S.2. Pointless Jolly Christmas Stuff: The Googology of Santa's Second Elfing

"There comes a time in every young googologist's life when he has to come to terms with the decision to gradually morph into an elf hunter while all his friends and loved ones watch in dismay."
—Hugo Steinhaus, Santa prophet extraordinaire


Christmas is finally here. It's a time where we can exchange presents to show how much we care about each other, a time where we can bake delicious cookies, a time where we get a tree from a farm and put it in our house to decorate, and a time where we learn as much as we can about the lore of Santa Claus. But most of all, it's a special holiday for googologists, because it's the best time there is to learn about the mysteries of how Santa Claus can deliver presents to seven billion people over the course of one night. If Santa does deliver presents over one night, which he obviously does, then seven billion people divided by eight hours equals 243,000 people per second. And how does he deliver presents at this impossible rate you may ask? Like the great Ronald Graham once said, that's a hell of a mystery that inexplicably nobody thought was a mystery but really needs solving, and today we will solve this mystery.

The Conundrum of Santa Claus's Lightning Delivery Speed

Everyone is familiar with Santa, who delivers presents to everyone in the world over the course of one night. Unfortunately, these days most people think of the amazing stories of Santa's exploits as fiction used to entice eager children rather than stone hard facts. Typically, parents will tell kids everything they need to know about Santa Claus, but as their kids grow older, they're like "fuck the things I said about Santa" and say that they give their kids presents rather than that jolly white-bearded man. I really wish that this is parents playing a joke on children rather than actually being deluded with Santa's reality. I really, really wish that they were elaborate pranksters, but I can tell through their cynicism alone that they aren't. Mysterious forces mercilessly sucked out of their minds the fact that Santa was real all along! Who else could deliver presents to everyone in the world so quickly? It sure as hell isn't anyone other than Santa Claus. Even clowns have been measured only to be able to deliver up to 100 presents per second, nowhere near the glory of Santa Claus.

Santa's combination of smells.

You might argue that it's multiple people doing the job, but that's so ridiculously wrong. I've caught impossibly lucky evidence that Santa is real. Santa Claus is an elusive man who goes at great lengths to prevent himself from being seen by snoopy kids. But he still lets people have just enough evidence to know that he exists, and here's my evidence. After last Christmas, my dog named Stanley started coughing at odd intervals. I took it upon myself to take my dear precious dog to the veterinarian. The vet was stumped, so I arranged weekly meetings with him in which we researched the deal with the dog. We stumbled upon an obscure website that catalogs everything about dog coughs, and we figured out that his coughs came from catching a whiff of a combination of three different things: microwaved eggnog, gingerbread cookies covered with brittle Betty Crocker frosting, and a scratch-and-sniff Lego set (believe it or not, those things exist). If that doesn't scream Santa Claus, then nothing does. Eggnog and cookies are obvious, but the scratch-and-sniff Lego set is more obtuse. I can safely associate it with Santa because scratch-and-sniff Legos were a trend around my neighborhood last winter and Santa loves following neighborhood trends. So there you have it, Santa is more real than the water spewing out of the White House's fountain to open the president's speech on inauguration day.

OK, next question. How does Santa deliver presents at such lightning speed? That's a hell of a question. We've already established that it is without doubt the efforts of the great and elusive Mr. Claus, but how? This is a question that has stumped the minds of even the most advanced pataphysicists since the 1800s. People have thrown about theories for many decades as to how Santa does this, such as the idea that Santa has the mind of a firefly who experiences tiny fractions of seconds in what feels like seconds do to us humans, or the idea that Santa's numerous elves do the manwork. The first idea is impossible since fireflies can't deliver presents, and the second is stupid because we already know that it is definitely Santa Claus himself. So what is the real reason? I have the surprising answer.

Hugo Steinhaus and Santa Claus

Enter Hugo Steinhaus, a figure usually known to googologists inventor of the two famous large numbers, the mega and megiston, using circle notation (a subset of Steinhaus-Moser notation) as an easy way to make numbers that blast through the roof of most people's conception of infinity. But very few know that Steinhaus knows more than he lets on: he figured out the connection between googology and Santa's strange mechanics, way before the ridiculous notion of Santa being fake was popularized by some bozos who cannot accept Santa's undeniable reality.

The reason most people don't know about Steinhaus's knowledge of Santa Claus is the same reason most people don't know about Conway drift: Steinhaus was too amazed by his discovery to be able to share it to the world. When Steinhaus discovered what we will learn about shortly, he was unable to figure out how to present it to the world in the best possible way before the publication date of one of his books was due; he even delayed the release by two years and still couldn't decide on a presentation method within the time allotted. At first he beat himself up about not being able to insert this information on Santa Claus into his poorly-acclaimed book about holidays around the world and thus not being recognizable by googologists as more than the creator of one of the "classic" large number systems. However, Steinhaus later developed a sense of gladness to be privy to this inside knowledge on the mysteries of Santa Claus. If he was alive today, he would be so pissed. :)

So how do I know about Steinhaus's amazing insider knowledge of Santa's mysterious ways? Thank Nathan Ho, the founder of Googology Wiki, for informing me about it. He emailed me an unfinished paper of Steinhaus's that appears to have come from the same source as John Conway's research on Conway drift. How he found it, I cannot say. But I will summarize Steinhaus's cryptic writings and share with you the ultimate answer to the question kids and scientists alike have spent innumerable sleepless hours in bed contemplating. Are you ready? I can feel your fingers tingling with anticipation of my reveal of a wondrous revelation about how Santa is as amazing as he is, and mine were tingling just the same way when I opened the document Nathan emailed me.

Red Hole Magic: The Secrets Behind Santa's Speed

Steinhaus learned that Santa accomplishes his incredible present delivery speed with the help of his loyal army of elves. The elves are exactly who allow Santa to be the magical man he is: everyone knows that they make the presents he gives to children, but very few know that they genetically breed his flying reindeer, they develop an item compaction system to allow seven billion presents to fit on one reindeer-fueled sleigh, they deliver subliminal messages to the world's kids that make sure they'll be sound asleep dreaming about cotton candy butterflies well before Santa comes to their houses, and here's the big one: they use thoughts about Graham's number to allow their jolly boss to travel so incredibly quickly. Yep you read that right: thinking about Graham's number is the key to delivering presents at such an impossible rate!

The YouTube channel Numberphile has several videos about Graham's number, and they claim that if you could think about all the digits of Graham's number, your mind would collapse into a black hole due to the sheer number of digits. That sounds impressive as all hell, but it isn't a great way to give you an idea of the size of Graham's number. Even if each digit of a number could be stored in a Planck volume in a universe a googolplex meters wide (likely much larger than the entire inflationary universe), then you wouldn't get much further than storing a number like a googolduplex (10^10^10^100). Even that would be way more than enough density to collapse the universe into a yottamassive black hole.

But not all is lost. Graham's number is just big enough that storing the number in your mind creates not just a plain old boring black hole, but a red hole. Red holes are something far more scary and mind-screwing than black holes. Black holes suck in whatever comes near them and rip it to shreds. In other words, they suck in space. Red holes, meanwhile, suck in time. Basically, by sucking in time instead of space, red holes let you travel back in time! It has long been thought that traveling forward in time is possible by traveling near the speed of light, while traveling back in time is only possible by somehow going faster than light. But by analogizing the duality of space and time to what black holes do, we can flip off the antiquated scientists who devised those light speed time travel theories and create a red hole, just by thinking about Graham's number! Along with red holes there are cyan holes, which do the opposite of what red holes do: they blow out time and let you travel forward in time, which means we can pull a flipoff x2 combo to those scientists. You make a cyan hole by storing negative Graham's number in your mind.

A red hole is what happens if you could store all the digits of Graham's number in your mind.

And making red holes by thinking about all the digits of Graham's number is exactly what some of Santa's elves are assigned to do. Few people know this, but Santa has a second identity as an acclaimed mathematician. I don't know which mathematician he masquerades as when he isn't commanding his loyal army of elves, other than that it's a close collaborator of Ronald Graham's. Yes you read that right: Ronald Graham is good friends with Santa Claus himself, and he doesn't even know it! Graham is the one who told Santa about Graham's number, and allowed him to store Graham's number in the minds of his elves. It should be noted that elves can store all the digits of Graham's number in their minds because they are elves rather than humans, and thus have vastly differently functioning minds. And Santa finding out about Graham's number through Ronald Graham when people had believed in Santa since the 1600s is what brings us to Santa's convoluted biography, spread across time thanks to red/cyan hole time travel.

Santa's Time Travel Biography

Even though Santa Claus has joyed the minds of children since the time of the Pilgrims, he was actually born in Alabama in 1953 and traveled back in time from there. His parents honorably named him after the jolly white bearded man who came to their houses every Christmas; this means that Santa's name is in fact an ontological paradox, just like the title of a demon whose real name is too dangerous to enunciate. Santa was a very strange child who loved exploring the forests more than anything—so much, in fact, that he started to hear funny noises at strange hours of the night. He investigated the noises, and found that they were coming from adorable little men in green outfits and silly hats. By Santa's tenth birthday, he had befriended a decent amount of those little men, and called them "elves". To avoid recognition as the guy who delivers your presents every Christmas, he developed his mathematician identity as he amassed an entourage of tens of thousands of elves. He started genetically breeding the elves, and made it so that each was designed to perform a certain specific task.

Santa learned about Graham's number shortly after it was shared with the public in 1977. He instantly decided that he must tell his elves about this number. To his surprise, the digits of Graham's number fit snugly in the minds of his elves; not only that, but those digits created a red hole within the minds of his elves! He also experimented with negative Graham's number, and created cyan holes. By the way, the duality of red holes and cyan holes was also the inspiration for red-cyan 3-D glasses, meaning that Santa was the one who brought you the ability to see Toy Story in 3-D!

If it weren't for Santa Claus, this wouldn't exist.

Santa Claus quickly figured out that red holes and cyan holes allowed you to travel through time. He wanted to travel back 24 hours, but ended up going too close to his elf's red hole and screamed as he and his elves ended up in the 1600s. There have been a few news reports here and there around the time of phonographs that people exploring forests vaguely heard what sounds like a record of someone screaming spinning very slowly in the the wrong direction. That's just the sound of Santa Claus screaming. Mystery solved, chumps.

Where were we? After arriving in the 1600s, Santa and his elf entourage spent some time figuring out what exactly to do. Amidst one of his many contemplation sessions, Santa accidentally let one of his elves loose. The elf visited the house of a quaint Pennsylvania family and told them all about his amazing boss, Santa Claus. Everyone was floored by the stories of Santa's amazing accomplishments, and the kids in particular wanted Santa to give them presents. Word gradually got around the city, and after some years the whole world knew about Santa Claus. The elf eventually left and reported back to Santa how everyone knows about him, and this event of the elf visiting a house came to be known as Santa's elfing. And one day, Santa decided to fulfill desires by giving all kids around the world presents, choosing to do so on the at the time rather bland holiday known as Christmas.

How the Santa Made Christmas

And so, on the night before Christmas (remember, we're in the 1600s), Santa decided to go around the world and give everyone presents, and here's where Santa's juicy secrets of how he delivers presents to billions in one night are finally revealed. Santa goes to one house at a time to deliver presents, and when he's done, he uses a red hole to travel back however long he took to deliver the presents, high-fives his past self just like how he was high-fived by his future self before delivering the present, and moves on to the next house. His elves tell him if he skipped a house, and he finishes all the houses at almost the same time of day as when he started his mission. He then did all that every Christmas since then, and he continues doing so to this day.

Before we move on, you may be wondering: how is Santa alive after delivering presents for 400 years plus time added from going back to the same point in time a number of times that is greater every year due to population growth? The answer is elves: Santa figured out how to use his elves to prevent his aging. Sadly, this clever elf trick has not been applied to the whole world to prevent aging from happening to people and causing them to eventually die, because all those amazing facts about Santa have not been publicized until now. You're welcome.

Another question you may have: didn't I say Santa delivered 243,000 presents per second? Despite Santa's time traveling, this is still in a way true: every second, a large amount of people have their present delivered by Santa. In fact, it's definitely more than 243,000 people, given that it wouldn't take anywhere near eight hours for Santa to deliver any single present before he travels back in time using his trusty elf's red hole.

Santa's Second Elfing

In the past few decades, people tragically started to lose faith in Santa's existence. This is probably because the long-term effect of the elf's presence in a family's house didn't last forever, and is starting to wear off. This is pretty unfortunate, given how amazing of a man Santa really is. Now here's where Hugo Steinhaus appears yet again: on the title quote of this article, I said that Steinhaus was a "Santa prophet extraordinaire". I didn't give him that title for nothing. He prophesized something very revolutionary: that Santa would have a second elfing as great in magnitude as Santa's elfing when an elf visited a 1600s family's house. An elf would visit an impressionable family and make them gain faith in Santa's existence once again. It would only make sense that an event of great magnitude that brings joy to the world would happen once again when its effect starts wearing off.

Imagine walking all the way to the center of this map from wherever you live.
That's what Hugo Steinhaus and his grandfather did for a passion.

Now how does Steinhaus know all this? Well, his grandfather was a great explorer who he admired very much. One day, Steinhaus's grandfather adventured to the North Pole, and he managed to get there and find Santa's place of residence there. Everyone knows that Santa lives on the North Pole, but not many know that Santa's office is hidden underground so that explorers who venture to the North Pole won't find it. Old man Steinhaus, however, was a very adventurous man, and he managed to find Santa's residence. He was vastly shocked by how big it was and how he managed to meet Santa Claus in person (this was back when people knew he was real), but Santa, being the jolly man he is, didn't mind having a rare guest. Santa showed Mr. Steinhaus around his office and told him about his amazing time travel life, his elf equipment, and the mind-wrenching physics of red and cyan holes.

When Hugo's grandfather came home, he told his whole family about everything he learned about Santa Claus. Hugo Steinhaus himself was particularly fascinated, and he and his grandfather would start visiting the North Pole every so often to learn all they can about Santa Claus; Steinhaus followed in his grandfather's footsteps after he died. Steinhaus compiled a great deal of research on Santa's life and the jobs of his elves, and planned to publish it in his books, but sadly failed; we might never know it if it weren't for me publishing this article.

The Googological Implications of Red/Cyan Hole Time Travel

We've established a while back that elves can make red holes or cyan holes by thinking about Graham's number or its negative respectively. Now, what if we take the idea of red/cyan hole time travel to the extreme? This is where the googological side of this article kicks into high gear—so high that the car engine blows the fuck up and you get arrested for community destruction. Beforehand, we haven't discussed all that much that directly relates to googology besides the connections between Graham's number and red holes. But now, we're going to learn about the weird things that happen when you go further and further through time using red and cyan holes.

I've already implied that the closer you go to the center of a red hole, the further you travel back in time. I've also implied that it's easy to screw up when using a red hole: Santa Claus of all people accidentally traveled to the 1600s when he meant to go back 24 hours. That's a bit misleading though; this is most likely the invisible forces of the Easter Bunny at work to fulfill the stable time loops of Santa's existence (remember that I said Santa's very name is a paradox). Wait. You aren't informed on the almighty glory of the Easter Bunny??? Well, the Easter Bunny is the only truly omnipotent thing in existence, and his existence is in fact a very curious paradox. If you want to learn more about the Easter Bunny read here.

So could you use a red hole to travel to, say, the Big Bang? I suppose so: you could go about 0.4 inches through the center of the hole, and bam, you fall right into the breath of the Easter Bunny as he creates the universe. If you go closer than that, you would be vaporized by the Easter Bunny since you have not reached the time where he chooses to create the universe. Wonder why every so often you don't get the right present from Santa Claus? One of his elves screwed with time travel and went to a time before the Easter Bunny created the universe.

So what is the relationship between distance to the center of a red hole and how far you travel back in time? Those two have the following relationship:

T = X(1/d)

where T is time in years, d is distance (in inches), and X(n) is a function defined like so:

X(1) = 1
X(2) = 2^2 = 4
X(3) = 3^^3 ~ 7.6 trillion
X(4) = 4^^^^4
X(5) = {5,5,5,5}
X(6) = {6,6(1)2}
X(7) = {7,7(2)2}

and extrapolate from that.

It happens that extrapolating from this is the very best way to define large numbers. Come up with a large number sequence, say that you'll extrapolate from there, and good ol' Santa Claus will do the rest. That's way easier than defining a complicated notation like Bird's array notation: since googology is about creating simple ways to make large numbers, this is a great way to make the largest numbers you can, and make BIG FOOT let out a muffled sob. X(100) is already way way way way WAY bigger than BIG FOOT ... raised to its own power!!! Don't tell LittlePeng9 of Googology Wiki (creator of BIG FOOT) any of this.

Cyan holes are about the same idea. You could use them to travel however far into the future you want. But they also have a limitation similar to how the 13.7-billion-year age of the universe limits how long you can safely travel without the Easter Bunny destroying you: the Easter Bunny delivers another Big Bang after the last proton in the universe decays (in about a googol years). It's just like in that episode of Futurama, no joke. The creators of that show were always subconsciously aware of the existence of the almighty Easter Bunny and how he reboots the universe over and over again; they just weren't directly aware that it is the Easter Bunny. The Easter Bunny doesn't take kindly to those who interrupt the process of the universe's creation.

So what if some person mysteriously finds his way to Santa's office and wants to use one of Santa's elves' red holes to travel back in time and kill Abraham Lincoln? Well, the Easter Bunny takes care of time paradoxes. He will alter your thoughts to prevent you from wanting to kill Lincoln. This also means that with red holes you can't change the past.

These restrictions combined with the timeline-housekeeping powers of the Easter Bunny are why the people who do get the chance to use red/cyan holes for time travel (read: Santa Claus and on rare occasions his elite elves) don't cause time paradoxes no matter how reckless they are. Since Santa is not the Easter Bunny, let alone his elves, he does make the occasional mistake, but the Easter Bunny has it accounted for.


It's such a shame Santa's existence isn't generally treated as more than a silly anecdote parents tell kids and promptly revoke its verity after a few years. This would have changed entirely if Hugo Steinhaus did something a little differently, namely managing to write his content on Santa Claus in time for his book's publication. But now I fixed that, thanks to luckily getting some information so invigorating that everything we learned about Conway drift months ago looks like the regular stuff people learn about the googol and googolplex. It's just that amazing, everything you now know about Santa Claus and his glorious exploits. I hope that what I presented in this article spreads around the world and restores everyone's faith in Santa, not just as the jolly man who discovers presents, but a true revolutionary genius whose mere presence is a strong positive force for humanity, and that's one hell of an understatement.

Just kidding! I hope you enjoyed this joke article. Merry Christmas everyone.

If you want to look at other spoof articles from this site, look here.