One thing that is full of confusion is figuring out relationships. It can also be full of surprises, like the fact that Wolfram|Alpha can do it for you. If you follow this blog, you already know that Wolfram|Alpha can figure out and calculate lots of different things, including the moon and planets, and you are about to discover what it can tell you about your relationships.

Or at least relationships between your relatives. For instance, my cousin just had a son”.

We get a family tree, and it tells us that my relationship to my cousin’s son is that he is my first cousin once removed. Confusion resolved.

Like many other Wolfram|Alpha outputs, we get more than we may have expected. A few genealogical properties are related to historical laws, and a few are biological. The plots for sharing a Mendelian trait are given at the bottom after clicking More. This helps me understand how much I may have in common with my new first cousin once removed.

A dominant trait only requires one allele, while a recessive trait requires two. The other piece of information needed to say how likely it is to share a trait is how common it is in the general population. It is possible to share a trait accidentally, and for recessive traits one needs to get the other allele from the other parent. For my cousin’s son, not surprisingly, we see that the probability of sharing a genetic trait in common doesn’t seem to depend much on whether it is dominant or recessive. We are too distantly related to have much in common, and the probability of a shared trait between us depends primarily on the chance coming from the frequency in the general population.

It turns out that most traits are not simple like this, and involve more than one gene and so on, but this gives a general sense of how much we may have in common.

You probably know people who get confused about second cousins and so on, but there is also another category for relationship confusion.

Wolfram Alpha can compute the possible relationships given any sequence of relationships, not just the ones that people might use in real life. For instance, consider “my cousin’s cousin’s niece’s grandfather”:

The first pod shows the family tree based on what we just entered. It assumes that none of the people we mentioned are the same. Only the first few on the family tree are related in a traditional sense.

The next pod shows possible simplifications. I would never have figured this out myself, but if my cousin’s cousin was myself and the grandfather referred to was on the same side of my niece’s family as myself then her grandfather would be my sibling’s father, which would be my father. We get the other possible relationships, and also the neat statistic on the number of relationships that don’t have a traditional label like “father” such as the one pictured in the first pod.

Sometimes it’s best to let another do the relationship thinking. That’s thinking best left to Wolfram|Alpha.