I was binge re-watching Breaking Bad when I started thinking about the opening credits. Each name has a chemical element symbol highlighted in green — Vince Gilligan’s name highlights V for Vanadium, for example.
I wondered: out of 118 identified elements, how common is it that we can find at least one element symbol inside a random name?
The data
I found a list of 5,163 unique first names and 88,799 unique last names and wrote a Python script to count how many element symbols could be inserted into each name.
I expected it to be rare to find a name with no possible insertions. I had no idea how rare.
Results
For first names, only 0.81% had no possible symbol insertions. The complete list of elementless first names includes names like ada, dee, emma, jade, mel, and zelda — 42 names total.
The most common number of possible insertions was 4, and the maximum was 11. One of the 11-insertion names was Catherine — despite having only 9 characters:
- Catherine (Carbon)
- Catherine (Calcium)
- CAtherine (Astatine)
- CaTherine (Thorium)
- CatHerine (Hydrogen)
- CatHerine (Helium)
- CathErine (Erbium)
- CatherIne (Iodine)
- CatherIne (Indium)
- CatheriNe (Nitrogen)
- CatheriNee (Neon)
For last names, just 0.18% had no insertions — there are roughly 160 such names.
Full names
For full names we can combine the distributions. If $P_{first}(i)$ is the probability of $i$ insertions in the first name and $P_{last}(j)$ is the same for the last name, then:
$$P(n) = \sum_{i=0}^{n} P_{first}(i) \cdot P_{last}(n - i)$$
The chance that a full name has zero possible element insertions: 0.0015%.
Full names show a distribution shifted even further right, with a tail extending to 25 possible insertions. An example: Catherine Bernasconi, only 19 characters, has 25 possible element symbol placements.
For my own name — Andy Bohn — there are 8:
- ANdy Bohn (Nitrogen)
- ANdy Bohn (Neodymium)
- AnDy Bohn (Dysprosium)
- AndY Bohn (Yttrium)
- Andy Bohn (Boron)
- Andy BOhn (Oxygen)
- Andy BoHn (Hydrogen)
- Andy BohN (Nitrogen)
Note: I didn’t consider elements that span the first and last name boundary.