The nature of Infinities

[shunyadragon]

Friends

There are at least two views of Infinity in things, time and space: One predominantly used in Philosophy and Theology, particularly traditional theology, which has a foundation in Aristotle's works. The second is that which is used predominately in math, physics and cosmology. I recommend the book, Infinity and the Mind by Rudy Rucker to get a basic understanding of Infinities in contemporary math and science. It is a fun book, as well as informative.

I propose the following based on our contemporary knowledge of science and math: Our physical existence, which includes our universe is possibly if not most likely infinite and eternal.

I will post more describing this view based on Rudy Rucker's work and other references.

This thread is in response to those who use 'actual' infinities as part of their basis for ontological arguments.

[shunyadragon]

The universe is not likely infinite unless it is found to demonstrated to be possibly infinitely cyclic. The physical existence which the universe is a part of is what is likely infinite and eternal.

In Rudy's bock he desrcibes three types: (1) Spacial Infinities (2) Temporal infinities. (3) Infinities in the Mindscape.

Type one and two are the most important in math, physics and cosmology.

Actual and potential infinities are Infinities of the Mindscape as first described by Aristotle. Actual infinities are sets of things described as infinite, such as: the number of possible universes, or the number of atoms in all of existence. Potential infinities are infinities that are described as having a starting point, such as the set of infinite whole numbers. It is important to remember one important point about time and space, no numbers. Humans use numbers to describe things from our perspective, so actual and potential infinites are descriptions of infinites from the human perspective only as infinities of the Mindscape.

One note of trivia; Our current symbol for infinity represents a type of 'Spatial Infinity' called 'finite and unbounded.' Circles and Spherical objects like balls are finite in extent, but unbounded (infinite) in that one can travel around them and never reach an end.

In contemporary cosmology, physics and math our physical existence is considered conceptually infinite and eternal.

This thread will emphasis Spacial and Temporal infinities, which are used to describe our physical existence as possibly infinite and eternal.

[NeilUnreal]

Rucker's book is a classic; I first read it as a undergraduate -- an infinity ago in the mindscape, lol. I think my copy is in storage; let me try to find it so I can follow the references more closely.

-Neil

[shunyadragon]

Rucker's book is a classic; I first read it as a undergraduate -- an infinity ago in the mindscape, lol. I think my copy is in storage; let me try to find it so I can follow the references more closely.

-Neil

Yes! It is a classic, but I some times jumps around, and makes things a little difficult. Other than that it is a fun easy read. Please contribute and add to the discussion.

[shunyadragon]

Friends

The book, page 18-19, refers to a Roman 1st century BCE philosopher Lucretius that gave an adequate concept of 'spacial infinity' that is still relevant to modern math and science. Here is a source that discusses his contribution in more detail. I believe he should be given more credit for his work than the current near anonymous state of affairs.

http://www.ams.org/journals/bull/1918-24-07/S0002-9904-1918-03078-4/S0002-9904-1918-03078-4.pdf

In any adequate historical survey of the role of the notion of infinity in our human thinking a consideration of the De Rerum Natura of Lucretius will have to be accorded the position of an important chapter. Most of the many great merits of the work have been long [neglected], if not generally nor even widely, recognized. One of its recognized merits is its superb daring and the unsurpassed magnificence of its enterprise; another is its probably unmatched union of literary excellence with scientific spirit and aim; still another, which includes many, being a highly composite merit, is its confident and often acutely argued presentation, sometimes in detail and sometimes in clear and striking outline, of ideas and doctrines that came into their own only in modern science. I refer to such concepts and dogmas as natural law, the atomic constitution of matter, the conservation of mass and of energy, organic evolution, spontaneous or chance variation of life forms, struggle for existence, survival of the fit, and sensation as the ultimate basis of knowledge and the ultimate test of reality, not to mention other equally brilliant anticipations of modern scientific thought.

In attempts to appraise the work of Lucretius his employment of the notion of infinity is commonly indicated, but only more or less incidentally. For example, in Masson's large volume, Lucretius, Epicurean and Poet, the term infinite has only a subordinate place in the index of important terms; in Munro's very extensive Notes the term receives but scant attention; and it receives even less in the Notes found in Cyril Bailey's recent and deservedly much praised English translation of the poem. What is missed in such appreciations and commentaries and what I wish to signalize here is the fact that the concept of infinity—of infinite multitude and infinite magnitude—is not merely one among the many ideas, but is indeed the dominant idea, in the work of Lucretius.

© source where applicable

[shunyadragon]

Friends

Thanks to shadowmaster's reference to online courses at MIT, there is section on 'Paradox and Infinity' that is great. It references Rucker's book heavily as one of the primary texts.

The course can be found here . . . http://ocw.mit.edu/courses/linguisti...ity-fall-2006/

[NeilUnreal]

I still haven't been to storage; it's at a dismal spot on a windy hill and it always depresses me, so I put it off. The place always puts me in mind of Edgar Allen Poe or Edward Gorey.

However, this morning I find myself in need of a particular type of light bulb for a light in the workshop, and I know there is one in storage, so I'll go this afternoon.

-Neil

[shunyadragon]

I still haven't been to storage; it's at a dismal spot on a windy hill and it always depresses me, so I put it off. The place always puts me in mind of Edgar Allen Poe or Edward Gorey.

However, this morning I find myself in need of a particular type of light bulb for a light in the workshop, and I know there is one in storage, so I'll go this afternoon.

-Neil

Take a Raven along with you.

[NeilUnreal]

I got it; it's a bit musty, like some kind of tome of forgotten lore, but I've got it.

-Neil