Re: DDD specifies recursive emulation to HHH and halting to HHH1

On 3/31/25 11:10 PM, olcott wrote:

On 3/31/2025 10:02 PM, dbush wrote:

>
The only requirements of an algorithm are to generate the results of a mapping.  How that is accomplished is irrelevant.

>
It may have been historically considered irrelevant.
When it comes down to determining that mere guesses
are not any sort of: "computing the mapping" then it
does become relevant.
>

One important thing to add, is you can't just look at an algorithm and necessarily say if it is right or wrong.
For instance, your program to add to numbers might be correctly done with a program that never actually directly added the two numbers.
If could have done the anti-log to some base of the two numbers, multiplied them, and then taken the log.
These operations might be obfuscated further, making it hard to see that this is what was done.
It is a proven fact in computation theory that the task of determining if two arbitrary machines compute the same mapping is uncomputable. We can easily prove if they are not, by showing a case where they differ, but we might not be able to prove that they always produce the same results (sometimes we can, but not generally).