24 February, 2022


I was told today that the number 45 was ruined by Trump. I found this difficult to parse at first — to me, a number is not ruined just because it has an association with something bad. But I think that there is more to it than just that. The weather service predicts rain as she'll come home from work today. As the day started (just after midnight here), Russia began an invasion of Ukraine. It really isn't the greatest start to Katherine's 45th birthday for several reasons. (And she was so looking forward to any day that represented a multiple of 5, her favorite number.)

At first, I pointed out Grover Cleveland. Sure, Trump is widely said to be the "45th" president. But since Cleveland was both the 22nd and 24th president (being elected both just prior to and immediately after the little-talked-about Benjamin Harrison), that means that Trump is only the 44th person to take on the mantle of the presidency overall.

Then, to bolster my claim, I remember the old claim that one person was President temporarily. David Rice Atchison has a plaque affixed to a statue in Plattsburg, Missouri, which states: "President of United States One Day". This refers to March 4, 1849, when he was chosen as president pro tempore in the Senate where he resided. The Senate's own website tells the rest of the story:

On March 2, 1849, Vice President George M. Dallas took leave of the Senate for the remainder of the session and the Senate elected Atchison as president pro tempore. ... Until the adoption of the Twentieth Amendment in 1933, presidential and congressional terms began and ended at noon on March 4. In 1849 March 4 fell on a Sunday. On the morning of March 4, President James Polk signed the last of the session’s legislation at the White House and at 6:30 a.m. recorded in his diary, “Thus closed my official term as President.” The Senate, having been in session all night, adjourned sine die at 7:00 a.m. President-elect Zachary Taylor, in observance of the Christian Sabbath, preferred not to conduct his inauguration on Sunday, March 4, and the ceremony was delayed until the next day. On Monday, March 5, Taylor took the oath of office on the Capitol’s east front portico and the transition of power was complete.

But if President Polk’s term ended on March 4 at noon, and Zachary Taylor was not sworn in until noon on March 5, who was president on March 4? Under the Presidential Succession Act of 1792 the Senate president pro tempore immediately followed the vice president in the line of presidential succession. Had Atchison been president from noon on March 4 to noon on March 5?

If the answer is yes, then, I at first thought, that might save the number 45. But then I realized that, if Athison had indeed served as president, then that would again make Trump the 45th person to take the role, since Cleveland served twice!

Thankfully, the answer is no. But I'm starting to suspect that this won't appease someone who feels that 45 is ruined anyway.

What, then, can rehabilitate 45? In the eyes of someone who loves the number 5, a strong contender is the fact that 45 is the conjectured value of the Ramsey number R(5,5). What is the least number number of guests that you must invite in order to ensure that at least five guests will know each other or at least five guests will not? Mathematicians are not sure, but we suspect it is 45.

To be slightly more general, R(m,n) gives an answer to the question of the least number of guests you'd need to invite in order to ensure that at least m guests know each other, or that at least n guests don't know each other. R(5,5) is known to be between 43 and 49 inclusive, and is conjectured to be 45. (See OEIS entry A120414 on Conjectured Ramsey Numbers R(n,n).) (To be even more general, R(m,n) refers to the idea that "complete disorder is impossible"; given a sufficiently large set, order will appear among its proper subsets. This is the first basic finding in Ramsey theory, which focuses on order amid disorder.)

Figuring out these numbers are deceptively difficult. Joel Spencer writes about Paul Erdős quip: if aliens come and demand to know the value of R(5,5) or they will destroy Earth, we should marshal all of our computers and mathematicians in an attempt to find the value. But if they demand to know R(6,6), we're better off attempting to destroy the aliens. In fact, Ramsey numbers appear to be difficult to calculate even with hypothetical quantum computers.

If 5 is a great number, and the most exciting parts of mathematics are the parts that lie just on our horizon, and if finding order within disorder is one of the enjoyable parts of being an artist, then R(5,5) must be a special case of representing something that might make up for Trump's taint. While we can't guarantee that it is 45 (some suspect 43 instead), it stands out as something that should make Katherine's 45th birthday special.

Happy birthday, Katherine. <3

I'll close with a poem by Ernest Davis entitled The Ramsey Number R(5,5):

There are fans, among math buffs, of e and of π.
The ratio golden has legions who sigh,
In reverent awe at its beauty ideal.
Euler's γ has got its own quirky appeal.
But what makes me feel tingly, aroused, and alive
Is the mystical integer R(5,5). [Read "R of five five"]

Like Batman and Robin, its everyday face
Is a secret identity quite commonplace.
It's an integer, experts on graph theory state,
At least 43 and at most 48.
And combinatorists laboriously strive
To narrow the bounds known for R(5,5).

It's a quite element'ry idea to define
(Though I don't want to try that in meter and rhyme).
A short, simple program in Python or C
Has no trouble at all finding R(3,3)
But the stars in the sky will no longer survive
Ere it prints out the value of R(5,5).

Said Erdos: "If aliens from far outer space
Want to know, or they'll wipe out the whole human race
If we join all our forces, perhaps we'll contrive
To tell them the value of R(5,5).
But we'll certainly be in a hell of a fix
If they ask for the value of R(6,6)."

15 February, 2022

A Long History of Gaming

I no longer have any of the video games I grew up with. Some were gifted to others; some were lost as I moved from place to place. Still others may very well be hidden in an obscure box I haven't opened in a decade or so. I played countless games on the NES, Game Boy, SNES, GBA, Playstation, GameCube, PS2, DS, Wii, 3DS, Wii U, and Switch, let alone the hours played on Steam and GOG.

Today, Nintendo released an app that lets you go back to your old 3DS and Wii U gaming memories. It was fun to look back on where I spent most of my time.

My 3DS gaming appears to have been dominated by single player games, with the exception of Tri Force Heroes, which I played through entirely with Katherine Hess and Jon Bockman. I apparently spent 94 hours in Animal Crossing alone, with another 61 hours in Bravely Default.

Not all of my 3DS memories are positive. There was a period of time where my personal life was very, very negative, and I used my 3DS as an escape mechanism — someplace I could go to avoid the harsh reality of life around me. Much of that experience occurred with Ghost Recon, which ended up with 82 hours of emotionless escape gameplay. I'm grateful that later games on the system represented much better times in my life, though apparently I didn't spend as much time with many of those later games as I did with Ghost Recon.

My Wii U gaming experience is a surprise to me: I would have guessed that Splatoon would have topped this list. But instead the top two positions go to Advance Wars: AW2 received 124 hours of my time and AW1 113 hours. These were both nostalgia plays for me — I feel certain that I put even more hours into the original games, and probably an even greater amount into Advance Wars: Days of Ruin on the DS. Meanwhile, poor neglected Splatoon had only 80 hours listed. (If you count Splatoon 2, this number becomes much, much higher, but that's on the Switch.)

The Wii U was a system that I played often with siblings, but I ended up playing mostly on their Wii U system when I visited, rather than on my own. This means the number of hours associated with Smash Bros., Nintendo Land, and several other local multiplayer games are undercounted here. The big surprise for me was that Super Mario 3D World didn't make the top three played games. I feel like I spent entire months of my life working on Champion's Road with Katherine. (Later, on Switch, I replayed 3D World online with three friends and have almost 100% completed it (still missing a Champion's Road finish with Toad).) I also feel like Mario Kart 8 must be missing many of the hours I spent online playing it, but maybe I'm combining in my head the portion of plays I've done on the Switch instead.

When the Switch came out, everything changed for me. Breath of the Wild alone took up entire days of my life when it came out. I can recall playing late into the evening, still playing in the morning when my partner left for work, and not yet finishing my gaming session by the time she returned home. I was obsessed.

In 2019, I logged 706 hours in 62 games on Switch. Considering that I spent a lot of time on StarCraft and a number of Steam games, this is fairly significant. My most-played games were Civilization, Slay the Spire, and WarGroove.

The following year, I became deathly ill, and my game playing reduced commensurately. In 2020, I played 535 hours on Switch in 39 games. My most played titles were Animal Crossing (209 hours by itself in 2020!), Killer Queen Black, and Divinity: Original Sin 2.

2021 had another 546 hours played in 35 games. Surprisingly, Animal Crossing continued to top the list, with Monster Sanctuary and Bug Fables not far behind. Killer Queen Black did not make the top three most played on Switch, but this is probably because I bought it on Steam and Stadia, opting to play on those platforms instead.

Unfortunately, these lists don't take into account the time I spent in 2018 nor in 2022 so far on Switch. I don't see a way to look at past play history in the settings, though the most recent 20 games played do get listed under my play activity. A glance there shows Killer Queen Black at 155+ hours, Grandia HD Collection at 70+ hours, Animal Crossing at 285+ hours, Monster Train at 55+ hours, & Loop Hero at 50+ hours. These are just the games with 50+ hours that exist in the last 20 games I've booted up on the system — I won't bother going through the trouble of going the full list of all 246 games I have on Switch, as that would take far too long. I'll instead just wait for whenever Nintendo decides to create an app that will showcase my Switch gaming memories.

14 February, 2022

A Valentine's Day Card

Giving something meaningful each Valentine's Day has become a sort of tradition between Katherine and myself.

This year, Katherine has truly outdone herself. Her handmade card quotes Carl Sagan's Demon-Haunted World, showcasing a principle that has guided my life ever since I first became a skeptic some twenty odd years ago. It's a principle that I've held close to my being and that has been at the heart of many conversations Katherine and I have about so many different things. She writes that the balance between openness to new ideas and ruthless skepticism is a dance where each of us often switch sides in our cooperative search for truth. Alongside the quote, she has made literal pinpricks of light, referencing the lone lights in the darkness that rational thinking helps us to uncover. These represent the deep truths that lie within the deep nonsense — the very same deep truths that we slowly aim to uncover as we dig through the arguments about the problems of our time.

Upon opening the card, we see that there is yet another layer to the quote on the cover. She says that I brighten her life, implying that, at a different level, the darkness of the card itself also represents our lives, separated, and the lights we have managed to uncover are the shining moments we have made in the course of our relationship. All of this is said within the confines of a Sierpinski triangle, a fractal shape of crystalline regularity that reveals yet another layer of meaning: here, the balance is in the construction of the shape, with its open spaces throughout (literally it has an area of 0) and the numerous lights that we nevertheless uncover via the application of strict logical rules within the triangle itself. It is a saga that shows us the things we can count on even within a field where nothing can be counted on. Here, she implies, is where our love resides.

On yet another layer of interpretation, we see that the lights themselves overwhelm the structure of the sierpinski triangle. The triangle itself is drawn in a dark color that is difficult to see on the black background even with the lights turned off — once they are turned on, it becomes impossible to see the logical order belying them. Only the front of the card, written in reflective ink, remains visible to the human eye when the lights wash out the scene on the dark void itself. Yet even then it is a difficult thing to make out: you must struggle to see the path before you. Ironically, it is the brightness of the lights, not the darkness of the background, that makes this so difficult. This, again, is in reference to our relationship: so many of our brightest moments sometimes overshadow our typical moments in life, and make it that much more difficult to see the structure beneath it all when we reside day by day.

I am completely taken aback at the various layers of meaning weaved into a single card. So many of our conversations over the past years point back to many of the points made on the card itself. I am sure that, to any other person, this must look just like a black card with lights embedded within. But, to me, I see the threads of our relationship here: the discussions and presented arguments, the successes within a background of seeming impossibility, and the simple joys that overwhelm even the lowest of lows in a relationship of this magnitude.

I don't know how I can top this, but I will have to up my game next year.

See also the Puzzle Portraiture she made for me, the screen print of The Tuft of Flowers, & her drawing of Jasper and the Amiibo. You can see more of her work at KatherineHess.com.