosmology, against which he was rebelling: the Big Bang as beginning of the universe, the Oort cloud as source of comets, the existence of dark matter, and so on. His reasoning presented in this post was, as I stated above, a priori and deductive.
I think Van Flandern's reasoning about the possibility of an infinite number of successively finer levels to the universe is interesting. As far as I can see, it is the only way in which the universe could work without action-at-a-distance.
His specific ideas on what is gravity and on the nature of the smaller planets, comets, moons and asteroids of the Solar System, are another matter. I might study these some time.
Thanks for your reply! As I remember, force field mathematics uses differential equations. These differentials are defined using limits. So force fields are really action at an arbitrarily small distance.
Then there is the Fourier transform, which can convert a continuous function into a discrete function, and back.
So it seems to me action at a distance and continuous action are both human mathematical models to describe reality. They can be converted into one another. Which one you use is a matter of choice, like the choice between cartesian and polar coordinates.
"Zeno’s Paradox deals with the ultra-small structure of space and time. In its essence, the paradox notes that if a moving body is in a specific place at every instant, then there is no instant when it is in transition from one place to another; and therefore motion is impossible. Since this contradicts everyday experience, it is called a paradox."
This is an interesting paradox for a number of reasons. Can we indeed have an 'instant in time'? Can time be disected into packets? Is time even linear? We make many lofty assumptions about Time but it is an artificial construct that we don't actually understand.
Time (t) is definitely in our "thinking apparatus"; it's not "out there", it's "in here". It can't be a physical dimension, like x, y, or z are positions.
We see "changes" but cannot discern, on any scale, the resolution limit for the "process" of change. We therefore invent "clocks" of ultra-fine precision, but they're just our change-measuring tools. They don't create what we are trying to measure with them. They limit our concept of "time" to "intervals", but ignore the "duration" aspect, which is (obviously?) continuous, or "analogue", not "digital".
Thanks for your blog series! Huygens observed reflection and created a model to predict refections. His model stands up to testing.
It seems to me Flandern starts with a model and ends with a model. What testable predictions do Flandern's models make?
@thinking-turtle, you are correct in stating that the principles from which Huygens and Van Flandern were working from were completely different.
Huygens started off with results known for centuries about reflection and refraction. He then took a mechanical model he had already developed for the collision of solid bodies, which was quite successful, and made a miniaturized version of it for light, explaining those aforementioned known results. In the two chapters that follow in his Traité de la lumière, he studies refraction in the air and in Iceland crystal using his model, and the model seems to stand up.
Van Flandern, on the other hand, was an astronomer who was tired about all sorts of concepts in currently accepted cosmology, against which he was rebelling: the Big Bang as beginning of the universe, the Oort cloud as source of comets, the existence of dark matter, and so on. His reasoning presented in this post was, as I stated above, a priori and deductive.
I think Van Flandern's reasoning about the possibility of an infinite number of successively finer levels to the universe is interesting. As far as I can see, it is the only way in which the universe could work without action-at-a-distance.
His specific ideas on what is gravity and on the nature of the smaller planets, comets, moons and asteroids of the Solar System, are another matter. I might study these some time.
Thanks for your reply! As I remember, force field mathematics uses differential equations. These differentials are defined using limits. So force fields are really action at an arbitrarily small distance.
Then there is the Fourier transform, which can convert a continuous function into a discrete function, and back.
So it seems to me action at a distance and continuous action are both human mathematical models to describe reality. They can be converted into one another. Which one you use is a matter of choice, like the choice between cartesian and polar coordinates.
There are serious philosophical differences between the two approaches. Have a look at my new post, "Peter and Neal Graneau Explain the Importance of Newton's Third Law and Action-at-a-Distance" (https://johnplaice.substack.com/p/peter-and-neal-graneau-explain-the).