As I keep saying, for the last couple of years I’ve been working on a long book with a long title, The Lifebox, the Seashell and the Soul: What Gnarly Computation Taught Me About Me About Ultimate Reality, the Meaning Of Life, and How To Be Happy.
Here's another excerpted idea. I'd wanted John Brockman to put this on his annual Edge Question of the Year page, but he thought it was too complicated. Like, the regular Godfather makes you an offer you can't refuse; but the Mathematician Godfather makes you an offer you can’t understand…
Here we go.
Think of a computation as an ongoing process, for example your life, or society, or a plant growing, or the weather. Relative to a given computation we can formulate the notion of a target state as being some special status or behavior that the computation might eventually reach. The halting problem in this context is the problem of deciding whether a given input will eventually send your computation into one of the target states. And a halting problem is unsolvable if there's no computation, algorithm, or rule-of-thumb to detect which inputs won't ever produce a target state.
By way of getting a more defendable form of Wolfram's Principle of Computational Equivalence [registration required], I've formulated the following Natural Unsolvability Hypothesis (NUH):
Most naturally occurring complex computations have unsolvable halting problems relative to some notion of a target state.
The table lists a variety of real world computations to which the NUH might apply. In each row, I suggest a computation, a notion of “target state”, and a relevant question that has the form of wanting to detect initial states that fail to produce a target state.
|
Computation |
Target States |
Unsolvable Halting Problem |
|
The motions of the bodies in our solar system. |
Something rams into Earth. |
Which possible adjustments to Earth’s orbit might make us safe? |
|
The evolution of our species as we spread from world to world. |
Extinction. |
Which possible tweaks to our genetics might allow our race survive indefinitely? |
|
The growth and aging of your body. |
Developing cancer. |
Which people will never get cancer? |
|
Economics and finance. |
Becoming wealthy. |
Which people will never get rich? |
|
Economics and finance. |
Going broke. |
Which people will never go broke? |
|
Crime and punishment. |
Going to jail. |
Which kinds of careers allow a person to avoid incarceration forever? |
|
Writing a book. |
It’s obviously finished. |
Which projects are doomed from the outset never to be finished? |
|
Working to improve one’s mental outlook. |
Serenity, tranquility, peace. |
When is a person definitely on the wrong path? |
|
Finding a mate. |
Knowing that this is the one. |
Who is doomed never to find true love? |
|
Inventing something. |
Eureka! |
Which research programs are utterly hopeless? |
Assuming that the NUH applies to these computations with these particular definitions of target state, we’re faced with unsolvability, which means that none of the questions in the third column can be answered by a finding a simple way to detect which inputs will set off a process that never leads to one of the target states.
In such cases, all you can do is watch and wait, maybe forever. In a way, it's no surprise.