Hubris battling humility. I considered anti-blogging the last 3 paragraphs of the previous Thought, removing them from existence. They sound too much like boasting. But hey, we're all pals here, so forgive me the occasional moment of weakness. Maybe you'll hate the ending of Resolution; maybe you won't read it. I dunno. I wrote those words while working on the 2nd draft, several days before cold fear gripped my heart as I reached the ending and saw how badly I'd written it first time round.

(And there was an important 'if you read the earlier books...' qualification: a conditional clause or, as computer scientists prefer to say, a guard condition.)

I've just handed in Resolution to my editor, the splendid Simon Taylor at Bantam (or, strictly, Transworld: Bantam is the imprint, Transworld is the company). I don't think we should wait till the New Year for Resolutions. Really.

It was a December resolution last year that got me out of the full-time day job rat race. In February this year I discovered a new way of training which found its way into my daily workouts: I'm talking about the bodyweight exercises used by Indian and Japanese wrestlers, variations on freehand squats and press-ups. If you've made a decision, don't wait for the right moment to strike (he preached)... go for it right now.

Want to join a gym? Don't wait until January. Now's the time to begin that liberating self-discipline. Want to write a novel? Get up an hour early tomorrow, and write for an hour in your private space. Repeat daily until the work is finished. (Then write something new.)

What with time passing and resolutions forming, we can talk about physics, or writing, or working out. To me they're all sensible and interesting and interwoven. I think I'll concentrate on physics, and put some abbreviated notes on other stuff at the end.

Feel free to skip forward to "END OF PHYSICS BIT..." at any time.

Can you stand a bit of elementary geometry here? Let's pretend we have two towns, Alphaville and Betaville, and we know they're 5 miles apart (or kilometres, if you prefer). To set out from Alphaville and reach Betaville, I need to know more than the distance: the direction would be helpful. So, I need an angle, with reference to some baseline (eg. an East-West line, so due East is zero degrees). Something we all agree on.

Alternatively, rather than an angle, I could say that one way (though not the shortest way) is to travel 3 miles due East, then 4 miles due North. By magic (I didn't pick these numbers at random) old Pythagoras tells us that the hypoteneuse will be 5 miles long. (In other words, 3 across and 4 up gives us a distance and an angle. The angle's tangent is 4/3. Opposite over adjacent, remember?)

Specifying a distance in terms of two right-angled components (a direction E-W, another N-S) is handy. Easy. 9 + 16 = 25. The hypoteneuse, the shortest distance between A and B, is root 25, or 5. Sorry to insult you graduate physicists and mathematicians. I'm talking about orthogonal vector components, of course.

Oh, I forgot to mention that while Alphaville is built on the ground, Betaville is a floating city. So we need an up-down component. Given 3 shifts at right angles -- east-west, north-south and up-down -- I can still find the shortest distance from A to B. If the three distances are X, Y, and Z, then ShortestDistance^2 = X^2 + Y^2 + Z^2.

(X^2 means X squared, just multiplying X by itself.)

Time passages... We're almost there.

Relativity is misnamed. Relative motion was part of Galileo's physics, never mind Newton. If I throw a ball forwards at 10 miles per hour, but I'm on a train travelling at 60 mph, then someone at standing at the side of the track will say the ball's going at 70 mph. Obvious.

What Einstein said was, if the guy at the side of the track shines a torch, the light will emanate from the bulb at a particular very high speed. Let's call that speed c, for convenience. (Everyone does.) According to Galileo, who knew bugger all about electromagnetism and the nature of light (but would have known that 'celeritas' is Latin for 'speed'), if there's a big headlight mounted on the train -- remember, the train's travelling at 60 mph -- then the light should be thrown forwards at (c + 60).

(We'd need to specify both speeds in the same units; c is 3 x 10^8 metres per second, or 186000 miles per second, or 186000 x 60 x 60 miles per hour.)

See, what Einstein sussed out is that everybody always detects light travelling at c... not c plus or minus the speed of something else. (Well, strictly we need to be doing all this in a vacuum; travelling through some material can slow light down. The train is travelling on the lunar surface, and our guy at the side of the track is in a vacuum suit, OK?) The speed of light is *constant* -- anything with zero rest mass travels at that same speed -- and is not relative to anything whatsoever. At all. Ever.

In principle you measure speed with a ruler (to get the distance) and a stop watch (to measure the duration) and a calculator (for people too young to be able to execute the lost art of mental arithmetic and divide distance by time in their heads). Speed = distance/time, all right?

Now here's a conundrum. Most speeds are relative, but c is constant, yet you measure 'em all the same way, with rulers and stop watches, whether you're standing on the ground or in a train or in a spaceship. You're only going to get consistent results if the guy standing still thinks that rulers inside the train shrink and the stop watches slow down. (Take my word for this one, or look it up; I haven't proven it here, but it's not hard. Wild physics, easy maths.)

We can spin off in a few directions on this, and reach fundamental concepts which are not understand by anyone, all with nothing more than Pythagoras's Theorem. If you wondered why teachers used to drill it into your heads... That's why.

One interesting thing is the time dilation: folk on the train think their stop watches are fine; the guy by the track thinks his own watch is fine, but the passengers' watches run slowly. The faster the train is travelling, the slower the watches get. If the time between 2 ticks on our guy's watch is t, then he thinks the time between ticks on the passengers' watches is t divided by a certain factor. (The factor's value is less than 1; dividing t by a number less than 1 gives a bigger number than the original t.) The interval between ticks is longer... the watches are slowing down.

That factor is usually represented by the Greek letter tau, which is a squiggly t. (The tau factor is the square root of (1 - v^2/c^2).) This is very basic to anyone who's studied physics, by the way -- I'm not looking any of this up as I write. (What did I say about hubris?)

In that factor, v represents the train's speed. The bigger v gets, the smaller tau gets, and the bigger the time between ticks becomes. (Divide by a small number, and you get a big result. One-thousandth is smaller than one-third.) But suppose you're considering something that is actually travelling at the speed of light (so v = c in this case). Now tau is equal to zero. Hence the classic Poul Anderson novel, Tau Zero.

If you divide a number by zero, the result is infinity. The time between ticks on a stop watch travelling at the speed of light is... infinite. TIME DOES NOT PASS FOR A PHOTON.

There are more photons in the universe than there are particles of matter. For most of the stuff that exists in the universe -- I'm ignoring dark matter, aka quintessence, since we don't know what it is -- duration in time has no meaning. (A photon can be created and destroyed, yet in between... no time passes.) John Gribbin pointed this out in one of his books: it's absolutely fundamental, yet everyone ignores it.

Oh, and an observation of my own along similar lines. Anything with zero rest mass can never be at rest. Come again? Do the words "if it somehow were at rest, which it can't be..." really belong in a fundamental definition?

(Fundamental definitions... A fun topic for another time, I think.)

Now I'm gonna twist your brain in another way. What with all these lights and stop watches, it turns out we can never agree on simple things like whether two events happen at the same time. It depends on where you're standing and how fast you're travelling; all you can do is observe and measure and make deductions, and different observers produce different deductions (about simultaneity, the rate of other people's watch ticks, etc.). Since time and distance measurements are always wrapped up in each other, we talk about spacetime, and the *separation* between two events.

Remember how we said the square of the shortest distance between Alphaville and Betaville is (X^2 + Y^2 + Z^2)? Well, each of those cities is going to fire off celebratory fireworks. The square of the *separation* between the two displays beginning is (X^2 + Y^2 + Z^2 - T^2), where T is the time difference. When you're working with stationary cities, you might as well talk about distance and duration in the ordinary way, but if they're moving relative to each other at significant fractions of the speed of light, the only sensible way to relate two events is via their separation.

So, did you notice that minus sign creeping in there? It wasn't a mistake. But we're into some strange territory now.

One interpretation is simple: that however much space and time are wrapped up together, time remains fundamentally different from space; it is not simply a fourth dimension.

Stephen Hawking, the devil, has a twisty way of looking at it. The root of 9 has 2 values, 3 or minus 3. (Minus 3 times minus 3 is plus 9, right? Multiply by a negative, and you reverse the sign. Multiply two negatives, you reverse twice: back to a positive.) What about the root of minus 9? Well, it's plus or minus 3 times the root of minus 1. Now the root of minus 1 is simply a weird quantity: you can't taste it, touch it, or smell it. We denote it by the letter i, but giving something a name isn't the same as knowing what it is. Anyway, the root of minus 9 is either 9i or minus 9i.

Hey, we can now rewrite our separation... Separation^2 = (X^2 + Y^2 + Z^2 + (iT)^2) where iT replaces T, and that bothersome old negative sign from before is now positive. We're now treating iT as a measurement along a fourth, spacelike axis. Hey... That's cool. Oh, what is iT, exactly? It's imaginary time, of course. (Any number times i is called an imaginary number. Due to that inability to touch, taste, smell, etc.)

Now I'm going to give your cerebral cortex a final twist, and leave you to lie down and recover. Let's go back to Alphaville and Betaville on the ground: no floating or moving cities. They're 5 miles apart. If I start at Alphaville, and travel 3 miles East (plus 3, I'm going to call that, along the x-axis) and 4 miles North (plus 4 along the y-axis), I will have travelled 7 miles really, because of the route I chose, but just 5 miles as the crow flies (square root of (3^2 + 4^2)) and I'll be in Betaville. (I could go North then East, and end up in the same place.)

If I start in Betaville, I might travel 3 miles West (minus 3 on the x-axis) and 4 miles South (minus 4 on the y-axis). Where am I going to end up? Alphaville, hopefully, and 5 miles from Betaville as the crow flies. The square root of ((-3)^2 + (-4)^2).

So I can travel from A to B, or (by reversing the signs) from B to A, and travel the same distance. Reversing the sign just means I'm driving my car in the opposite direction, right?

Oh, but... If we're talking about the fireworks taking place in the moving cities, then perhaps I need to travel for 5 hours to reach event B. But that's the same as travelling along the fourth (imaginary time) dimension for, say, 5i imaginary hours, in order to reach event B. But once I'm there, I can just as easily reverse sign and travel -5i imaginary hours from the later event back to the earlier event A. Can't I? If imaginary time is spacelike, you can travel either way along it.

I knew you'd like that.

(And you'll notice that we didn't go quantum. Not once. Or thermodynamic.)


Oh, and for French movie buffs... I have seen Alphaville, though not for a long time. Recognized the satire on World of Null-A, a book which I could quote huge sections of -- verbatim -- when I was fourteen years old. (But not since.)

I'm not well versed in movies, but Nikita is my favourite French film. I'm going to nominate Heat as my favourite Hollywood crime pic, with the ever-watchable Messrs Pacino and de Niro, under Michael Mann's excellent understated direction.

Oh, hey... Did you want to talk about writing?

Look, I was serious when I said, if you want to write, do it. (What Nicola Griffith calls the Nike school of writing: Just Do It.) If you're working on a novel and not short stories, then I say: be strict (and joyful) and write every day. (It's harder with short fiction, to keep working daily, but Roger Zelazny did it when he was starting out. But he was a genius.) It's just like working out.

Books on writing? I read Characters and Viewpoint by Orson Scott Card just when I needed it. Stephen King's On Writing is superb. I read books by Natalie Goldberg on someone's recommendation, and personally picked up only one writer's tool, but one I use all the time: tying the scene together by being specific about one item. We're in a room with a blue formica-topped table, right? Not just any table, but blue formica... Fine. Let the reader construct the rest of the room in their mind, from that starting point.

Writing classes? Don't ask me: I've never been to one. Writers' groups? Joined one for a little while -- after I had 2 novels published -- spent some very pleasant hours socializing, but to no other benefit. But that's just me. When you've got a complete first draft -- and I mean a complete draft, not just a few chapters, damn it: committees can't write books -- then you need people to read it. Maybe a writers' circle is the only place to get a sympathetic readership. (A spouse is far better. No diplomacy. Your partner will give you the Real Deal, with no messing.)

What do you want those readers to tell you? What do you want to know? The bits that are boring... Cut them out. Or rewrite totally. The bits that are incomprehensible. The personalities, the events that don't work because they're inconsistent with the people.

When I first wrote Paradox, no one believed the way Tom's mother just ran off with the Oracle. Now, one of the things I've always done is read anything that my favourite authors ever wrote about their craft. The introductions in Roger Zelazny's short story collections, for example. Somewhere, the late great Mr Zelazny told of the way he began every novel: by writing a short story about each main character. A story that would remain forever unpublished, but would inform the background, the personality, bringing depth and life to the primary actors in his cast of characters.

So I wrote the story of Ranvera Corcorigan's early life. It produced no more than 2 or 3 sentences in Paradox, but that was enough.

Hemingway said: Writing can be learned, but not taught.

(Of course, he was a terrible role model in many ways. Personally, I don't drink alchohol, smoke anything, or even eat meat. Science Fiction, as they say, is the only true mind-altering drug. Though I'm pretty fond of crime fiction and caffeine, too.)

Well, we've talked about physics and writing. Fitness is good, but I won't harp on about it. Maybe some URLs would be in order.

Dave Draper is a 60-something bodybuilder from Arnold's time. Go to for words of gentle wisdom. A sentence in his book Brother Iron, Sister Steel begins: "Be a happy bodybuilder..." Marvellous.

For bodyweight exercises that are fantastic for combat athletes, the Combat Conditioning book from will tell you all about it. Or just google these 2 terms until you find how-to descriptions: baithak and dand.

Or, starting tomorrow, get out of bed first thing, drink a glass of water, go out for a 20 minute jog. Repeat daily forever. (I'd rather write first, train afterwards. But the trick is, if you need to work out first, the glass of water helps.)

One last story... Some years back, I was in Dublin for a week, doing some IT consultancy. Had a few adventures, including going to a very shady-looking district to find a dojo I'd been told about, going through a narrow doorway in a warehouse, up the steps and into the unknown... and finding a wonderful, tough traditional shotokan dojo. Polished, sprung wooden floors; serious, dedicated people. Lovely place.

Anyway, I still had time to kill in the evenings. Tried ringing Anne McCaffrey, but she was globetrotting somewhere. So, stretching in my hotel room after a run, I committed an act of total desperation, and decided to watch television. (Writing and TV are mutually incompatible. Stephen King and William Gibson say so. I add my tiny voice to theirs. Here endeth the lesson.) Switched on Channel 4, and saw some muscular black dude performing martial arts, and thought: He's pretty handy. Man knows what he's doing.

What was I watching? A documentary on Afro-American SF writers, as it turned out. As far as I know, Chip Delaney and Octavia Butler have nothing in common with Bruce Lee, but the third featured writer was Steven Barnes, and that's who I was watching.

Steve's website at has good stuff to say about writing, and a nifty weight training routine called The Cube that requires a couple of dumb bells and some of that joyful self discipline we've been talking about.

Other writer-martial artists that I've met are legion. Well... Walter Jon Williams and Joe Lansdale and Juliet McKenna. I'd back them against a legion any day.

Enjoy your Christmas, or your Hanukkah, or whatever holiday you celebrate. Be strong and peaceful. Only time and love matter.