I Had To Physycally Restrain Myself From Bringing Up All Other Details And Thoughts To Not Overload This Analysis Any Further - Blog Posts

William and the Fibonacci sequence

While math isn't really the main focus of the story, being a mathematician is still an important element of William's personality and mindset. It's the lens through which he views the world, incorporates experience, and thus gives meaning to things around him.

That's also the reason why I find so peculiar one little remark that he tells Sherlock at their first meeting:

"While that was a slightly forced deduction, you did make quite a good observation. However, rather than the golden ratio, I am more interested in the Fibonacci sequence."

The question is: why in this particular case does William correct Sherlock and specifically point out that he's interested in the Fibonacci sequence, but not in the golden ratio itself? The golden ratio and the Fibonacci sequence are closely intertwined with one another. There isn't any real reason why he would be interested in one thing but not in the other if he were solely curious about the properties of the spiral.

So, maybe, it isn't about the math and the spiral at all?

To answer this question, I'd like to look at the chapter's context first.

In a sense, ch. 5 is quite special by itself, as it represents the point of no return in the story. It has two major points to focus on. One of them is the final introduction of William's grand plan, which he had not revealed in full up until now. Another one is the moment when William meets Sherlock for the first time, or the staircase scene in question.

Now, as William states, at the core of his plan lies "the play of death". He means to turn London into a grand stage, and so, every step he takes is a carefully written plot that has an underlying message and a running theme, connecting one act with the other. Everything is measured and well within his control, as if he were indeed a screenwriter writing a play.

Luring Lord Enders into committing a crime serves to prove William's intention as well. While carefully guiding him to a breaking point, William is even shown to think of each step of his plan as a "scene". And right up to the meeting at the staircase, he ensures to execute this project through and through, not leaving a single possibility unattended, and not a single moment unaccounted for.

In other words, a good chunk of the chapter is dedicated to showing William's approach to what he's doing, as well as to his vision of himself as a director of a play. which he is not, but that's a topic for another time

Coming back to the Fibonacci sequence, it is evident that here it resembles exactly William's grand plan. It's the sequence of actions, or rather deaths, that he intends to carry out. While taking a step back to observe the stairs, he also takes in the whole picture of the stage that he so carefully set, and the actors at play.

But what's even more interesting to me here is the golden ratio and William's lack of attention to it. The golden ratio is an irrational number. It is the limit, towards which all ratios of the sequence must converge, but one that cannot be reached. It's the ideal.

It's William's wish to create the ideal country, or even world, devoid of all humanity's corruption.

So, why won't he look at his ideal, for which he yearns so much?

Being a mathematician, one of William's problems throughout the story is that he's constantly seeking a single, clear-cut solution. He dedicated his whole life to coming up with an equation that could've led him to his desired outcome, his ideal world. And the equation he came up with was that of utilizing the fear of death in people's hearts.

But the reality of a human heart and mind is far more complex for any possible calculation. It's just as irrational and ever-present, as the golden ratio itself.

Seeing how William constantly adjusts his plans, I think that he, as a true mathematician (and a perfectionist to the bone), at one point became far more obsessed with finding the ideal solution for his equation, rather than the end goal itself. On the other hand, he also feels a desperate need to hold every possible thing within his control. And especially Sherlock Holmes, who very much dislikes playing his assigned role in William's play.

But another reason would be that William must really not be able to imagine how this beautiful world of his is supposed to look, as he never intended to see it for himself.

In William's eyes, he's just another one of many numbers in the sequence.

Another devil to die before wrapping up the ultimate solution that he was searching for all this time.