Monday, October 6, 2014

One Reinhardt and counting...

The original post has been changed: the attribution of the game has been clarified.

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.

Now, Chris is so kind to suggest you not to play to the big version, but I am evil and I push you to try that instead of Reinhardt. It is called 1=0, and it is cleaner and more strategical.

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.


  1. So I guess my 32768 on the 5x5 grid is kinda lame...
    How many different tiles there are in this Reinhardt game?

  2. Good question. I haven't finished the game, so I don't know. In Reinhardt, I counted 10 different types, the equivalent of 1024. But the last one is empty. Is that a glitch? Is it a way to say that the Reinhardt cardinal does not exist? Nobody knows. Well, Chris knows.

    In 1=0, I arrived at superstrong, that should be the 12th, therefore the equivalent of 4096. Still a long way to go.

  3. Brought here by Vsauce@ytb. This game was originally made by me. Chris followed some peoples' suggestions and changed the large cardinals without changing the font sizes. This is why some of the large cardinals are oversized. Yizheng.

  4. Sorry Yizheng, I didn't know that! I immediately changed the post, I care about sources. Do you have a link for your original version?

    1. This comment has been removed by the author.

    2. I got bored. The big one was simply a joke. I didn't expect anybody to seiously play it, but to my surprise...
      You see the big one has "remarkable". This is because it was spread in Muenster (and remarkable is very small).

  5. I would love to get an explanation of the 0=1

  6. "And why the big one is called 1=0? This is more difficult to say, probably I will write it in another post."

    I'm really looking forward to that post, i've enjoyed your other articles Vincenzo.

  7. Sorry Marc and James! I forgot to add the link.

    Actually I have already answered that in my post about the movie "The Zero Theorem". In the end it is just an inside joke, it's the so-called principle of explosion, but I think it unveils something deep about mathematics.

    And I'm happy you enjoyed the articles! Thanks!

  8. Speaking of forgetting... yeah... I think I read that one already and forgot that i did ha ha!

  9. I know it's been a while, but the link for the game is down :(