Some time ago, I wrote a couple of posts distinguishing All Possible Math from the Math We Know. In short, people only study the mathematics that is interesting or useful to us, and not too hard. When you think about that it becomes clear that there’s a lot more mathematics possible than the stuff Homo Sapiens talks about. Much of All Possible Math would be uninteresting for us, useless and/or too hard to grasp.
By contrast, the Math We Know is surprisingly practical. Two questions that puzzle scientists and philosophers are
- Why is there a physical universe?
- Why can it be described mathematically, or; Why is math so practical?
Steve Landsburg, an author of a number of good books, feels he has an answer to these questions. He believes that the ultimate reality is All Possible Math. He says the physical universe exists because it can be described mathematically, and so does every other thing that mathematics can describe. He explains this on his blog, and in more detail in this book.
I can see how this would be an attractive idea, especially to an atheist mathematician. The universe becomes a created thing, beautiful because the Creator (Mathematics) is beautiful – without the need to invoke a traditional idea of a conscious Deity. The so-called Queen of Sciences is promoted to King, for if mathematics were the Primum Movens, or First Cause, we could call it “God” and insist that students of theology enrol in advanced calculus courses.
On reflection, however, Steve Landsburg’s idea has problems. If the First Cause is All Possible Math, and the universe exists because it can be described within All Possible Math, then any universe so describable must also exist. However, All Possible Math is not bound to create only logical universes. We learn how logic works in math courses, but mathematics can be used to describe quite illogical theories of logic. We don’t have these in “Math We Know” because they are neither practical nor interesting. Nonetheless, they are right there in All Possible Math.
In fact, it’s not too much of a stretch to think that All Possible Math could describe anything at all. For any conceivable universe (and, I think, any inconceivable one), it would be possible to describe the universe in some mathematical form, even if this form were merely a completely detailed “list” everything in that universe and the relationships between them. As a direct result of Steve Landsburg’s idea, we could say not just that the physical universe exists, nor just that many physical universes exist, nor even merely that every logical universe exists. As Terry Pratchett points out with his concept of L-space, as soon as you have a language capable of describing ideas, anything imaginable can be described. All Possible Math contains many such languages, with unlimited descriptive power. If all the things that All Possible Math describes all actually exist, then Steve Landsburg’s idea tells us “Everything Exists.”
Think what it means for “Everything” to exist. It means that including C. S. Lewis’ Narnia and Terry Pratchett’s Discworld are really real, even though we happen not to live there. It means that every major religion (and every minor one) is simultaneously true, at least somewhere. The fact many religions are logically incompatible is no problem, since All Possible Math describes illogical logics as well as logical ones. Far from being a way to explain the universe without God, Steve Landsburg’s idea necessitates that all possible Gods exist. All Possible Math is not pretty.
To exclude the ugly side, one might try to modify Landsburg’s original idea. Maybe not everything that All Possible Math describes is real, but only what Some Possible Math describes. Our first cause becomes some Cosmic Mathematician that decides which bits of All Possible Math get to create reality and which bits don’t. However, what is this Cosmic Mathematician like?
Human mathematicians use practicality or aesthetics to trim All Possible Math. The former implies some sense of purpose, the latter some sense of pleasure. If the Cosmic Mathematician has purpose and/or pleasure, it becomes, I suspect, too much like a “Who” for an atheist to be comfortable with. On the other hand, if this Mathematician remains an It and still exists at all, Steve Landsburg’s idea seems somewhat too incomplete to be intellectually satisfying. It begs the question of what It is like.
Hmm… I wonder what Steve Landsburg would say to all this?