I might be able to do the paradox better than Zeno did. To get from A to B you have to go half the distance, since if there is any distance at all it has a half. But the half, if it is any distance at all, has a half. There is no end to the process. If you don't go another half you are already there. Hence the paradox: the finite appears to be infinite. What we call those "things" at the bottom are infinitesimals nowadays

https://www.academia.edu/343657/Inevitability_of_infinitesimals

There's the article, I got the name slightly wrong. It goes into a lot of stuff. Very little was useful for me. I didn't get what was meant by "of course, with ultraproducts of rational numbers come infinitesimals." It makes intuitive sense to me, but that's all. I thought Newton did fine talking about infinitesimals as fluxons, half there and half not. Leibniz might have understood this the best. People latter on added stuff about "limits" but I don't know anything that it added to what Newton and Liebniz had already said. Newton already had a limit towards which an infinite series goes towards. Non-standard analysis, it seems to me, claims to show that Cantor was right in arguing that actual objects have an infinity of points, and the Britannica Encyclopedia says it uses the mathematical logic of Godel.

What does Banach-Tarki's paradox do to Euclid's system and proposition 7? I only know about the paradox from Vsauce on youtube, but at least Zeno's cubes are getting a closer look into

Which of his books talk about points and quantity? Wikipedia says Whitehead wrote stuff that was wrong about wholes and parts, while Husserl wrote good things. This is stuff that I'm interested in

Great post. I'm tending more towards Hegel than Aristotle though.

Im not sure what you mean. An abstract number can be divided into infinite fractions. So can a brownie. The brownie clearly is finite though, while 1 is finite by our definition alone

Well I tried to read over Alezandre Bolovak's article The Inevitability of Infinitesimal but I could my grasp her main argument. Check it out on Google if your interested

Let me try. Euclid is assuming he can construct ADB as identical to ACB and then show the contradiction with how angles add up. I am not sure Proposition 5 is enough to prove this. Up to prop 7 I haven't seen a fully proven system yet. Even what it means for point A of ADB to be right there with point A of ACB seems ambiguous to me. I learned up to book IX in college 16 years ago and I've read a tiny bit about non-Euclidean geometry, and pondered Zeno's paradoxes endless times in my life. I wanted to start very basic and learn the essential nature of math from the ground up but Euclid hasn't been doing it for me. This is the first time I've read him since I was 19

Internet Encyclopedia of Philosophy, Nagarjuna

"Let us take the claim that something can be proven to be true on the basis of other facts known to be true. Suppose, to use a favorite example from the Logician Gautama, I want to know how much an object weighs. I put it on a scale to measure its weight. The scale gives me a result, and for a moment that satisfies me; I can rely on the measurement because scales can measure weight. But hold on, Nagarjuna flags, your reliance on the trustworthiness of the scale is itself an assumption, not a piece of knowledge. Shouldn’t the scale be tested too? I measure the object on a second scale to test the accuracy of the first scale, and the measurement agrees with the first scale. But how can I just assume, once again, that the second scale is accurate? Both scales might be wrong. And the exercise goes on, there is nothing in principle which would justify me in assuming that any one test I use to verify a piece of knowledge is itself reliable beyond doubt. So, Nagarjuna concludes, the supposition that something can be proven through reference to some other putative fact runs into the problem that the series of proofs will never reach an end, and leaves us with an infinite regress.... [T]he Logician might, and in fact historically did, try an alternative theory of mutual corroboration. We may not know for certain that a block of stone weighs too much to fit into a temple I am building, and we may not be certain that the scale being used to measure the stones is one hundred percent accurate, but if as a result of testing the stones with the scale I put the stones in the building and find that they work well,I have reason to rely on the knowledge I gain through the mutual corroborations of measurement and practical success. This process, for Nagarjuna, however, should not pass for an epistemologist who claims to be as strict as the Brahminical Logicians. In fact, this process should not even be considered mutual corroboration; it is actually circular. I assume stones have a certain measurable mass, so I design an instrument to confirm my assumption, and I assume scales measure weight so I assess objects by them, but in terms of strict logic, I am only assuming that this corroborative process proves my suppositions, but it in fact does nothing more than feed my preconceived assumptions rather than give me information about the nature of objects."

Nagarjuna was followed in the West by Hume, who said the same thing. It seems one has to allow some subjectivism in in order to have a rational understanding of the world.

I'd say that objective patterns (interrelationships) are all we see in the world. — Gnomon

This answers my objection. Thanks

Hence patterns are "objective", their degree of repetition indicated by the Shanon Entropy of their encoding. — Banno

If patterns are all we see, then this example is of complex patterns. The ground, however, of it might might be subjective. Have you seen anything from Donald Hoffman? I would explain his thesis by saying that the proprioception (also called kinaesthesia or kinesthesia) of a bird might be totally different from ours. If the bird could see our physics, he would say "there is no way things move that way". So physics, and thus the world, might be subjective at the last level, but we might have to regard everything as patterned because we are human.

If you have all the fractions from 1/2 to the infinitesimals (what are they?), you can add them up to make 1. 1 can contain that infinity because it's an abstract number. But an object is finite extension. It has uncountably infinite points yet it is finite in form. Maybe add time to the equation and finitute+infinity+time=beauty (which in turn equals patterns once consciousness is added).

That's how I look at patterns, entities spontaneously impinging upon our consciousness from out of nowhere, but in orderly ways provisional of a baseline objectivity. — Enrique

The human mind seems to organize the pattern through reflection and "noticing". Although the mind is "noticing", this is not enough for me to say the pattern is out there. Take a beautiful cathedral or the arabesques of the Alhambra. Are these different styles compatible? Some people like one, some the other, some both. Saying there is something rational objective about patterns that applies to every creature in the universe is what I am questioning. I took the most basic example I could above. Take a blank white piece of paper. Does it have pattern? When exactly, once one starts drawing, does patterns start? It doesn't seem to be clear to me what a pattern is, objectively. Seeing patterns might be more connected to our spiritual side than to our mathematical side. What you guys think?

Thanks for the post. People are capable of seeing space thru proper eye adjustment and intuiting. Time can never be seen. We only feel it. The infinite and the finite can make beautiful things, but the world is contingent so it's the movement of time which makes these patterns. I can't comment any more on Plato

Addition: The finite seems to contain the infinite. But how the infinite got contained in the finite is a physical, mathematical, and philosophical puzzle.

My only answer is philosophical (and maybe even esoteric), because I don't know enough non-Euclidean geometry to deal with that question. I imagine the universe started from gravity and quantum uncertainty, as I suggested already, but I don't read up on modern physics so I can't really take an authoritative stance.

This guy thinks an infinite regress which does not reside in a divine mind is impossible:
https://www.youtube.com/watch?v=ZJDYPZYMt0Q

I just say simply that potentiality (infinite vagueness) turns into actuality (finite objects). I think Heidegger already answered that Youtuber in the 20's. The thread on Heidegger going on right now is great for anyone out there wanted to know more about this

"Nagarjuna reminds his readers, all change in the world, including the transformations which lead to enlightenment, are only possible because of interdependent causality (pratityasamutpada)"

The Indian words for physical Pratityasamutpada are anitya, anepikrita, nihsvabhava, or shunyata. The last is the most used word. Just because I don't like infinite regress (A cause B, because B cause C which cause A because A causes C), that alone doesn't mean it's not true. But I like ideas about the world to be clear: "A literally cause B". However, Zeno seems to have prove Heraclitus true instead of Parmenides. If the world is pure fluidity, what kind of mathematics would even apply anymore to the world? I thought that might be an interesting question for those schooled in mathematics

The model I use to conceptualize time is cyclical. The two types of singularity in the Cosmos are interconnected, and movement from one to another creates what I call Cosmic Time. The universe in this model is a perpetual motion machine, self-causing, self-creating, self-contained. I admire the working analogy for time as a single line of dominoes, but this analogy doesn't fit in with the Cyclical Model. it doesn't apply. Its more like the inflating and deflating of a balloon. The fundamental physics of Cyclical Time at as of yet very basic, at least mine are. They will improve their explanation power with time. — Josh Alfred

Tonight I've been reading about Nagarjuna on the Internet Encyclopedia of Philosophy. I feel like most of us on this forum are Westerners. Modern physics is getting into more Eastern ideas even since Borh, and our philosophical culture is resistant, and maybe it should be. I read the Tao of Physics book and felt it was purely a philosophical work. Modern physicists speak of pure nothing, while even the Eastern idea of sunyata-nihsvabhava doesn't mean “non-existence”. The word for that is actually Abhava. But when the world's existence was granted, Indian thinkers still thought the answer was the interconnection of all within one motion, within which is allowed infinite regress (Anavastha in Indian thought) and circularity (karanasya asiddhi). Some Vedic philosophers did believe in what they called svabhava, which can be compared to the modalities of Liebniz, so there is division within Eastern thought as well

What I wanted to say though was that we are culturally Westerners (most of us) and unless we want to be like Pyrrho, we want a satisfying explanation of how this world came about. Pyrrho said he doubted and doubted that he doubted. Stephen Hawking had a paper trying to argue that this type of paradox (i guess introduced into math by Godel?) could be in matter (in the universe) itself as well. That's a little too loopy for me.
It's been a good day

https://plato.stanford.edu/entries/descartes-physics/

And the man who directly tried to refute his whole philosophy:

https://plato.stanford.edu/entries/leibniz-physics/

If you say that 1 + 1 = 4, what do you mean? Esoteric as in woo? — fishfry

Well I had a thread a few days ago that got closed because I claimed math maps out the impossible and that the opposite flip side is true of every mathematical statement. So perhaps the negative numbers are positive and vice versa, e.g. I was trying to start a conversation but people got upset. I don't deny math's usefulness and it's beauty, but math might not be the last statement about math itself.

What does Hawking have to do with this? I wonder if you mis-tagged me perhaps? None of this convo sounds familiar. Free lunch is contingent? What am I supposed to make of that? I apologize if I was at one point having the other side of this conversation and no longer remember. — fishfry

Well I tagged you because other people weren't responding to posts I was making here. I started out ny explaining what I meant about the math thing so you don't think I'm a nut. The OP here, however, was talking about Aquinas, who said that the world was contingent and needed a necessary God. Physicist are now saying nothingness was before the big bang, making the world contingent without the need for "the necessary". Sean Carroll explicitly says this. He says the world is a brute fact of quantum fluctuation, using Russell's old phrase btw

Descartes's vortex theory is a discredited and discarded theory of gravity that lost to Newton's. It has absolutely nothing to do with quantum uncertainty. — fishfry

I think any mechanical theory can be resurrected in the search for a "theory of everything". I said quantum physics is answer to Descartes, but perhaps Descartes is the answer to QM. Newton replaced Cartesianism with a lot of forces. God was the ultimate one that Descartes had wanted one force to control everything and thought God could be found only in the mind. Perhaps that "one force" is pure leverage, as he thought. It's a thought that needs to be worked out for sure, but the Stanford Encyclopedia says there is growing interest into Cartesian physics again

Ok. I can't argue with you there! Is the heart of contingency near the root of physics? — fishfry

Probably. There are studies that literally argue our brains control time. There are lots of Youtube videos that run with this and say we are in almost complete control of our "free lunch", given us by the universe. There might be some truth in these videos that the universe gives itself to us freely. And then there are Napoleon Hill types (the forerunner of The Secret), that say our thoughts are in complete control of everything. These ideas may have a kernel of truth still

The point here would be that transfinite numbers are an abstraction but not an isolated one. They're an abstraction that arose naturally from the study of heat; just as the infinity of natural numbers is an abstraction that arises from everyday counting. — fishfry

Well I think my point was that objects are finite on one side, but flip the coin and it's infinite was well. There no end to the descent into an object. Imagine taking a spaceship (one that forever shrinks) into a banana. Only infinity is in there. This seems to be a contradiction of logic. I have had enough trouble trying to explain the problem to people, let alone getting a satisfactory explanation. Think about it: objects are finite and infinite in the same respect

Thanks for your response man :)

I'm reading Hegels lesser logic and just got his greater logic in the mail. The latter has the smallest print I've ever seen and there aren't even page numbers. In the next few.months a i want to have some type of answer to Zeno. The mathematical community does not recognize that we have a contradiction with the core of matter. Matter is inherently finite and infinite in the same respect

Touché . . . Good point! — jgill

But if objects are trans-finitely infinite, how can they remain finite as well

When I say for example that 1+1=4, I mean it esoterically. When Hawking says time acts as a fifth direction of space, he is talking as a scientist. He says nothing was before this curve in spacetime, meaning I think that the free lunch is contingent. Quantum uncertainty may be the root of physics, the answer to Descartes's vortex of the universe. Any talk of the "necessary" is sitar music thinking, and if our brains control time we have access to the heart of contingency

Objective idealists have no problem with the beginning of the universe. Neither has Hinduism or most non-theist religions. A materialist would say that everything is governed by uncertainty. But is there actuality at the beginning and potentiality at the end, or conversely?

I might have struck at something you guys will find interesting. If time goes back through descending fractions, as has been suggested here and by Hawking as well, than the limit of the segment of time is potentiality, an infinitesimal. It starts the beginning of time because the segment is on a slant and gravity pulls the potential into actuality. It's self contained. Potentiality will always remain some thing mystical or mythical for homo sapiens because we live in actuality. In an instant though of self creation the physical (gravity) would act on the vague (potentiality) and walla the start of casual motions, governed by uncertainty, would start to roll forward

Maybe potentiality is like an infinitesimal

There can't be a potentiality infinite past. Unless it's a koan of sorts, it's a contradictory statement

"What is the perspective of the universe from the mind of a bird?" John Lennon

Maybe a bird would experience force and gravity differently with his body than a homo sapien

Descartes wanted one principle to rule the material realm. A clock was his favorite model. It's clearly incomplete though. What about time before the clocks unwinds?

I see Relativist's point now. It's interesting though to think about matter itself and try to distinguish what is philosophical about it and what is scientific about it

Descartes thought everything in the world worked through leverage. Newton said "no, because for every action there is an equal reaction so there is more to force than leverage". How could Newton possibly prove this though? Anyone out there who can explain this briefly

It would be good to hear from an actual physicist regarding these comments. — jgill

Very good.

Tetens, who lived in the 17 hundreds, said: "The idea of a body set in motion, which neither acts upon any other body nor is acted upon, leads the mind to the idea that the motion of the body will continue unchanged; and even though the latter idea be derived from perceptions, yet its connection with the former ideas is an effect of the power of thought, which according to its nature brings about in us this relation between the two ideas; and the connection between predicate and subject, which is made by this operation of the mind, is far more reason for the conviction that our judgment is true than the mere association of ideas based on perceptions."

I think Teten's point is that we have to have some sort of philosophy to start out doing science. Otherwise we just have sequences of perceptions that could change in order, intensity, and quality at any time. Hume developed this to it's logical conclusion and took the West to the East (Shunyata). Maybe there is something deeper in the mind which actually can understand matter, and which faculty can be analyzed. Yet what some people call "scientific common sense" other people call philosophy. Such disagreements are interesting! Hegel wrote in 1807 (long before Einstein) that the "reality of time has the solid form and shape of space". He came to this by way of philosophy

And what do physicists mean when they say something like "we can just change the math on this one a little". They literally say stuff like this all the time!! If the math merely reflects the quantities measured, it would seem ALL of physics is about experimentation. So where does that leave theoretical physics? I think in philosophy, but I am willing to be corrected

All we can go on is sense data, says empiricism about physics. How one views that data is entirely philosophy as I see it. What does a theoretical physicist even do if he's not doing experiments? To my mind he could only be doing philosophy

I think the whole is prior to the parts (in order to avoid Zeno's paradox and establish the unity of the object against complete Shunyata), and yet from another perspective the parts are prior because they compose the whole unity. This metaphysical balance has to take into account the geometry of magnitude, where infinity meets finitude. I personally think it not a contradiction to say those opposite principles merge to form objects. Maybe material things cannot be either completely finite or infinite. Finitude and the infinite come from the prior world of the Potential. I don't see how you can have a bird's eye view of the universe's history and have no problem at its start with regard to physical mechanics

I love Heraclitus. Someone can regard a jungle as entity, or a branch of a tree. It's all about one's personal perspective. The world has all the reality it needs to exist on its own while remaining contingent. That's what I meant when I said the world is neither contingent nor necessary in the Thomistic sense. Also, I feel like using curves at the beginning of the universe is no more useful than string theory. One leads to circular regression while the other leads to infinite past universes. I doubt you can demonstrate the mechanism of the origin using only science.

Finally, I wanted to say I smoked some bud a few minutes ago and it immediately accord to me that time goes on forever and should reach an infinity but cant. Therefore logic says the universe will end

An accidental infinite just means "one with God supporting it". An essential one is one without God. Thomists make it easier for people to think of this by saying the accidental is one where the effect doesn't need to cause to exist. But God could actually create a series where each effect is supported by the previous, according to Aquinas's thought. This really is not always explained very well. Aquinas thought he could avoid the argument which goes "how can there be an infinity of effects when each motion in the series is intermediate" by saying God holds it together from the outside. Again, I don't buy that argument either. The universe had a beginning in the primal realm of potentiality, which you might describe as halfway between nothing and something

There is no mechanized or unmechanized minds in your sense. Only what part of reality is from you and that which isn't. — substantivalism

Douglas Hofstadter I think argues in his books that we can avoid paradoxes in set theory (and Godel too of course) by realizing we are not mechanized thinkers. Our intellects seem to have something substantial about them that avoids strict mechanism. This might be connected to the mystical part of the mind. (It's all quite complicated) Also, like I said, physicists are never going to find the physical mechanism by which the world started. They are starting with the wrong basics. Time and again they have tried to drive the truck around the turn but it always turns over, as a Thomist once told me. Thomas Aquinas's argument was that an infinity of past events cannot stand on it's own. It needs to rest in a mind. That makes sense, but I don't believe in an infinite universe anways. As I said, I take a more Heideggerian approach to the beginning of the universe. Think with primordial thinking, as he says

Hawkings solution is like jgill's above. Imagine the sequence of events as a segment (not a line). You go back further and further towards a limit but the fractions go on forever. Hawking said time becomes more and more like space as this happens, and basically everything gets lost in fuzziness. It's a nice try but it's not satisfying. Penrose said it was wrong, but he keeps going on circles with the circular universe stuff. The fact, the reality, is you can't avoid using the mystical part of your mind in thinking about "the beginning". All you need to do is imagine pure potentiality flowing or falling, or however you like, into actuality. I really have no problem doing this, and so the whole God thing doesn't matter to me anymore

I agree partially with your stance. Even many scientists, as you said a couple of times, say we create the world. But I don't believe anything is necessary. If thoughts of necessity are Platonic in nature, I consider that spiritual but not realistic. You know that feeling you get when your with a romantic partner early in the courting, kissing in the dark at a park, and watching the stars? You can feel the contingency of everything. Sinatra captured that feeling in some songs. I think that is reality. Every thing is contingent and there is no reason for the necessary except as a mental escape. There is some book on Amazon, I think it's called Necessary Being... But I don't buy it (pun intended)

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Your post is Spninozian. But I object to the ending when you say infinity implies necessity

Eternity is infinite. But if you can't make sense of the beginning of time, pushing it back forever doesn't give you a more logical explanantion. There are illogical things in this world, but the logical is prior. How a physical timeless universe goes from being still and then into the flow of time without outside causality is a question scientists are breaking their heads over. They have no forrm of natural faith so they can't see creation out of nothing. I reject the idea of God for certain reasons but if there was a God I can perfectly well see him creating our of nothing. I do have natural faith but I reject supernatural faith as the dreams of trolls

If the model is an infinite casual past, you should be able to plug in any accidental figures to see if it works. An infinity of humans with no start. That's too crazy for me. I think set paradoxes which are only resolvable by an unmechanized mind proved an infinite past would require a divine mind, but I still think it's impossible

An infinite series of, say, dominoes going into the past does indeed need a prime mover or movers (Aristotle) or a Trinity (Aquinas) to keep it well ordered. I'm a little stricter and think there can't be an infinite past. Try if you can to imagine humanity with all the births and deaths going back forever with no first human or evolution. It verges on the illogical. So I say potentiality flung into actuality along Heideggerian lines.

Were they scientific, though? You know, as opposed to those unscientific Dunning-Kruger studies? — InPitzotl

There is no such thing as a "scientific" psychological study. There are way too many factors for that. The establishment says all the time "that's just anecdotal" about an herb or something. Of course what people tell people in white coats in a laboratory is also anecdotal. There is way too much dogmatism over this stuff. All you can do is accept your observations and run with them. It's you guys who are making this stuff into dogma