You shouldn’t trust people who claim to know 4 digits of accuracy for a forcast like this.
You shouldn’t trust a human person who makes that claim. But if we are using ‘person’ in a way that includes the steel-Vulcan from the quote then yes, you should.
The uncertainity involved in the calculation has to be greater.
It is all uncertainty. There is no particular reason to doubt the steel-Vulcan’s ability to calibrate ‘meta’ uncertainties too.
In the face of all the other evidence about the relative capabilities of the species in question that the character in question is implied to have it would be an error to overvalue the heuristic “don’t trust people who fail to signal humility via truncating calculations”. The latter is, after all, merely a convention. Given the downsides of that convention (it inevitably makes predictions worse) it is relatively unlikely that the Vulcans would have the same traditions regarding significant figure expression.
You shouldn’t trust a human person who makes that claim. But if we are using ‘person’ in a way that includes the steel-Vulcan from the quote then yes, you should.
There inherent uncertainity in the input. The steel-Vulcan in question counted one specifc case as being 24% relevant to the current question. That’s two digits of accuracy.
If many of your input variables only have two digits of accuracy the end result shouldn’t have four digits of accuracy.
If many of your input variables only have two digits of accuracy the end result shouldn’t have four digits of accuracy.
Almost-inaudibly, whispering in a small corner of the room while scribbling in a notebook that the teacher is totally stupid while said teacher says something similar to the quote above:
under the assumption that all variables have equivalent ratios of weight to the final result and that the probability distribution of the randomness is evenly distributed across sub-digits of inaccuracy, along with a few other invisible assumptions about the nature of the data and calculations
Yep, that’s me in high school.
In your example, the cited specific case only means that the final accuracy to be calculated is +- 0.01 individual ship relevance, which means that at the worst this one instance, by the standard half-the-last-significant-digit rule of thumb (which is not by any means an inherent property of uncertainties) means that there’s +- 0.5% * 1 ship variance over the 542 : 2 000 000 ratio for this particular error margin.
Note also that “24% weight of the relevance of 1 ship in the odds” translates very poorly in digit-accuracies to “3745 : 1″, because 3745:1 is also 0.026695141484249866524292578750667% chance, which is a shitton of digits of accuracy, and is also 111010100001 : 1, which is 12 digits of accuracy, and is also (...) *
As you can see, the “digits of accuracy” heuristic fails extremely hard when you convert between different ways to represent data. Which is exactly what happened several times in the steel-vulcan’s calculations.
Moral of the story: Don’t work with “digits of accuracy”, just memorize your probability distribution functions over uncertainty and maximal variances and integrate all your variables with uncertainty margins and weights during renormalization, like a real Vulcan would.
Edit: * (Oh, and it’s also 320 in base-35, so that’s exactly two significant digits. Problem solved, move along.)
If many of your input variables only have two digits of accuracy the end result shouldn’t have four digits of accuracy.
That is indeed the (mere, human) convention as taught in high schools of our shared culture. See above regarding the absurdity of using that heuristic as a reason for rejecting the advice of what amounts to a superintelligence.
It’s not about accuracy, it’s about not privileging 3700 over 3745. Neither is a particularly round number in, say, binary, and omitting saying “forty five” after converting this number into decimal system for human consumption is not much of a time saver.
But re-mentioning the “forty five” after a human asks you “three thousand seven hundred?” is mostly pointless nitpicking, and demonstrates a lack of understanding of human (well, at least, of neurotypical human) psychology IMO.
Either that, or it reflects an accurate understanding of the things that humans (justifiably or otherwise) treat as signals of authoritative knowledge. I mean, there’s a reason people who want to sound like experts quote statistics to absurd levels of precision; rounding off sounds less definitive to most people.
You shouldn’t trust a human person who makes that claim. But if we are using ‘person’ in a way that includes the steel-Vulcan from the quote then yes, you should.
It is all uncertainty. There is no particular reason to doubt the steel-Vulcan’s ability to calibrate ‘meta’ uncertainties too.
In the face of all the other evidence about the relative capabilities of the species in question that the character in question is implied to have it would be an error to overvalue the heuristic “don’t trust people who fail to signal humility via truncating calculations”. The latter is, after all, merely a convention. Given the downsides of that convention (it inevitably makes predictions worse) it is relatively unlikely that the Vulcans would have the same traditions regarding significant figure expression.
And lo, Wedrifid did invent the concept of Steel Vulcan and it was good.
Do we actually have enough fictional examples of this to form a trope? (At least 3, 5 would be better.)
There inherent uncertainity in the input. The steel-Vulcan in question counted one specifc case as being 24% relevant to the current question. That’s two digits of accuracy.
If many of your input variables only have two digits of accuracy the end result shouldn’t have four digits of accuracy.
Almost-inaudibly, whispering in a small corner of the room while scribbling in a notebook that the teacher is totally stupid while said teacher says something similar to the quote above:
under the assumption that all variables have equivalent ratios of weight to the final result and that the probability distribution of the randomness is evenly distributed across sub-digits of inaccuracy, along with a few other invisible assumptions about the nature of the data and calculations
Yep, that’s me in high school.
In your example, the cited specific case only means that the final accuracy to be calculated is +- 0.01 individual ship relevance, which means that at the worst this one instance, by the standard half-the-last-significant-digit rule of thumb (which is not by any means an inherent property of uncertainties) means that there’s +- 0.5% * 1 ship variance over the 542 : 2 000 000 ratio for this particular error margin.
Note also that “24% weight of the relevance of 1 ship in the odds” translates very poorly in digit-accuracies to “3745 : 1″, because 3745:1 is also 0.026695141484249866524292578750667% chance, which is a shitton of digits of accuracy, and is also 111010100001 : 1, which is 12 digits of accuracy, and is also (...) *
As you can see, the “digits of accuracy” heuristic fails extremely hard when you convert between different ways to represent data. Which is exactly what happened several times in the steel-vulcan’s calculations.
Moral of the story: Don’t work with “digits of accuracy”, just memorize your probability distribution functions over uncertainty and maximal variances and integrate all your variables with uncertainty margins and weights during renormalization, like a real Vulcan would.
Edit: * (Oh, and it’s also 320 in base-35, so that’s exactly two significant digits. Problem solved, move along.)
That is indeed the (mere, human) convention as taught in high schools of our shared culture. See above regarding the absurdity of using that heuristic as a reason for rejecting the advice of what amounts to a superintelligence.
It’s not about accuracy, it’s about not privileging 3700 over 3745. Neither is a particularly round number in, say, binary, and omitting saying “forty five” after converting this number into decimal system for human consumption is not much of a time saver.
But re-mentioning the “forty five” after a human asks you “three thousand seven hundred?” is mostly pointless nitpicking, and demonstrates a lack of understanding of human (well, at least, of neurotypical human) psychology IMO.
Either that, or it reflects an accurate understanding of the things that humans (justifiably or otherwise) treat as signals of authoritative knowledge. I mean, there’s a reason people who want to sound like experts quote statistics to absurd levels of precision; rounding off sounds less definitive to most people.