If any part of mass is infinitely divisible, what would that mean?
A question risen out of the library seminars that i am organising on presocratic philosophy, cause that is pretty much the position of the Eleatics. That any part of mass (or other extendable volumes/surfaces/lines) is (mentally, but arguably they claimed the human mental world was closer to the truth than our senses) infinitely divisible, and therefore nothing can actually ever take a different position in any progression.
You can also read the largish spoiler for some background on the presocratic idea of infinite divisibility, but i merely want some guiding to current notions of infinite systems and what is theorised to be the relative position of their distinct particles within them.
Spoiler Alert, click show to read:
The argument (termed a paradox in Zeno's examples of it, but originally Parmenides did not use this line of presentation) seems (to me, but also others i read a bit) to mostly consist of the following parameters:
1) If something is infinitely divisible then it already can be said to be in all parts of its own divisions, which would likely render it as being tied to other things of its likeness through the same infinite divisions and therefore be in Oneness with all those as well. The Eleatics famously argued that the Cosmos is a Monad (a One) and the senses makes us believe it alters, but they are part of the problem with understanding the actual truth.
2) The senses obviously make us think there is change around us or in us. But if there was change then we would have no notion of infinity given it would be un-natural as an idea. Eg in the paradox with Achilles and the tortoise the latter has a headstart and Achilles can't reach it due to first having to reach the first position of that headstart, upon which the tortoise would have moved slightly more, and so on to infinity. While the senses tell us that regardless of that syllogism a faster runer will overtake a slower one given enough time, this would require the cosmos to operate in a system of finite division, which idealistically is not true. The start of what by now is termed as idealism is argued to be Parmenides (and maybe before him Xenophanes), and Plato regards Parmenides of Elea as the father of his own (platonic) philosophy of ideas as well.
Λέων μεν ὄνυξι κρατεῖ, κέρασι δε βούς, ἄνθρωπος δε νῷι
"While the lion prevails with its claws, and the ox through its horns, man does by his thinking"
Anaxagoras of Klazomenae, 5th century BC
Re: If any part of mass is infinitely divisible, what would that mean?
Two things.
The Zeno arrow paradox issolvable using modern mathematics. If the arrow is cutting the distance in half, you get an infinite series, but the sum of that series can be proven to be nothing more than 1, the total distance
Achilles and the Tortoise is the same idea; it was only paradox before we had the tools to really analyze infinite series.
As to infinite divisibility in general. Due to experiments in the 20th century it is generally accepted that energy is quantized and not infinitely divisible. There is a minimum "packet" of energy, and everything else is a multiple of that. This is fundamental to quantum mechanics, and very well supported at this point.
There are theories that have space and time quantized in the same way as energy is "packeted" in quantum mechanics, but none of these have been supported by experiment yet. Indeed, it is very hard to come up with a quantum theory of space-time that is consistent with General Relativity (which has been proven by experiment).
So right now we are living with two different paradigms; on the small scale world of quantum mechanics where energy comes in "packets" and is not infinitely dividable. And space and time in the large scale world governed by Einsteins General Relativity and in theory infinitely dividable.
Re: If any part of mass is infinitely divisible, what would that mean?
Thank you
Archimedes also used his own (proto-calculus) methods for examining Zeno's paradoxes, but in my view the essense of those is not in the (trivial by now) infinite series they create, cause Zeno and Parmenides argued that the divisions are infinite 'in reality' while our senses present the illusion that they are cancelled by other factors (eg the faster speed of Achilles etc).
A very dark point which i would wish to know more about is that Democritos (who in direct response to the eleatics formed his 'atomic theory', ie that divisions end at some last, atomic level, where there are only atoms (you might say particles) moving around in a vastly large next to them 'void') agreed with the Eleans that if space/time/mass etc were infinitely divisible then there would be no change to anything (in reality, not in our senses). I am wondering why this was deemed as so. If the divisions never end why would that have to mean that 'in reality' the cosmos is a changeless Oneness as the eleatics argued?
Λέων μεν ὄνυξι κρατεῖ, κέρασι δε βούς, ἄνθρωπος δε νῷι
"While the lion prevails with its claws, and the ox through its horns, man does by his thinking"
Anaxagoras of Klazomenae, 5th century BC
Re: If any part of mass is infinitely divisible, what would that mean?
A very dark point which i would wish to know more about is that Democritos (who in direct response to the eleatics formed his 'atomic theory', ie that divisions end at some last, atomic level, where there are only atoms (you might say particles) moving around in a vastly large next to them 'void') agreed with the Eleans that if space/time/mass etc were infinitely divisible then there would be no change to anything (in reality, not in our senses). I am wondering why this was deemed as so. If the divisions never end why would that have to mean that 'in reality' the cosmos is a changeless Oneness as the eleatics argued?
Physicists jumped the gun when they named the elements "atoms" after Democritos. At the time they understandably thought elements were the fundamental building blocks of matter, as they weren't observed to break apart. But eventually when radioactivity and atomic decay were discovered, it became obvious that "atoms" must be made up of smaller parts. But today we still have the Democritos idea of "atoms" in physics, they are just called "fundamental particles". For the normal, everyday matter that you and I are made of they are the 'Up Quark' the 'Down Quark' and the 'Electron'.
As to why infinite divisibility would mean a changeless Oneness, I have nothing insightful to say.
Re: If any part of mass is infinitely divisible, what would that mean?
Thanks I will try to find some info on that.. Btw the Eleatics regarded 'God' as a perfect sphere Starting with Xenophanes (6th century BC) and then Parmenides, who in his poem (sole remaining work, partly at least) claims specifically that the god is a sphere cause it extends without any reason to be stopped or stop anywhere (ie extends the same towards all directions).
But curiously Parmenides (iirc also Xenophanes, and i suppose Zeno too) argued that the god/cosmos sphere was infinite in its own divisions, but had a border to something else. While the last of the Eleatics, Melissos of Samos (famously defeated Pericles in a naval battle) argued that the Sphere was infinite by itself and as the whole of anything there is (ie nothing bordering it).
I think Heraklitos also spoke of spheres, but his main thesis is more of a synthesis between the earlier Milesians like Anaximander, and the Eleans who came a few decades later, cause he argues that we cannot even know what is the origin, since we only can know why there is a cosmos as a strange set-up and flow of that origin.
Λέων μεν ὄνυξι κρατεῖ, κέρασι δε βούς, ἄνθρωπος δε νῷι
"While the lion prevails with its claws, and the ox through its horns, man does by his thinking"
Anaxagoras of Klazomenae, 5th century BC
Re: If any part of mass is infinitely divisible, what would that mean?
A famous astronomer named Fritz Zwicky once said his collegues were "Spherical bastards" because "they were bastards, when looked at from any side"
He actually was the first person to observe and coin the phrase "dunkle materie" or "Dark Matter" in a scientific paper. This discovery was basically ignored for 50 years, in part because nobody liked him. But eventually other people made similar observations and redeemed his discovery.
Re: If any part of mass is infinitely divisible, what would that mean?
Originally Posted by Sphere
A famous astronomer named Fritz Zwicky once said his collegues were "Spherical bastards" because "they were bastards, when looked at from any side"
He actually was the first person to observe and coin the phrase "dunkle materie" or "Dark Matter" in a scientific paper. This discovery was basically ignored for 50 years, in part because nobody liked him. But eventually other people made similar observations and redeemed his discovery.
Sadly i immediately thought of how much he looks like a HORRIBLE highschool chemistry professor i had, who was an UTTER creep. A sort of imp-like being (i think he would be at roughly 1,5 metres if he did not wear some kind of half-covert heal-like shoe), he was easily the most annoying person in the professors for myself. He first singled me out in the first year of highschool cause i solved some stuff at the first day, then deliberately cancelled me when he thought i would not become a student in his private-tutoring class.
Still think of him as a creep :/ (he is probably dead by now though). (and obviously Zwicky at least contributed something to the science of his field, unlike the person i briefly spoke of ).
Λέων μεν ὄνυξι κρατεῖ, κέρασι δε βούς, ἄνθρωπος δε νῷι
"While the lion prevails with its claws, and the ox through its horns, man does by his thinking"
Anaxagoras of Klazomenae, 5th century BC
If any part of mass is infinitely divisible, what would that mean?
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Starting with Xenophanes (6th century BC) and then Parmenides, who in his poem (sole remaining work, partly at least) claims specifically that the god is a sphere cause it extends without any reason to be stopped or stop anywhere (ie extends the same towards all directions).
Originally Posted by Sphere
