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Psychological and Physical Time and Space

The other night I was having dinner with an erstwhile collaborator (academic, not WWII) and we were talking about the relation between psychological time and calendar time in finance.

I once long ago wrote a paper on this, in which I regarded psychological or trading time as the time ticked off by a clock that counts trading events rather than seconds. The trading frequency, the number of trades per second, can vary from moment to moment, so that there might be more psychological events in one minute and less in another.

I considered the possibility that neoclassical finance and its approach to risk might in principle be correct, but that it might be correct only in psychological time, not in calendar time. I was trying to do a kind of behavioral finance?.

From the point of view, calendar time is global, the same for everyone, and psychological time, the time between psychologically significant events, is local.

This suddenly reminded me of the literally wonder-full Hockney photo collage Pearblossom Hwy. which seemed to me to do for psychological and physical space what I was thinking about for time.

Then, I realized, it’s analogous but not quite the same. The relation between psychology and physical for space is different to that for time.

For time, I was arguing, physical time is global and psychological time is local.

But in Pearblossom Hwy, which constructs an entire space out of detail fovea-image-style bits of everything visible, in sizes that are significant psychologically rather than physically, the relation is reversed. Each local photograph of something small in space is in fact physical, not psychological. The fovea of the eye cannot, like a camera, witness the entire scene sharply; the mind constructs the entire scene from little bits of sharp darting images. For space, at least as perceived by vision, ?physical space is local and psychological space is global.

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? This led to a version of the Capital Asset Pricing Model in which excess return was proportional not to volatility, but to ?(volatility x sqrt[trading frequency]), which I called temperature, and had the dimensions of 1/time. The Sharpe ratio, the excess return divided by the temperature, in this scheme became dimensionless.?

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