Can you hear it? Do you hear that sound? It's something like streeeeeeeeaaaaaaatch. It's me stretching the theme of the blog to accomodate this topic.
You know 2048? Of course, everybody knows it. It's a very addicting game by Gabriele Cirulli, and the Wall Street Journal called it "almost Candy Crush for math geeks".
Addiction has a face.
I cannot describe it. Just play it. Or don't! You have to read this blog, don't get distracted.
The game is open source, so anybody can make a personal version. But then, don't you feel that the numbers here are a bit... small? 2048 is so tiny, is there a way to go really big?
If you dare to adventure the deep, deep academia web you'll find a specific version... with large cardinals! Now also you can climb up the large cardinals hierarchy! The name of the game is Reinhardt. The original idea was by Yizheng, and then it was picked up by Chris La Sueur, that changed the large cardinals and published it.
I thought about giving you the list of the cardinals involved, but why ruining the fun? Part of the delight is in the exploration!
But why it is called Reinhardt? This is the skeleton in the closet of all set theorists.
The reaction of set theorists when asked about Reinhardt and large cardinals
Once upon time (1969, to be precise), William Reinhardt was studying some large cardinal, and had an idea: to build the largest cardinal ever, the king of large cardinals, the most powerful! We now call it Reinhardt cardinal.
But just after months, Kenneth Kunen proved that it was too big and powerful. In fact it just couldn't exist! Set theorists wanted the absolute power, but they overshot and reached a contradiction, and now the tale of the non-existing Reinhardt cardinal is taught to all students, as a sombre reminder that in trying to achieve too much, one risks to destroy everything. Anyway, Reinhardt cardinal is the largest cardinal, even if it does not exists, and the aim of the game is to reach it.
And why the big one is called 1=0? This is more difficult to say, probably I will write it in another post. (Edit: here it is!)
Now you can go playing! Have a nice waste of time!
Many large cardinals that appear in the game already appeared here. Interested in just one large cardinal? Make it this one, says Sheldon.