A finite infinite

[Vajradhara]

Hi Vajradhara -

Yes - definition 3 is the closest.

No, I don't think a ray is infinite - but then it depends on the context. A ray has a source, and it is not normally considered omnidirectional (although, of course, the sun emits rays in all directions - but then we tend to the plural). These would seem to imply limitation.

If something is perceived as infinite it must necessarily comprise all modes of possibility, whether that possibility is realised or not - ie whether it remains a potentiality - is a secondary consideration.

Abstract concept - a concept that is theoretical rather than demonstrable?

Thomas

Namaste Thomas,

i'm speaking of a mathmatical ray. it begins at one point but extends infinitely, in a single direction. it's true that it's not emmanating omnidirectionly.

ah... something perceived as infinite. our perceptions could be wrong in this instance... however, let's stipulate that they aren't for the sake of conversation. i'm still not clear why infinite must comprise all modes of possibility... isn't that simply Sum Over Histories?

that's a good working definition of abstract concept though i'm not sure what it's "nature" is. perhaps the nature of an abstract concept is it's unexpressibility?

 

[Thomas]

i'm still not clear why infinite must comprise all modes of possibility... isn't that simply Sum Over Histories?

Pax, Vajradhara

I have never come across 'Sum Over Histories'?

If the Infinite does not comprise all modes of possibility, then it is not infinite, as there is a mode of possibility that exists 'extra' to it - which cannot be (either it is not extra, or the infinite is not infinite).

Thomas

 

[mikie8]

time is definatly not constant as was proved but a pratical experiment some time ago .the question of infinate depends on what context as the word infinate has a finate meaning so maybe it would be easier to answer your question if a context or datum was put in place .

Quote: Originally Posted by I, Brian
would it not also state "We are all a part of God"?

i dont think it would state this as god does not exist in everyones universe only some

i see abstract concepts as theoretical exersises but not always with a practical purpose .

the infinate realises the finate but goes beyond where as the finate can only realise the infinate as it is in its presnt state or any state but not in its conclusion .

 

[Vajradhara]

Pax, Vajradhara

I have never come across 'Sum Over Histories'?

If the Infinite does not comprise all modes of possibility, then it is not infinite, as there is a mode of possibility that exists 'extra' to it - which cannot be (either it is not extra, or the infinite is not infinite).

Thomas

Namaste Thomas,

here's a brief description of Sum over Hisotries:

In non-gravitational physics the approach to quantum theory that has proved most successful involves mathematical objects known as path integrals. Path integrals were introduced by the Nobel prizewinner Richard Feynman, of CalTech. In the path integral approach, the probability that a system in an initial state A will evolve to a final state B is given by adding up a contribution from every possible history of the system that starts in A and ends in B. For this reason a path integral is often referred to as a `sum over histories'. For large systems, contributions from similar histories cancel each other in the sum and only one history is important. This history is the history that classical physics would predict. For mathematical reasons, path integrals are formulated in a background with four spatial dimensions rather than three spatial dimensions and one time dimension. There is a procedure known as `analytic continuation' which can be used to convert results expressed in terms of four spatial dimensions into results expressed in terms of three spatial dimensions and one time dimension. This effectively converts one of the spatial dimensions into the time dimension. This spatial dimension is sometimes referred to as `imaginary' time because it involves the use of so-called imaginary numbers, which are well defined mathematical objects used every day by electrical engineers. The success of path integrals in describing non-gravitational physics naturally led to attempts to describe gravity using path integrals. Gravity is rather different from the other physical forces, whose classical description involves fields (e.g. electric or magnetic fields) propagating in spacetime. The classical description of gravity is given by general relativity, which says that the gravitational force is related to the curvature of spacetime itself i.e. to its geometry. Unlike for non-gravitational physics, spacetime is not just the arena in which physical processes take place but it is a dynamical field. Therefore a sum over histories of the gravitational field in quantum gravity is really a sum over possible geometries for spacetime. The gravitational field at a fixed time can be described by the geometry of the three spatial dimensions at that time. The history of the gravitational field is described by the four dimensional spacetime that these three spatial dimensions sweep out in time. Therefore the path integral is a sum over all four dimensional spacetime geometries that interpolate between the initial and final three dimensional geometries. In other words it is a sum over all four dimensional spacetimes with two three dimensional boundaries which match the initial and final conditions. Once again, mathematical subtleties require that the path integral be formulated in four spatial dimensions rather than three spatial dimensions and one time dimension.

you can visit this link for more information:

http://www.damtp.cam.ac.uk/user/gr/public/qg_qc.html

 

[Thomas]

here's a brief description of Sum over Hisotries

Pax, Vajradhara

Thanks for the post. I've read it a couple of times, but obviously I'll take some time to let it all sink in.

isn't that simply Sum Over Histories?

My inital response would be no. Certainly as the proposition I've expressed is much older than Sum over Histories - or physics as such - and the equation adds nothing to the concept, rather it appears to me to be an attempt to explain it.

Interesting though, and if time allows I shall pursue it further.

Thomas

 

[Susma Rio Sep]

biography of the infinite

May I just start from the biography of the infinite?

Whatever the infinite is or might be, whether outside or inside our mind, our first acquaintance with the infinite is in our mind.

Now, how did we arrive at this thought of the infinite which is in our mind.

By the knowledge of the finite founded upon our functioning senses. Whatever we sense has a beginning and an ending, for example, earthly biological life.

Then in our mind we deny a beginning and an ending to anything we have derived in our mind from our sense acquaintance of things outside our internal awareness or external senses.

Imagine yourself never having sensed anything, not even your internal physiological and cerebral operations, would you have any concept of the infinite?

The OP asks:

The question then is what prevents the Infinite realising the finite.

My answer is that the infinite is all in the mind insofar as human perception is concerned. Is there any other kind of perception that is worth its salt? It is not the infinite realizing the finite, but rather the finite responsible for the conception of the infinite.

May we ask the physicists and cosmologists here to tell us whether outside the mind the infinite exists, as in an infinite universe.

Now the question of an infinite series of odd numbers or even numbers or just a count of numbers upward and downward, right of zero and left of zero, that would seem to be also in the mind of man. But without a mind, would they exist?

We can say that such series are independent of the mind, inasmuch as if we do not’think of them they don’t stop being true or factual on a cosmic perspective, independent of human thought. But they don’t exist as like a ladder that we can climb endlessly outside our mind and before any mind surfaces to be mindful of it.

My own conclusion: the infinite does not exist before the emergence of the mind.

Susma Rio Sep