The Theoretical Minimum: Lecture 1, The Nature of Classical Physics

This is part of my series of commentary on the physics book The Theoretical Minimum.

Notable Quotes

The job of classical mechanics is to predict the future. (p. 1)

I love this.

The rule that dynamical laws must be deterministic and reversible is so central to classical physics that we sometimes forget to mention it when teaching the subject.  In fact, it doesn’t even have a name.  We could call it the first law, but unfortunately there are already two first laws — Newton’s and the first law of thermodynamics.  There is even a zeroth law of thermodynamics.  So we have to go back to a minus-first law to gain priority for what is undoubtedly the most fundamental of all physical laws . . . (p. 9)

As a number-lover, this sort of thing just makes me all kind of amused.

But there is another element that [Laplace] may have underestimated [when he said the laws of physics could theoretically predict the whole future]: the ability to know the initial conditions with almost perfect precision. [...] The ability to distinguish the neighboring values of these numbers is called “resolving power” of any experiment, and for any real observer it is limited.  In principle we cannot know the initial conditions with infinite precision. [...] Perfect predictability is not achievable, simply because we are limited in our resolving power. (p. 14)

This concept, I am keenly aware, is what makes my Russell’s Attic books science fiction.  My main character is only able to do the calculations she can on the world around her because I permit her to have indefinitely good resolving power.  It’s kind of a required secondary power for what she does.  And reading this section, it completely tickled me that it has a name!

Thinky Thoughts

I’ve said before that I reduce all physics to doing math.  I felt like I was cheating a bit in this section, because saying a system is deterministic and reversible is the same as saying you can model it with a one-to-one function.  So I bopped along just thinking of the functional invertibility of the the rules, most of which I knew off the top of my head.

Sigh.  You can take the mathematician out of mathematics . . .

The Theoretical Minimum: Preface

So. I’ve always wanted to learn physics.

I know this will sound bizarre to most people.  I went to freakin’ MIT — one of my physics professors as an undergrad won the Nobel Prize the semester after I was in his class.  But I’ve never felt I’ve had a good intuitive grasp of physics, nor studied it to a depth where I felt like I understood it.

A confession: Physics doesn’t come naturally to me.  It’s not intuitive.  (I always end up reducing it to mathematics, and then it makes sense.)  Because physics ran a bit against the grain of my brain, I didn’t study it heavily in college beyond my undergraduate requirements, and I always regretted that.  I’ve always wanted to know more, and felt a bit like the physics world was this fascinating enchanted universe but I’d only ever managed to have my face pressed up to the glass, catching glimpses without being able to be a true party to the wonder.

While I was down with cancer, a college friend of mine gave me a book called The Theoretical Minimum, by Leonard Susskind and George Hrabovsky.  He billed it to me as, “for people who have a decent foundational background and know calculus, but who were never able to study physics to the point they wanted to.”  I said, “Hey, that’s me!”

Well, I’ve been reading it, and it’s quite excellent!

To keep myself on track with it, I’m going to blog about a chapter every week or thereabouts.  I apologize if people find these boring — I’ll try to keep them pithy.  I started the book a while ago so hopefully I should be able to keep up with the posts  (in fact, I’m going to write a few of these and buffer them before posting, and then send them up every Saturday or so).

So, these posts will be some commentary on The Theoretical Minimum, whatever I feel like writing about it.  I shall start with the Preface, since it’s quite worth starting with:

Notable Quotes

As it happens, the Stanford area has a lot of people who once wanted to study physics, but life got in the way.  They had had all kinds of careers but never forgot their one-time infatuation with the laws of the universe.  Now, after a career or two, they wanted to get back into it, at least at a casual level. (p. ix)

This is pretty much exactly me.  Also, I often regret that there aren’t more opportunities for hobby academics — thanks to online endeavors like Coursera and edX, that’s changing, happily, but it can sometimes be hard to find courses that are just that bit beyond the basics.  Especially for more theoretical scientific disciplines.

Okay, now next week — on to the physics!

Why/Why Not: “The Invisible Orientation: An Introduction to Asexuality”

It’s been a privilege for me to know Julie Sondra Decker for some time.  In addition to being a fiction writer and artist, she’s a passionate advocate and educator on asexuality (check out her recent excellent article for The Toast here!), and is a lovely person to boot.  I’m beyond delighted to have her join the blog today — the very day her book The Invisible Orientation comes out, a book I’ve been waiting to see hit the shelves for a while.


Why was this a book you needed to write, or only you could write?  What parts speak to who you are as a person, your life experiences, or the things you want to see more of?

Julie Sondra Decker: There were literally no books out there for general audiences on the topic of asexuality. NONE. One fellow wrote a textbook, but it was both academic and written from a non-asexual point of view. Another fellow released the partial contents of his blog in a self-published book, but most of the promotion he does is through the same blog where you can read its contents online—it’s not marketed in a mainstream way. So basically, asexual people and their loved ones go to the bookstore, look for books about this topic, find a whole lot of nothing, and conclude that they’re alone or asexuality isn’t real. There’s a ton of power in a book being there for those people. I wanted it to exist, so I wrote it.

Part of the reason I decided it should be me to write the book was that I’ve been writing all my life, and people seem to pay attention when I write about this. I’m one of the only asexual people who had developed a really significant platform online, and because I’d already started pursuing publication for my fiction when my fairy tale trilogy got signed to an agent, I had some idea of how mainstream publishing worked. I was in a unique position to both develop the content and get it out there. So I did.

The book has very few personal bits; the introduction is a personal story of how I came to identify as asexual and why I think it’s important, but the rest is general. Despite that, every piece of it reflects my experience living in a world that doesn’t recognize asexuality or wants to erase it, and while it’s the first book of its kind, I hope it helps pave the way for more asexual people becoming secure in their identity, more non-asexual people supporting and nurturing their asexual friends and loved ones, and more asexual narratives in mainstream culture—including fiction.

Why was this a book that you couldn’t write—why did it force you to grow as an author? What terrified you along the way? What parts of it stretched you, made you think, made you research? What parts were you most afraid of getting wrong?

I have so much to say about this! First of all, I was afraid the book would feel too much like a single person’s perspective if I spoke in my “I” voice throughout, so for the most part I kept the personal content to the introduction and backed off the personality for the rest of the book. However, I worried that the audience would find it dry and disconnected if I didn’t find another way to make it feel personal, so I decided to incorporate illustrative quotes from asexual bloggers to facilitate reader connection. And it also served to feature diverse asexual narratives throughout—I had contributions from asexual people of color, asexual people with autism, asexual people with disabilities, asexual people of various gender identities, asexual people of many different romantic orientations; it ended up being the perfect solution to the problem of giving the audience a “who” to connect to without stealing it all for myself. Because believe me, I worry that being the author of the first book that’s probably going to be THE asexuality book for at least a while will necessarily make it seem like I’m speaking for my entire community, and I never wanted to do that. So I decided, in the limited ways available to me, to let some of them speak using the microphone I handed them.

As for being terrified, there are several places in the book that I am sure are controversial, and the entire time I was writing them I kept cringing, thinking I just know this is going to get someone angry. I know you can’t please everyone, but I wanted so badly not to get it wrong—especially since it’s so easy to make a mistake and be judged ignorant. The section I’m thinking about specifically was my discussion of asexuality’s intersection with the queer communities. In some circles, suggesting asexual people are queer—or that they experience overlapping or analogous struggles—can get you flamed so hard you will turn into a crunchy piece of ash and crawl under your bed. But then other queer communities absolutely think asexuality is queer and/or marginalized because of heteronormativity, and are dedicated to inclusion. I addressed the reasons asexuality makes sense as a queer identity and also the reasons why certain queer communities may have legitimate, non-xenophobia-related reasons for not wanting to include asexual people, and I follow up with a section on queerness in general. And the section finishes off with a long bulleted list of experiences asexual people have that contributes to their marginalization as an identity, along with some bullets that they share with LGB and T populations. I did as much homework on this section as I possibly could, but I wasn’t satisfied with it. I decided to reach out for help—and in so doing, I also invited help on other sections in the book in which I was discussing parts of asexual experience that did not intersect with my own experience.

I posted a request for people with certain identities—including non-asexual people—to contact me if they’d like to read short sections of the book and react to them with their unique perspective. And I got a surprising amount of support; more than eighty readers of my blog e-mailed me offering up their demographic information and an offer to react to excerpts, and more than two thirds of them actually delivered on their promise. The section about inclusion in queer spaces kicked up very few dust bunnies, happily, but I was pleasantly surprised at the opportunity to expand, refine, and correct other sections in which I’d initially had minimal or misleadingly sparse content—most notably asexual people of color, religious asexual people, asexual men, autistic asexual people, and kinky asexual people.

Ultimately, I could not have served my community anywhere near as effectively with this book if I had not explicitly invited them into it. It was an amazing experience and the outpouring of support was humbling.

You should see my acknowledgments page. (Pages, actually.)

Give us the blurb or an excerpt from The Invisible Orientation.

A short description of the book’s content, along with lovely blurbs and reviews from others, can be read here on the book’s page. My book was also excerpted in TIME Magazine recently, with a short excerpt from the book that they titled “How to Tell If You Are Asexual.”

But here, I will offer a short excerpt that hasn’t appeared elsewhere, from a sub-chapter of the book’s section about misconceptions: “Shouldn’t Asexual People Let an Experienced Sexual Partner Change Their Minds?”

One of the most frustrating misconceptions about asexuality is the widespread belief that asexual people must not have tried sex—or, similarly, must have tried sex with the wrong partner(s)—and that they can be “converted” through a good sexual encounter. Amazingly, a very high percentage of the people who come up with this one believe themselves to be just the one to carry out the experiment! What do asexual people have to lose by “just trying it,” right? Can’t those stubborn people just open their minds and let someone show them a good time?

Some asexual people have tried it. Some asexual people don’t want to for the same reason that many heterosexual people don’t feel obligated (or even able) to have sex with a member of their own gender to find out if they’re really straight. Asexual people don’t have to try sex to make sure they wouldn’t like it; whether they’re attracted to others is the basis of whether they’re asexual, and attraction tends to play a big part in most people’s choices of who to sleep with. People usually want sex long before they get it. It’s not common for a person to suddenly start finding other people attractive because someone gave them good sex.

No, sex with a talented partner is not going to flip a switch for asexual people’s ability to become attracted to others. And no, it’s not close-minded of asexual people to refuse to “try” a self-proclaimed master of the art. If, for instance, there’s a straight guy and his feelings about getting oral sex from a man can’t be described as “indifferent,” he may understand why he can’t expect an asexual person to “just try.” Some asexual people aren’t only expressing that they aren’t excited about or interested in sex; some are actually repulsed by it (as many heterosexual people would be if the only sex available was with their own gender). No one should offer to try it with an asexual person as if it’s a favor to them for the benefit of their self-exploration, and no one should act like their unwillingness to have sex is an attitude problem.

Unfortunately, many asexual people feel pressured to go through with it even if they really, really don’t want to . . . because they’re told over and over again that something worthwhile and fulfilling and beautiful is waiting in coitus, and they’re told they “just can’t know” until they do it. What if they do try it, still don’t experience sexual attraction to others, and realize they were right about themselves in the first place? Do critics nod and finally agree that they did everything reasonable to make sure they were really asexual, and finally start accepting the orientation?

Of course not. Asexual people then hear “If you tried it once and didn’t like it, try again! You did it wrong, or with the wrong person! You didn’t give it a chance!”

“I didn’t enjoy it because I don’t enjoy sex with people I’m not attracted to” does not exist to these folks. That just doesn’t compute.

Some people who say this are assuming asexual people tried and had a bad experience, which led them to conclude once and for all that sex was not worth it. The first problem with this is that sexual attraction is something people usually experience before ever having sex for the first time, and they don’t have to prove that they’re feeling it or get “switched on” to the idea despite having no inkling that it would feel good. They’re compelled by sexual attraction. Asexual people are not. Trying it anyway isn’t going to change whether they’re attracted to others, though it may help them understand what they’re willing to do sexually.

And the second problem with this is that trying “again” still isn’t going to satisfy anyone who says this. If an asexual person tries a second time, a third time, a fourth time to like sex and they fail, they will continue to be bombarded with suggestions that they try a different partner, a different gender, a different position, a different time of the month, whatever—as long as they keep trying until they like it. This is absurd because, again, a negative can’t be proven.

Lots of people enjoy the idea of making an indifferent or even a gay person realize how great heteronormative sex is, after which, of course, the “converted” will thank the “converter” profusely for the eye-opening, transformative experience. People love thinking that they’re so good at sex they could even make an uninterested person crave it. And this, yet again, is a symptom of ego—this “experiment” would not be for the benefit of the asexual person, but for the purpose of fueling the other person’s self-esteem and feelings of accomplishment, as well as confirming their preconceived ideas and narrow perspectives. Again, it’s about them, not about the asexual people.

Asexual people would really rather their experiences be about them.

Finally, give us a funny or unusual piece of trivia about yourself.

I have a very long list of ways in which I am a living contradiction:

  • I love babies but don’t want to have kids.
  • I like buses, trains, and airplanes but I don’t like travel because I don’t like getting there.
  • I hate school and I got a degree in education. (Then proceeded to not be a teacher.)
  • My body thinks it’s left-handed except when I write.
  • I love baking and then I’m meh on eating what I bake.
  • I hate sports but I’m obsessed with inspirational sports movies.
  • I don’t enjoy public speaking but I’m decent at it and not afraid of it so I do it all the time.
  • I’m a vegetarian for anti-cruelty reasons but I’m not an animal lover.
  • I read and write fantasy but have zero interest in role-playing (video games or tabletop).
  • I love eating very bitter or very sour food, but will roll over and die if I eat something even slightly spicy.
  • I grew up hearing you’re supposed to be good at either math & science OR language & history. I excelled at science and language. And failed miserably at math and history.
  • I’m introverted and mildly asocial but I don’t mind crowds and have a lot of friends.

Thank you so much for joining me today, Julie, and best of luck with release day!  The Invisible Orientation is available from the following retailers:

Barnes & Noble
Book Depository
And is on Goodreads here.

Julie Sondra Decker is a versatile author from Tampa, Florida. Her fiction is primarily focused on speculative subjects—science fiction, fantasy, magical realism—and she writes for young people as well as for adults. Her nonfiction addresses awareness efforts for underrepresented subjects, most notably asexuality. Julie has been a prominent voice for the asexual community since 1998, spreading asexuality awareness through her popular videos and blog essays. She has been interviewed in many mainstream publications, including Marie Claire, Salon, and The Daily Beast, and she was a prominent interviewee in the documentary (A)sexual by Arts Engine. She is a regular contributor to Good Vibrations. Julie is also a webcomic artist, a singer, and an avid reader. As an aromantic asexual woman, Julie is happily single. In her spare time (on the rare occasion that she has any), she enjoys baking, playing tennis, blogging, and posting wordy rambles on the Internet.

Find Julie Sondra Decker on:
Google Plus

Hugos 2014

I’ve only got a minute here — I’m buried in edits — but I wanted to drop a quick note about this year’s Hugos before we’re too far out.

The full list of winner and nomination votes is here:

First, congratulations to all the winners!

Second . . .

I’m on record as having problems with the Hugos.  But this year has made me feel a lot more invested and a lot more excited about both the Hugo process and SFF awards in general.  Not because everything I wanted won — in fact, I think my first choice lost in more categories than it won, giving me a few wallops of disappointment! — but because I observed so much passion in the discussions surrounding the Hugos this year, so much love for the genre, so much desire even by people who had problems with the awards to make their voices heard, to vote, to make it be better.

I can’t say I still don’t have problems with the awards.  But in one year I’ve gone from not caring at all about the Hugos to caring quite a lot, and I think that’s down to the people in the SFF community around me, the people who put so much passion into recognizing the voices in our genre that speak to them.  You’ve made me care, y’all.

Also, the Hugo packet?  Pretty rad reading.  I’ve gotten way more into short fiction the past few years, and I really dug having such a great collection of it to immerse myself in.  And I’ve gone on to recommend a bunch of the short pieces I read this year to others.  (I’ll probably be making rec posts for some of them here, too, as soon as I get some time.)

I’m very much looking forward to nominating and voting next year now.  And I hope even more people consider nominating and voting as time goes on.  I have to say, it felt rather excellent to cast my ballot for honoring some remarkable talent, and I’m excited to keep doing that.

Truly, congratulations to everyone who won.

(And hey, now maybe I’ll finally send in my application to be in the Emmy academy.  After all, Orphan Black NEEDS that nomination . . . ;) )

I Am An American, and This Is Not Okay

The violence in Ferguson is still happening.  Another journalist was arrested today.  The National Guard is coming in.  By all appearances, the local PD seems to be invested in fanning the flames and working against the Missouri Highway Patrol (who briefly had things under better management) and the DOJ/FBI.  Follow the links from my previous post for coverage.

I want to say something about what’s happening here.  It’s not as important as what other people are saying — go read them — but I want to say it.

There’s a fairly vocal subset of the US-based Internet who seems to like to cry, “Free speech!  First Amendment!” at the drop of a hat.  Even when it doesn’t apply.  Like when people’s words get criticized (not a free speech violation).  Or when people lose the platform that was previously provided by another free person (also not a free speech violation).  Or when people are banned from privately-owned spaces (seriously, NOT a free speech violation).

You know what qualifies as actual First Amendment violations?  Gross, extreme, no-American-should-be-okay-with-this First Amendment violations?  What’s happening in Ferguson right the fuck now.

Journalists being arrested.  Press and citizens being told by authorities to stop recording.  Police aggressively preventing citizens from engaging in peaceful assembly or protest.  News helicopters being banned.  People having guns pointed at them or handcuffs slapped on them because they were standing or walking or talking or shouting or protesting or recording or associating in a manner a police officer didn’t like.  Curfews.  Snipers.  Tear gas.


The people of Ferguson are my fellow Americans.  And this is what it looks like when Americans’ rights are being violated.

For God’s sake, get angry.

Ferguson: Everyone Needs to Be Following This

I haven’t said much on Ferguson because I don’t have anything smart to add, and also I’m here safe on the West Coast and not in St. Louis having tear gas thrown in my fucking yard.  But I realized: I can and should signal boost, even to my small audience here.  To anyone I can.  Because if you’re not following what’s going on in Ferguson, start right now.  Police are assaulting unarmed protesters with tear gas — journalists are being arrested — a no-fly zone has been instituted — police are ordering citizens and reporters to turn off their cameras –


And there’s no substantive response — none — from the state or federal governments.

A lot of media outlets aren’t giving full coverage.  Places to start:

#Ferguson on Twitter

@AntonioFrench is a St. Louis alderman tweeting from the ground in Ferguson, he’s giving a stunning level of coverage eta: It’s being reported on Twitter that he’s now been arrested.

Here’s a Twitter list of people tweeting from Ferguson

Here’s a Twitter list of journalists tweeting from Ferguson (thank you to those journalists — media, we need more, send more)

This article summarizes responses from horrified military and vets: “We rolled lighter than that in an actual war zone.”

This livestream is no longer live (as of this writing) but you can see prior footage of police attacking a group of unarmed protesters with hands raised — police demand that they turn off cameras but they keep filming.

Talk about this — tell people — link about it — especially my fellow USAians, let our government know that this is not okay.  That our leaders MUST respond.  Let the people of Ferguson know they are not alone.  Make #Ferguson trend across the country, demand a response from the government of Missouri and our president.

I am angry, and I stand with Ferguson.

Why/Why Not: “The Glass Sealing”

A very warm welcome today to Andrew Leon Hudson, who’s here to talk about his novel The Glass Sealing. You know, I always feel like the best speculative fiction reflects the real world and makes us think, and it sounds like Andrew feels the same way . . .

The Glass Sealing

Why was this a book you needed to write, or only you could write?  What parts of the premise, plot, or characters speak to who you are as a person, your life experiences, or the things you want to see more of in fiction?

Andrew Leon Hudson: I don’t know if I’d claim to be the only one who could have done anything (that kind of thing always sounds a bit Matrixy, and I doubt I’ll ever save the cheerleader or the world), but that fits since one of the themes of The Glass Sealing is the power of groups against the power of individuals, and the weaknesses of both. The same person can be a hero to their supporters and a villain to those they oppose; a state’s use of strength can either protect its citizens’ rights or persecute them; and for every peaceful sit-in there is a riot… though the balance probably weighs in favour of burning cars, not incense.

I live in Madrid, Spain, and in 2011 the legacy of the Occupy Wall Street movement reared its head almost on my doorstep. For about a year, protesters held their ground in the city’s centre protesting the Spanish government’s austerity measures, and they’d probably still be there if it wasn’t for a visit from the Pope in 2012—the kind of thing that motivates authorities to clear the streets! When I learned about the Darkside Codex—the Steampunk shared world project my novel is a part of—all this was still fresh in my mind, and the result was relocating OWS to my version of the industrial revolution and the Luddite protests. Steam-powered robots won’t take our jobs!

However, I didn’t want to set up a battle between evil fat-cats and noble workers, since the world is rarely so easy (although the two sides in the financial crisis looked pretty stark, I’ll admit). Rather than pure heroes and absolute villains, I wanted to present leaders and followers on both sides of a conflict who have mixed, even questionable motives but which spring from good intentions, at least from their own points of view. Lofty ideals are useful: they offer great heights to fall from.

Why was this a book that you couldn’t write—why did it force you to grow as an author? What terrified you along the way? What parts of it stretched you, made you think, made you research? What parts were you most afraid of getting wrong?

There are some great female characters in fiction but there are also pit-falls to be watched for, and one concern I had was of seeming patronising. The pseudo-Victoriana of Steampunk is often used as a frame for female liberation, the casting aside of gender repression, and one of my two protagonists was created in this vein, but it would be very easy to go two-dimensional. I’ve tried to present a strong personality that gradually reveals its flaws, just as I have for the male character who stands in opposition to her goals—but gender is not an important part of that dynamic, and it is really via her personal relationships that I’ve tried to present her challenge to conventional social expectations. I told myself while writing that it would be interesting to seek out a feminist analysis of the character and story to see how well, or how poorly, they both comes across in that context. So far I’ve chickened out, but I’m open to requests!

Give us an excerpt from The Glass Sealing:

One of the workers was watching the yard, and Ben heard him whisper, “Here they come,” in an oddly unafraid tone. That changed when the man got a better look at what was coming. “Gavin,” he hissed, “fellas, look at this!”

The workers turned, and Ben spotted their bearded leader immediately. “That’s him, boss,” he said. “The big one in the middle.”

“Of course it is,” Black Tom murmured and then raised his voice as the gang spread out. “Hello, gents. Nice night for a walk, eh? But you know, this here is private property. I’d suggest for you to go walking somewhere else, but oh, you’ve only gone and knackered the gate lock coming in here.” The gang formed a loose semi-circle, fencing the cluster of workers in against the factory doors. “That makes this ‘breaking and entering’, and that’s a crime. And crimes call for a little punishment in polite society, don’t they?”

“This is none of your business,” said the leader, Gavin. “Leave us to ours.” He hefted a long-handled spanner that probably weighed as much as Ben did. Give the man credit, his deep voice didn’t waver. Ben wouldn’t have been so bold if faced by twice his number.

Black Tom obviously felt the same. “My my, you’re a one,” he chuckled. “So look, if you all line up facing the wall there and give us no trouble, we’ll send you off with just a tickle.” Then the smile left his voice. “Or we can scrap over it, and you can crawl home.”

The nervous workers shifted their feet, each brandishing heavy hand tools, but Gavin just squared his jaw. “We’re not here to be cowed, and we’ll leave when we’re finished.”

“You’ve got that right, mate.” Black Tom shrugged. “Fair warning, have at ’em.”

The gang began to close in, swinging their clubs. In the face of chanting strikers they’d have yelled, but in the night’s quiet their silent approach was even more unnerving. Then, in the brief moments between the end of the talk and the start of the fight, Ben heard something else in the dark—from behind them.

At first he saw nothing but the empty yard, the high walls, the open gates, and the dark of the street beyond. Then figures began to emerge from the gloom, each one carrying a tool.

“Tom,” he said. “There’s more.”

Black Tom took in the building crowd outside the yard, barked an order, and the gang stopped before they’d so much as landed a blow. A few watched the first group while the rest turned to face the newcomers. They kept coming in through the gates, and the yard started feeling a lot less empty. There were more than just the thirty-odd from the alehouse—at least twice that. Ben hoped his earlier estimate of the gang’s capabilities was a conservative one.

Black Tom slipped a short-barreled revolver from inside his jacket. A slender knife dropped from one sleeve into his free hand. Ben had the sudden, highly unwelcome realization that he was the only man in sight not armed with anything.

The last of the workers were inside the yard now, the Roughnecks outnumbered by at least four-to-one and with opponents front and back.

Black Tom turned to Gavin. “There’s still time for you to leave it at this and go home,” he said, utterly brazen in face of bad odds—but that was always a basic requirement of rising to the top in the Southwatch underworld.

“Your position’s a bad one, mister,” Gavin’s voice rumbled back. “Maybe you’re the ones who should be going quietly.”

Black Tom yanked off his hood and threw it on the ground, making sure everyone got a good look at him. “You know who I am, I hope,” he called, loud enough for all to hear. “Think twice before you start a fight you won’t be finishing.”

“Our fight is with Longstone and what’s in there.” Gavin jerked a thumb at the factory doors and raised his voice to a shout. “Make a gap, lads!” Waving them to either side, he had the mass of workers part down the middle, leaving a passage between them to the gateway.

Black Tom fumed, fingers flexing around gun and knife. Ben could see he was weighing up the balance between the lot of them getting out clean and the blow a retreat would be to his credibility with the rest of the Roughnecks. One way or another, he’d have a fight on his hands soon enough. The question was, which would he be most likely to win?

Before he made a decision, the quiet was broken by an echoing bang and the factory doors shook on their hinges. They burst open under a second great impact from within, knocking the nearest workers off their feet. Something moved inside. Flickering lights glowed. Then, in a cloud of smoke, to the grinding of metal, it moved out from the shadows and into sight.

Finally, give us a funny or unusual piece of trivia about yourself.

All right… I once had a job sandpapering Sylvester Stallone’s armpits. Probably you feel that statement needs qualifying. Reluctantly I concede that, in fact, it was only a slightly larger-than-life-size fibreglass statue of Rocky and not the man himself, but in fairness to the let-down there were about twenty of them and I had to apply that sandpaper from head to toe. Later we got to decapitate them all. That was a fun nine weeks.

Thank you so much, Andrew!  The Glass Sealing is is available through the following retailers:
Barnes & Noble
Musa Publishing (publisher’s own website)

Andrew Leon Hudson is an Englishman in Madrid and has been writing full-time since 2012, partly in an attempt to appear as unemployed as everyone else in the country, partly in an attempt to lead a fulfilling life. In preparation for this he has worked in fields as diverse as prosthetic make-up, teaching, contact lens retail, “intoxicant delivery” and the services (customer and military). He used to have his own company, but it died. He never tweets as @AndLeoHud, and you can fall in love with him further on his pseudonymous website,

Guns and Math: Does 1 MOA *Really* Equal 1 Inch at 100 Yards?

I’m doing rifle marksmanship training right now, and the rule of thumb for sight adjustment is that 1 minute of angle (MOA) equals one inch at 100 yards.  That means that if you adjust your sights to sweep in a certain direction (left, right, up, or down) by an angle measuring one minute, your point of impact on a target 100 yards away will move in that direction by 1 inch.  So, for example, if you adjust your rifle by 1 minute of arc left, your point of impact will shift left by 1 inch on the 100-yard target.

Of course, being a mathematician, my thought is automatically, “One MOA equals 1 inch at 100 yards?  How convenient!  I should do the math to see how close it actually is.”

It’s pretty easy to convert the angle measure of an arc to the arc length.  Take a look:

Here, theta is the angle, r is the radius (imagine the pie slice as a sector of a circle with radius r), and s is the length of the arc.

Here, theta is the angle, r is the radius (imagine the pie slice as a sector of a circle with radius r), and s is the length of the arc. (Wikimedia Commons, public domain.)

If you have the measure of the central angle in radians, the measure of the arc length — denoted s here — will be that number times the radius:

s = \theta r

Since the angles we’re looking at are so small, we can use a small angle approximation to say that our length of shift on the target equals the arc length –

. . . OKAY FINE, I shudder when physicists use the small angle approximation, but when I did it ABSOLUTELY EXACTLY without using the small angle approximation, the length of the chord matched the length of the arc out to 7 decimal places, which means our error here is about the width of an atom.  SO FINE.  We’ll use it and say the chord approximately equals the arc.

Arc / chord comparison

The red curve is the “s” we’re finding; the blue line is the actual straight-line distance on the target. For angles as small as we’re examining, the difference in length between them is about the width of an atom or two.

Let’s go back to the above formula.  We need one minute in radians.  One minute is 1/60 of a degree, so we get

\left(1/60 \text{ degrees}\right) \left(\frac{\pi}{180 \text{ degrees}}\right) = 0.000290888209 \text{ radians}

s = 0.000290888209 * \left(100 \text{ yards}\right)

s = 0.0290888209 \text{ yards}

Which equals about 1.0472 inches.

(Look at me, truncating before we get out to 7 decimal places so the small angle approximation holds!  To find the exact number, you’d have to do 2 times the sine of half the angle you’re looking at (so, 2 times the sine of half of 1 minute converted to radians, in this case), and then multiply by the radius (100 yards) and then convert to inches.  Again, for angles this small it’s equal to the above out to an absurd number of decimal places.)

So, yeah, 1 MOA is 1.0472 inches of distance at 100 yards — it’s pretty close to one inch!

The rifle marksmanship rule of thumb continues to say that we’re at 1 inch of point-of-impact change per 100 yards out, so at 200 yards 1 MOA would be equivalent to 2 inches on the target, at 300 yards 1 MOA would be equivalent to 3 inches on the target, etc. (and at 50 yards or 25 yards, 1 MOA would be equivalent to .5 inches or .25 inches on the target respectively).  Here’s what the actual numbers are:

Distance 1 MOA Equivalence (Rule of Thumb) 1 MOA Equivalence (True)
25 yards .25 inches  0.2618 inches
50 yards .5 inches  0.5236 inches
100 yards 1 inch  1.0472 inches
200 yards 2 inches  2.0944 inches
300 yards 3 inches  3.1416 inches
400 yards 4 inches  4.1888 inches
500 yards 5 inches  5.2360 inches
1000 yards 10 inches  10.4720 inches

So we’re edging up to half an inch difference at 1000 yards.  That’s a lot!

Now the question becomes — well, scopes often adjust as 1 click = 1/4 inch.  But are they adjusting 1/4 of an MOA (and thus 1/4 of 1.0472 inches), or 1/4 of a true inch?  Wikipedia had the answer:

One thing to be aware of is that some scopes, including some higher-end models, are calibrated such that an adjustment of 1 MOA corresponds to exactly 1 inch, rather than 1.047″. This is commonly known as the Shooter’s MOA (SMOA) or Inches Per Hundred Yards (IPHY). While the difference between one true MOA and one SMOA is less than half of an inch even at 1000 yards,[5] this error compounds significantly on longer range shots that may require adjustment upwards of 20-30 MOA to compensate for the bullet drop. If a shot requires an adjustment of 20 MOA or more, the difference between true MOA and SMOA will add up to 1 inch or more. In competitive target shooting, this might mean the difference between a hit and a miss.

Hey, look how useful math is!