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fix: typo

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NunoSempere 2023-03-01 23:46:24 -06:00
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blog/2023/03/01/computable-solomoff/index.md
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@ -6,7 +6,7 @@ Thinking about [Just-in-time Bayesianism](https://nunosempere.com/blog/2023/02/0
### The key idea: arrive at the correct hypothesis in finite time ### The key idea: arrive at the correct hypothesis in finite time
1. Start with a finite set of turing machines, \(\{T_0, ..., T_n\}\) 1. Start with a finite set of turing machines, \(\{T_0, ..., T_n\}\)
2. If none of the \(T_i\) predict your trail bits, \((B_0, ..., B_m)\), compute the first \(m\) steps of Turing machine \(T_{n+1}\). If \(T_{n+1}\) doesn't predict them either, go to \(T_{n+2}\), and so on^1 2. If none of the \(T_i\) predict your trail bits, \((B_0, ..., B_m)\), compute the first \(m\) steps of Turing machine \(T_{n+1}\). If \(T_{n+1}\) doesn't predict them either, go to \(T_{n+2}\), and so on[^1]
3. Observe the next bit, purge the machines from your set which don't predict it. If none predict it, GOTO 2. 3. Observe the next bit, purge the machines from your set which don't predict it. If none predict it, GOTO 2.
Then in finite time, you will arrive at a set which only contains the simplest TM which describes the process generating your train of bits. Proof: Then in finite time, you will arrive at a set which only contains the simplest TM which describes the process generating your train of bits. Proof:
@ -31,7 +31,6 @@ Interestingly, that scheme also suggests that there is a tradeoff between arrivi
### A distracting epicycle: dealing with Turing machines that take too long or do not halt. ### A distracting epicycle: dealing with Turing machines that take too long or do not halt.
When thinking about Turing machines, one might consider one particular model, e.g., valid C programs. But in that case, it is easy to consider programs that do not halt, like:[^2] When thinking about Turing machines, one might consider one particular model, e.g., valid C programs. But in that case, it is easy to consider programs that do not halt, like:[^2]
[^2]: Readers might find it amusing to run gcc loop.c and check it
``` ```
void main(){ void main(){
@ -63,4 +62,5 @@ This can easily be fixed as follows:
^1: Here we assume that we have an ordering of Turing machines, i.e., that T_i is simpler than T_(i+1) [^1]: Here we assume that we have an ordering of Turing machines, i.e., that T_i is simpler than T_(i+1)
[^2]: Readers might find it amusing to run gcc loop.c and check it