Everyday entropy: mapping information

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“The Hopi, an Indian tribe, have a language as sophisticated as ours, but no tenses for past, present and future. The division does not exist. What does this say about time?

Matter, that thing the most solid and the well-known, which you are holding in your hands and which makes up your body, is now known to be mostly empty space. Empty space and points of light. What does this say about the reality of the world?”
Jeanette Winterson, Sexing the Cherry

And yet even this is an overstatement.  The particles of matter – quarks, electrons gluons and photons – take up no space at all, so a map of matter is nothing but empty space.  But they all create waves in the fields of vacuum space that establish their boundaries as if they filled the space entirely.

The confusion between quantum and classical physics arrises out of the failure to rigorously define information, not a problem of measurement. Momentum, charge and spin are all bits of real information that a particle can communicate directly to the instrument, so they appear to be true and fundamental. Because quantum information slotted straight into the information of description, it seduced physics into giving it a privileged position in the map the universe in the same way that it seduced Plato into the cave.  This, despite Einstein’s proof that no privileged position exists in real space and Bohr’s admonition to understand the difference between the observed information and its subsequent explanation.  Position is not information.  It takes an un-quantised composite of information and material to create a map with which to make meaning of the instrument’s measurements of position.

But it turns out that this problem of mapping extends to all scales and frames.  From Zeno’s paradox to general relativity to zero point energy, dark matter and dark energy, all of the conundrums in physics have been mapping problems.   You cannot make a map without an inertial frame of reference in thermodynamic equilibrium.  Because the information must be laid out on a stable substrate to preserve its meaning, a map is a composite of information and entropy that can only exist as a classical tool.  It has no quantum counterpart.  Not only that, but the information never maps the entropy of the mapped configuration, so that all maps are off, skewed and incomplete.  A holographic universe is no better than a cork-board full of tacks.

If information is taken as real but formally distinct from entropy, the paradoxes of quantum mechanics and classical relativity disappear. The difference between a wave and a particle is not the important distinction.  The fundamental distinction is between position and information.  There is no record of position in space, and as quantum entanglement shows, fundamental information is indifferent to position anyway.

In the end, everyday entropy is an exegesis on the importance of entropy in a world dominated by information and energy.  Position and configuration may be quantitatively uncertain, but the are not insignificant.  Words, maps and clocks are all composites of information and entropy.

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