2006-08-26 by
qntm

I will say right now that I am not an avid Lost fanatic. I lost interest in the show after the anticlimactic finale of season one. I *am* curious as to what the ultimate solution to the whole island mystery is going to be, but I have strong suspicions that the final answer will not be entirely satisfactory or make much sense, so I am reluctant to invest much of my personal time agonizing over the deeper meanings of the show, when it would be simpler to wait for the entire series to finish and then watch the whole thing at once.

I am, however, a mathematician. And these numbers, **4, 8, 15, 16, 23 and 42**, are interesting. They were first brought to my attention by a Lost fan I know online. He knew I was into maths so after the episode "Numbers" aired he IMed me asking me if this was a known sequence. I didn't recognise it - I found nothing in the On-Line Encyclopedia of Integer Sequences either. Mathematically these number have no real structure - they appear to have been chosen to be as random as possible.

However, it is possible to force any sequence of numbers to have structure by a method called Lagrange Interpolation. By this method we can construct a polynomial which passes through each number one at a time.

Seeing as there was no other way to make sense of the numbers, I have constructed a Lagrange Interpolating Polynomial for the Lost numbers. Just out of idle curiosity, you understand.

What I found was this, which I shall call the **Lost Number Function**:

2400 - 4896n + 3670n^{2}- 1175n^{3}+ 170n^{4}- 9n^{5}f(n) = --------------------------------------------- 40

This formula gives

f(1) = 4 f(2) = 8 f(3) = 15 f(4) = 16 f(5) = 23 f(6) = 42

Which you can see graphed here:

From this we can see that the next number in the sequence is

f(7) = 46

And also that the *zeroth* number in the sequence, the one coming before 4, is

f(0) = 60

Beyond these points the graph shoots off towards infinity or minus infinity. The eighth Lost number is -52, the ninth is -426, and so on.

What can we make of this? Well, nothing really. I just thought that you Lost nutters might be interested. Does the number 46 turn up anywhere on the island? Probably...

Enjoy!