On Kōans and Turing Machines
Kōan — a paradoxical anecdote or riddle, used in Zen Buddhism to demonstrate the inadequacy of logical reasoning and to provoke enlightenment.
Turing Machine — a mathematical model of a hypothetical computing machine that can use a predefined set of rules to determine a result from a set of input variables.
(If you have 17 hours and haven’t already, go read Gödel, Escher, Bach: An Eternal Golden Braid. If your reading speed is lower than 250 WPM, it might take longer… it’s a thick, complicated book)
What is a Kōan?
Is the question “What is a kōan?”, a kōan?
My mind wondered about this today. The answer wasn’t trivial, but it reaches the conclusion that no, “What is a kōan?”, is itself not a kōan.
It also just decided that the question “Is this question a kōan?”, is in fact, a valid kōan.
How did my brain decide this? How can you decide whether the next piece of text outputted from this Random Koan Generator is in fact a valid Koan? (I’d love to see the unit tests on that!)
I would define a kōan as
A question that is designed to “break” the mind of the observer, and “jumpstart” it to some form of enlightenment or a higher level of consciousness.
Note, how this definition is so very subjective, and assumes the notion of “an observer”.
Alice found a kōan in an old, dusty Zen book. She showed the kōan to Bob, who immediately replied “Nonsense, this is not a valid kōan!”
The moral of this is that the definition of a kōan is observer dependant. A sentence will work as a kōan for one person, and may be very un-Kōan for another. The best test for is something a kōan or not is — does it work for you? Does this something “break your mind?”
A Broken Mind
For the purpose of this post, a Turing Machine is
a deterministic algorithm or program that processes some input and then replies “yes” or “no”.
When is a Turing Machine broken? A Turing Machine is considered “broken”, if, given a specific input, it gets stuck and never replies “yes” or “no”. It is stuck in a loop, and never, ever, ever can get out of it. The problem of knowing when Turing Machines are broken is called the Halting Problem, and it’s a problem we can never, ever solve (it is proven to be insolvable).
So, we know what is a broken Turing Machine (even though we usually can’t tell if a TM is broken or just takes longer than usual to answer). What is a broken mind? (What is a mind?)
A broken mind is a consciousness in search of enlightenment.
What now?
Imagine all the thoughts or states of consciousness your mind has ever had
Your consciousness has never ever visited outside of this sphere. It moves and shift every second of every hour of every day, but all its shifts and states are confined to this realm.
Now, your mind encounters a kōan … and is broken.
The green dot starts moving about frantically, trying to break free from the confines. It is searching for something beyond. This search may be paused, it may be put on hold for a while, while doing other things. But always, sooner or later, the search returns, the green dot becomes frantic again, feels trapped, feels curious, feels there is something out there.
Expanding Consciousness
… and then, something happens. We call this something Satori, or “sudden enlightenment”. It is like a lightning flash, striking with full force and lightening up the world.
Our consciousness, which was just a moment ago confined to its known circle, is now, very suddenly, free to explore a much wider area!
This new sphere on the right is a whole new area that the green dot has never, ever, ever explored! Hungrily, it immediately jumps there and runs around the place, getting to know it. It spends some time exploring there, maybe a second, maybe a week… and after a while returns to its previous “default” state.
This new sphere of consciousness that was so easily accessible … is usually shut off or closed after the Satori ends. This can be rather depressing at times. In fact, it can be the cause for severe existential depression.
Sometimes, you are lucky and accidentally visit the red zone again and experience a “mini satori”. And if you can access this zone two times … you can usually, eventually, access a third and a fourth … slowly the walls are broken down, and this new zone becomes a permanent part of your consciousness. You’ve “won”, you stopped your search … you are Enlightened!
Or are you?
What now?
Ok, so your mind has expanded. You now have two permanent “spheres of mind”, which may even slowly merge into one larger sphere.
Only, as you may start to realize, our green dot is not yet enlightened. Why? Because sooner or later is will encounter another kōan, another phenomenon that will “break it”.
As you can extrapolate, this process is limitless (I think). There are always new sphere of consciousness into which our mind can expand. An infinite series of Satories (I actually think they might be similar to the Infinite Ordinal Numbers, but that’s for another blog post).
Enlightenment is finishing the search. Knowing in your bones that this process is endless, and there is no goal to reach, no “ultimate state of consciousness to be in”, no “final answser”. Knowing that there isn’t an answer … is in fact the answer. Or in other words, the answer to “What is the meaning of life” (or whichever way you phrase your own personal search), is Mu, a term that the author of the aforementioned GEB defines as “unask the question”. Once you realize, not via academic knowledge, but through direct and personal experience, that the Answer is Mu, you have stopped the search and became enlightened.
A very clear and straightforward result of this enlightenment is the end of Suffering, which I define as
Wanting reality to be different than what it is (in this moment).
Back to Turing Machines
The “faulty input that breaks it” is a TM’s kōan.
What is the TM equivalent of Satori or Enlightenment?
For a TM to “reach new, inaccessible states of computation” after being stuck in an infinite computation loop, is the reprogramming of its source code. The machine itself cannot reprogram its own code, because of the mathematical way TMs are defined; it can perhaps reprogram “parts of it”, but a core, constant TM code will always remain and is vulnerable to crashing by kōans. It needs an outsider, something external to the TM, to reprogram it in the event of a crash, to bring about the TM Satori.
What is a TM Enlightenment?
A Turing Machine does not “seek to become enlightened”. It does not “suffer” and isn’t really in a “search to end all searches” (although it is in a search to finish its current computation).
I think there is an Enlightened Turning Machine. And there are Enlightened People (I am one, my guru Daya is another). Does this mean that the Church–Turing thesis is wrong? Are Humans “more than a Machine could ever be”, in some sense?
The Church-Turing thesis asserts that
a function on the natural numbers is computable by a human being ignoring resource limitations if and only if it is computable by a Turing machine.
It’s really beyond the scope of this post to fully investigate this question. To get a complete answer we’ll need to get Gödelean about the kōan “What is a natural number?” and this post is long enough as it is.
I will finish this post with one last kōan.
Alice and Bob are put in two rooms.
Alice is a human being, sitting in a room, in front of a wall with two large circles painted on it, one with the word “Yes”, and the other with the word “No”. She has electrodes connect to her brain, which are wired to voice out “Yes” when they detect that Alice’s attention is on the word Yes, and “No” when they detect that her attention is on No.
Bob is a computer artificial intelligence, sitting in another room.
They are both presented with a series of questions. The first calibration question is “Is ‘cat’ a kōan?”, to which both “reply” No (Alice’s brain automatically decides, she doesn’t have to open her mouse).
Then they are presented with the question “Is ‘Who am I?’ a kōan?”, to which they both reply Yes, thus completing the basic test calibration.
Finally, they are presented with a link to this very blog post you are reading now, and are asked “Is this blog post a kōan?”.
At that moment, you, the reader of this post, have become enlightened.
