This result reminds me of a paper I read last week via Andrew Gelman's blog [1]. It's a very thorough review of the, so called, bat and ball problem and is an up to date summary of something brought to many people's attention via Kahneman's Thinking Fast and Slow. As other commenters have suggested, the most reasonable explanation for the mathematicians to get this problem wrong is something more like carelessness than a lack of logical reasoning ability.
As an English speaker myself it's astonishing the number and range of features that other languages have built in, so to speak. Years ago I took Latin and the idea of declension just blew my mind. And that's basic in the grand scheme.
Great article. As someone with a geology background working in an Earth and space science department, I've greatly appreciated everything I've learned from the planetary scientists and meteorite researchers. There's just so much that we now understand about how our solar system formed and arrived at its current state. The explosion of exoplanet research on top of that and how those two fields inform each other has also been exciting to follow.
That's just playing with words. Putting Gordon Ramsay in the same bucket as "burger flipper" makes as much sense as putting Linus Torvalds in the same bucket as "keyboard monkey".
Why are you pivoting to "value"? The original discussion was about skilled vs unskilled labor and whether that assessment is subjective vs objective. You might think that accountants are useless paper pushers whereas burger flippers are Hard Working People That Get Actual Things Done™, but that's orthogonal to how much skill[1] is needed to flip burgers vs be an accountant.
So you're trying to derail the discussion to something about "value", because the page I linked about "skill" has a passage about how skilled laborers were historically important to the economy? What does this have to do with the subjectivity/objectivity of "underpaid", "unfair wages", "unskilled labor", or whether a burger flipper is more "skilled" than an accountant? As I said earlier, even if you think that accountants are useless paper pushers, the fact that they're pushing papers in a very specific way that takes years to learn, makes them more skilled.
First I'm pivoting now I'm trying to derail, when all I've done is answer you question; but to make it plain: yes, it's subjective. How else are certain skills valued more that others? There's no objective measurement to these. Comparing the skills of one disapline to another doesn't work, like apple to oranges.
The objective measurement for "skill" is how much training/experience/talent is required to carry out a particular job. Sure, there might be some fuzziness/ambiguity to this, and there's various degrees of freedom to how you compute a "skill score" or whatever (eg. what's more skilled an accountant or an auditor?), but it's hard to argue that a burger flipper is more skilled than an accountant. You can make the argument that the value of a burger flipper vs an accountant is subjective, but that's irrespective of the skill required.
Whether someone is getting "underpaid" or a "fair wage" on the other hand is entirely subjective, and you can come to whatever conclusion you want depending on your politics. On one side of the spectrum you could argue any sort of situation where the employer is capturing surplus value from the employee is inherently exploitative[1] and therefore "underpaid" and a "unfair wage". On the other end of the spectrum you argue that supply and demand curves are the ultimate arbiter of what's "fair", and any wage that is determined by the free market can't by "underpaid" or "unfair" by definition.
Yeah I don't think we're going to agree about skills in this, especially since I'd consider usefulness as a main objective measurement of skill. Using your "objective" measures could lead to a juggler of knives having the same level of skill as your accountant.
> With the two examples you chose, I‘d say there is not much of a skill gap.
Unless we're talking about really high end burgers, you can take almost anyone off the street and train them to flip burger patties within a day. They might not willingly do it on account of it being boring/tiring/poorly paid work, but it's not exactly hard to learn either. I doubt you can do the same for an accountant, unless your idea of an accountant is something like "manually copying entries into a ledger". Even teaching excel to someone who hasn't used excel ever, to a capacity where they can do meaningful financial reporting probably can't be done within a day.
On a relative scale, I agree with you that the amount of training involved differs for accountants and burger flippers, thus this is a good example.
On an absolute scale, comparing skills of burger flippers, accountants, aeronautical engineers and surgeons, the first two basically lump together.
I look at skill gap more in terms of „how hard is it to completely automate/autonomize this job“. Which is fiercely easy both for the burger flipper and the accountant, yet a bit harder (though not impossible) for the other two.
I think this can be seen as a change to acknowledge the need for context in order to make a robust (and hopefully correct) argument for possible evidence of life (fossil, trace, or otherwise). In all likelihood you're not going to find this uncontestable smoking gun and so you're going to need your robot geologist to collect much more than one sample in one place in order to rule out alternative interpretations. The Viking approach doesn't get you that.
Low content reply I know but it's great to see ICAP having the mindshare to appear in this discussion on HN. It's such a great paper and concept. I also think it has a lot to offer practitioners by making "active learning" a defined and delineated idea.
Absolutely! I based my dissertation on analyzing how students selected different lower level CS exercises (typing exercises, Parson Puzzles, output prediction, etc.) based on ICAP. What I observed was lower Active exercises benefit all students, the general order of exercise selection follows a sawtooth wave (work upwards to assessment, then reset for the next week), completers and non-completers in a MOOC selected 'next exercises' similarly, and no one likes pop ups recommending you to 'downgrade' if you're struggling on a problem. There are limitations to my work, like the order of how exercises were presented primed their selections, but the overarching theme I tried to convey was that lower-level drilling is an absolute necessity for learning.
It's always great for more people to know this. As another comment said, this is in no way "new" information. In fact, it may be interesting for you and others to read about the long study of organic compounds in meteorites. You could start with Murchison[1], which contains not just simple molecules, but over 70 amino acids. It even smells.
[1] https://statmodeling.stat.columbia.edu/2024/04/21/now-heres-...
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