Posts by Cassius

Thank you Don! That will give us a foundation for dealing with the Latin references, because just the differences between Yonge and Rackham we've seen already indicate that there's a lot of speculation going on about the implications.

The whole issue of limits and absence of limits seems fundamental to everything and carry over from physics to ethics and probably to canonics as well. I would think that Lucretius and people writing in the Latin period understood what was going on and are largely reliable, but the further away we get from people who had access to the wider set of texts the less I would trust the translations.

This is going to feed also into the differences in the way "ut omnia omnibus paribus paria respondeat," is viewed by Rackham as "match and counterpart," vs. Yonge's "everything in it is made to correspond completely to some other answering part."

And on the issue of whether infinity leads to an infinite number of identical things, or simply an infinite number of "like" things, we'll need to scrutinize the words referencing the concept of "like" and "unlike."

Ok this one is up. Note that we recorded this Sunday morning, before many of our recent conversations on isonomia and infinity, but I think the result is pretty current with recent postings.

Episode 237 of the Lucretius Today Podcast is now available. This week we explore isonomia and the implications of infinity!

OK maybe I misinterpreted your post above -- I was thinking you meant that the Epicureans did not think that there was no limit to the amount of distance you could travel in any direction.

These would be the key sections from Lucretius (Bailey Edition) supporting the conventional view that Epicurus held that the universe is limitless in size in all directions.

[951] But since I have taught that the most solid bodies of matter fly about for ever unvanquished through the ages, come now, let us unfold, whether there be a certain limit to their full sum or not; and likewise the void that we have discovered, or room or space, in which all things are carried on, let us see clearly whether it is all altogether bounded or spreads out limitless and immeasurably deep.

[958] The whole universe then is bounded in no direction of its ways; for then it would be bound to have an extreme point. Now it is seen that nothing can have an extreme point, unless there be something beyond to bound it, so that there is seen to be a spot further than which the nature of our sense cannot follow it. As it is, since we must admit that there is nothing outside the whole sum, it has not an extreme point, it lacks therefore bound and limit. Nor does it matter in which quarter of it you take your stand; so true is it that, whatever place every man takes up, he leaves the whole boundless just as much on every side.

[968] Moreover, suppose now that all space were created finite, if one were to run on to the end, to its furthest coasts, and throw a flying dart, would you have it that that dart, hurled with might and main, goes on whither it is sped and flies afar, or do you think that something can check and bar its way? For one or the other you must needs admit and choose. Yet both shut off your escape and constrain you to grant that the universe spreads out free from limit. For whether there is something to check it and bring it about that it arrives not whither it was sped, nor plants itself in the goal, or whether it fares forward, it set not forth from the end. In this way I will press on, and wherever you shall set the furthest coasts, I shall ask what then becomes of the dart. It will come to pass that nowhere can a bound be set and room for flight ever prolongs the chance of flight. Lastly, before our eyes one thing is seen to bound another; air is as a wall between the hills, and mountains between tracts of air, land bounds the sea, and again sea bounds all lands; yet the universe in truth there is nothing to limit outside.

[984] Moreover, if all the space in the whole universe were shut in on all sides, and were created with borders determined, and had been bounded, then the store of matter would have flowed together with solid weight from all sides to the bottom, nor could anything be carried on beneath the canopy of the sky, nor would there be sky at all, nor the light of the sun, since in truth all matter would lie idle piled together by sinking down from limitless time. But as it is, no rest, we may be sure, has been granted to the bodies of the first-beginnings, because there is no bottom at all, whither they may, as it were, flow together, and make their resting-place. All things are for ever carried on in ceaseless movement from all sides, and bodies of matter, are even stirred up and supplied from beneath out of limitless space.

*Loeb here has* [998] Lastly, one thing is seen before our eyes to be the limit of another; air separates hills and mountains air, earth bounds sea and contrariwise the sea is the boundary of all lands; the universe, however, has nothing outside to be its limit.

I need to know exactly what Aristotle said, but I could see Epicurus agreeing that the 'concept of infinity" is a mental construct only, while at the same time holding that the number of atoms actually existing is uncountable and extends without limit or boundary out into space "forever."

I see the javelin example as highly useful - it illustrates that the limit is in US, not in the reality of space or atoms, because "if we could live forever" we could go on throwing the javelin outward, and counting atoms, forever and ever.

I am not sure you can square that with the "javelin" example in Lucretius, Don. Can you?

Editing is coming along -- this should be out no later than tomorrow - hopefully sooner.

In the meantime, this part of section 19 (book one) is clearly one of the sections that is most critical - here is the Rackham version, with the focus on "that in the sum of things everything has it's exact match and counterpart."

Here is Rackham's Latin:

It looks to me like that is a rendering of a section of "ut omnia omnibus paribus paria respondeat," so Rackham's "match and counterpart" is as open to question as is Yonge's "everything in it is made to correspond completely to some other answering part." In this instance Yonge's "answering" may be a better rendering of "respondeant" than Rackham's "exact match or counterpart." The decision we make on what words to use is going to greatly influence one's conclusion on what is being said. What would seem most likely for an Epicurean to be thinking in terms of "answering" or "corresponding?" We know the basics of Epicurean physics and canonics which cannot be violated in answering the question, so what are the possibilities?

This is a line at which we'll want to train our best big guns of Latin translation expertise!

All of the perspectives you've expressed in the last several messages Tau Phi, are fine if they work for you, but as you say and know - they are not Epicurean perspectives. Would that the world were filled with people like you, but it's not. It's filled with "lost" people who are in the grip of supernatural religion, and unable to think their own way out of it, just like they were in the time of Lucretius and the time of Diogenes of Oinoanda, not to mention the time of Epicurus.

Epicurean philosophy was then, and can be today, an organized method of bringing answers to such people. If there are individuals like you who don't need its help, and can do it on your own, then that's all to the better for you, but it does nothing for the large numbers of the "hearts in darkness" that Lucretius was talking about in his poem.

Not everyone has to participate in the kind of organized activity that the ancient Epicureans were engaged in, but at the same time, if some don't, then the same patterns of deception and manipulation will go on and on and on and never be challenged. Maybe you see it differently, but to me it is in the nature of things that lone individuals, especially lone individuals who focus on retreating into their own gardens, can do little or nothing to change that situation. And of course I'm not at all referring to you as retreating into your own garden, but referring to the allusion often applied to the ancient Epicureans, which I will never admit to be true. The ancient Epicureans were part of an organized campaign, not lone rangers.

That's the value Epicurus saw in putting together a team and a community, and the same thing holds true today. People have to work together to accomplish anything, and to accomplish things they have to be aware of the situation around them. Again, I would wish that the world were full of Tau Phi's, but there are far too few of them. The great majority fit the description of the people Diogenes of Oinoanda referenced on his wall. They won't and can't think through a system of philosophy for themselves, and they will forever be at the mercy of the organized manipulators if those who know better don't step up to help them.

i guess we'll just have to agree to disagree on our assessment of the general situation and how to deal with it. No one is ever going to force you to accept any position of Epicurus with which you don't agree, but just like in the ancient world the teachings of Epicurus formed the basis of the "movement," and that's where this forum and our organized activities needs to remain focused.

Quote from TauPhi

As of now, infinity of the universe (among other infinities) is neither obvious nor easy to understand (or prove) to humanity.

Probably they were neither obvious or easy in the ancient world either, and that was a large part of the undertaking of studying and applying Epicurean philosophy. I don't recall Epicurus or Lucretius of Diogenes of Oinoanda implying that the philosophy was easy -- the closest I recall in the texts to calling it easy or simply was Cicero making a similar comment, and that's in his own words in a statement I'm happy to consider to be one to take with a grain of salt.

But it makes sense to me that Epicurus would start out personally motivated with an interest in where the universe came from and then continue to the end of his life seeing the importance of that conveying that very same issue to others. If you're going to wrestle people out of the jail of supernatural religion you're going to need to replace "god" with something, and "atoms" is only a part of the picture. The rest of the picture as a whole requires "infinity" to be plausible and persuasive to people of normal intelligence - and people of normal intelligence shouldn't be asked to accept "trust the scientists" or "trust the mathematicians" any more than they accept "trust the priests" as an explanation.

In fact, I would say that the implication of what Epicurus has stated that we should do - MOST OF ALL -- is that we should study the principles of infinity and take them to be correct. We should not consider them to be "mind-blowing' at all, but they should be second nature and taken to be as obvious and easy to understand as anyone for the past 2000 years has taken the incorrect "In the beginning GOD created the heaven and the earth...":

Quote from Epicurus Letter to Pythocles

All these things, Pythocles, you must bear in mind; for thus you will escape in most things from superstition and will be enabled to understand what is akin to them. And most of all give yourself up to the study of the beginnings and of infinity and of the things akin to them, and also of the criteria of truth and of the feelings, and of the purpose for which we reason out these things. For these points when they are thoroughly studied will most easily enable you to understand the causes of the details. But those who have not thoroughly taken these things to heart could not rightly study them in themselves, nor have they made their own the reason for observing them.

Quote from kochiekoch

The bottom line is, all this stuff is hypothetical, and may not be real at all, but it's mind blowing to contemplate.

Difficult perhaps, but not for that reason something that we should not do. In fact the "recommendation" or "command" that we do spend our time considering it is probably one of the most clear "recommendations" that Epicurus gives. Lots of the other material ends up being "Choose what makes the most sense in terms of pleasure and pain in your own situation." In this case, he's giving a flat statement to students that this is something we should definitely do. I am on board that this is a much-neglected aspect of Epicurean philosophy that needs to be dramatically elevated in focus.

Quote from Godfrey

Then there's Nietzche's eternal recurrence. I'm not too familiar with it, but it seems to me that this was just a thought experiment and not a serious proposal of the way things are. But I could be wrong on that.

Yes apparently there is a question as to whether he believed this himself or not. And some quick googling links "eternal recurrence" to the STOICS, of whom he generally disapproved, so that's another mark against it. It seems that the Stoic version may have been based on their ideas of fate/necessity, so they may have seen it as inevitable from that point of view, which Epicurus would reject. We need a lot more detail on both Nietzche's version and the Stoic version.

Quote from kochiekoch

But you might end up with infinite multiverses too, all with different laws of physics, so infinity is the limit!

Whenever I hear "multiverse" my blood runs cold, especially with references to "different laws of physics." Apparently "multiverse" needs closer definition too, and anyone who wants to explore that is welcome, but it's not likely to be me. I am firmly in the camp that "universe" should be taken to mean "all that exists" - and if that's what the word means then fine, but I see no reason to change the traditional meaning of "everything." But the "different laws of physics" is a showstopper too, from an Epicurean perspective, it seems to me. Sure different circumstances lead to different outcomes, but that's different circumstances, not different "laws of physics."

At the moment I am thinking that:

1 - "Infinity on the downside" (infinite divisibility) is a total dead end. That kind of thinking leads to the "it's impossible to walk across the room" which we observe to be nonsense.

At the opposite extreme, on the "up-side":

2 - Infinity meaning "different laws of physics" and "anything goes" and anything is possible" is also a non-starter. By definition this is postulating something that we have never seen, and for which we have no evidence, and you might as well start postulating pink elephants on the other side of the moon, and supernatural gods. All that is a total non-starter in Epicurean terms.

The most interesting questions to me seem to be along the lines stated above, including:

1. Whether infinity means that any combination of atoms which *is* possible does in fact happen,
2. Whether any combination which does happen, happens and infinite number of times.
3. Whether the swerve of the atom, or something like irrational numbers / fractals / fibonacci sequences, should make us expect that "classes" of "like" events will happen an infinite number of times, like snowflakes or grains of sand, but that recurrence in IDENTICAL ways should not be expected.

These are basic questions that would have occurred to Epicurus, and the texts maybe already indicate in fact *did* occur to Epicurus, and which we can use to shed light on how to reconstruct our interpretation of what Epicurus in fact taught.

Notes on directions to research to look for proper ways to reconstruct basic Epicurean reasoning on infinity:

1. Wikipedia: Infinity
   1. Philosophical nature of infinity.
      1. Anaximander - first Greek to propose the universe to be infinite. Mostly right?
      2. Anaxagorus - first Greek to propose infinite division - Mostly wrong?
      3. Aristotle - rejected actual inflnity but allowed potential infinity?
         1. In Book 3 of the work entitled Physics, written by Aristotle, Aristotle deals with the concept of infinity in terms of his notion of actuality and of potentiality. Physics 207b8 It is always possible to think of a larger number: for the number of times a magnitude can be bisected is infinite. Hence the infinite is potential, never actual; the number of parts that can be taken always surpasses any assigned number.
      4. John Locke - in common with most of the empiricist philosophers, also believed that we can have no proper idea of the infinite. They believed all our ideas were derived from sense data or "impressions," and since all sensory impressions are inherently finite, so too are our thoughts and ideas. Our idea of infinity is merely negative or privative. "Whatever positive ideas we have in our minds of any space, duration, or number, let them be never so great, they are still finite; but when we suppose an inexhaustible remainder, from which we remove all bounds, and wherein we allow the mind an endless progression of thought, without ever completing the idea, there we have our idea of infinity... yet when we would frame in our minds the idea of an infinite space or duration, that idea is very obscure and confused, because it is made up of two parts very different, if not inconsistent. For let a man frame in his mind an idea of any space or number, as great as he will, it is plain the mind rests and terminates in that idea; which is contrary to the idea of infinity, which consists in a supposed endless progression."  Essay, II. xvii. 7., author's emphasis --- Mostly wrong (?)
2. Especially Likely to lead to something fruitful?
   1. Georg Cantor
      1. The concept of the existence of an actual infinity was an important shared concern within the realms of mathematics, philosophy and religion. Preserving the orthodoxy of the relationship between God and mathematics, although not in the same form as held by his critics, was long a concern of Cantor's.^[71] He directly addressed this intersection between these disciplines in the introduction to his Grundlagen einer allgemeinen Mannigfaltigkeitslehre, where he stressed the connection between his view of the infinite and the philosophical one.^[72] To Cantor, his mathematical views were intrinsically linked to their philosophical and theological implications – he identified the absolute infinite with God,^[73] and he considered his work on transfinite numbers to have been directly communicated to him by God, who had chosen Cantor to reveal them to the world.^[5] He was a devout Lutheran whose explicit Christian beliefs shaped his philosophy of science.^[74] Joseph Dauben has traced the effect Cantor's Christian convictions had on the development of transfinite set theory.^[75][76]
      2. Debate among mathematicians grew out of opposing views in the philosophy of mathematics regarding the nature of actual infinity. Some held to the view that infinity was an abstraction which was not mathematically legitimate, and denied its existence.^[77] Mathematicians from three major schools of thought (constructivism and its two offshoots, intuitionism and finitism) opposed Cantor's theories in this matter. For constructivists such as Kronecker, this rejection of actual infinity stems from fundamental disagreement with the idea that nonconstructive proofs such as Cantor's diagonal argument are sufficient proof that something exists, holding instead that constructive proofs are required. Intuitionism also rejects the idea that actual infinity is an expression of any sort of reality, but arrive at the decision via a different route than constructivism. Firstly, Cantor's argument rests on logic to prove the existence of transfinite numbers as an actual mathematical entity, whereas intuitionists hold that mathematical entities cannot be reduced to logical propositions, originating instead in the intuitions of the mind.^[78] Secondly, the notion of infinity as an expression of reality is itself disallowed in intuitionism, since the human mind cannot intuitively construct an infinite set.^[79] Mathematicians such as L. E. J. Brouwer and especially Henri Poincaré adopted an intuitionist stance against Cantor's work. Finally, Wittgenstein's attacks were finitist: he believed that Cantor's diagonal argument conflated the intension of a set of cardinal or real numbers with its extension, thus conflating the concept of rules for generating a set with an actual set.^[10]
      3. Some Christian theologians saw Cantor's work as a challenge to the uniqueness of the absolute infinity in the nature of God.^[6] In particular, neo-Thomist thinkers saw the existence of an actual infinity that consisted of something other than God as jeopardizing "God's exclusive claim to supreme infinity".^[80] Cantor strongly believed that this view was a misinterpretation of infinity, and was convinced that set theory could help correct this mistake:^[81] "... the transfinite species are just as much at the disposal of the intentions of the Creator and His absolute boundless will as are the finite numbers.".^[82] Prominent neo-scholastic German philosopher Constantin Gutberlet was in favor of such theory, holding that it didn't oppose the nature of God.^[8]
      4. Cantor also believed that his theory of transfinite numbers ran counter to both materialism and determinism – and was shocked when he realized that he was the only faculty member at Halle who did not hold to deterministic philosophical beliefs.^[83]
      5. It was important to Cantor that his philosophy provided an "organic explanation" of nature, and in his 1883 Grundlagen, he said that such an explanation could only come about by drawing on the resources of the philosophy of Spinoza and Leibniz.^[84] In making these claims, Cantor may have been influenced by F. A. Trendelenburg, whose lecture courses he attended at Berlin, and in turn Cantor produced a Latin commentary on Book 1 of Spinoza's Ethica. Trendelenburg was also the examiner of Cantor's Habilitationsschrift.^[85][86]
      6. In 1888, Cantor published his correspondence with several philosophers on the philosophical implications of his set theory. In an extensive attempt to persuade other Christian thinkers and authorities to adopt his views, Cantor had corresponded with Christian philosophers such as Tilman Pesch and Joseph Hontheim,^[87] as well as theologians such as Cardinal Johann Baptist Franzelin, who once replied by equating the theory of transfinite numbers with pantheism.^[7] Although later this Cardinal accepted the theory as valid, due to some clarifications from Cantor's.^[8] Cantor even sent one letter directly to Pope Leo XIII himself, and addressed several pamphlets to him.^[81]
      7. Cantor's philosophy on the nature of numbers led him to affirm a belief in the freedom of mathematics to posit and prove concepts apart from the realm of physical phenomena, as expressions within an internal reality. The only restrictions on this metaphysical system are that all mathematical concepts must be devoid of internal contradiction, and that they follow from existing definitions, axioms, and theorems. This belief is summarized in his assertion that "the essence of mathematics is its freedom."^[88] These ideas parallel those of Edmund Husserl, whom Cantor had met in Halle.^[89]
      8. Meanwhile, Cantor himself was fiercely opposed to infinitesimals, describing them as both an "abomination" and "the cholera bacillus of mathematics".^[41]
      9. Cantor's 1883 paper reveals that he was well aware of the opposition his ideas were encountering: "... I realize that in this undertaking I place myself in a certain opposition to views widely held concerning the mathematical infinite and to opinions frequently defended on the nature of numbers."^[90]
      10. Hence he devotes much space to justifying his earlier work, asserting that mathematical concepts may be freely introduced as long as they are free of contradiction and defined in terms of previously accepted concepts. He also cites Aristotle, René Descartes, George Berkeley, Gottfried Leibniz, and Bernard Bolzano on infinity. Instead, he always strongly rejected Immanuel Kant's philosophy, in the realms of both the philosophy of mathematics and metaphysics. He shared B. Russell's motto "Kant or Cantor", and defined Kant "yonder sophistical Philistine who knew so little mathematics."^[91]

I am going through and upgrading the "Infinity' forum to emphasize its importance. For the moment it is renamed "The Universe Is Boundless - Infinity And Its Implications," however we need to greatly expand it in the direction of exploring general implications of infinity, of which "life on other worlds" is just one major subtopic. The implications for "how many things there will be of a kind, given the limited shapes of the atoms" are wide and deep. I feel sure there are many good discussions of this, both in nonfiction and in science fiction literature, that ought to be added in for consideration.

Future visitors here will want to check out Lucretius Today Podcast Episode 237 for our strongest focus on Principles of Infinity to date. Feel free to open new discussions in this forum, because we need to flesh out in full the implications of infinity as explored by Epicurus and others of similar mindset.

One question on my mind at the moment relates to question of whether "nature never makes a single thing of a kind" means that "single things can be and are duplicated exactly an infinite number of times, given the infinite universe" or "kinds will have infinite numbers of examples of their kind over the infinite universe, but the individual examples within the kind are not duplicated. In other words, do the principles of infinity imply that the universe has within it: (1) infinite earth-like plants, or (2) infinite beings which are essentially "human," or (3) infinite numbers of humans who look like Epicurus, or (4) infinite numbers of actual Epicurus clones?

What did Epicurus (and do we now, if different) observe here on earth? Are there in fact never two snowflakes exactly the same, even though within the class of snowflakes there are virtually boundless instances of snowflakes? Is there something in the formation of bodies (perhaps related to irrational numbers / fibonacci / fractal issues) that lead to vast numbers of similars but imply that no two natural objects are ever *exactly* duplicated?

I will also add to the above list of cites those we collected for Episode 237.

Thank you Joshua. I am processing this quickly so I may be mistaken, but what I see is :

1 - The introduction is by Dunster's SON, and contains nothing of interest, but typical clerical affirmation that the soul has an eternal existence.

2 - The text itself is wholly clerical and contains nothing of interest. To the extent it refers to the ancients, it doesn't mention any Epicurean views - just circular representations of god and the like.

So what we are missing, which might have been of interest if it still existed, was Dunster's OWN commentary on the issue of eternity. Looks doubtful we will find anything based on this.

Yes bravo Joshua - it was worth the wait! i will have lots of comments before this is over but something caught my eye that you and I have not discussed:

Quote from Joshua

He further published a sermon on the book of Proverbs, advocating in defense of public education, in 1708. In 1709-1710 there appeared two translations; The Considerations of Drexelius on Eternity, which ran through a number of subsequent editions,

Do you think there is any possibility of us getting our hands on this?

This 1743 edition is one of my favorites because there are several passages that I think Dunster (I will assume the question for the moment) translates better than anyone else. My prime example of that is how Dunster uses events rather than accidents early in the poem in that section referencing the Trojan War.

I therefore have developed a notion that Dunster was more "in tune" with Lucretius (and Epicurus) than many other writers, so I would expect him to be drawn to some of the same questions that we are pursuing now -- especially the question of infinity / eternality of the universe.

I would love to read what Dunster wrote about eternality. I want to know what "Drexelius" said too (don't know who that is at this point) but I would expect Dunster to have wanted to follow up on many of the leads that we are following today.

Did you see anything indicating that any of Dunster's other works (especially on eternality) have still survived?

EDIT: Well it pays to Google before typing too much! https://books.google.com/books/about/Th…id=2mNiAAAAcAAJ

Writing before post 3 is updated: I can't wait for the conclusion! Cliffhanger!

Some of the cites to discuss in this episode:

1. Epicurus to Herodotus 45 - These brief sayings, if all these points are borne in mind, afford a sufficient outline for our understanding of the nature of existing things. Furthermore, there are infinite worlds both like and unlike this world of ours. For the atoms being infinite in number, as was proved already, are borne on far out into space. For those atoms, which are of such nature that a world could be created out of them or made by them, have not been used up either on one world or on a limited number of worlds, nor again on all the worlds which are alike, or on those which are different from these. So that there nowhere exists an obstacle to the infinite number of the worlds. [46] Moreover, there are images like in shape to the solid bodies, far surpassing perceptible things in their subtlety of texture. For it is not impossible that such emanations should be formed in that which surrounds the objects, nor that there should be opportunities for the formation of such hollow and thin frames, nor that there should be effluences which preserve the respective position and order which they had before in the solid bodies: these images we call idols.
2. Epicurus to Pythocles 117 - All these things, Pythocles, you must bear in mind; for thus you will escape in most things from superstition and will be enabled to understand what is akin to them. And most of all give yourself up to the study of the beginnings and of infinity and of the things akin to them, and also of the criteria of truth and of the feelings, and of the purpose for which we reason out these things. For these points when they are thoroughly studied will most easily enable you to understand the causes of the details. But those who have not thoroughly taken these things to heart could not rightly study them in themselves, nor have they made their own the reason for observing them.
3. Epicurus to Menoeceus - [135] ... Meditate therefore on these things and things akin to them night and day by yourself; and with a companion like to yourself, and never shall you be disturbed waking or asleep, but you shall live like a god among men. For a man who lives among immortal blessings is not like unto a mortal being.
4. Lucretius Book 2: 1077 - Bailey: [1077] This there is too that in the universe there is nothing single, nothing born unique and growing unique and alone, but it is always of some tribe, and there are many things in the same race. First of all turn your mind to living creatures; you will find that in this wise is begotten the race of wild beasts that haunts the mountains, in this wise the stock of men, in this wise again the dumb herds of scaly fishes, and all the bodies of flying fowls. Wherefore you must confess in the same way that sky and earth and sun, moon, sea, and all else that exists, are not unique, but rather of number numberless; inasmuch as the deep-fixed boundary-stone of life awaits these as surely, and they are just as much of a body that has birth, as every race which is here on earth, abounding in things after its kind.
5. Lucretius Book 2, Bailey: [522] And since I have taught this much, I will hasten to link on a truth which holds to it and wins belief from it, that the first-beginnings of things, which are formed with a shape like to one another, are in number infinite. For since the difference of forms is limited, it must needs be that those which are alike are unlimited, or else that the sum of matter is created limited, which I have proved not to be, showing in my verses that the tiny bodies of matter from everlasting always keep up the sum of things, as the team of blows is harnessed on unbroken on every side. [532] For in that you see that certain animals are more rare, and perceive that nature is less fruitful in them, yet in another quarter and spot, in some distant lands, there may be many in that kind, and so the tale is made up; even as in the race of four-footed beasts we see that elephants with their snaky hands come first of all, by whose many thousands India is embattled with a bulwark of ivory, so that no way can be found into its inner parts: so great is the multitude of those beasts, whereof we see but a very few samples. [541] But still, let me grant this too, let there be, if you will, some one thing unique, alone in the body of its birth, to which there is not a fellow in the whole wide world; yet unless there is an unlimited stock of matter, from which it might be conceived and brought to birth, it will not be able to be created, nor, after that, to grow on and be nourished.
6. Lucretius Book 3 Bailey - [843] And even if the nature of mind and the power of soul has feeling, after it has been rent asunder from our body, yet it is naught to us, who are made one by the mating and marriage of body and soul. Nor, if time should gather together our substance after our decease and bring it back again as it is now placed, if once more the light of life should be vouchsafed to us, yet, even were that done, it would not concern us at all, when once the remembrance of our former selves were snapped in twain. And even now we care not at all for the selves that we once were, not at all are we touched by any torturing pain for them. For when you look back over all the lapse of immeasurable time that now is gone, and think how manifold are the motions of matter, you could easily believe this too, that these same seeds, whereof we now are made, have often been placed in the same order as they are now; and yet we cannot recall that in our mind’s memory; for in between lies a break in life, and all the motions have wandered everywhere far astray from sense.
7. Diogenes of Oinoanda Letter to Antipater - Fr. 63 So, as I was saying, having had my appetite most keenly whetted by all the advantage of the voyage, I shall try to meet you as soon as winter had ended, sailing first either to Athens or to Chalcis and Boeotia. But, since this is uncertain, both on account of the changeability and inconstancy of our fortunes and on account of my old age besides, I am sending you, in accordance with your request, the arguments concerning an infinite number of worlds. And you have enjoyed good fortune in the matter; for, before your letter arrived, Theodoridas of Lindus, a member of our school not unknown to you, who is still a novice in philosophy, was dealing with the same doctrine. And this doctrine came to be better articulated as a result of being turned over between the two of us face to face; for our agreements and disagreements with one another, and also our questionings, rendered the inquiry into the object of our search more precise. I am therefore sending you that dialogue, Antipater, so that you may be in the same position as if you yourself were present, like Theodoridas, agreeing about some matters and making further inquires in cases where you had doubts. The dialogue began something like this: «Diogenes,» said Theodoridas, «that the [doctrine laid down] by Epicurus on an infinite number of worlds is true [I am confident], ................ ................., as [if] ............. Epicurus .......

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3. Repeated exposure to images creates pathways of thought just like repeated vision creates afterimage?
4. Fractals - Fibonacci sequences
5. Pleasure as related to smooth motion as held by Cyreniacs - Did Democritus also hold this? Did Epicurus?

Thank you - never heard of that - very interesting!