Time’s Arrow Paradox

Spiralling Clock

The Moving Finger writes; and, having writ,
Moves on: nor all thy Piety nor Wit
Shall lure it back to cancel half a Line,
Nor all thy Tears wash out a Word of it.
(Omar Khayyám)

In 1928, the British astronomer Arthur Eddington published his book The Nature of the Physical World explaining the concept of the arrow of time. This paradox involves the “one-way direction” or “asymmetry” of an arrow converted into an expression of time. Likewise, evolution follows specific patterns predetermined by the inorganic nature of the earth and its thermodynamic processes.

Following a lengthy argument upon the Second Principle of Thermodynamics, which says that in an isolated system, entropy tends to increase with time, Eddington stated that time’s arrow is a property of entropy:

Let us draw an arrow arbitrarily. If as we follow the arrow we find more and more of the random element in the state of the world, then the arrow is pointing towards the future; if the random element decreases the arrow points towards the past. That is the only distinction known to physics. This follows at once if our fundamental contention is admitted that the introduction of randomness is the only thing which cannot be undone. I shall use the phrase ‘time’s arrow’ to express this one-way property of time which has no analogue in space.

Centuries ago, when Robin Hood shot his arrows at the troops of the Sheriff of Nottingham and Prince John Lackland the path of his darts would have led them toward the same target as if he opt for a hand-to-hand fight. But in adverse conditions, the archer of Sherwood would not put much effort to take the same route back. Arrows, couldn’t back off because they have a single vector without any possibility of return. Like breaking a plate against the floor or a liquid when mixed with another, there is no involution at all.

As Eddington proved with his paradox, the arrow is just a vector of time. Its trajectory is entropic. Its movement aims toward disorder. Its effect multiplies a uniform distribution of energy throughout space. The arrow is a path and not a trace. Knowing its direction is penetrating the fourth dimension, pointing to the future, collimating to the immediate, the transient, and the final target.

That is just like our creativity momentum at work. The concept of the arrow refers to the direction in which time takes place, flowing without interruption from the past to the future. One of the time most important features is its irreversibility, which prevents to progress unlike the path followed by the arrow. Eddington’s challenge lead us to apply his statements on our entrepreneurial mission. Innovation and serendipity are, in the same direction of time, our entropic arrows. A risky drive toward the unknown with no return.

Fernando Gallardo |

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