Oxford philosopher Adrian Moore explains the infinite: http://www.youtube.com/watch?v=6s0TFBml_z4

This was so fascinating, the lecturer made this very simple to understand. Thanks for sharing friend.

Peace and love

..good lecture and topic thanks primordium..

a book which really expanded my mind was 'Infinity And The Mind' by mathematician Rudy Rucker..
highly recommended and readable..can preview/read here>
http://www.scribd.com/doc/125958327/Infinity-and-the-Mind ..easy to find for sale..

the 'orders of infinity' through the Alephs to Omega is a deep thing to grasp..

the contemplation of Infinity takes us to the limits of Mind..

WOW. knew lots about this already but it never ceases to amaze me! wish the lecture would go on forever (excuse the pun!)

This is an interesting one as well.

Thanks for the links will check them out later..
I always see infinity as like a long journey in a car whereby just when you think you have nearly arrived there is yet another road or turning you to have to take.
While on this subject does anyone know where π fits into many worlds/multiverse theory?

Had a thought earlier about dmt enabling us to access these other universes where the properties of that universe are different to our own however that raises more issues such as it implies our conciousness can separate from our bodies and that dmt has some way of doing this. Also that our conciousness can bypass the contempary laws of physics such as light speed and space-time. Wormholes? I dunno its probably just my understanding of the muliverse theory is wrong but interesting to think about anyway, just thought I would throw that one out there..

infinity plus1

While mathematics is commonly called the language of nature, in fact it is the human translation of this language. It is a science of relation between mind made objects and also those which have their material representation in nature either technology that wouldn't exist without mathematics. The point is, in fact it is a system that reflects in its symbols a way of logic and rational understanding, a relatively small part of the mind. Except every form that arises in consciousness can be described in certain limits by this system, unfortunatelly it is not efficient to go beyond those forms. I mean by that behind every form of mind stands the consciousness, undescribable by any equasion but imaginable in geometrical forms nevertheless still without measurement. In fact consciousness is an infinite potential of imagination for the mind. A plane that upon any form can really exist. The mathematical representation of consciousness and only one that truly represents its character is infinity itself.
Through our consciousness we can create in mind countless problems to solve and find a way through discovery of relation between them to solution, the logic of a phenomena. The universal consciousness is in fact the bigest set of possibility. There are many smaller sets within consciousness that can be called dimensions of reality, our world is one of them and human form is just a part of it, an even smaller set of ideas, concepts and assumptions.
Going deeper into the mind we can make a map of fractal sets that would go deeper and deeper into the vastness of mindspace, by adding forms and creating another within them. The possibilities the same as consciousness are infinite. While every set means limits, the defining boundries of the set, infinite number of sets can be infinite within.
The question which infinity is bigger, is only solvable by comparison of the sets, which includes which and if they are not codependent solution do not exist. It would be like comparing two other cathegories by the same mesure. Perhaps there is a way to do that but very fragile. If one type of infinity exist on a certian level of a mind complexity, it boundries are the complexity itself and that creates an opportunity to compare by the levels of mind, the relation between them.
In that context all paradoxes about infinity are somekind of logical and rational boundries of the mind or assumptions that point us to step outside the box to a higher level of understanding. After all it is just a play of the mind upon the plane of consciousness and question about infinity that goes together with view points on this subject are also infinite. In fact they belong to a certain set within the mind, the same as my way of describtion. There is no solution of infinity, we can only bring out of it what we want.
What the profesor does is just rising a problem out of infinte potential of creation, a play between consciousness and the mind. However there is a solution to the infinity, it is reduction and concentration of the mind to the one point and stand in front of pure consciousness without any problematic mask upon. It is to become infinity. That's how incredible is consciousness and the mind.
Just like Aldous Huxley on mescaline saw in every form infinity and William Blake wrote - "if the doors of perception were cleansed everything would appear to man as it is infinite".

^ nice observations

..it's like endlessly ascending..

even if you make the 'set of everything',
absolute infinity is beyond that..

When I write "consciousness", "mind", I am reffering to whole universe, not single being but oneness of all that exists.

To say that the absolute inifinity is beyond anything is to say that it is out there, already created, independent from the consciousness and the mind.
For the consciousness the only thing that trully exist is the experience and consciousness itself - the space of the mind manifestation (which is spaceless by itself). That means things becomes to existance while they are present in the consciousness. While imagining infinity we can create some picture of a certain set but this picture is limited by its intelectual/visual boundries. We can only imagine the absolute infinity by constant creation within our consciousness. That brings conclusion about absolute infinity - it dose not exist but is an effect of constant creation.
That's why it is more like potential of the consciousness itself than already mind made object. Perhaps thank to this universe is constantly developing, moving "forward" towards greater and greater complexity and existance will never be "boring" (the same) couse we can always and we do expirance something new, that have never manifested itself before, in the consciousness presence, the moment of existence.
We can say that absolute infinity is beyond anything that already exist but it still dosen't exist either. Fractal mind will go on and on, with the consciousness presence, constantly observing it. On the other hand we can stay as empty as we trully are, without any manifestation.
Final conclusion is that the only existance was and ever will be in present moment but the moment of the existing universe includes all single subjective consciousnesses in all already created spaces, times and dimensions, that are brought into one single expirance in "front" of "God" presence, which penetrates them all. (This quality of the consciousness also makes DMT, other entities comunication, telepathy, dimensions and time travel, expirance possible. With DMT as a key to cross the boundaries of the mind.)

^absolutely! more good points..
..i meant 'beyond' in the 'mathematical' sense (i.e the set of everything is not contained within the set, leading to a yet another set, and so on...)

there is no beyond awareness...

(some quotes from INFINITY AND THE MIND: THE SCIENCE AND PHILOSOPHY OF THE INFINITE by Rudy Rucker 1981)

"Set theory is, indeed, the science of the Mindscape. A set is the form of a possible thought. Set theory enables us to put various facts about the Mindscape into one framework in the same way that the atomic theory of matter provides a framework in which the diverse physical and chemical qualities of matter can be simultaneously accommodated.
...
A set is the form of a possible thought. So the question of whether or not there are any infinite entities in the Mindscape is really equivalent to the question of whether or not there are any infinite sets."


"THE ABSOLUTE INFINITE
There is a certain type of non-physical entity that was not discussed in the last section. God, the Cosmos, the Mindscape, and the class V of all sets -- all of these are versions of what philosophers call the Absolute. The word "Absolute" is used here in the sense of "non-relative, non-subjective." An Absolute exists by itself, and in the highest possible degree of completeness.
...
Suppose that I want to add thought after thought to my mind until my mind fills the whole Mindscape. Whenever I make an attempt at this, I am collecting together a group of thoughts into a single thought T. Now, when I become conscious of my state of mind T, I realize that this is a new thought that I had not yet accounted for . . . so I improve my image of the Mindscape by passing to the thought that includes all the elements of T plus T itself, viewed objectively.
...
This is a dialectic process in the sense that the thetic component is one's instantaneous unconscious image of the Absolute, the antithetic component is the conscious formalization of this image, and the synthetic component is the formation of a new unconscious image of the Absolute that incorporates one's earlier images and the awareness that they are inadequate.

...
In terms of rational thoughts, the Absolute is unthinkable. There is no non-circular way to reach it from below. Any real knowledge of the Absolute must be mystical, if indeed such a thing as mystical knowledge is possible."


"The Reflection Principle as formulated in set theory goes as follows: every conceivable property that is enjoyed by V is also enjoyed by some set. (Recall here that V is Cantor's Absolute, the class of all sets.) Philosophically it would run: every conceivable property of the Absolute is shared by some lesser entity; or, every conceivable property of the Mindscape is also a property of some possible thought.

The motivation behind the Reflection Principle is that the Absolute should be totally inconceivable. Now, if there is some conceivable property P such that the Absolute is the only thing having property P, then I can conceive of the Absolute as "the only thing with property P." The Reflection Principle prevents this from happening by asserting that whenever I conceive of some very powerful property P, then the first thing I come up with that satisfies P will not be the Absolute, but will instead be some smallish rational thought that just happens to reflect the facet of the Absolute that is expressed by saying it has property P.

Let me give an example of a Reflection Principle argument. For every thought S in the Mindscape, the thought "S is a possible thought" is also a thought in the Mindscape. By Reflection there must, therefore, be some thought W such that For every thought S in W, the thought " S is a possible thought" is also in W. This W reflects, or shares, the italicized property of the Mindscape. But note now that this W must be infinite. So an infinite thought exists.
...
The point I wish to make is that if one accepts the existence of any of the various infinite Absolutes, then one is fairly well committed to accepting the existence of infinite thoughts and sets. For to deny the Reflection Principle is practically to assert that the Absolute can be finitely described, which is most unreasonable."

α(∞)Ω