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Molly’s Nifty Trick

Molly’s Nifty Trick published on 2 Comments on Molly’s Nifty Trick

In the Dresdenverse short story “Bombshells,” the only story told in first-person POV by Harry’s apprentice Molly Carpenter, she describes a way to incorporate math (!) into her version of the first spell she learned from him- the tracking spell- and uses it to estimate the distance to her target (Thomas Raith, using a few of his hairs) without having to actually go all the way there. This occurred to me as pretty significant because it’s not something Harry ever showed her how to do (or even figured out for himself) and it’s a vivid demonstration of Molly’s own strengths and intelligence.

Here’s how she did it.

The basic idea is that if the target of your tracking spell is close to you, and you’re moving, it will appear to shift a lot relative to your position. If it’s really far away, it won’t appear to move much at all when you move- it stays pretty much the same direction from you. Compare looking at faraway things as you drive past them to the things right at the side of the road that whoosh by your window. You may have even used some form of this trick in video games like Call of Duty, Skyrim, Arkham City, or anything else that lets you see a pinned location relative to which way you’re facing. For many years (before electronics got decently sophisticated) airplane pilots used bearing changes and a mechanical calculator to fudge estimates of their distance from radio navigation aids.

Jim Butcher didn’t stick an actual equation into the story, and rightly so, because it would have dragged the pace down to nothing and alienated the readership. But for those of us who are obsessive nerds who enjoy that level of detail, it’s surprisingly easy math to do. Despite the implication that Molly’s technique would involve high-school-level trigonometry, you can do it in your head, using only an ordinary magnetic compass and a tracking spell (or its equivalent).

Step 1: Go ahead and put that blood or hair or whatever in your mouth and follow the tingle of your lips (like Molly does) or dangle it from a string or a chain (like Harry Does, if you don’t relish the idea of putting such things in your mouth) and determine the direction of your target. Use the compass to determine the exact number of degrees that is relative to magnetic north. For now, let’s say that the target happens to be directly (0°) north of us.

Step 2: Turn so you’re facing perpendicular to the way the tracking spell points, so the target is directly to your right or to your left. For example, with our hair donor directly north of us, we’d need to face directly east or west. Now, walk a reasonable distance to measure (Molly uses the convenient unit known as a “Molly-pace”) keeping the target exactly off your shoulder. Make sure to go at least far enough to register a slight change in the direction you’re facing according to the compass.

Step 3: Measure the change in your compass bearing. Continuing our example, let’s say we started with our target directly north of us, and walked fifteen paces west. Checking the tracking spell against the compass, our target is now four degrees east (004°) of dead north, and we’re not facing directly west anymore- we’re facing four degrees north of that (274°). We’re now ready to plug in some numbers. Do not fear trigonometry- that’s not what we’re doing. Instead, do this:

Step 4: (Molly-paces x 60) ÷ degrees changed = Molly-paces to the target
To finish our example, we took fifteen paces to travel four degrees. Fifteen times sixty is nine hundred. Divide that by four degrees, and we’ve got a result of two hundred and twenty-five paces to the target… however far that is. If you’re not as tall as Molly, your results may vary.

I’m certain that the math nerds in the crowd started mumbling about cosines and reached for their scientific calculators before this last step. The reason this trick works, however, is not because it’s a 30-60-90 triangle, nor because it approximates an isosceles triangle. What we’ve done is approximate an arc-length of a circle.
As we already know, a circle (a) contains 360 degrees, and (b) has a constant ratio between its circumference and diameter, known as pi, or 3.1415926blahblahblah, which, for the sake of rough simplicity, we will approximate as 3. What Molly’s trying to figure out is the distance (in Molly-paces) from the center of the circle (the target) to the perimeter, a portion of which she’s just paced off. That distance (the radius ) is half of the diameter, so we’re going to use (in rough simplicity, 6) as the total number of Molly-paces it would take to walk around the entire circle, and then solve for

Since we know how much of the circle we’ve walked around (“degrees changed” out of 360), we also know what portion of the circumference we’ve paced off (“Molly-paces” out of 6). Since these are equal portions, all we need to do is simplify:

degrees changed = Molly-paces 360 6r

degrees changed * 6r = Molly-paces * 360

degrees changed * r = Molly-paces * 60

r = Molly-paces * 60/degrees changed


It’s not terrifically precise, but it doesn’t have to be. It was close enough for Molly to locate Thomas in Svartalheim, and now you’re just that much cooler (and/or more dorky) for knowing it. Now, for your homework, go find Mouse. Ten paces off your shoulder gives you two degrees of bearing change.

Did Jim Butcher sit down and figure out the mathematics in Bombshells as Andy Hammond describes in his guest article, Molly's Nifty Trick?

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This wonderfully nerdy guest post was brought to you by Andy Hammond!

The Duck Quacks

The Duck Quacks published on 4 Comments on The Duck Quacks

Theory 1: Molly/ Mab
Part 1

“You should not presume wizard. I adore Freedom. Anyone who doesn’t have it wants it”


This all started with the headaches. Harry has them, we all know this. There have been a few suggestions as to why; Lash coming back, permanent brain damage at the end of WN, perhaps he has strained his magic too much, but then I realized we know at least one cause for this headaches; he has them in SF, when Mab messed with his head while she borrowed his blasting rod, and reprogrammed his head to forget he had ever had it. While discussing this, I wondered well then, if she caused that headache, what else could have happened during the books that she could have taken or messed with?

Which gives us, in discrete mathematics, our starting point?

STATEMENT: Mab caused the headaches.

I am not saying this is the truth, I am stating it as the point of argument. In discrete math, you start with an assumption, then build on it one point at a time, as a test to determine if the original point is true. (For all rational numbers N, if N is F(N) is true, then F( N+1) is true; if you then can reverse it from the final conclusion, the theory is true ; this is called the principles of incursion and reduction.)

So, following this point, what other headaches could have been caused by Mab? It was He Whom Walks who first noted that in the book Turn Coat, that little Chicago was not mentioned. Which is strange, as Harry was desperate to find Thomas; and in every other book, Harry mentions it in every other book, and it had been repaired form it’s damage taken in WN as it was used in SF. Furthermore, when Harry does refer to the table, it is covered by a heavy tarp; which are the same words he used to describe his missing memories of the blasting rods on SF, page 312. And we know Mab caused those headaches, it describes the headaches, right on that very page.

Additional point, Namshiel’s missing coin. We have been assuming That either Marcone, Hendricks, or Gard took it. But Marcones says he did not, Hendricks has shown no signs of it, and Gard was driving. But what if there were other people on the island, undetectable to mortal eyes? Mab cannot interfere directly in mortal affairs, but she can claim anything Harry owns or has rights to. His “life, his fortune, his future”; once he defeated Namshiel was defeated his coin by right of battle was Harry’s and Mab could step in and claim it. ( I will admit this one may be stretching things, but it’s just a side idea.)

STATEMENT: Mab fixed little Chicago in Proven Guilty. “even if there HAD been a threshold, it wouldn’t have done diddly to stop any number of supernatural baddies. The fetches in PG hammered down the /Carpenters’/ front door, and that’s a threshold like the rock of firkin’ Gibraltar. The loup-garou sneered at such things. A threshold wouldn’t slow down a Denarian for a moment, nor would it stop ghouls, ogres, or any number of largely physical (as opposed to manifested spiritual) beings. And even if the skinwalker had been something summoned from the Nevernever into a manifested physical body, the toad demon was one of those too, and IT stomped through Harry’s pathetic threshold in the very first book”

-Jim Butcher

Which leaves questions of how Mab got past the wards, Past Bob- something I consider a point in her favor actually; of all the suspects she could mess with Bob the easiest; and most importantly, how could she have predicted this chain of events?

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