If that is what you want to do, you can do that in any language. It's just that when you do it in e.g. Java, you have to spend a lot longer proving correctness before discovering that it doesn't work.
Yeah, just last week I updated the numeric precision of a value across an entire user journey in a big enterprise application, spanning many functions and data types. Thanks to Haskell, I could do it in a day.
In any other language I've used (barring maybe Ada) that is a refactoring that would take at least days, if not weeks, to manually track down all the places it interacts with the system directly or indirectly, because mixing e.g. int with long long is not a type error.
In Haskell, I change the type and the compiler spits out a list of locations that needs to change. This is repeated for a few iterations until all transitive interactions are worked out. Done!
The calculator cannot know whether there are no negative terms. For example, if people's net worth is distributed 0.2–400, there's likely a significant chunk of people who are, on the whole, in debt. These will be represented as a negative term, even though their distribution was characterised by positive numbers.
The calculator in Emacs has support for what it is you request, which it calls "interval forms". Interval form arithmetic simply means executing the operations in parallel on both ends of the interval.
It also has support for "error forms" which is close to what the calculator in OP uses. That takes a little more sophistication than just performing operations on the lower and upper number in parallel. In particular, the given points don't represent actual endpoints on a distribution, but rather low and high probability events. Things more or less likely than those can happen, it's just rare.
> I'm not especially good at stats
It shows! All the things you complain about make perfect sense given a little more background knowledge.
Is it actually just doing it at both ends or something nore complex? Because for example if I did 7 - (-1~2)^2 the actual range would be 3-7 but just doing both ends of the interval would give 3-6 as the function is maximised inside the range.
This looks like a much more sophisticated version of PERT than I have seen used. When people around me have claimed to use PERT, they have just added together all the small numbers, all the middle numbers, and all the big numbers. That results in a distribution that is too extreme in both lower and upper bound.
I have no familiarity with blue whales but I would guess they're 1--5 times the mass of lorries, which I guess weigh like 10--20 cars which I in turn estimate at 1.2--2 tonnes, so primitively 12--200 tonnes for a normal blue whale. This also aligns with it being at least twice as large as an elephant, something I estimate at 5 tonnes.
The question asks for the heaviest, which I think cannot be more than three times the normal weight, and probably no less than 1.3. That lands me at 15--600 tonnes using primitive arithmetic. The calculator in OP suggests 40--320.
The real value is apparently 170, but that doesn't really matter. The process of arriving at an interval that is as wide as necessary but no wider is the point.
Estimation is a skill that can be trained. It is a generic skill that does not rely on domain knowledge beyond some common sense.
I would say general knowledge in many domains may help with this as you can try and approximate to the nearest thing you know from that domain.
How you get good at being a generalist is the tricky part, my best bet is reading and doing a lot of trivia (I found crosswords to be somewhat effective at this, but far from being efficient)
No, that has nothing to do with it. Trivia helps you narrow down an interval. It is not necessary to construct a correct interval, which can be of any width.
It is producing a useful number. As more truly independent terms are added, error grows with the square root while the point estimation grows linearly. In the aggregate, the error makes up less of the point estimation.
This is the reason Fermi estimation works. You can test people on it, and almost universally they get more accurate with this method.
If you got less certain of the result in the example, that's probably a good thing. People are default overconfident with their estimated error bars.
Read a bit on Fermi estimation, I'm not quite sure exactly what the "method" is in contrast to a less accurate method, it's basically just getting people to think in terms of dimensional analysis? This passage from the Wikipedia is interesting:
By contrast, precise calculations can be extremely complex but with the expectation that the answer they produce is correct. The far larger number of factors and operations involved can obscure a very significant error, either in mathematical process or in the assumptions the equation is based on, but the result may still be assumed to be right because it has been derived from a precise formula that is expected to yield good results.
So the strength of it is in keeping it simple and not trying to get too fancy, with the understanding that it's just a ballpark/sanity check. I still feel like the Drake equation in particular has too many terms for which we don't have enough sample data to produce a reasonable guess. But I think this is generally understood and it's seen as more of a thought experiment.
They are meaning the same thing. The original comment pointed out that people’s qualitative description and mental model of the 95% interval means they are overconfident… they think 95 means ‘pretty sure I’m right’ rather than ‘it would be surprising to be wrong’
I have made a similar tool but for the command line[1] with similar but slightly more ambitious motivation[2].
I really like that more people are thinking in these terms. Reasoning about sources of variation is a capability not all people are trained in or develop, but it is increasingly important.[3]
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