In which I string together a series of videos, links and text that use Mario as a base for Science. First is Mario and the Many World Interpretation of Quantum Physics
…So what’s this about quantum physics? Oh, right. Well, I kind of identify the branching-paths effect in the video with the Everett-Wheeler “Many Worlds Interpretation” of quantum physics. Quantum physics does this weird thing where instead of things being in one knowable place or one knowable state, something that is quantum (like, say, an electron) exists in sort of this cloud of potentials, where there’s this mathematical object called a wavefunction that describes the probabilities of the places the electron might be at a given moment. Quantum physics is really all about the way this wavefunction behaves. There’s this thing that happens though where when a quantum thing interacts with something else, the wavefunction “collapses” to a single state vector and the (say) electron suddenly goes from being this potential cloud to being one single thing in a single place, with that one single thing randomly selected from the different probabilities in the wavefunction. Then the wavefunction takes back over and the cloud of potentials starts spreading out again from that randomly selected point.
But, we can kind of think of the multi-playthrough Kaizo Mario World video as a silly, sci-fi style demonstration of the Quantum Suicide experiment. At each moment of the playthrough there’s a lot of different things Mario could have done, and almost all of them lead to horrible death. The anthropic principle, in the form of the emulator’s save/restore feature, postselects for the possibilities where Mario actually survives and ensures that although a lot of possible paths have to get discarded, the camera remains fixed on the one path where after one minute and fifty-six seconds some observer still exists.
This video is the winner of the Mario AI competition, in which an algorithm is tasked with completing Mario all by itself. Here, the many worlds are not actualised but are predetermined by the code.
There's also the guy who graphed out the change in gravity over the years and came upon the conclusion that the gravity in Mario is nearing towards a more realistic gravitational pull, similiar to earth. There's also the physics paper (done as an in class project, but still) Acceleration Due to Gravity: Super Mario Brothers which looks at the decline in gravitational forces in Mario over the years as it nears something similiar to earth.
Once we knew the time, we needed to figure out the distance Mario fell in each game. We used a screen shot of Mario next to the ledge he fell from in each game, and found the height of Mario and the ledge in pixels. According to Wikipedia, Mario is "a little over five feet tall.", so we used 5 feet, or 1.524 meters, as Mario's height. We used the formula:
HeightMario[m] / HeightMario[pixels] = Distance[m] / Distance[pixels]
Distance = (HeightMario[m] / HeightMario[pixels]) x Distance[pixels]
Once we had the distance Mario fell in each instance, we were able to use the formula
s = s0 + v0t + ½ at2
to find Mario's acceleration in each game. Mario was in free fall in each case, so this acceleration was equal to gravity.
Moving further up the ladder of unneccessary but totally valid science is mapping the gravitational pull on the various levels in The Physics of Super Mario Galaxy to see not just how implausible the game is but how hard it would be to recreate it. I should add that this game is still in my top 5.
So, if you want to get earth-like gravity on the surface of a 230-foot-diameter sphere, you’re going to need about 1.8 * 10^14 kg of mass. This is not that much! Checking Wikipedia I find even the smallest moons and dwarf planets in the solar system get up to about 10^20 kg. in fact, 2 * 10^14 kg is just about exactly the mass of Halley’s Comet. This sounds attainable; other characters are shown hijacking comets for various purposes elsewhere in Mario Galaxy, so no one will notice a few missing.
Meanwhile, Wikipedia’s formula for escape velocity for a planet ( sqrt( 2GM / r ) ) tells us that escape velocity from this planetoid will only be about:
sqrt((2 * G * (1.8043906 × (10^14) kilograms)) / (115 feet)) = 26.2110511 m / s
Which is about 60 MPH. So the cannon stars Mario uses in the video to move from planet to planet should work just fine. (Although platforms might not work so well, at least not tall ones; since the planetoid is so small, you’d only have to get about 45 or 50 feet up off the ground before the amplitude of gravity is halved. Actually gravity will fall off so quickly on the planetoid that there would be a noticeable gravity differential between your feet and your head: a six-foot-tall person standing on it would experience about 1 m/s^2 more acceleration on their feet than their head. So expect some mild discomfort.)
So, we know the density; the ratio of electrons to protons has to be 1 (Otherwise the white dwarf would have an electric charge. Of course, if you can somehow find a positively charged white dwarf somewhere, you can reduce your required pressure noticeably!); and everything else here is a constant. Plugging this in we get:
P = ( (pi^2*((6.626068 * 10^-34 m^2 kg / s)/(2*pi))^2)/(5*(9.10938188 * 10^-31 kilograms)*(1.67262158 * 10^-27 kilograms)^(5/3)) ) * (3/pi)^(2/3) * (1.00023843 * 10^9 kg/m^3)^(5/3) = 9.91935718 × 10^21 kg m^-1 s^-2
Or in other words, if we neglect the assistance that the white dwarf material will be providing in holding itself together in terms of gravitational pull, the shell for our planetoid would need to be able to withstand 9.91935718 × 10^21 Pascals of pressure in order to keep all of that degenerate matter in. That’s a bit of a problem. Actually, it’s more than a bit of a problem. It’s most likely impossible.
Which then brings me to Paper Mario. The joke being that it's a game long Flatland reference. Which I had every intention of reading and comparing the two. There's an annotated version of the book at my favourite bookstore, which I've been meaning on buying for several years. I think that same copy is sitting in the same shelf, waiting for me and mocking me. I guess this admission of guilt is me realising that I'm just never going to get around reading it. Shame. Anyway, the point being that it's another way in which Mario, being the broad stand in reference for interpretating the physical world. In a perfect world I would have finished the game while reading Flatland and a tidy comparison would have occured. Instead you just get some hazy recollections and a bit of whinging.
Or you could read Clive Thompson talking about this aspect of the game as well:
Tt completely renews the age-old Mario conceits -- like the bricks, the tubes, the platforms. They're all here, except that often they're concealing new stuff only visible in 3-D. I found tons of hidden areas lurking behind boulders, and secret enemies "inside" objects that appeared to be solid blocks in 2-D.
In essence, the game instills the exact mentality with which a good mathematician, geometrist or theoretical physicist views the world. Seriously, they ought to make this thing mandatory in grade 3 math; it's that good. Better yet, Nintendo includes several gorgeously sharp in-jokes that directly reference Flatland. At one point, you rescue a 2-D man who's trapped in 3-D, unable to interact with his normal plane of existence (which is similar to the basic plot of the novel). When Mario is being trained to use a new power, his trainer tells him to "hit the 2 button." Then he mutters that while Mario himself probably won't know what a "2 button" is, "the being that watches over you from another dimension" -- i.e. the game player -- will.
Mario 3D Land for the 3DS seems to take the best parts of Paper Mario and use the 3D slider as a gameplay mechanic. It seems like the proper way to explore this idea, although it'sa bit of a shame that it's not pushed to the conclusion it should be, based off the screengrab and video. Not that I intend on playing it. Or getting a 3DS. But still. I very badly need to download Fez and play that instead.
Yet, while all of these are fascinating, none of them have the same existential punch as the Goomb'a Lifetime.