US politics

American Crypto

In 1982 three computer scientists funded by the US Army Office published a highly influential article on the ‘Byzantine Generals Problem’. 

Imagine a wealthy 14th Century city under siege from a coalition of a dozen generals and their armies. After blockading the city over a bitter winter, the armies are nearly out of food and must either attack or retreat. However, the armies must all move simultaneously, otherwise the city’s still-functioning cavalry will ride out and eliminate them each in turn from the rear.  The generals are coordinating their plans using mounted couriers.

But the city has hidden supporters.  Each of the generals suspect the city may be intercepting their couriers , and replacing some of their messages to each other. Worst of all, each general wonders if one or more of the others has secretly sold out, so even if their messages aren’t intercepted, they fear they may still be betrayed by some of their allies.

Now imagine you are one of the generals.  A courier enters your tent one night with a message saying one of the general saying they will move at dawn. Then another courier arrives with a message from a different general, with the same message – they will move at dawn.  Then another courier arrives, with the same message again. Do you believe them and move at dawn yourself?  If the messages are genuine, and everyone moves at once, you will all be safe.  But if they are faked in some way, and you move too late, your army may be slaughtered or the prize lost.  What do you do? When will you know what you should do?

According to the computer scientists, it depends on the messages.  Apparently, if you can tell whether a message has been intercepted and substituted, you only need half of your fellow generals to be honest for the coalition to prevail. But if you can’t tell if the messages have been intercepted, more than two thirds of the generals must be honest if they are to survive. 

This computing research is a foundation for modern cryptography and many kinds of software, including the emergency decentralised economy powered by cryptocurrencies like Bitcoin and Ethereum. 

I’d always assumed that any social or economic system based solely on mistrust only leads to ruin.  But it seems it depends on the numbers.  If a two thirds supermajority hold fast, believers in rainbows and unicorns thrive. If over half stay true, honest soliders can still survive.  But if a majority are compromised, all are as good as lost.

What proportion of my fellow citizens do I trust?

Image on homepage: Siege of Constantinople by Sultan Mehmett II (1432-81) in 1453 (fresco), by Romanian School, (16th century); Church of St George, Voronet Monastery, Bukovina, Romania. Copyright Archives Charmet / Bridgman Images.

Divining the rules of the game

I’ve been watching a lot of news during the lockdown. Of outrage followed by protest followed by outrage. Of statues toppled, erected and toppled. Of politicians one upping each other for electoral gain. But after a few rounds of grim ‘tit for tat,’ one side or the other would do something that I just did not see coming. 

Maybe it’s the stress of watching it all, but I’m reminded of how my brother and I would start a game of Go, when we first learned it.

I thought I was familiar with the general rules of how politics is ‘played,’ but after being shocked and surprised too many times, I realised I have no clue what will happen next. I guess there are no clear rules to any of these games  Or maybe the diversity of players with different styles and agendas makes prediction impossible.

Take Lee Sedol, one of the greatest Go players of all time. In 2016, the 33-year old Lee agreed to a play five, time-limited games of Go for a $1million prize. His opponent was Google’s artificial intelligence DeepMind. 

The tournament was live-streamed globally, and having done his research on DeepMind’s previous games, Lee was confident he would win at least 4 of the 5 games.

In their first game, each player worked steadily and hard through their gameplay. Around 90 minutes in, Lee had to stop and think for five minutes or so before resuming at his usual pace. 30 minutes later, in the 102nd move of the game DeepMind made Lee exclaim out loud. He sat and considered the board in silence… for 10 minutes. The TV commentators were transfixed, and one observing grandmaster described Lee as ‘stunned.’ Lee eventually responded and the game went on. But things had changed, and in the end DeepMind won. In the post-game interview, Lee said the 102nd move was “a move that a human never would have played.”

Their second game was equally stunning. According to DeepMind’s programmers, after 36th moves DeepMind had an 80% chance of winning by about twenty points. But DeepMind did something that commentators said was “overturned hundreds of years of received wisdom.”  It made a move that its programmers predictedd would extend the game’s duration and reduce its margin of victory, but increase its chance of winning to 99%. No professional human player of Go has every attempted such an ambitious ‘play it safe’ strategy. With that move, DeepMind of course went on to win the game. And the third game as well.

Coming into the fourth game, Lee had already lost the tournament. Maybe this freed him up in some way, because in the 78th move of the game, Lee play what Korean commentators call a ‘divine move’:  it combines tactics, strategy, and a reversal of fortune in a move that a professional Go player might play only once in their life. For its brilliance, Lee’s ‘divine move’ is apparently on a par with a one played in 1846 by the Japanese Go master Hon’inbō Shūsaku.

Even without this historical awareness, DeepMind’s programmers knew something uncanny had happened. The software had judged the probability of a human making this particular move at ‘one in ten thousands,’ yet Lee played it. But then something even stranger occured. DeepMind’s subsequent ten moves were described by its programmes as ‘sub-optimal’ and reduced its probability of winning from 70% to below 50%. It looked to me like DeepMind’s software got rattled.

In his post-tournament interview, Lee said he had learned something new from his 4-1 loss: “I enjoyed playing DeepMind without question. And as I watched how he fought, I began to question the established conventions about how you should play.”

What was going through Lee’s mind during that ten minute silence in his first game, and in the fourth game when he made his divine move?  I suspect he himself doesn’t know. And what was going through DeepMind’s circuitry in the second game when it upended centuries of human understanding, and in the fourth when it lost its way after Lee’s inspiration? I suspect its programmers themselves don’t know. 

I guess all great human games see brilliant new players from time to time. They play in the same arena as their opponents, and in a superficially familiar style. But they are in a league of their own, playing a different stort of game, tuneded into music even they can barely hear. And they change the game forever.

When I see the news of political grandmasters playing off against each other, I can only look on in wonderment and not a little fear, trying to divine the games they are all playing at.

Image: Created using skillgamesboard.com.

His next escapade

While most families worry about neighbors or bikes for us it’s high places.  But no way would we have guessed he’d try the maple in our own front yard.  I’d been watching the inauguration on TV when he started so I missed the first logic-defying leap, and the second.  It was only when I heard dad’s shout and ran out that I saw, and yes, it was an awesome sight. 

Such a crazy dude, scrabbling and hauling his way up.  Occasionally he’d taken a breather, head cocked as if listening to something on the wind, but after a moment he’d continue on with his quest for the sky. 

I wasn’t convinced by mom’s explanation about why he stopped.  After all, he’d needed a larger jump to get started so the branch above should have been easy.  Personally, I think he’d reached the perch he’d been eyeing all along. 

Whatever the reason, he stopped.  He’d blink quietly at the sun or occasionally glance down at us and shuffle a bit, otherwise he just sat there.  We thought he was simply basking in the experience but after a while we realized he was stuck with no way down.

We tried the more obvious tactics like food and toys.  No luck.  A stick was thrown and I have to confess that another was even thrown at him.  Nothing doing.  Weirdly, none of us could repeat his first jump to climb up and get him down.  How was that even possible?  In the end we had to call animal control. 

His ability to spot an opportunity is infuriating but it’s also pretty genius.  So even with a $50 call out fee none of us have the heart to punish him.  We can only look on as the black sheep of the family sprawls out on the lawn, pantingly pleased with himself and no doubt planning his next escapade.

Image: Pascale, Carol. A Tree. 2015. Watercolour. Carolepascale.com