Everyday I will blog a Book Club post since I am reading the book Where Mathematics Comes From: How the Embodied Mind Brings Mathematics Into Being by George Lakoff and Raphael Nunez. Now I must admit that I have not read Philosophy in the Flesh in which the embodied mind theory is fully laid out. I don’t think this should hurt my understanding too much, though.
OK. So everyday I will probably summarize the main points, and then sadly say what bothers me about them. I really want to believe this book since it is so pertinent to what I want to argue (an aesthetic theory for mathematics), but so far not so good.
Chapter 1 argues that humans are born with innate number sense. I’d buy this if they just said it, but the experiment to verify it seems very sketchy from a philosophical standpoint. I’m sure psychologists think it is perfectly fine. Let’s see what you think.
A few day old baby is shown two objects. A screen is put up and the baby sees one of the objects get removed from behind the screen. The screen is taken down. If the baby looks at two remaining objects for longer than (what I’m assuming is a control group that wasn’t mentioned in which only a single object remains) average, then the baby didn’t expect there to be only two objects. This happened with experiments in both adding and subtracting combinations of 1, 2, and 3 objects. Thus, the baby understands addition and subtraction of small numbers! Moreover, this was done with varying spatial arrangements and objects. Thus, the baby isn’t using some sort of concrete object specific reasoning, the baby is legitimately abstracting what numbers are and doing theoretical calculation!
I really wish I had a copy of the original experiment. It might clear up some of my concerns. Uh, when we say longer than average, what does that mean? What is significant? Are we talking milliseconds, or like 20 seconds. This makes a difference in my mind. Second, how much error is involved. Are we talking about 50% of the time this happened, but we can hypothesis test away the error, or like 99.9% of the time this happened? This also makes a difference in my mind.
Outside of experimental concerns there are many philosophical ones. Suppose the experiment is true. What sort of conclusions can we actually draw from it? We have no idea that the baby is looking at the objects longer for that reason. “Expected” that is funny. This baby has been alive for a few days. What in the world does “expected” mean? It’s memory probably isn’t long enough to remember how many objects were there in the first place. My guess would be that there was something else near the objects keeping the babies attention (if that length was even significant). Let’s not even go to the abstract number conclusion.
Overall, I have little doubt that babies (probably a little older than a few days…maybe a year or so) have innate small number sense. I just don’t understand why these authors decided to try to justify it with such a shaky experiment.