# What Can We Know?

Put bluntly, metaphysics asks simple albeit deep questions:

- Why do I exist?
- Why do I die?
- Why does the world exist?
- Where did everything come from?
- What is the nature of reality?
- What is the meaning of existence?
- Is there a creator or omnipotent being?

Although these questions may appear idle and futile, they seem to represent an innate longing for knowledge of the human mind. Indeed, children can and often do pose such questions, only to be faced with resignation or impatience of adults.

To make things simpler and tractable, one can focus on the question "What can we know?".

When you wake up in the morning, you instantly become aware of your self, i.e., you experience an immaterial inner reality you can feel and probe with your thoughts. Upon opening your eyes, a structured material outer reality appears. These two unsurmountable facts are enough to sketch a small metaphysical diagram:

### Outside

Focussing on the outer reality or physical universe, there exists an underlying structure forming and selforganizing process starting with an initial singularity or Big Bang (extremely low entropy state, i.e., high order, giving rise to the arrow or direction of time). Due to the exact values of physical constants in our universe, this organizing process yields structures eventually giving birth to stars, which, at the end of their lifecycle, explode (supernovae) allowing for nuclear reactions to fuse heavy elements.

One of these heavy elements brings with it novel bonding possibilities, resulting in a new pattern: organic matter. Within a couple of billion years, the structure forming process gave rise to a plethora of living organisms. Although each organism would die after a short lifespan, the process of life as a whole continued to live in a sustainable equilibrium state and survived a couple of extinction events (some of which eradicated nearly 90% of all species).

The second law of thermodynamics states, that the entropy of the universe is increasing, i.e., the universe is becoming an ever more unordered place. It would seem that the process of life creating stable and ordered structures violates this law. In fact, complex structures spontaneously appear where there is a steady flow of energy from a high temperature input source (the sun) to a low temperature external sink (the earth). So pumping a system with energy leads it to a state far from the thermodynamic equilibrium which is characterized by the emergence of ordered structures.

Viewed from an information processing perspective, the organizing process suddenly experienced a great leap forward. The brains of some organisms had reached a critical mass, allowing for another emergent behavior: consciousness.

### Inside

The majority of people in industrialized nations take a rational and logicall outlook on life. Although one might think this is an inevitable mode of awareness, it actually is a cultural imprinting as there exist other civilization putting far less emphasis on rationality.

Perhaps the divide between Western and Eastern thinking illustrates this best. Whereas the former is locked in continuous interaction with the outer world, the latter focuses on the experience of an inner reality. A history of meditation techniques underlines this emphasis on the nonverbal experience of ones self. Thought is either totally avoided, or the mind is focused on repetitive activities, in effect deactivating it.

Recall from the conceptual overview of the understanding of the fundamental and complex workings of nature that there are two surprising facts to be found. On the one hand, the physical laws dictating the fundamental behavior of the universe can be mirrored by formal thought systems devised by the mind. And on the other hand, real complex behavior can be emulated by computer simulations following simple laws (the computers themselves are an example of technological advances made possible by the successfull modelling of nature by formal thought systems).

### Outlook

This conceptual map allows one to categorize a lot of stuff in a concise manner. Also, the interplay between the outer and inner realities becomes visible. However, the above mentioned questions remain unanswered. Indeed, more puzzles appear. So as usual, every advance in understanding just makes the question mark bigger...

# Finite vs. Infinite

There is an interesting observation or conjecture to be made from the Mataphysics Map illustrated above, 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?