Posted by: @coder1987

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But they would need to use a computer.  There is just no way around that.  Too many possibilities that need to tested, and a human isn’t going to be able to do that.  You might get lucky subjectively, that is possible, but how would you prove what you found is right, when you didn’t try all of the others?  That is what I did, as we see with the code.

(Emphasis added—S)

And this is very much the issue. How would we go about selecting a set of candidates that we could then argue comprised all of the others?

Well, of course we can’t.

As with your coded example, we have to start somewhere with a set (perhaps) of formal templates and a lexicon to populate the former, to then permit testing. Yet, in the act of doing so we are already pruning down the ‘all’ set to just those that match with the choices we have thereby imposed. On this reasoning, then, we are – even at the outset – denying ourselves (as we must) the option of being able to come back later saying “what my code has found is right.”

In your code, for example, you have – what is it – 12 templates, under a couple of exclusion tests foremost:

f"{pre}{dist_word}{frac_str}{rad}{angle_word}"
f"{pre}{angle_word}{rad}{dist_word}{frac_str}"
f"{pre}{dist_word}{frac_str}{angle_word}{rad}"
f"{pre}{angle_word}{dist_word}{frac_str}{rad}"
f"{pre}{rad}{angle_word}{dist_word}{frac_str}"
f"{pre}{rad}{dist_word}{frac_str}{angle_word}"

f"{pre}{dist_word}{frac_str}{dunit}{rad}{angle_word}"
f"{pre}{dist_word}{frac_str}{dunit}{angle_word}{rad}"
f"{pre}{angle_word}{rad}{dist_word}{frac_str}{dunit}"
f"{pre}{angle_word}{dist_word}{frac_str}{dunit}{rad}"
f"{pre}{dunit}{dist_word}{frac_str}{rad}{angle_word}"
f"{pre}{rad}{angle_word}{dunit}{dist_word}{frac_str}"

and a rather limited lexicon:

_WORD_TOKENS = [
"THIRTEENSIXTEENTHS", "FIFTEENSIXTEENTHS", "ELEVENSIXTEENTHS",
"SEVENSIXTEENTHS", "NINESIXTEENTHS", "FIVESIXTEENTHS", "THREESIXTEENTHS",
"THREEQUARTERS", "THREEFOURTHS", "THREEEIGHTHS", "SEVENEIGHTHS", "FIVEEIGHTHS",
"TWOTHIRDS", "SIXTEENTH", "RADIANS", "RADIAN", "INCHES",
"TWELVE", "ELEVEN", "QUARTERS", "QUARTER", "FOURTHS", "FOURTH", "EIGHTHS", "EIGHTH",
"SEVEN", "THREE", "EIGHT", "NINE", "FOUR", "FIVE", "ZERO", "THIRDS", "THIRD", "HALF",
"INCH", "RADS", "ONE", "TWO", "SIX", "TEN", "RAD", "AND", "THE", "FROM",
"IN", "AT", "TO", "BY", "GO", "ON", "A",
]

from which it would seem hardly justifiable to claim that your code, in contrast to others’ attempts, has tried all of the other candidate options. Others have chosen some set to begin from, you have likewise; as we must.

In short, if that is our aim – to evaluate under the claim that we have taken into consideration all possibilities –  then we are already stymied by the very nature of the problem, even before we have had begun to run out code or trimmed our spreadsheet.