The Incompleteness of the Abortion Debate

Mehdi Hasan has provoked a big online debate about abortion, after publishing a column in the New Statesman on whether abortion is a Left/Right issue in politics. Mehdi says that although the Left is usually identified with the pro-choice* argument and the Right with pro-life*, the arguments deployed are (in his view) the opposite of what the Left and Right usually deploy. The Left use the language of individualism and choice, while the Right use the language of vulnerability and equality.

This article sparked a furious online debate about the central issue – Kenan Malik has an excellent pro-choice rejoinder to Hasan’s piece.  There has also been a meta-debate about whether it was even possible to have a reasoned debate about the issue. I was taken with Hopi Sen’s analysis, comparing what a person thinks they said with what people on the opposing side actually hear (see these amusing stanzas for a shortened version).

I tend to think of the central question as a Devil’s Alternative type question. Whatever you choose, the outcome is bad. Trying to devise rules – legal or ethical – for a Devil’s Alternative problem seems futile. Is abortion right? is a trick question: The stuff of utilitarian philosophy lectures and episodes of 24, where you try to work out the course of action that causes least hurt… Knowing full well that any choice you make leads to permenant unpleasant consequences. Perhaps the only way out of the mire is to punt on the central ethical question, declaring it essentially incomplete in Gödel‘s sense: we are not equipped to process such a question properly. It is undecidable. A paradox that exposes the limits of our language and ethical structures. Continue reading “The Incompleteness of the Abortion Debate”

Trainyard and Neural Pathways

By far the best iPhone game I have come across is Trainyard. Is a deceptively simple puzzle, in which the player lays tracks to guide a set of coloured trains from their starting points to a goal. It has all the features of a great game: the rules are few, simple and intuitive. The puzzles are solved on a 7×7 grid, which gives the impression that a correct solution is on the cusp of revealing itself. The graphic design and sound design give you a satisfying mental ‘pay off’ when a puzzle is solved. This all adds to the addictive quality. It is no surprise it is one of the highest ranking games in the App Store.

Until recently, Trainyard’s only flaw was that it had a set number of puzzles to play. When they were solved, the payer had to go cold turkey. Playing a pre-solved puzzle was dull. However, with the latest update, the game’s creator Matt Rix has solved this problem, by providing an ‘engineer’ feature. Players can now create their own puzzle and upload it to Trainyard site for others to download and solve. This adds an element of competitiveness, and also social play, which makes the project as perfect as can be on it’s own terms. Highly recommended.

The ‘engineer’ feature has an interesting constraint. You cannot upload a self-made puzzle to the website unless you have solved it yourself. For a while I wondered why the computer could not already perceive which puzzles were solvable, and which were unsolvable… But then I remembered Godel’s Incompleteness Theorem, as explained to me in the sprawling Pulitzer Prize winning meditation on symmetry, mathematics, loops and consciousness, Godel, Escher, Bach by Douglas Hofstadter. Trainyard is, I think, a perfect little companion to this bizarre, genre defying book.

The cover of Godel, Escher, Back gives some clue to its esoteric subject matter
The cover of Godel, Escher, Back gives some clue to its esoteric subject matter

Godel’s Incompleteness Theorem says that in any consistent mathematic system will have certain “undecidable statements” which the system will not be able to answer either way. There will be true statements that nevertheless cannot be proven within that system. This holds for Trainyard, which is definitely a mathematic system with just a few logical rules. If you translate the elements of a puzzle (the starting points, gates, tracks, switch points, the colours of the trains, the goals, and the grid) into a mathematic formula (which, of course, you can do because the iPhone is essentially a mathematical machine, manipulating millions of 1’s and 0’s each second) there would be no equation or test that could consistently tell you whether the puzzle could be solved or not. The only way to tell is to run the puzzle, set off the trains, and see what happens. With some puzzles (such as this one) it is actually quite easy for even a novice player to work out that the puzzle has been solved, but the computer has to run it (all 10,603,843 steps) to confirm that fact.

Kurt Gödel
Kurt Gödel

The second link with Godel, Escher, Bach is to do with synapses, and how elements as simple and as binary as a neurones can give rise to enough symbols and signals to constitute a consciousness. Trainyard works wonderfully well as a metaphor for neural pathways, but it is only with the addition of the ‘engineer’ feature that this becomes apparent.

What do we notice when we look at the game in this way? (1) First of all anyone playing the game can see how the same track layout can result in completely different outcomes, depending on the number of trains sent from any given start position. On a related point, it is also interesting to see tiny changes to the track layout can fundamentally alter the outcome, once the trains are set in motion.

One of 3403 solutions to 'A Barrel Roll', one of the puzzles on Trainyard
One of 3403 solutions to 'A Barrel Roll', one of the puzzles on Trainyard

Through this, one can begin to comprehend how a brain, with very simple building blocks can give rise to huge, complex patterns, which is what is required to perceive and interact with the world. We can see how an apparently fixed set of neurones can act in different ways, depending on the precise nature of the stimulus.

A different insight – one only needs to play Trainyard for a short period of time to see how the same outcome can be achieved in a near infinite number of different ways – for each puzzle in game, users have submitted hundreds of unique solutions. It’s not really important how you get there, just so long as the right pattern emerges. When thinking about brains (artificial or biological), the lesson might be that trying to discover a particular set of pathways could be a red herring. If you were to do so, you would only understand one brain, not The Human Brain. We all have different patterns and pathways in our cerebal cortexts, and it is the different pathways we take to make the same patterns, that makes us unique.

Finally, it is worth remembering the insight of Godel’s Incompleteness Theorem. When you get to a sufficiently complex puzzle solution,you can never know whether it will produce the desired outcome, until you set the train running. This will hold for the artificial brains we create on circuit boards and in the RAM of computers – we won’t know whether the pattern we have created will work, until we have tried it. Which means we can’t work out the ‘correct’ pattern in advance. We’ll need to create some process of trial and error – a metaphor for evolution – before we hit on a correct pattern, and win our mental payoff.