# Phases of the Moon, from Victor Niederhoffer

April 28, 2008 |

In considering the phases of the moon I found the following two passages partially illuminating:

"Considering the moon as a circular disk, the ratio of the area illuminated by direct sunlight to its total area is the fraction of the moon's surface illuminated; multipled by 100 it is the percentage illuminated. At New Moon the percent illuminated is 0; at First and Last Quarters it is 50%; and at Full Moon it is 100%." Source

"When a sphere is illuminated on one hemisphere and viewed from a different angle, the portion of the illuminated area that is visible will have a two dimensional shape defined by the intersection of an ellipse and circle where the major axis of the ellipse coincides with a diameter of the circle; if the half ellipse is convex with respect to the half circle then the shape will be gibbous, bulging outwards, whereas if the half ellipse is concave with respect to the half circle then the shape will be a crescent." Source

The explanations made me start thinking of the angle of incidence and the angle of reflection, and the % of the time that a market is above zero and below zero, and other concepts engendered by the phases of the moon.

I wonder what other ideas about markets are generated by considerations such as the above. Also, a layman's proof of the ellipse/circle statement might be helpful to speculation.

## Jim Sogi writes:

Speaking of moon effects, there is one of Vic and Laurel's classic penumbras forming off the 1400 round in S&P off this recent high.

Also, the other image I got is the kids playing jump rope with a kid at each end spinning the line around. There is a definite drift to the spin in one direction, but one can play the spin until tapping out or whatever they call it. Its definitely tradeable though may or may not show on radar of a fixed wavelength. The game is different at the bottoms than at the tops for sure. Do kids play this game anymore?

Reminds me of earnings season. First Alcoa, then a handful of others. The first sliver of the waxing moon. As the days pass, the number of companies reporting earnings steadily increases until a full globe of information illuminates the markets. Hunting/gathering levels peak just as the flow of earnings begins to dissipate. Next comes the struggle for survival on diminishing resources as the moon wanes into oblivion. Only the strong will survive the dark days until the cycle begins anew.

## Phil McDonnell enlightens:

The side of the Moon facing the Sun always looks like a circle from the perspective of an observer on the Sun. The simplest way to understand how the shape of the visible lighted portion of the Moon changes is to view the circle of light as a rotating circle. It is well known in mathematics that a circle rotating on a North South axis will appear as an ellipse in general. It will only be a true circle when viewed full on.

From the perspective of a viewer on Earth the circle of light on the Moon is rotating once every 29.5 days. So from the Earth perspective the line between day and night on the Moon will generally be visible as an ellipse because it represents the edge of our rotating circle of light. However the lighted edge of the Moon is still circular at all times so the edge of the lighted portion will always be described by a circle. Thus the combination of one edge bounded by a true circle and the day-night line of demarcation by an ellipse will always be true.

To understand the convex concave claim we need only consider the ellipse formed by our North South rotating circle. When the Moon is exactly half full corresponds to when the circle is rotated by 90 degrees and faces us edge on. At this time the ellipse appears to collapse to a straight line because the circle is edge on. This is what happens at first quarter and last quarter Moons. During the Gibbous phase the ellipse will appear convex from Earth because what we are seeing is the convex portion of the lighted ellipse. Similarly during the crescent phase (either waxing or waining) the visible ellipse will be the concave portion of the lighted circle.

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