Afterthoughs on Banach Tarski and the Miracle of loaves and Fishes

I posted about using the Banach-Tarski Paradox(BT) to explain the miracle of Loaves and Fishes (LF) here.

Darling says that whenever I fool my readers or my students then I have to tell them later, so I'll tell you now: The story about me meeting with Pope and talking about the BT Paradox (that would be a good name for a rock band: B-T-Paradox) was not true. I think my readers know that.

1. I first learned the Banach-Tarski Paradox as a grad student in 1981 when I read Hillary Putnam's article Models and Reality where he writes on Page 470:

One cannot simply sit down in one's study and decide'' that V=L'' is to be true, or that the axiom of choice is to be true. Nor would it be appropriate for the mathematical community to call an international convention and legislate these matters. Yet , it seems to me that if we encountered an extra-terrestrial species of intelligent beings who had developed a high level of mathematics, and it turned out they rejected the axiom of choice (perhaps because of the Tarski-Banach Theorem), it would be wrong to regard them as simply making a mistake. To do that would, on view, amount to saying that acceptance of the axiom of choice is built into our notion of rationality itself; that does not seem to me to be the case.

I agree with him and I wonder if we accept AC too readily. See my blog post on the BT paradox and my wife's strong opinion (she's against it).

1. Back in 1981 my first thought was I wonder if someone has thought to use the BT paradox to explain t he LF? And if so, were they serious or was it some kind of joke? And does the Pope really get a discount at Pope-Yes?

I also had the meta-thought (which I could not have said as cleanly as I will now):

I wonder how I could find out if anyone else has thought of the BT-LF connection?

Recall that back in 1981 the Internet was but a glint in Al Gore's eyes. So back then I could not find out if anyone else had that thought of BT-LF.

But now I can! And indeed, as I expected, some other people have made the connection of BT to LF:

A tweet and a Reddit thread discussing the tweet: here. Not serious

A serious article, I think, here

A 24-page article about Holy Water and BT. I can't imagine an article that long being a parody so I think its serious, see here. On the other hand, there is a 12-page article about Ramsey Theory and History that I think is supposed to be a parody, see here.

A parody article, I think, here

I am sure there are more.

1. I had thought of doing a blog post about BT and LF a long time ago, but Pope Leo having a math degree was the final push I needed.

2. The word cardinal has three very different meanings: (a) a type of infinity, (b) a position in the Catholic church, (c) the bird. Same for large cardinal

3. One of my students who proofread the post thought that people will know it's a hoax since I am a vegetarian and hence would not eat at Pope-Yes, even if the Pope was paying.

By gasarch