# Re: Keesey on a mathematical approach to defining clade names -- or -- Whatever Happened To Baby New Papers?

```On 9/27/07, T. Michael Keesey <keesey@gmail.com> wrote:
> > A branch definition would not be difficult: we have just to *divide*
> > by the sister-group clade-number.
>
> Branch-based definitions use species or specimens (or genera or clades
> within the sister group, outside of the PhyloCode) as external
> specifiers, not the sister group itself. (And it's possible for a
> branch-based clade to have multiple sister groups, although let's not
> get into that right now.)

External specifiers end up being sister groups anyway.

> Also, that strategy could potentially result in numbers with unending
> sequences after the
> decimal point --

No problem. Pi and euler are even worse - since they do not form a
periodic decimal expansion - and are more or less well operated by
computers. In such a system, all number will be rational (at worst
case will have periodic decimal expansion).

> (And what about apomorphy-based definitions.)

Good point. No definite answer by now. But maybe apomorphy could be
treated as an number too.

> Using primes to represent specifiers would be wasteful from a database
> point of view, when you could just use integers as lookup keys and
> form definitions based on lists of keys.

Yes, but we would loss some interesting properties. With prime numbers
we could assign a unique number to clades - that could be decomposed
into their specifiers numbers. It would be more suitable to computers
operate with. If we just use normal integers we could get the same
value for differente inputs. 3*8 = 6*4. The uniqueness of prime
product is the advantage of that system.

> Figuring out the primes that constitute the multiples of a large integer is
> not an easy
> calculation -- certainly a

Actually an impossible calculation. By definition, a prime number is
not a multiple of any other number (except for itself and 1). But yes,
factoring some huge numbers is a so harsh task that we could use it in
encryption - but they use keys with 64 or more digits, and the upper
biodiversity estimation is about 100 million species: just 9 digits
(any present day desktop could handle this in less than a minute).

> Math is more than just numbers.

Surely. And I'm not mocking on your work.

[]s,

Roberto Takata

```