A few days ago a solution was finally submitted for the Mirroshambo fumpetition.

At this point - with Fumpetition.org just having started to warm up and with minimal promotion having been performed so far - the interest in that (first) fumpetition was quite low; there was some interest among people who learnt about the challenge through real-life communication but the word didn’t spread. As a result, there were zero ideas posted regarding the theoretically possible (albeit practically infeasible or rather difficult/costly) approaches. So much opportunity for easy fun has been missed! I won’t let it vanish. Here you go:

Take advantage of the time delay

It takes time for the light reflected from your hand to travel to the mirror and bounce back from it into your eyes. If you can synchronize the thrown shape of your hand with the reflected shape from the previous cycle the desired effect is achieved.

Note that in order for the final image to qualify as a reflection any artificial delay line must be built with purely optical components (that is, any conversion of the optical image to electronic, chemical or any other form and backwards is not acceptable).

The following three ideas fall into this category.

Mirromoon

Convert (mirraform) the Moon into an ideal concave spherical mirror with curvature radius slightly below the radius of the lunar orbit around the earth. Get to LEO during new moon and arrive at the exact trajectory of the center of curvature of the mirror. Float in space at an arm’s length from that point (so that you could grab it if it was real), facing the Moon. You will see right in front of you your upside-down inverted reflection of exact your size¹. Try to shake hands with your reflected self - there is no glass between you two, only 2.5 seconds of time delay! Then play roshambo in paper-scissors-rock-paper-scissors-and-so-on order (and at the right pace!) and observe your reflection lose all games.

The main problem with this solution is that making shapes with your hand in the spacesuit glove requires significant strength; scissors will be particularly challenging. Another difficulty is the need to sustain the ideal shape of the mirror in the presence of self gravitation, tidal forces, temperature gradients, light pressure, solar wind, bombardment by meteorites and malfunctioning lunar landers, etc.

Slow light

Use light slowing methods. But be prepared to face issues with the colour, shape and intensity of your reflection (provided that you at all manage to produce a discernible reflection, ha-ha!).

Play fast enough

Instead of attempting to increase the time delay of the reflection generation system through modification of the latter, it can be more productive to rather adapt your performance. After all – time is money. If you engage in this fumpetition for the monetary prize only, then the faster you play the higher your effective hourly rate will be. The typical distance from the mirror being on the order of one meter, you will have to move your hand at a frequency of just around 1 GHz (if that’s too much, please stand farther away from the mirror). For a set of 3 games – you don’t have to play the other 2 if you win the first 3 – and the announced starting prize value of ֏10K, you will gain the right to brag of the hourly rate of ~3 petadram/hour; news stories like “Elon Musk Just Got $36 Billion Richer in a Single Day” are dwarfed by such staggering rate of wealth growth offered to you by Fumpetition.org.

Time travel

Invent a time machine, travel back in time and play roshambo alongside your past self playing roshambo in front of the mirror. With sufficiently reliable memory you will defeat not only the reflection of your past self but your past self too. Alternatively, when training for this match of all times, if you notice your future self appearing by your side, you can try to defeat his/her² reflection (but note that you are at a disadvantage here, unless you can predict your future self’s tactic by planning your actions in advance and executing the plan strictly).

One arguable point with this approach is whether the reflection of your temporally other self can be considered as your own reflection. I’ll leave the answer to that objection to lawyers and philosophers, since I’d rather spend my time on building a time machine regardless of the conclusion they arrive at.

Distorting the reflection

Use a curved mirror of sophisticated shape together with carefully crafted illumination of the scene in space and time.

You and the spectators see your hand from one side whereas the opposite side of your reflection’s hand is visible. Hence, by throwing your hand against the right segment of the curved mirror and into the right sector of the spotlight you can achieve the intended distortion of the apparent shape of the reflected hand (even if only when seen from a narrow sector of angles). A more advanced variant of this approach is to utilize technics similar to adaptive optics - the mirror’s curvature as well as lighting can be controlled by a computer “watching” the game through a video camera and favouring the real player over their reflection.

Wrapping up

Quite naturally, the winning solution belongs to none of the above categories. Consistent with my expectations, it happens to be a second-hand approach, taking advantage of the fact that human beings - the only extant creatures known to play roshambo - are two-handed by design. However, technically the submitted solution fell largely short of the perfect one that I hoped to see. When posting the challenge, I overlooked the possibility of such a simple implementation and formulated the requirements looser than they should be. I now feel somewhat like Elliot Richards³ after his first wish went awry⁴. Which thought smoothly takes us to the next fumpetition.

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Footnotes

¹ In this configuration, in order to fit your entire reflection the mirror must be a few dozen times larger (linearly) than the current lunar disk. A cheaper solution, requiring a ~6x smaller mirror is to put its curvature center at the L1 Lagrange point of the Earth-Moon system. The downside of this workaround is the proportionally reduced value of the time delay, which can be somewhat countered by using multiple reflections. The simplest setup only needs an extra flat mirror under your feet across the L1/curvature-center point, both you and the flat mirror facing the mirromoon (a picture is worth a thousand words).

² After the Wachowskis precedent, for me this he/she uncertainty sounds a little ambiguous in the context of time travel. I wrote “his/her” only because of the absence of information about the gender identity of the reader, and not because I meant to imply that the person considering time travel might undergo sex reassignment therapy.

³ Brendan Fraser’s character from the Hollywood movie Bedazzled.

⁴ That sentence sort of implicitly assigns Susanna (the winner) as the Devil in the Mirroshambo story. I sincerely believe that she is not and will work with her towards improving her solution. In any case I will publish later the setup that I had in mind. Meanwhile, anyone is welcome to provide their own versions just for fun.