PROFIT: (or is that Prophet?) Pick a specific message, such as one pretending to be from God announcing myself as the Messiah, translate it via ASCII into a single number, then search the digits of Pi to find the message.
IMPROVE THE WORLD: Run infinitely many infinite size simulations of Conway's life for an infinite duration. In each one, fire a stream of gliders (with the presence of a glider being a "1" and an absense being a "0") containing a message. Eg a repeated sequence, then build up to numbers, representation, alphabets, etc. The message would be finite in length but basically request a confirmation of understanding message be sent back to a specific point at a specific time, using the same glider gun code. Set the complexity of return message to be such that it is less likely to randomly occur than intelligent stable life is to evolve. Pick a sampling of those game of Life instances that passed this test, and ask them for advice on solving the world's problems (eg "Here's the structure of DNA and the human genome. Here are the diseases that affect the world. Please provide structure of immortality virus.")
WHAT WOULD I DO? Use the Conway life evolving trick, but combined with a test for superior intelligence and good will. I could then trade with them, running infinity machine programs on their behalf to solve problems for them. Ask an infinite number of such civilisations to each come up with a program they think I ought to run, run them, and store the questions and answers. If I don't have the storage to take an infinite answer away with me, I could use infinite peer review to pick out the best problems and answers. Another trade point would be to act as a communication channel between the infinite number of such benign civilisations, allowing them to send messages to each other.
Three Ideas
Pick a specific message, such as one pretending to be from God announcing myself as the Messiah, translate it via ASCII into a single number, then search the digits of Pi to find the message.
IMPROVE THE WORLD:
Run infinitely many infinite size simulations of Conway's life for an infinite duration. In each one, fire a stream of gliders (with the presence of a glider being a "1" and an absense being a "0") containing a message. Eg a repeated sequence, then build up to numbers, representation, alphabets, etc. The message would be finite in length but basically request a confirmation of understanding message be sent back to a specific point at a specific time, using the same glider gun code. Set the complexity of return message to be such that it is less likely to randomly occur than intelligent stable life is to evolve. Pick a sampling of those game of Life instances that passed this test, and ask them for advice on solving the world's problems (eg "Here's the structure of DNA and the human genome. Here are the diseases that affect the world. Please provide structure of immortality virus.")
CURIOUS:
Prove Reay's Lemma:
http://www.toothycat.net/wiki/wiki.pl?ReaysLemma
WHAT WOULD I DO?
Use the Conway life evolving trick, but combined with a test for superior intelligence and good will. I could then trade with them, running infinity machine programs on their behalf to solve problems for them. Ask an infinite number of such civilisations to each come up with a program they think I ought to run, run them, and store the questions and answers. If I don't have the storage to take an infinite answer away with me, I could use infinite peer review to pick out the best problems and answers. Another trade point would be to act as a communication channel between the infinite number of such benign civilisations, allowing them to send messages to each other.