Paradoxes of complexity

This article is about several apparent paradoxes of nature. For the 3D printing feature, see Complexity paradox.

A paradox of complexity is a name for any claim that some aspect of the observable universe is either vastly more complex, or vastly less complex than might reasonably be expected. This may be an illusion, or an actual mystery of reality.

Background

Albert Einstein wrote that the "most incomprehensible thing about the world is that it is at all comprehensible". Einstein considered it remarkable that he and others were able to deduce the principles of general relativity from only limited observations, yet these principles were later verified to very high accuracy.

The universe appears to be governed by precise laws that are approximated by the Standard Model of physics. Everything that is known to physically exist can be described with relatively few dimensionless physical constants. Approximations of these numbers are used to predict the future positions of particles with very high accuracy. However, no one knows if these numbers have a finite or an infinite number of digits, or why this should be so. For example, the fine-structure constant includes the number Pi and the strength of the elementary charge, which has been measured to be about 1.602,176 × 10-19 coulombs. It is not known how many digits precisely describe this charge, or if the string of digits ever ends. Nor is it known whether physical processes use the actual number Pi, or just an approximation. It has been suggested that quantum processes may be actually infinite, though this is debated. This is an unsolved problem of the philosophy of physics.

Claims of paradoxical simplicity

The human mind appears to be of finite size. The average brain is said to contain under one quintillion bits of meaningful information.

This may be a paradox if there is no theoretical limit controlling the largest possible mind size, and if all mind sizes are equally likely to exist. In that case, a mind selected at random from the list of all possible minds could be expected to be infinitely large.

One possible solution may be that reality generates far more copies of smaller minds (with shared awareness) than it generates larger minds.

Claims of paradoxical complexity

Alternatively, nature may be considered to be "unreasonably" complex. No one knows why this should be.

In classical physics, which is considered a simplification of reality, the Einstein field equations governing even a single particle are still extremely difficult or impossible to solve exactly (though they can be closely approximated). The same is true for all other fundamental interactions. The most powerful supercomputer can not predict the exact trajectory of any particle, no matter how precise the initial data. Even with approximations, the known forces and variables controlling the internal and external interactions between any two particles are too complex to calculate. An early and simpler example of this is the three body problem.

This issue becomes even more difficult with quantum mechanics, in which the internal interactions of any particle are sometimes said to be infinitely complex. These infinities can be reduced through renormalization, but they can't be eliminated entirely.

The universe, and even the human brain, are said to contain vastly more particles than the minimum needed to generate conscious structures. The game physics used in computer games is immensely simpler than that found in nature, but already looks quite realistic. It has been estimated that a picotechnology computer the size of a human brain would have the computing capacity of an entire country. However, this may be difficult to achieve because of Bonini's paradox and other reasons.

Other issues

• If the future is infinite, why do we live relatively close to the beginning of the universe? Futurists have suggested that social and technological evolution have barely begun, and that almost all history will occur after an upcoming technological Singularity. However, the fact that we exist before this Singularity may imply that these events are unlikely to happen. The fact that we live in the relatively "simple" present might then be an anthropic shadow.

• It would appear that most possible minds should be inconsistent. There are many more ways to have irrational or absurd thoughts and perceptions than rational ones. However, human reality appears to be perfectly consistent. This may imply that natural processes like the laws of physics create vastly more mind copies than random processes like those that may generate Boltzmann Brains.

• Some philosophers suggest that the most "natural" state of being is non-existence. Human minds do exist, but compared to most possible minds (which would be infinitely large) they may have an almost minimal existence. Any finite mind might then be close to the limit of non-existence.