Dual Frontier Analysis

I. Introduction, with Example in Population and Area of Countries and Country-Like Entities

In this post, I introduce a way of looking at correlated data I will term “dual frontier analysis”.

What motivates this idea? Often, we like to compare entities via a certain “rate”, how much of one quantity there is for a unit amount of another quantity, across a set of entities. One example of this is population density. But if you, like me, have glanced at a population density chart of, say, the countries, you may have had one of the same first reactions as I have had: “the top of the chart is pretty much just a listing of city-states!” You might then proceed with questioning whether it really makes sense to compare this quantity for city-states versus for “more normal” countries. Maybe we want a way of looking at this data that better captures what our prior idea of what an “impressively high” or “impressively low” population density is: Bangladesh’s population density definitely “feels” more impressive, even if it’s not as numerically high as Bahrain’s.

There are probably solutions to this problem involving designing a prior distribution of likeliness of one variable in terms of the other, and then comparing percentiles along respective distributions, but going down this path requires crunching a lot of numbers and, more importantly, extensive knowledge in the ideas being analyzed already.

Here is another solution: output the data on the dual frontiers. If two attributes are somewhat correlated, a scatterplot for entities in these attributes probably looks something like this.

scatterplot_example

What we’re outputting is this.

scatterplot_example_2

That is, we’re outputting entities for which no other entity has both more of one attribute and less of the other attribute than this entity.

In this way, we would capture, for instance, the country with the highest population density among countries of similar size. (We could even extend this to become a quantitative metric for entities not on this frontier: the percentage of the way an entity is from one frontier to the other.)

One could also look at an entity in this data and compare it to neighboring entities and see how much larger in one attribute another entity must be to be larger in the other attribute as well (as otherwise, this entity would also be in the frontier), which shows how prominently impressive a particular entity is in the ratio.

Continue reading “Dual Frontier Analysis”

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Periodic World

Here’s a map of the world, with countries and country-like entities given periodic-table-like one- or two-character symbols.

periodic_world.png

My Hobby

subtly altering world maps in ways that only map geeks notice

messed-up-world

And if you are in fact a map geek, one of the tiniest changes on the map above may very well be one of the first discrepancies you notice. You might even question if it’s too small to show up at this resolution. It’s not too small.

Answers to the MIT Campus Scavenger Hunt

This post contains the answers to the MIT scavenger hunt I posted 40 months ago, excepting items in the 16 advanced item expansion known as the “Navigator’s Quest”.

I decided to end this due to changes that have occurred to MIT’s campus, the rate of which has been much speedier than I could have imagined 40 months ago. Buildings have been demolished, buildings have been built, buildings have been renovated, stuff has moved around, and permissions to various locations have changed such that original foundational ideas of the hunt could no longer hold. The Picture Scavenger Hunt, on the other hand, I still plan to run indefinitely, and it now has an established mechanism for pictures that become outdated.

In any case, congratulations to jakobw for the most items found during the duration this hunt was up.

As for the answers, long story short:

MITscavanswers

I decided to not chart locations that are answers to 39 here on a post on the internet. Ask me in real life for an answer to 39.

There are of course probably many more locations that several of these items can be found at than plotted in the map above.

Notes:

For item 1, solidly shaded buildings have the floor numbered 0 aligned with the ground. I also accepted buildings just outlined in the map above, though, as those are cases where ground is between floors numbered 0 and 1, but the floor numbered 0 is closer to the ground level than the floor numbered 1.

For item 8, Senior House was my original intended item. When I was designing the hunt, I momentarily forgot about graduate dorms when writing this item. I was later informed that at least Edgerton House among the graduate dorms have both A/C and elevators. Eventually, Senior House closed, but Edgerton House does still remain, so this item had an answer through the end of this hunt, despite this not being true of the set I was originally thinking of.

I parenthesized the Building 8 answer for item 9, even though I accepted it, because Building 1 is a case where the building is the fairly indisputable central home of a course, whereas Course 8 has substantial portions outside Building 8.

For item 20, there’s many tiny buildings that satisfy the item that I did not bother to mark on the map above. Probably my favorite case of this is Building W55, whose bottom doesn’t even touch the ground. (I was actually fairly sad they did not number its singular floor 2, so that MIT could have the amusing feature of containing a building whose lowest floor is numbered 2.) Of course, Building W55 hadn’t been built yet when I published this hunt. Building 34’s lowest floor is in fact 1 because what lies underneath it is actually not grouped with 34. This is in fact the reason for one of the answers to item 33.

Item 21: the Pharos color printer is in W20-575. This is a quite useful thing to know as an MIT student. When I wrote this hunt, though, the Pharos color printer was in 12-182, a room that no longer exists.

Item 24: the elevator services floors 4, 5, and 6. Without additional permissions, though, travel is restricted to oscillating between 4 and 6.

Continue reading “Answers to the MIT Campus Scavenger Hunt”