I made the following chart which gives an array of all the Bayer-designated stars of each of the 88 constellations (in other words, the ones labeled with Greek letters), with the lightness of the fill indicating the brightness of the star and the hue of the fill reflecting the color of the star. There’s quite a few interesting patterns that can be noticed from this method of organizing stars (anyone want to start categorizing “blue constellations” and “red constellations”?).

# Month: January 2012

## List of All Stars Brighter than 3.00 Magnitude Categorized by Bayer Designation

Alpha (43)

Canis Majoris: -1.46 (Sirius)

Carinae: -0.72 (Canopus)

Boötis: -0.05 (Arcturus)

Centauri: -0.01

Lyrae: 0.03 (Vega)

Aurigae: 0.08 (Capella)

Canis Minoris: 0.34 (Procyon)

Eridani: 0.45 (Achernar)

Orionis: 0.58 (Betelgeuse)

Aquilae: 0.76 (Altair)

Tauri: 0.87 (Aldebaran)

Virginis: 0.98 (Spica)

Scorpii: 1.06 (Antares)

Piscis Austrini: 1.17 (Fomalhaut)

Cygni: 1.25 (Deneb)

Leonis: 1.36 (Regulus)

Crucis: 1.40 (Acrux)

Geminorum: 1.58 (Castor)

Persei: 1.79

Ursa Majoris: 1.81 (Dubhe)

Trianguli Australis: 1.91 (Atria)

Pavonis: 1.94

Ursa Minoris: 1.97 (Polaris)

Hydrae: 1.99 (Alphard)

Arietis: 2.01 (Hamal)

Andromedae: 2.07 (Alpheratz)

Ophiuchi: 2.08 (Rasalhague)

Coronae Borealis: 2.22

Cassiopeiae: 2.24

Lupi: 2.30

Phoenicis: 2.40

Cephei: 2.45

Pegasi: 2.49 (Markab)

Ceti: 2.54

Librae: 2.61

Serpentis: 2.63

Columbae: 2.65

Muscae: 2.69

Arae: 2.84

Hydri: 2.86

Tucanae: 2.87

Canum Venaticorum: 2.89

Aquarii: 2.95

Beta (34)

Orionis: 0.18 (Rigel)

Centauri: 0.61

Geminorum: 1.16 (Pollux)

Crucis: 1.25

Tauri: 1.65 (El Nath)

Carinae: 1.67 (Miaplacidus)

Gruis: 1.73 (Alnair)

Aurigae: 1.90

Canis Majoris: 1.98

Ceti: 2.04

Andromedae: 2.07

Gruis: 2.07

Ursa Minoris: 2.07 (Kochab)

Persei: 2.09 (Algol)

Leonis: 2.14 (Denebola)

Cassiopeiae: 2.28

Ursa Majoris: 2.34 (Merak)

Pegasi: 2.44 (Scheat)

Scorpii: 2.56

Leporis: 2.58

Librae: 2.61 (Zubeneschamali)

Arietis: 2.64

Corvi: 2.65

Lupi: 2.68

Ophiuchi: 2.76

Eridani: 2.78

Herculis: 2.78

Draconis: 2.79

Leporis: 2.81

Hydri: 2.82

Trianguli Australis: 2.83

Arae: 2.84

Canis Minoris: 2.89

Aquarii: 2.90

Gamma (20)

Orionis: 1.64 (Bellatrix)

Velorum: 1.75 (Regor)

Geminorum: 1.93

Leonis: 2.01

Andromedae: 2.10

Cassiopeiae: 2.15

Centauri: 2.20

Cygni: 2.23

Draconis: 2.24

Ursa Majoris: 2.41 (Phad)

Corvi: 2.58

Aquilae: 2.72

Virginis: 2.74

Lupi: 2.80

Pegasi: 2.83 (Algenib)

Trianguli Australis: 2.87

Persei: 2.91

Eridani: 2.97

Sagittarii: 2.98

Hydrae: 2.99

Delta (12)

Canis Majoris: 1.83 (Wezen)

Velorum: 1.93

Orionis: 2.25 (Mintaka)

Scorpii: 2.29

Leonis: 2.56

Centauri: 2.58

Cassiopeiae: 2.66

Sagittarii: 2.72 (Kaus Meridionalis)

Ophiuchi: 2.73

Capricorni: 2.85 (Deneb Algiedi)

Cygni: 2.86

Corvi: 2.94

Epsilon (13)

Canis Majoris: 1.50 (Adhara)

Orionis: 1.69 (Alnilam)

Ursa Majoris: 1.76 (Alioth)

Sagittarii: 1.79 (Kaus Australis)

Carinae: 1.86

Centauri: 2.29

Scorpii: 2.29

Boötis: 2.35

Pegasi: 2.38 (Enif)

Cygni: 2.48

Virginis: 2.85

Persei: 2.90

Leonis: 2.97

Zeta (10)

Orionis: 1.74 (Alnitak)

Puppis: 2.21 (Naos)

Ursa Majoris: 2.23 (Mizar)

Ophiuchi: 2.54

Centauri: 2.55

Sagittarii: 2.72 (Ascella)

Herculis: 2.81

Persei: 2.84

Tauri: 2.97

Aquilae: 2.99

Eta (8)

Ursa Majoris: 1.85 (Alkaid)

Centauri: 2.33

Ophiuchi: 2.43

Canis Majoris: 2.45

Boötis: 2.68

Draconis: 2.73

Tauri: 2.85 (Alcyone)

Pegasi: 2.93

Theta (5)

Scorpii: 1.86 (Sargas)

Centauri: 2.06

Aurigae: 2.65

Carinae: 2.74

Eridani: 2.88

Iota (5)

Carinae: 2.21

Aurigae: 2.69

Centauri: 2.75

Orionis: 2.75

Scorpii: 2.99

Kappa (3)

Orionis: 2.07 (Saiph)

Scorpii: 2.39

Velorum: 2.47

Lambda (3)

Scorpii: 1.62 (Shaula)

Velorum: 2.23

Sagittarii: 2.82 (Kaus Borealis)

Mu (2)

Velorum: 2.69

Geminorum: 2.87

Nu (0)

Xi (0)

Omicron (0)

Pi (3)

Puppis: 2.71

Sagittarii: 2.88

Scorpii: 2.89

Rho(1)

Puppis: 2.83

Sigma (2)

Sagittarii: 2.05 (Nunki)

Scorpii: 2.90

Tau (2)

Scorpii: 2.82

Puppis: 2.94

Upsilon (2)

Scorpii: 2.70

Carinae: 2.92

Phi (0)

Chi (0)

Psi (0)

Omega (0)

## One Year of Minesweeper

On 23 January 2011 (for the record, Rhyzyxian IA.2FA), I downloaded Arbiter (which is one of the Minesweeper clones accepted by the official Minesweeper records (ironically, they don’t accept the original one installed with Windows because it’s too easy to cheat on that)), so that I could join the professional Minesweeper world. I really like Arbiter among the clones because it provides tons of statistics…possibly too much. In any case, here’s some of my statistics over the past year. I didn’t include the daily average for expert, because with the very low number of expert games I play, the data is very erratic.

## Conditional Probability and the Fermi Paradox

Certainly most of you have stared into the skies and wondered if somewhere light-years away some form of life is doing what you are doing (or maybe they’re narcissistic enough to not care whether there’s another intelligent life form out there). Well, the thing is, most people suggest that there’s a very high probability, as might be calculated from their inputs into the Drake equation, for life to exist elsewhere in the universe. And yet…we still have not found any. Why? The universe was miraculous enough to bring us to life, so why would the similar occasion not happen in many places in the universe?

I believe the best way to communicate my opinion is through conditional probability. First, an analogy. Suppose there’s a rare but serious disease that 0.01% of the population has. There happens to be a test developed for the disease that is incredibly accurate—in fact, is has a 99% chance of reporting the correct result given a particular patient; if they have the disease, there’s only a 1% chance that this hypothetical test fails to detect this disease. If they don’t, there’s only that 1% chance that the patient should end up being falsely alarmed by the test. Sounds like a good test right?

So you go to take the test…and it reports that you have tested positive for the disease. You are in shock. What has just happened? Can you only hope for that 1% chance that the test is wrong?

Thankfully, yes. Because the chance that you do not have the disease is in fact not 1%. Take into account all possibilities that could be happening: either you have the disease and test positive or you don’t have the disease and test positive. You have the disease and test positive with a 0.0001(0.99)=0.0099=0.99% probability. You don’t have the disease and test positive with a 0.9999(1-0.99)=0.9999(0.01)=0.009999=0.9999% probability. You actually have a higher probability of not having the disease than having it by that small sliver of a percentage (50.2488%). Although if this is truly a serious disease, even 50% might not be that great to learn about, but it certainly is many times greater than that 1% chance. This is the thing about conditional probability; specific information can narrow possibilities down substantially and thus make probabilities different from what may be intuitively expected; in this case, one has to realize that the 1% of the population occupies (only) 50% of the positive test.

But surely conditional probability isn’t messing with the existence of another civilization?

Not so. Remember how it seems like a miracle that there is life in a universe, and hence there should probably be other life? Well, what’s the probability the life exists in a universe? Small?

Well, let’s change that question a bit. What’s the probability that given a universe exists, life exists in it?

Wait, what has changed? Oh, potentially quite a bit. Because the probability that given a universe exists, life exists in it is…1.

Let’s consider the cases of life existing and life not existing and see what happens. What is the probability of a universe existing given that life does not exist in it?

Think about it.

Life is the only thing that can recognize and verify a universe’s existence. In fact, only a subset of life can: the conscious portion. (I would argue that consciousness is actually a prerequisite for a reasonable definition of life.) Suppose multiple universes existed, but many of them had no life in them…let’s call them sterile universes. If information is leaked from one universe to another, the definition of a universe is violated. What would life from a non-sterile universe perceive regarding such potential sterile universes? Well, they’re clearly nonexistent, as there’s nothing to trigger such life forms to believe in the existence of them. There are zero ways to prove such a universe’s existence. Now realize here, that the following might not be the case, since we might be dealing with an indeterminate form, but it is conclusively literally impossible for no life to exist in an existent universe. If a universe exists, it contains life. Existence implies life.

So in actuality, it would actually be more of a miracle if life didn’t exist, because it is impossible to have a lifeless universe, unless one argues that the abovementioned indeterminate form resolves otherwise after taking d/dx of the numerator and the denominator of the existence of the universe, or something. It is a reasonable thing to consider, but as I mentioned, there could actually be sterile universes all over the meta-universe, but they by all reason nonexistent to us. And thus, the burden of the miracle of life is placed not on the first civilization in a universe, but in a similar form on the second.

Now think about this second civilization. Try to apply this existential manipulation once more and see what happens. I’ll tell you right now that following this reasoning I’ve landed on some amazingly absurd paradoxes within themselves.

I would say that wondering about the universe is like integrating functions with negative integer exponents of the integrated variable. We could divide a universe up into all sorts of philosophical pieces, and integrating them one by one, we get to -6/x^4, 2/x^3, -1/x^2, 1/x; we’re used to thinking normally, seeking the definition of unknown under our established line of logical “politeness.” But once we start thinking about the “all,” the “everything,” we integrate ourselves from the 1/x, the universal level, to a level strange to us, where our nice hood of logic breaks open into a strange logical chaos, sending neuronic doubt through all our functions. If we never come to naturalize what might occur out of this tailgrating of logic with the universe’s secrets, we ride along the finest and most well-integrated familiar line of logic, the universal level of philosophy, the 1/x level. And though we solve paradoxes, there will be a new paradox that jumps out at us somewhere down the line, probably smaller. We will never absolutely rid ourselves of paradox, and only approach perfect logic asymptotically. And if we do it properly, we will also enjoy and accept such paradox as paradoxically integral to non-paradox, that out of the greatest of wonders of the 1/x level of thinking, we have asymptotically reached the absence of paradox while integrating along our way an infinitude of paradox accumulated.

## Which states are best at electing good presidents?

It’s election time, so I thought that I might post about something election-related.

As some of you know (I didn’t take APUSH, so if I’m ever wrong with these facts, do correct me), Nixon won his second election in a landslide. As Nixon in his second term turned out to be the president some considered the worst president the United States has ever had, and Massachusetts was the only state that didn’t go for Nixon (well, so did the District of Columbia, if you consider that a state), there was a popular bumper sticker that circulated after Nixon’s resignation that read “Don’t blame me—I’m from Massachusetts.” Well, according to data I collected, Massachusetts not only made the evidently good choice of not choosing Nixon, but also has the best record of choosing good presidents in United States history (and Alaska has the worst).

Here’s what I did. I took the latest Times, CSPAN, Siena, and USPC polls of ranking the presidents in the history of the United States and took the average ranking of each president (for example, Lincoln is on average considered the best president we’ve had, while Buchanan, the one right before him, is on average considered the worst (of course, in my opinion, I don’t agree with these; I believe that the best president we’ve had is Polk and that there were many presidents worse than Buchanan, say, the earlier Harrison or Fillmore; of course, I’m not a historian, so one should take my commentary with a larger grain of salt than you take historians’ (remember, you should *always* take anyone else’s opinion with a grain of salt; always question; never blindly follow anyone else’s advice (yay massive parenthetical comment stack)))). (Wow, that was quite a tangent of parenthetical comments. Back on topic…). Then, I took data on the choices of each state in voting for presidents in all the elections in the United States’ history, and I assigned scores based on how well the presidents that they chose were ranked (which is a point gain for a president in the upper half of the ranking and a point loss for a president in the lower half of the ranking, and has a magnitude proportional to how extremely good or extremely abominable they were). In the case of split votes, I assigned the proportional percentage of the point gain or point penalty. Then, I summed up the point deviations over all elections, and came up with a final score for each state that represents how good they are at electing presidents that people end up liking…and it turns out that Massachusetts does indeed end up on top, so not electing Nixon was not the only good decision they made.

I represented the data in the map below, where the lighter the shade of a state, the better they were historically at electing good presidents.

Now you might ask if there’s a bias for states that joined the union earlier, since they seem to be generally lighter. Keep in mind that although they had more time to accumulate point gain, they also had more time to accumulate point penalty, so the two should cancel out. Instead, what’s actually happening is that historians seem to think that the earlier presidents of the United States were generally better than the later presidents. If you say that’s not the fault of the states, well, that’s not quite true, since the states that joined more newly helped to elect these new presidents. Whether there’s hindsight bias on the side of the historians is a different question, but that aside…listen to Massachusetts!

UPDATE: There is a majorly fancier version of this analysis that takes into account more recent elections over at wywing.