Jen Jen Chung

Interesting Times

Probabiliscuit

For a while now, N has been an avid consumer of the Honey Maid Graham biscuits. Initially we bought the packs with the Minions characters, but when the Star Wars biscuits came out, there was no question as to which set of flour-based fictional characters we’d rather be eating (our one weakness in an otherwise steadfast resistance against the nation-wide compulsion to throw money at the megalithic franchise). In any case, both N and I lack self-control when it comes to snacking on things that can be eaten by the handful. In an effort to retain some dignity in the matter, N devised a biscuit-sampling strategy that would:

1. Curb our mindless snacking behaviour, and
2. Stay faithful to our probabilistic roots.

The strategy is simple: you randomly sample and eat one biscuit from the pack at a time, and you stop once you pick out Yoda.

“Stop eating biscuits, you must.” – Yoda

At once you have plunged your dreary junk food-eating habits into the beautiful swirling cup of randomness stirred vigorously by the spoon of mathematical probability. You may not share my passion in this matter, but there is no denying the satisfaction of being able to hold the universe accountable for your personal vices.

It also helps that there is a rather stern-looking Yoda on the front of the pack holding a lightsaber in... not exactly a menacing way, but certainly one that suggests to the viewer that they ought to rethink reaching for another one of those biscuits shown floating around the fluorescing weapon.

The question that remains, of course, is how many biscuits do you actually expect to eat each time? To answer this succinctly and without the hassle of pouring out all the biscuits and counting the number of times each character occurs, allow me to assume that each time I reach into the box, I am drawing from a limitless biscuit universe where there is an equal probability of drawing out any of the characters. If there are $m$ different characters in this biscuit universe, then for any draw $n$, the probability of Yoda appearing and ruining my diet is $\left(\frac{1}{m}\right)$. The $\left(n-1\right)$ biscuits that I would have happily consumed up to that point would all be sampled with a joint probability of $\left(\frac{m-1}{m}\right)^{n-1}$. The expected number of biscuits I get to eat can then be calculated by solving:

$$\sum _{n=1}^{\infty }n{\left(\frac{m-1}{m}\right)}^{n-1}\left(\frac{1}{m}\right)$$

which, with great satisfaction, turns out to equal $m$.

So for the Honey Maid Star Wars Graham biscuits, our expected serving size is in fact 7 biscuits. We’re positively dieting compared to the recommended 17 biscuits per serving! Although methinks the latter number more accurately accounts for the hysteresis apparent in our will to stick to one sampling sequence per serving. Frankly, my fat-kid mentality now has me on the lookout for biscuits with more varieties of characters or shapes in one box so that I can innocently bump up the expected serving size. My nerd mentality has me thinking of ways to justify additional biscuit consumption if the sample size falls below $1\sigma$. Perhaps this was all an exercise in futility. Nevertheless, there is something distinctly human about deriving the truth of something that you’ve always suspected with certainty, and then devising ways to outmanoeuvre the consequences in favour of old habits.

 

J²

23 February, 2016

 

The Final Pong

For centuries, the most noble and glorious traditions of mankind have seen brave men and women face off on the battlefield: jousting, arm wrestling and duelling at high noon. Yet the praise for victors of such battles cannot compare to the majesty and splendour bestowed upon those who may truly call themselves champions; those who crush their opponents with keen eyes, swift hands and sharp tongues; those who conquer in beer pong.

Beer pong is truly the sport that turns men into heroes. No other sport calls for such a unique combination of strength, dexterity and wit. A golden combination that we believed mankind was singular to possess. But grown proud and brazen of our skills we dreamed of an opponent who could compete against us in such an arena. Could we create such a being? Could we contain such awesomeness within a single earthly creation? What mechanism? What robot would this be?

We had so recently witnessed what many proclaimed to be the height of robotic technology; elegantly designed machinery with purposeful intelligence. Yet these creatures with their smooth finishes and precise movements were shown to be clumsy and unwieldy. Time and time again, they were so easily befuddled by what would be deemed the simplest of tasks for a man. It seems appropriate, then, following the stratospheric expectations over the weekend that were so resoundingly disappointed, that a true hero should emerge today to reclaim the lost glory of robotkind.

To fully realise the magnitude of the events we witnessed today, you must understand them as we saw them unfold. While we ourselves are still processing the implications of what we saw with our own eyes, we will attempt to present as faithful a retelling as we can possibly put on paper.

ZZZZ best was not the challenger we were expecting. Slim, some may say, frail, with a thin tangle of wires haphazardly attached along its frame; this unassuming creature whirred almost apologetically before gracefully ejecting a single ping pong ball across the table and, occasionally, into a cup on the other side.

It wasn’t difficult to find competitors who saw this as an easy victory. Many were eager to crush this robotic upstart in the name of humanity. However, it wasn’t long before the aisles were filled with those who had fallen in battle against it.

The tally of victories ticked ever in its favour as one after another each successive challenger conceded defeat. At 7-0 the gravity of the situation could no longer be ignored. This was no ordinary robot, there was something calculated in its demeanour, as if it had been built for the singular purpose of defeating its opponents at beer pong. Crushing human pride was merely collateral damage.

In this hour of need, a new hope emerged to carry the banners of mankind forth into battle against this robotic menace. Where had she come from? Some say she had travelled across the land and seas to take up arms against this new terror, driven by haunting visions prophesizing the rise of the machines. Could she be the one? Could she be our Sarah Connor?

A bloody struggle ensued with both opponents dealing heavy damage to one another. The arena was soon lined with red, with a single cup remaining on either side. Rallying for this final skirmish, Connor struck the deadly blow. But the cheers that erupted from the sidelines were quickly dashed when ZZZZ best parried artfully, forcing a rebuttal. Connor returned to the field with steely determination, but the battle before had taken its toll. She was no longer its opponent. It finished her off as an afterthought. 8-0.

Who was left to challenge this creature? Surely, given the circumstances, only the bravest or perhaps the most foolish would dare. The line between heroes and fools is often blurred, and from within this mist arose Skeeler. Skeeler, the high priest of the Order of the Pong, Slayer of a Thousand Cups, and of course, the reigning beer pong champion. Unfortunately, what was immediately obvious as the two squared off was that ZZZZ best cared little for title or fame or the struggles of men. The cut and thrust of Skeeler’s jibes, which would have fed the trickle of doubt in any other opponent until it became an insurmountable torrent of confusion and dread, were simply reflected by the unrelenting whir of the motors. Unceremoniously, ZZZZ best deposed the former champion and claimed his crown. 9-0.

There was only one possible battle remaining, the masters of the machine versus their mechanical offspring. If ZZZZ best could defeat its own creators then truly the robots had arrived.

The creators went into the battle with no illusions, despite their pride in their robotic protégé, this was their time to show that they were still the masters. They could build a monster, but still hold its powers in check. They both knew the robot. They had seen it rise from a simple sketch to the ball-belching behemoth that stood facing them impassively across the table. Caley had been at the controls of the beast for all of its human conquests. He knew the corrupting power of ZZZZ best more intimately than anyone else. But here and now he had to show that he was still in control of that power, that the automaton was simply that, without its true masters the machine would fail. The Zhanger was confident, his very clothes were channelling the spirits of those legends of launching: Curry and Skeeler. Humanity's best hopes crystallised in these men at this moment. They knew the robot, and they knew themselves.

Immediately, it was obvious that this was no ordinary contest. The early stages of the game were mostly a battle of wits, the crimson of fallen cups steadily flowing from both ends of the table. To an outsider it would not have appeared such an extraordinary game, but to those who had witnessed the prior battles it was immensely clear that every shot, every hit and each near miss, was carefully calculated not just to finish the game but to manipulate the minds of players at both ends of the table. For the first time in history the robot fell behind a human competitor. ZZZZ best quickly levelled, and with one cup remaining at each end, the final throws drew near. After a calculated miss from Caley, the Zhanger confidently stepped up, it was time to finish this, restore humanity to dominance and finally put this robot back in its place. With a deft throw, the Zhanger potted the final cup, no flashy rimshots, no bouncing off sides, just a direct shot that left no doubt of its intentions. The robot was left with two remaining shots, if these missed, the battle, and the war, for now, would be over.

The first rebuttal shot was well wide, ZZZZ best clearly shaken by the confidence and dominant skill of the Zhanger's final shot. After a moment of reflection and a quiet assessment of the situation, ZZZZ best settled, whirred its motors and launched its last shot.

The focus of the crowd slowed time to a syrupy crawl as the ball arced through the air. The die was cast and only divine intervention could change what was to follow. As the ball passed the apogee and began its inevitable descent towards the cup, it dawned slowly on the crowd that the shot was bad. It could not go in. The ball bounced long and wide of the only cup holding back the future of robots. The humans had won. As one, Caley and the Zhanger threw their arms in the air, roared at their success and cast their eyes skyward. Humanity was redeemed, ZZZZ best was fallible.

Robots do not have emotions. They do not suffer from the shame or spite that inspires humans to cruelty. Or so we believed. While the human victors celebrated, the rest of the crowd continued to watch the ball. Unbelievably, incredibly and then impossibly, in a trajectory that seemed to defy the laws of physics, the ball bounced, spun backwards and landed neatly in the cup. The Zhanger, almost tearful with victory, turned to see a field of wide eyes and accusing fingers pointed at the last cup. With the slow dawning of human faculty he attempted to process the impossible situation he was presented with. The masters had won, defeated their own creation, restored humanity to the apex of known intelligence, and yet, there, floating serenely in the cup, was the clear sign of their defeat. It was impossible, a logical dissonance. ZZZZ best impassively recorded the final image, a small white ball floating in a red cup, signaling the now unstoppable rise of the robots.

It wasn’t the victory itself that that made us realise that this was no ordinary event. Had the robot coldly, methodically and robotically defeated its human adversaries it would not have given us pause for thought. But this was something different. ZZZZ best showed that it could not only win, but do so in a way that maximized the suffering of its opponents. It toyed with that uniquely human emotion, hope. It allowed its opponents to be convinced, to have total belief, that not only could they win, but that they had won. It showed the ability to control every aspect of the emotions of each member of the crowd. Throughout the night every human spanned the complete spectrum of dismissing, then respecting, then detesting, then cheering for the tumbled mess of wires and wood that is ZZZZ best. In a single evening it created what can only be described as a personality. And with that understanding and manipulation of those most basic of human emotions, it crushed every competitor it faced.

As we ponder the future we have only one thought: we welcome our new robot overlords, and may they learn the meaning of mercy as fully as they demonstrated their knowledge of cruelty.

 

Dr Jen Jen Chung and Dr Nicholas Lawrance

First-hand witnesses of the battle that surely signals the inevitable outcome of the war to follow.

9 June, 2015

Video courtesy M. Biederman, 2015.