On 12 Oct 2013, at 01:36, Russell Standish wrote:
On Fri, Oct 11, 2013 at 04:08:05PM -0700, meekerdb wrote:
Maybe I'm not clear on what UD* means. I took it to be, at a given
state of the UD, the last bit output by the 1st prog, the last bit
output by the 2nd program,...up to the last prog that the UD has
Its not the output, because the UD doesn't actually output
anything. Rather its an internal view of the states the machines
emulated by the UD pass through, rather like what the Helsinki man
experiences when being duplicated to Moscow and Washington.
Its a subtle point, and I fell into the same trap you did (and Liz did
also, this morning) a few years ago. I'm not sure anyone has a clear,
crisp mathematical explanation of what UD* is - I certainly don't.
To do that needs the phi_i, or the W_i. It is the sequence
phi_0(0)^0, phi_0(0)^1, etc.
With the three numbers (i, j, k) going through all element of NxNxN, and
phi_i(j)^k = the kth state /step of the computation of machine/number
i, on input j.
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