a list compiled by Alex Kasman (College of Charleston)
|Though it is presented as if it were non-fiction, it is generally believed that this account concerning a very thoughtful six year old girl is a work of fiction. It is primarily about the girl's philosophy of religion, but mathematics appears frequently as an object of discussion itself or in metaphor.
At one point, she and Fynn reveal that each of them independently discovered the joys of doubting mathematical rules. In particular, the question "What if 2+3 were 10 or 7 instead of 5?" They both find this line of questioning exciting and revealing. In fact, I would have to agree that this sort of thinking is valuable. For one thing, it helps the person thinking understand and appreciate the fact that the rules were constructed by people. (I suppose it depends on how you think about it. For me, mathematics is a human invention which has taken many thousands of years to become what it is...and it is still growing. Others may see math as a separate universe with an independent existence which we are merely exploring. In either case, there is a huge role for human involvement.) Moreover, many of the rules one comes up with in such games turn out to lead to a real mess...in which case you may gain some appreciation for the rules as they are generally taught. But, most interesting is when an alternative mathematics turns out to be interesting and even useful. Quite a lot of what mathematicians do is along these lines. We've created alternative number systems (such as the quaternions or the p-adic numbers) and alternative geometries (non-Euclidean, non-commutative, etc.) and some of these are as beautiful and useful as the "classical" versions!
There is also a long and interesting discussion about 0-dimensional points and how they represent an object after all other identifying information has been stripped away. For instance, a collection of 5 points could represent the contents of a bag with 5 apples, five possible states for an electron in an atom, the fingers on my right hand, etc. This is contrasted against lines and higher dimensional objects with "Mister God" being the eventual outcome of the sequence according to Anna.
Mathematical physicists may be interested in Anna's observation that a shadow can move faster than the speed of light, even with relativity taken into account. Those who have not thought Einstein's theories through may find this shocking, as Fynn seems to. In fact, it is just one example of a rather common situation in relativity. It is objects with mass that are forbidden to increase their speed beyond "c" in relativity. Other things, including abstract things which really exist only in our mind (like shadows) have no such restriction. A more physical version of this is the observation that wavefronts in quantum mechanics can travel faster than the speed of light. These things do not contradict relativity, in particular, because no information can be sent between points at super-luminal speeds using these apparent violations of the "speed limit".
The mathematics discussed in the book is deep and interesting for a six year old child, but I'm afraid that I did not get much out of the theological side of the book. Others, however, have found it to be quite an epiphany. Hopefully, some people who were moved by this book will write in with some comments so that visitors to this site can hear their viewpoint as well.
|More information about this work can be found at .|
|(Note: This is just one work of mathematical fiction from the list. To see the entire list or to see more works of mathematical fiction, return to the Homepage.)|
(Maintained by Alex Kasman, College of Charleston)