A uniformitarian view is that everything is equally important. For example, there are 118 elements in the periodic table, so all 118 are equally important to know about.
The Pareto principle would say that importance is usually very unevenly distributed. The universe is essentially hydrogen and helium, with a few other elements sprinkled in. From an earthly perspective things aren’t quite so extreme, but still a handful of elements make up the large majority of the planet. The most common elements are orders of magnitude more abundant than the least.
The uniformitarian view is a sort of default, not often a view someone consciously chooses. It’s a lazy option. No need to think. Just trudge ahead with no particular priorities.
The uniformitarian view is common in academia. You’re given a list of things to learn, and they all count the same. For example, maybe you have 100 vocabulary words in your Spanish class. Each word contributes one point to your grade on a quiz. The quiz measures what portion of the list you’ve learned, not what portion of that language you’ve learned. A quiz designed to test the latter would weigh words according to their frequency.
It’s easy to slip into a uniformitarian mindset, or a milder version of the same, underestimating how unevenly things are distributed. I’ve often fallen into the latter. I expect things to be unevenly distributed, but then I’m surprised just how uneven they are once I look at some data.
It figures that a (more or less) Bayesian would write this…
*grins, ducks and runs*
As somebody who is on his fourth language now, the Spanish example is rather poorly chosen. Those vocabulary lists (or grammar points, or expressions) aren’t randomly chosen, but likely all so close to equally important that any weighing would be meaningless. They’re already optimized at the learning unit level.
The first five words you learn in English will likely be something like “Hi, I, you, book, am” or something like that. Not, “dessert, glucinum, thoroughwax, gothicism, baffler” (source: http://www.wordgenerator.net/random-word-generator.php), that a uniformitarian approach would give you.
And I’d say the same goes for much of academia (at least the areas I’ve encountered). At the level of subject areas and units, things are pretty well optimized for usefulness and importance. You can of course argue about the relative merits of disciplines, but that’s a different question (and one whose answer depends on your subjective point of view as much as any utlititarian measurement approach).
Did a little research. The 10 most common elements make up 99.4% of the earth’s composition. The top 10 elements in alphabetical order make up 3.3%.
John: Speaking as a chemist, the abundance is a really poor way to look at importance. For example, by abundance, silicon is one of the most important elements in the earths crust. However, its chemistry just isn’t that interesting or useful. Carbon is only the 15th most abundant element in the earth’s crust, but it’s chemistry is the basis for most drugs, polymers, biochemistry, etc.
A more extreme example: By the abundance logic, we’d never study a lot of the transition metals or lanthanides. However, they are some of the best and most useful catalysts around. Sure, we’d like to make iron do anything, since it is much cheaper and we’ve got a pretty much unlimited supply, but it simply can’t do a lot of the things we can do with the later transition metals (though we are putting a lot of work into that).
I don’t know of any chemist who thinks all elements are equally important to study (You don’t find much happening with Francium for example, and as far as I know Halfnium chemistry isn’t a hot area), but a lot of the big, useful discoveries come from weird elements and odd places, so neglecting those areas because they aren’t common or are a bit obscure would have missed most of the useful chemistry we do today.
@Cannageek: Importance depends on context.
I agree on that; I was just pointing out that your specific example was very flawed. Doubly so as helium has almost no chemistry to study, being a very small noble gas– It and Neon have the least known chemistry of any non-radioactive element, as I recall.
I completely agree. I just wrote a post sort of on the same subject. I see statistics professors who require students compute every equation for every statistic by hand and look up values in a table of the t, z or F distribution. They teach every single thing in the textbook equally.
I suppose they think I’m a slacker because I focus on the topics I think that students most need to know.
Context is key. Each context has a long tail of its own. Each of us engages with that context with our own long tail. Professors same. Universities same.
At one particular university, students came last. I wasted a year there regrettably. That was a year of negative use costs, costs that have their own tail. Everything has two tails, not one. That’s two separate distributions in a binomial distribution. There could be more.
Cognition is logarithmic, so those tails would likewise be logarithmic.
Books are graphs. Curriculums are graphs. Presentation forces orderings. Each their own long tails.
AnnMaria, The data in the sense of the nth data item has its own order of importance. Since a normal can’t be estimated until the 20th data item, and a normal won’t actually be normal until the 36th data item, there is an ordering by importance. This ordering of discipline-specific knowledge changes as one is taught more of the discipline, more of the nuance.