jbg

There is an interesting observation or conjecture to be made from the Mataphysics Map in the post what can we know?, concerning the nature of infinity.

The Finite

Many observations reveal a finite nature of reality:

• Energy comes in finite parcels (quatum mechanics)
• The knowledge one can have about quanta is a fixed value (uncertainty)
• Energy is conserved in the universe
• The speed of light has the same constant value for all observers (special relativity)
• The age of the universe is finite
• Information is finite and hence can be coded into a binary language

Newer and more radical theories propose:

• Space comes in finite parcels
• Time comes in finite parcels
• The universe is spatially finite
• The maximum entropy in any given region of space is proportional to the regions surface area and not its volume (this leads to the holographic principle stating that our three dimensional universe is a projection of physical processes taking place on a two dimensional surface surrounding it)

So finiteness appears to be an intrinsic feature of the Outer Reality box of the diagram.

There is in fact a movement in physics ascribing to the finiteness of reality, called Digital Philosophy. Indeed, this finiteness postulate is a prerequisite for an even bolder statement, namely, that the universe is one gigantic computer (a Turing complete cellular automata), where reality (thought and existence) is equivalent to computation. As mentioned above, the selforganizing structure forming evolution of the universe can be seen to produce ever more complex modes of information processing (e.g., storing data in DNA, thoughts, computations, simulations and perhaps, in the near future, quantum computations).

There is also an approach to quantum mechanics focussing on information stating that an elementary quantum system carries (is?) one bit of information. This can be seen to lead to the notions of quantisation, uncertainty and entanglement.

The Infinite

It should be noted that zero is infinity in disguise. If one lets the denominator of a fraction go to infinity, the result is zero. Historically, zero was discovered in the 3rd century BC in India and was introduced to the Western world by Arabian scholars in the 10th century AC. As ordinary as zero appears to us today, the great Greek mathematicians didn’t come up with such a concept.

Indeed, infinity is something intimately related to formal thought systems (mathematics). Irrational numbers have an infinite number of digits. There are two measures for infinity: countability and uncountablility. The former refers to infinite series as 1, 2, 3, … Whereas for the latter measure, starting from 1.0 one can’t even reach 1.1 because there are an infinite amount of numbers in the interval between 1.0 and 1.1. In geometry, points and lines are idealizations of dimension zero and one, respectively.

So it appears as though infinity resides only in the Inner Reality box of the diagram.

The Interface

If it should be true that we live in a finite reality with infinity only residing within the mind as a concept, then there should be some problems if one tries to model this finite reality with an infinity-harboring formalism.

Perhaps this is indeed so. In chaos theory, the sensitivity to initial conditions (butterfly effect) can be viewed as the problem of measuring numbers: the measurement can only have a finite degree of accuracy, whereas the numbers have, in principle, an infinite amount of decimal places.

In quatum gravity (the, as yet, unsuccessful merger of quantum mechanics and gravity) many of the inherent problems of the formalism could by bypassed, when a theory was proposed (string theory) that replaced (zero space) point particles with one dimensionally extended objects. Later incarnations, called M-theory, allowed for multidimensional objects.

In the above mentioned information based view of quantum mechanics, the world appears quantised because the information retrieved by our minds about the world is inevitably quantised.

So the puzzle deepens. Why do we discover the notion of infinity in our minds while all our experiences and observations of nature indicate finiteness?

Taken from http://j-node.homeip.net/knowledgebase/metaphysics/

tags: metaphysics, infinity, finite

This entry was posted on Friday, July 13th, 2007 at 3:51 pm and is filed under This'n'that, meta. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.