I was planning on ignoring this one, but tons of readers have been writing
to me about the latest inanity spouting from the keyboard of Discovery
Institute’s flunky, Denise O’Leary.
Here’s what she had to say:
Even though I am not a creationist by any reasonable definition,
I sometimes get pegged as the local gap tooth creationist moron. (But then I
don’t have gaps in my teeth either. Check unretouched photos.)
As the best gap tooth they could come up with, a local TV station interviewed
me about “superstition” the other day.
The issue turned out to be superstition related to numbers. Were they hoping
I’d fall in?
The skinny: Some local people want their house numbers changed because they
feel the current number assignment is “unlucky.”
Look, guys, numbers here are assigned on a strict directional rota. If the
number bugs you so much, move.
Don’t mess up the street directory for everyone else. Paramedics, fire chiefs,
police chiefs, et cetera, might need a directory they can make sense of. You
might be glad for that yourself one day.
Anyway, I didn’t get a chance to say this on the program so I will now: No
numbers are evil or unlucky. All numbers are – in my view – created by God to
march in a strict series or else a discoverable* series, and that is what
makes mathematics possible. And mathematics is evidence for design, not
The interview may never have aired. I tend to flub the gap-tooth creationist
moron role, so interviews with me are often not aired.
* I am thinking here of numbers like pi, that just go on and on and never
shut up, but you can work with them anyway.(You just decide where you want
to cut the mike.)
It’s such concentrated stupidity, it’s hard to know quite where to start. So
how about we start at the beginning?
Denise O’Leary claims not to be a creationist by “any reasonable
definition”? Yeesh. No point even trying to argue with that. She’s just playing
the usual ID’ers games with the definition of “creationist”.
Then, very rapidly, we get the usual victimization rant. Poor, poor
Denise. Such an unfortunate soul, so looked down on. I mean, she spews
non-stop nonsense, and all she gets for it is a nice salary, lots of attention,
a publishing contract, and some television interviews. Those IDers sure are
put upon, aren’t they?
Then – shock! – she gets something right. The subject of
the interview was goofy people who want their house numbers changed, because
they think that they got unlucky numbers. Yeah, that’s pretty stupid.
It brings to mind an interesting story. Back when I was in college, my
family had to move. My parents had taken out a ten-year renegotiable mortgage,
and they couldn’t afford the increased payments while also making the tuition
bills for me and my brother. They ended up selling the house very quickly. But
it was really strange. The people who bought it were Chinese, and they hated
just about everything about the house. They hated the landscaping.
They hated the kitchen. They hated the tiling. They hated the slate foyer.
They hated the windows. They hated the parquet wood floors. They thought it
was too big. Honestly, if there was anything that they actually liked
about the house, I don’t know what it was. But they bought it. Because it
faced in the right direction, and it was the only house facing exactly
that direction on the market. Their feng shui master had told them that they
must have a house that faced in that direction – that anything else
would bring them terrible luck. So they bought it.
People believe all sorts of strange things. There are all sorts of peculiar
superstitions, about numbers, names, shapes, colors, directions. It’s all silly.
And it’s amazing how many of us still hold on to those odd ideas, or at least
the behaviors that they imply. To get personal, I know perfectly well that
nothing I say is going to cause the world to turn on me and make something
bad happen. But European Jews have a lot of superstitions about drawing attention
to themselves, and I never say things like “Well, things couldn’t
possibly get any worse”, or “Things are so great, I can’t imagine how they could
get better”. Those are both statements that “draw attention”. I know how stupid
it is, but that doesn’t change the feeling I get in the pit of my stomach when
someone says something like that.
So yeah, superstitions like that are silly, and they do deserve to be
mocked. Mine included. But I’ll bet you dollars to donuts that Denise wouldn’t
buy a house where a satanist had performed his phony rituals without getting
it purified by a priest with holy water, and that she wouldn’t see anything
remotely silly about it. She sees her superstitions as legitimate,
but others as mockable.
ANyway, enough of that. Let’s get to the good part.
She says “No numbers are evil or unlucky. All numbers are – in my view –
created by God to march in a strict series or else a discoverable* series, and
that is what makes mathematics possible. And mathematics is evidence for
design, not superstition.”
Oy, oy, oy.
Numbers were not created by a supernatural being. No deity, no matter how
powerful, could have created a universe where numbers didn’t exist, or didn’t
This is a surprisingly difficult and subtle point. But numbers, in some
sense, aren’t real. They’re purely conceptual. There’s no such thing
in the real universe as the number 2. There are plenty of examples of “two
objects”, but the number 2 doesn’t exist. Far worse, there is absolutely no
way of claiming that π really exists. There are no perfect circles in the
universe. And the only sense in which π can possibly exist in the real
universe is as a measurement.
Numbers are an artifact of reasoning. They don’t exist out there in the
void, waiting for someone to find them. They’re a consequence of a simple set
of rules. And those rules must work. There’s no way that God can
change the nature of an abstraction that doesn’t really exist. He could make
it impossible for us to conceive of those rules. But the rules would
still work. Even if there was no universe at all, those
rules could still be said to exist, and therefore, that the numbers still
It comes down to a deceptively simple question: “What is a number?”. And
there is no single answer to that question! I can define numbers informally,
by counting. I can formalize that a bit, and get two different kinds of
numbers: ordinals and cardinals. I can formalize differently, and get surreal
numbers. Still another way, I can start with different rules, and get Piano
numbers. Or another way, and get computable numbers. I can define real
numbers, complex numbers, vectors, quaternions. Those are all perfectly valid
concepts – and they’re all different. Which one really
defines numbers? All of them. None of them. Take your pick. Numbers are
what you want them to be. They don’t exist outside of your mind. They’re a tool
that we use to understand the universe – but they don’t have any real,
But Denise’s stupidity doesn’t end there. She needs to qualify things – the
numbers “all proceed in a strict series, or else a discoverable series”.
You can look at that statement in two ways. One way of looking at it – which
I think is the one she meant – is just completely, utterly, wrong. The other way,
which you could reasonably argue is the correct interpretation, is totally
fouled up by that qualification.
“The numbers all proceed in a strict series”. My initial reading
of this is that “series” implies a listing or enumeration of one number after
The problem with this is that you can’t put the real numbers into
that kind of series. The real numbers are an uncountable set: you can’t
enumerate the elements of an uncountable set. So they can’t possibly be
put in a series.
You could weasel out of that problem, by saying that the
qualification solves the problem: you can enumerate the rational
numbers: you can put them into a kind of series. Since she explicitly mentions
numbers like π as being exceptions, you could argue that she meant
that the rational numbers could be put into a series, and that the “discoverable
series” qualification was meant to cover the irrational numbers.
Alas, that doesn’t work either. First, from her wording and description, I
really don’t think that when she said the numbers are in a strict series, that
she had in mind an ordering where, for example, 2 comes before 1/3, and
1/3 comes before 1/100. But you can’t enumerate the rationals in
anything like comparison order, which is what I think she was trying
In addition to that point, I’d say that there’s something seriously wrong
with a definition where the exception covers the overwhelming
majority of cases. Most numbers are irrational – but her phrasing implies that
the irrationals are sort-of strange exceptions.
But I left the worse for last. As I’ve mentioned before, most
numbers are undescribable. You can’t discover them. You can’t
describe them. You can’t name them. You can’t point at them. And yet, by the
definition of real numbers, they must exist. So even forgetting about
the whole ordering issue, the idea of all numbers being discoverable, is just
totally wrong. They’re not. Numbers are much stranger, much less
rational, less intuitively comprehensible, less well-behaved than her naive
The second interpretation is that “the numbers all proceed in a strict series” is a poorly
phrased way of saying that the real numbers are totally ordered. That is a fact:
given any two distinct real numbers X and Y, either X<Y or Y<X. That’s correct. But if
that’s what she meant, then she blew herself out of the water with the qualification: because
irrational numbers like π are still part of the total ordering of the real numbers.
Pulling them out by that qualifier implies that she doesn’t believe that they’re part of
the series – which in this interpretation means that you can’t always compare them. But even given
two irrational numbers, they’re always comparable. Even the undescribables.
And the qualification still fails exactly the same way it did in case one: most
numbers aren’t discoverable, describable, nameable, identifyable, or enumerable.
So again, she fails miserably.
The takeaway point here is that numbers are both less real, much stranger,
and frankly a whole lot more interesting than Denise O’Leary imagines. As
usual for Creationists (and yes, Denise, you are a creationist!),
she’s taken a simplistic understanding of something, mistaken her simplistic
understanding for a deep comprehension of it, and then argued that on the
basis of its alleged simplicity that it must have been designed by her deity.
Her version of numbers can’t account for undescribable numbers. It can’t
account for much of the beautiful strangeness of numbers. It can’t account for
logical wierdness like Gödel’s incompleteness theorem, which relies on the
logical structure of numbers. It can’t account for some of the magnificent strangeness
that people like Greg Chaitin have studied. As is all too common, she’s so satisfied
with her simplifications that she’s completely missed both the pathology and the beauty
of numbers. It’s sad.
It should be obvious, looking at this blog, that I’m deeply in love with
mathematics. Math is beautiful, and fascinating, and frustrating, and strange.
People like Denise O’Leary try to sap out everything that makes it wonderful
in order to be able to say that they understand it, and that their personal
deity created it. God didn’t create math. Math is a collection of formalisms
that we created from the basic rules of logic – and those rules
must hold, no matter what the universe is like. Because they aren’t
rules about the universe – they’re self-contained rules about concepts that
If you’re religious like me, you might believe that there is some deity that
created the Universe. Or you might not. But whether there is a God or not has nothing
to do with whether A∧¬A == false.