Feb 10, 2018

On the affinities between retirement tools and optical systems

Somewhere on this blog I have a post about optical systems.  I was once a telescope builder (four of them if I am counting right, here was one of them).  One of the things that most people misunderstand when they look into the eyepiece of a telescope is that what they are looking at is not actually a star even though they think it is. That sounds like it is at odds with common sense but here is how it works.  Because of the geometry and distance involved, a star is too far away to actually be able "see" the disc of the star like one can see the disc of a planet (I suppose it is possible if the telescope is big (wide) enough or the star close enough and I should double check the current science to see if someone somewhere has done it).  For small telescopes what one sees is actually the aftereffect of a wave-front of light (remembering here that light has "dual nature" as both particle and wave) interacting with the aperture of the instrument.  The aperture (the opening at the front of the telescope) is like an opening in a sea wall.  The wave front is like, well,  like a wave front.  The wave hits the opening and bends around the corners and creates wavelets (diffracts). At some point near the beach if one were to "look," the combinations of the various waves creates high spots and low spots (interference).  This is also what happens to light (or, rather, it is a pretty flat-ish wave front at that point) from a star.  It hits the (usually round) aperture* of the telescope and diffracts and when the image is examined at the eyepiece the combination of diffraction and interference means that the waves are combined to a really high point at the center (i.e., a bright point, you can see it) then there is a dark ring around the center where the interference cancels things out and another fainter light ring around that and another dark ring and another faint light ring and so on.  It gets geometrically fainter away from the center so what one sees is mostly the center diffraction/interference peak (called an "Airy disk" for the guy that wrote the first theoretical treatment of the phenomenon) or a combination of the first couple rings, not a star.  What one "sees" is entirely an artifact of the interaction between an aperture and a wave front of light. In fact, counter-intuitively, the smaller the aperture, the larger the "disk." One is not really "seeing" a star at all. It's an an illusion of sorts.

I propose that something vaguely similar happens when using retirement tools to examine retirement risk.  In this metaphor the instrument or aperture might be software/math while the wave front is data and assumptions (or maybe the assumptions are part of the instrument? I don't know. I guess I haven't thought about it carefully enough).  The image that is examined would be the output of the system: fail rates, "optimal" asset allocation recommendations,  glide paths, and so forth.  The point here is that the results created by the interaction of instrument (software) and wave front (data) creates an illusion that looks like retirement or the future but is nothing but an artifact of the interaction between the two components.  It may be useful but it is not "real" especially if one is very far away from the object of interest. On the other hand the closer one gets to the endgame the easier it is to see and judge the risk  Maybe some of this metaphor breaks down somewhere in there because the wave front of light is real and live where the data used in planning is usually past and dead but I'll have to work that out.


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* Think in terms of Newtonian telescopes here where the light is un-intermediated at the aperature and no refraction through glass is involved at or near the aperture to complicate the point of the post. In other words, light is just going through a round hole.



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