Richard Baker's Journal

The causal structure of black holes, part two

In the previous part of what has now become an ongoing series on the causal structure of various general relativistic spacetimes, I discussed the causal structure of the flat, Minkowski spacetime of special relativity, and of the Schwarzschild vacuum outside a spherical, uncharged, non-rotating star which collapses to form a black hole. In this part, I'd like to discuss the so-called Kruskal extension of the Schwarzschild vacuum. This is the general solution for a static, asymptotically flat vacuum (that is, a matter-free spacetime that looks like Minkowski spacetime when one is far away from the event horizon) containing a black hole. In other words, this time we'll consider a black hole that exists for all time, rather than one which forms from the collapse of a star.

As commenters have noted, the astrophysical black hole in the last article is not a time-symmetric solution as there's a star early in time and a black hole late in time. The time reverse of this solution is a "white hole", from which matter can emerge into the outside universe but into which no matter can fall. The Kruskal extension of the Schwarzschild metric is time symmetric and it contains both a black hole region and a white hole region (and is thus occasionally called a "grey hole"). The former contains a singularity that is in the future of some lightlike and timelike paths - those that enter the black hole - but in the past of none. Similarly, the latter contains a singularity that is in the past of some lightlike and timelike paths but in the future of none. More surprisingly, the full solution contains two asymptotically flat external regions, each of which is causally isolated from the other!

Causal structure of maximally extended Schwarzschild spacetime

Figure 1 The causal structure of a maximally extended Schwarzschild spacetime

Even though these posts are about the causal structure of the spacetimes in question rather than their geometries, I feel that at this point I ought to say something more about coordinates I've used in this diagram. For observers at rest with respect to the hole and far away from it in one of the asymptotically flat regions, the t coordinate is just proper time as measured on a standard clock. Suppose this distant clock emits a regular "time signal": a flash of light to mark every second of its proper time. An observer elsewhere in the external vacuum who is at rest with respect to the distant clock will not in general receive one time signal flash per second of her proper time. If she's closer to the hole then she'll receive more than one flash per second as measured on her clock. (If she emits her own time signal flash once per second of her proper time, the distant clock will receive them less often than once per second of its proper time. This is the famous phenomenon of gravitational time dilation, which leads immediately to gravitational redshifts and blueshifts. Unlike the time dilation of special relativity its not symmetric with respect to the two clocks.) However, by adjusting the mechanism of her clock so it runs more slowly she can make it tick in synchrony with the time signals arriving from the asymptotically flat region. In this way - provided a timelike hypersurface is chosen as a "zero" of coordinate time - the t coordinate can be extended across the external region.

The r coordinate is much easier to grasp. It's a radial coordinate with respect to the hole that's chosen such that a sphere of constant r coordinate has an area of 4 pi r^2. (Every point in the Penrose diagram is such a sphere at a certain time.) Note, though, that this means that r is not a proper distance (that is, a distance measured by using measuring rods). As the spacetime is spherically symmetric it's easy enough to finish off our coordinate system by picking two angular coordinates, but these won't concern us here.

The event horizon of the hole is at an r coordinate of 2m (where m is the mass of the hole and I'm using coordinates in which the gravitational constant and the speed of light are both equal to 1). (This distance is called the Schwarzschild radius, but it's not, of course, a proper radius.) As I described in the last part, a distant observer watching an object fall into the black hole sees it fall ever more slowly towards the horizon (and at the same time it appears to get ever more redshifted and ever dimmer). The black hole's event horizon is thus at a t coordinate of +infinity. (Remember, though, that the falling object crosses the event horizon in a finite amount of its proper time.) In a similar way, the distant observer sees any objects that emerge from the white hole as having done so infinitely long ago in coordinate time. The white hole's event horizon is thus at a t coordinate of -infinity.

At some future time, I'd like to say something about the causal structure of rotating and/or electrically charged black holes, but in the next part of the series I'm going to focus on the causal structure of open and closed universes.

The causal structure of black holes

A commenter writing about my earlier post, "Relativity, FTL and Causality" said:

As far as FTL being equivalent to time travel, the above explanation is correct. As far as FTL being impossible at present, it is not quite. Richard's explanation lacks a mention of black holes. An object (with non-zero mass), falling into a black hole from rest, will cross the event horizon AT THE SPEED OF LIGHT. Unfortunately we (the distant observers) would not be able to witness this event, since the falling observer would take forever (from our viewpoint) to reach the event horizon. In the falling observer's reference frame, however, he'd be flying at the speed of light all right! Moreover, he'd probably be able to time travel as well, as his speed continues to increase (to >c) inside the event horizon. Whether this would lead to any causality violations is unknown, since we can't see past the event horizon, and the unfortunate falling observer has a short time to live before he hits singularity, causality violations or not. However, from a purely theoretical point of view, we know that FTL travel is possible with black holes.

This comment about black holes is not true, at least in general relativity, the relativistic theory of gravity. It's correct that the radial velocity of an infalling object goes to zero at the event horizon when expressed in the coordinates of an inertial observer who is stationary with respect to the black hole and far away from it. In other words, the distant observer sees the falling object approach the horizon but never cross it. However, if a second observer falls in a windowless[1] spaceship she would notice nothing out of the ordinary, except for tidal effects, as she crosses the event horizon. If the tidal effects are sufficiently small (they can be made arbitrarily small by increasing the mass of the black hole) then she'd have no way of knowing whether she was falling into a black hole or just drifting through space. This is one aspect of a general feature of general relativistic spacetimes: as the region considered gets smaller and smaller it looks more and more like the spacetime of special relativity. Moreover, there's no frame in which her trajectory becomes spacelike so she can't be said to be travelling faster than light.

On the other hand, there's clearly something special about the event horizon of a black hole, and the singularity in its interior. What happens in a black hole spacetime is that the light cones near the black hole are "tilted" compared with what a naive observer at far away from the hole might expect. At the event horizon the tilting becomes so great that there are no future timelike or lightlike trajectories that can escape to infinity. The singularity is therefore not really at the "centre" of the black hole - although it looks that way in the coordinate system of the distant inertial observer - but rather in the future of all observers who fall across the horizon. And typically, and unfortunately for our daring black-hole explorer, not that far in the future.

One way to visualise this is through the use of Penrose diagrams. These are diagrams of the causal structure of a spacetime in which the points infinitely far away in space or time have been drawn at finite distances on the diagram through the use of a "conformal mapping" that leaves the causal structure intact. (The conformal mapping distorts the geometry of the spacetime to more clearly show its causal structure.) Rays of light in these diagrams still travel at 45 degrees to the vertical as in all of my Minkowski diagrams. The edges of the diagram are then the regions of timelike, spacelike and lightlike infinity - and singularities at a finite distance. This all sounds rather arcane, so let's look at an example:

Figure 1 The causal structure of Minkowski spacetime

On this diagram I've shown two possible paths for freely falling observers. (These paths are technically called "timelike geodesics".). Just as in my other diagrams of spacetime, at each event along the timelike path the path itself is in the light cone of the event, so all observers with mass travel slower than light. If we follow either of the two example paths - or indeed any timelike geodesic - forward in time we reach the region called "future timelike infinity". If we follow them backwards in time we reach "past timelike infinity". Similarly, light rays can shine from "past null infinity" and can extend in the future to "future null infinity". As we might expect, all the edges of this diagram are the appropriate kinds of infinity as Minkowski spacetime extends infinitely in space and time from any given event.

Now let's take a look at the causal structure of a spacetime that contains a spherical, uncharged, non-rotating star collapsing to form a black hole. (The spacetime for an eternally existing black hole has features I don't wish to discuss here.) In this case the spacetime outside the star isn't a Minkowski spacetime but a Schwarzschild spacetime. However, causally - and remember that Penrose diagrams show only the causal structure and not the geometry - the outside region is very much like Minkowski spacetime. The inside is very different though.

Causal structure of black hole spacetime

Figure 1 The causal structure of a physically realistic black hole spacetime. (The wiggles in the singularity are a notational convention and are not supposed to indicate any structure in the singularity itself.)

Once again, outgoing light rays originating from anywhere in the exterior vacuum region can reach future null infinity and (some) freely falling matter particles can reach future timelike infinity. But the diagram clearly shows that a light ray or matter particle from the region inside the event horizon of the black hole cannot reach future null or timelike infinity respectively. No matter in which direction or at what speed particles inside the horizon move, they can only ever reach the singularity. The singularity itself is a spacelike hypersurface on which all world-lines passing through the event horizon terminate. To escape from it, one would have to be able to travel faster than light. Otherwise it is, very literally, the end of time.

[1] If she were fortunate(?) enough to have windows to observe the outside world she'd see some strange things that I won't discuss here.

Integration modelling, part one

Data modelling is the art of abstracting aspects of reality relevant to a given problem and then representing those aspects in a database schema or collection of classes or other concrete form. Data modellers thus deal with deal with several different worlds simultaneously:

The problem domain, a part of the real world (or at least a part of the world considered "real" from the point of view of the system being designed);
The conceptual schema, an abstract model describing the problem domain in terms of entities and their properties and relationships;
The logical schema, which in this article will mean a relational database schema

(There are other layers that might be considered too, such as the physical schema, which describes how the logical schema is implemented in some specific database management system. This won't concern us at all here.)

Analysing a problem domain and building conceptual and logical schemata to capture its essence is an art rather than a science. The outcome of any particular attempt will tend to depend on subtle - or not so subtle - differences in judgement about the relative likelihood of different ways in which the parts of the real world being analysed can vary, and the signficance or otherwise of those variations to the operation of the system which will be built on top of the logical schema. People also vary in their skill at modelling and their practical and aesthetic preferences for one design option or another. This means that multiple attempts at modelling the same domain will almost certainly result in divergent conceptual schemata, and the subsequent logical schemata are likely to be wildly divergent.

Real organisations tend to face problems in multiple domains which overlap to varying degrees. Typically they build or acquire separate systems for dealing with each domain - the cost of developing a system which encompasses the union of all the problem domains is almost always prohibitive - and then later face the meta-problem of enabling the flow of data - or control - between the separate systems. To pick an example from the organisation with which I'm most familiar, an independent school might have an academic database (which stores details of teachers, pupils, pupils' contacts, timetables, assessment and attendance data and so forth), a network directory (which stores details about user permissions, home folders and so on), a personnel system, an alumni database and possibly one or more commercial databases. Making these database systems work together is the problem of enterprise integration.

It's now commonly accepted that the most promising approach to large-scale integration problems is to connect the component applications with an asynchronous message-passing system. Events in one component system generate messages that are sent over the integration infrastructure to other systems and on reception at each target system trigger events there. For example, a change to a contact's address in the first system will trigger the sending of a notification message which will make its way to all the other systems that share the contact, and these systems will then update their own address records. It's often possible to add the required messaging endpoints to each component system without access to the application's source code, for example by directly adding triggers to relevant tables. The integration system will contain components that translate, route, aggregate, decompose and otherwise transform the messages in transit. Integration systems designed along these lines have a minimal effect on each component's performance, and also provide the compelling benefits of loose coupling, resilience in the face of component shutdowns or crashes, and clarity of structure.

However, even when the integration architecture has been designed, it's often not clear exactly what information the actual messages should contain. As I'll describe in the next part, the key to message design is thinking clearly about the conceptual and logical levels of abstraction for the whole system and its constituent parts.

The Carnival of Software Development, number 4

The fourth edition of the Carnival of Software Development is now up at CoderBattery. The fifth edition will probably be back here at Sharp Blue.

Fair use

The staff at John Wiley & Sons do not understand the "fair use" provisions of copyright law, and furthermore seem intent on using their no doubt substantial legal resources to attempt to suppress free discussion in the scientific community. I think all readers should consider this apparent opposition to freedom by John Wiley & Sons while making future purchasing decisions.

http://scienceblogs.com/retrospectacle/2007/04/antioxidants_in_berries_increa.php

The above article contains copyrighted material in the form of a table and graphs taken from a recently published paper in the Journal of the Science of Food and Agriculture. If these figures are not removed immediately, lawyers from John Wiley & Sons will contact you with further action.

Update (26/4/2007): It seems that Wiley have backed down.

Absolute future and absolute past

<< Previous Article: "The relativity of simultaneity"

In the last installment we saw that observers in different inertial frames (each of which is moving with respect to the others at a uniform velocity) will consider different sets of events to be simultaneous. It's as if the various inertial observers have space and time axes that are tilted with respect to those of the other observers. This is very unlike the situation in Newtonian physics, in which all observers agree on simultaneity. In this installment we'll investigate the consequences of the relativity of simultaneity in more detail, focusing on its implications for the ideas of past and future.

Firstly, let's consider a single inertial observer, Alice, and an event P that's at the origin of the coordinates in her frame as shown in figure 1. In this diagram I've shaded all the events that Alice considers to take place later than P. As we might expect, these are the events with time coordinates in Alice's frame that are greater than the time coordinates of the events that Alice considers to be simultaneous with P (in other words, the events that are above Alice's space axis). It's not standard terminology but we might consider these events to make up the relative future of P in Alice's frame. Similarly, the unshaded events below Alice's space axis make up the relative past of P in her frame. (If we were considering Newtonian physics, that's all that we'd have to say about this as past and future would be not relative but absolute.)

Figure 1 The relative future of P in the Alice's frame.

Next, let's consider the situation as seen by Bob, who is flying past Alice at a constant speed in the positive x direction. As usual, in figure 2 I've chosen to draw Bob's axes in Alice's coordinates so we can easily compare the situations of our various inertial observers but there's nothing special about Alice's frame and we might just have easily drawn things in his coordinates instead. As previously described, Bob's space and time axes are tilted towards the light cones with respect to Alice's in such a way that he sees the same speed of light as Alice does. As Bob considers a different set of events to be simultaneous with P, the relative past and future of P in Bob's frame will contain different events to its relative past and future in Alice's frame. Once again, I've shaded the relative future of P in Bob's frame. Quite a lot of the events in the future of P relative to Alice are also in its future relative to Bob. However, Alice and Bob also disagree about two "wedges" of events: those taking place between their respective space axes. Alice considers the wedge in the positive spatial direction to be in P's future but to Bob they're in P's past. Similarly, Alice considers the wedge in the negative spatial direction to be in P's past but to Bob they're in P's future.

Figure 2 The relative future of P in the Bob's frame, which is moving in the positive x direction with respect to Alice.

If we recruit Carol to fly past P at a constant speed in Alice's negative spatial direction then we see the situation in figure 3. As expected, Carol's axes are tilted with respect to Alice's (and Bob's, although Bob is not shown). Once again, I've shaded the relative future of P with respect to Carol. The situation is very like the previous one we've considered, with Alice and Carol disagreeing on two wedges of events. You might like to imagine the situation of Carol as seen by Bob or vice versa: they too will disagree about two wedges of events. When we consider all three of our observers, they will disagree about even more events, but notice that there will still be some events that they all agree happen later than P and some that they all agree happen earlier than P.

Figure 3 The relative future of P in Carol's frame, which is moving in the negative x direction with respect to Alice.

Finally, consider a whole family of inertial observers moving at a range of velocities with respect to each other, as shown in figure 4. To reduce clutter I've only shown the spatial axes of the observers, but you should be able to imagine the time axes too without much difficulty. For each observer I've shaded the events in the relative future of P in his or her frame, and I've overlaid all of these different relative futures. The more saturated the yellow at an event, the more of our family of observers agree that it occurs later than P. As we consider inertial observers that move ever faster (but never faster than light) we must consider spatial axes that tilt ever closer to the light cones (which are the paths taken by light rays) but never cross them. This means that all inertial observers agree that the events within the future light cone through P occur later than P. This region, shown in saturated yellow on the diagram, is the absolute future of P. Similarly, all of our observers agreee that all events in the region within the past light cone of P occur earlier than P. These events, shown in dark blue, make up P's absolute past.

Figure 4 The absolute future (and absolute past) of P.

We can analyse any event in the special-relativistic spacetime ("Minkowski spacetime") in the same way, so each event has an absolute past and an absolute future (but not the same absolute pasts and futures!). The light cones through each event and the absolute pasts and futures form a sort of "causal grain" that runs through spacetime, and are the absolute structures in special-relativistic spacetime that conceptually "replace" the absolute simultaneities of Newtonian physics. Structures such as the absolute pasts or futures which are agreed upon by all inertial observers are called Lorentz invariants. These are extremely important in relativistic physics. Figure 5 shows the past and future light cones and the absolute past and future of an event P in Minkowski spacetime stripped of clutter (the white lines are Alice's coordinate grid). Notice that there are events such as Q that are in neither P's absolute future nor P's absolute past. For such events there will be some inertial observer for whom P and Q are simultaneous.

Figure 5 Minkowski spacetime

We have now learned quite a lot about space and time in special relativity. In the next few installments we will investigate some of the more striking consequences of the theory. First we will consider the way in which faster than light signals would cause violations of causality (fortunately for causality but unfortunately for our science-fictional dreams there are no known phenomena which allow faster than light signalling). Then we will look in more detail at the phenomena of time dilation and length contraction, before moving on to the celebrated "twins paradox" (which will turn out to be not so paradoxical after all).

Next Article: "Relativity, FTL and Causality" >>

The relativity of simultaneity

<< Previous Article: "Spacetime and Coordinates"

We've disussed how an observer, Alice, can apply coordinates to a special-relativistic spacetime using just a clock and rays of light. Now we need to consider how things look to Bob if he's moving with respect to Alice at uniform speed. First let's consider two events, P and Q, that are simultaneous in Alice's frame as shown in figure 1.

Figure 1 In Alice's frame the events P and Q are simultaneous.

Because of the principle of relativity one inertial frame is as good as another, Bob can use the same procedure as Alice to assign coordinates to the events P and Q. Let's watch him from Alice's frame as he does this. To draw the diagram of this situation we'll have to make use of the second postulate of special relativity: inertial observers always measure the same speed of light in a vacuum. This means that any light rays transmitted or received by Bob travel at 45 degrees to Alice's coordinate axes in just the same way that any rays that Alice transmits or receives herself do. (In this sense, special relativity is simpler than non-relativistic physics, in which we'd have to concern ourselves with the possibility that light emitted by moving observers might travel more rapidly than light emitted by stationary observers.)

As shown in figure 2, Bob must transmit light at event T1 to bounce it off event Q and receive it back at event R1. To bounce light off event P he must transmit it at event T2 and he receives the reflection at event R2. By symmetry - a powerful tool in physics - the same interval elapses on Bob's clock from T1 to R1 as from T2 to R2. Remember from our discussion of the method for assigning coordinates that event Q happens at the time in Bob's frame which is the average of his times at T1 and R1 and similarly event P happens in his frame at the time which is the average of his times at T2 and R2. As the two intervals are the same and T1 is earlier than T2, it follows that event Q happens earlier than event P. This is a striking conclusion: events that are simultaneous in one inertial frame are not simultaneous in other frames. As the description in any inertial frame is as good as that in any other it follows that there is no absolute notion of simultaneity. This is the famous phenomenon of the relativity of simultaneity. It follows directly from the principle of relativity and the constancy of the speed of light.

Figure 2 In Bob's frame Q occurs earlier than P.

To investigate the relativity of simultaneity in more detail we must next consider the sets of events which are simultaneous in Bob's frame. Once again we'll watch Bob from Alice's frame. Consider the collection of events and light rays shown in figure 3. The intervals from T1 to T2, T2 to C, C to R2 and R2 to R1 are all equal. This means that the average of the time from T1 to R1 is the time at event C, as is the average time from T2 to R2. Thus, by the procedure for assigning coordinates to events, the events A, B, C, D and E are all simultaneous in Bob's frame (although manifestly not in Alice's frame in which they increase in time from A to E).

Figure 3 Simultaneous events in Bob's frame as seen from Alice's frame.

Alice and Bob slice up the same spacetime into space and time in different ways because of their relative motion, and neither slicing is in any sense better than the other. (There's nothing special about Alice's frame; we could just as well work entirely in Bob's frame and we'd reach the same conclusion.) This mixing of space and time is very different to the situation in pre-relativistic physics (or most people's intuitive picture of the world) in which everyone agrees on what is space and what is time. Moreover, the experimental evidence strongly suggests that it's a fundamental aspect of the way the world works. This won't be the last time that our naive intuitions turn out to be a poor guide to the nature of the universe.

Finally, let's draw Bob's coordinate grid as seen from Alice's frame. Bob's time axis is his worldline and his space axis passes through all the events simultaneous with event C in his frame, as shown in figure 4. The other spatial gridlines of his coordinate system are all parallel with this simultaneity surface and the temporal gridlines are parallel with his worldline. Therefore, his coordinate grid is skewed as seen by Alice. (Likewise, Alice's coordinate grid is skewed as seen by Bob.) This skewing, however, preserves the speed of light: light rays move one unit of space in one unit of time in Bob's coordinates just as they do in Alice's coordinates. It's just that what constitutes a unit of space or time is different. The relationship between the two sets of coordinates is called a Lorentz transformation. We will have much more to say about these transformations later.

Figure 4 Bob's coordinate system as seen from Alice's frame.

From the discussion so far you will no doubt have the impression that very many things have values that are only valid relative to one inertial observer or another. On pondering the relativity of simultaneity you may start to worry that the theory of special relativity has fatally undermined even such everyday notions as "past" and "future". However, soon we'll see that the spacetime of special relativity has its own absolute causal structure in which past and future acquire new meanings. Later we will meet various absolute quantities that have values that are independent of the state of motion of the observer. A certain solidity will thus be restored to what might now seem a disturbingly insubstantial spacetime.

Next Article: "Relativity, FTL and Causality" >>

Spacetime and coordinates

(This series begins with Maps of Physics)

In physics an event is something that takes place at a given location at a given time. This conforms closely to our everyday notion of an event. The collection of all events is called spacetime. In this series we'll often be concerned with sets of events and their relationships to each other (especially their causal relationships). To talk more clearly about these relationships it's often helpful for an observer to assign a unique label to each event in some region of spacetime. As space has three dimensions and there's also a time dimension it's possible for our observer to label an event with three numbers representing its position and one number representing the time at which it occurs. A label of this kind is called a coordinate and the collection of labels is called a coordinate system or coordinate frame.

(In special relativity it's possible to produce coordinate systems that include every event in spacetime. This is not true when we introduce gravitation. In that case the best we can do is to cover spacetime with a set of overlapping coordinate systems that each label some region uniquely, and then translate between one coordinate system and another on the overlaps.)

Different observers will typically assign different coordinates to the same event and we'll often consider how events labelled in one way by one observer are labelled in another way by a second observer. Coordinate systems are thus useful, but you shouldn't read too much into them. There are deeper properties of spacetime which don't vary from one coordinate system to another and modern physics is formulated in terms of these properties in ways which I will describe more fully as this series progresses. However, this is getting ahead of ourselves: in this installment I want to talk about a concrete procedure that an observer can use to assign coordinates using a clock and rays of light.

Firstly, we'll need to consider the concept of spacetime diagrams, which I'll use extensively through these articles. As I'm not sufficiently artistically skilled to draw four-dimensional diagrams I'll restrict our view to one dimension of space as well as the time dimension. I'll always draw the diagram so that time increases from bottom to top and space extends from left to right. Lines running from bottom to top (which don't slope too much) are possible paths that particles can follow through spacetime. Such a line is called the worldline of the particle. It's really a collection of events, each of which is a place and time at which the particle exists. I'll typically plot the diagram from the point of view of an observer moving uniformly (that is, an observer who isn't accelerating). The vertical axis will then form both the time axis and the worldline of that observer. I'll also scale the space and time coordinates so that light rays travel at 45 degrees to the axes.

Our first problem is this: how can Alice, a uniformly moving ("inertial") observer, decide whether or not a second observer, Bob, is at rest relative to her? She can do this using a simple method that requires only a clock and a flashlight. Alice shines flashes of light at Bob and times the interval between a flash being sent and her reception of the reflected flash, as shown in figure 1. If the interval between each flash being sent and its reflection being received is constant then Bob is at rest relative to Alice. (If each successive flash takes less time than its predecessors to get to Bob and back then Bob is moving towards Alice; if each one takes longer than its predecessors then Bob is moving away from Alice.)

Figure 1 Two observers at rest relative to each other.

Using this same apparatus, Alice can do something even more useful: she can assign coordinates to the events at which the light pulses are reflected. The time coordinate of the reflection event is simply the average of the times on her clock at which the pulse was transmitted and its reflection received. An inspection of the diagram reveals that this is a rather intuitive definition. Giving the reflection events a spatial coordinate is a little more subtle. The spatial coordinate is proportional to the interval elapsed between the pulse being sent and its reflection received. (The constant of proportionality is half the speed of light, as the light flash has to travel twice the distance from Alice to Bob.) It should be clear that if the flash of light takes longer to return then it must have travelled further. In this case the two intervals shown are the same so the two reflection events are at the same distance from Alice, as they must be if Bob is at rest relative to her.

Alice can extend this process to give coordinates to all events in the (Newtonian or special-relativistic) spacetime (at least if there's something going on at each event that reflects some of the light and she's patient enough to wait for reflections from distant events). Figure 2 shows her using this process to assign coordinates to the events P, Q and S. To reflect pulses from events P and Q she must transmit flashes towards them from event T. She receives the reflections at event R. From this she deduces that the two events happen at the same time (in her coordinate frame but not necessarily, as we will see later, in other frames). They also happen at the same distance from her, but in different directions. From the interval between T and R she can deduce the times and distances of P and Q. She can use the same process to give coordinates to event S, this time transmitting from T' and receiving at R'. As the interval from T' to R' is less than the interval from T to R, event S happens closer to her than event Q. As the average of the times at T' and R' is greater than the average of the times at T and R, event S happens later than event Q (in her frame). Once again, she can do detailed calculations to give S space and time coordinates. She can do the same for any other event of interest. Essentially she's just using radar.

Figure 1 Using a clock and light rays to assign coordinates to events

Given this process, Alice can lay down a coordinate grid on spacetime. Bob or any other observer moving uniformly can do likewise. However, the coordinate grids deduced by different observers will be different. As Bob is at rest relative to Alice it's easy to translate between their coordinate systems. All we have to do is to compensate for Alice and Bob each thinking that they are at the centre of their own coordinate system, and possible make use of a simple process to synchronise their clocks to compensate for the possibility of each starting the local clock at a different time. In Newtonian physics we can also translate between coordinate systems set up by observers in uniform relative motion by using another simple and intuitive process. However, things are not quite so simple in special relativity. One of the postulates of the theory is that the speed of light is the same as measured by any inertial observer. This will have profound consequences for our coordinate translations and for many other things. In the next installment in the series I'll extend this discussion to consider the intriguing phenomenon of the relativity of simultaneity: observers in uniform motion relative to each other will differ on their deductions concerning simultaneous events.

The Carnival of Software Development, number 3

The third edition of the Carnival of Software Development has just been posted at Mark Levison's weblog, Notes from a Tool User. Check it out!

The Carnival of Software Development, number 2

Welcome to the second edition of the Carnival of Software Development. This time around there were many more submissions than for the first edition, but some of them were fairly liberal in their definition of "software development"...

Carnival regular Mark Levison's contribution is Online Code Reviews suck - even Guido van Rossum can't fix that. I think he's absolutely right that the bandwidth of technologically mediated communication is much lower than that of face-to-face conversation, and that this can't be fixed by any amount of clever design. Furthermore, specific tasks such as code reviews are only a small part of what developers get out of talking to each other in person. In a world of distributed development teams this is going to become an increasingly serious problem.

Scott Sehlhorst also has interesting things to say on the subject of the development process. His entry is How To Use Timeboxes for Scheduling Software Delivery, a discussion of the management of tradeoffs between resources, time, functionality and quality through the use of timeboxes, which are units of developmental capacity. I think that anything that makes clear to non-developers that these four quantities cannot be abitrarily varied by fiat is a good thing.

Magnus' advice is to Choose your distributed component name wisely. While I've put a lot of thought into naming things clearly for other developers, I certainly hadn't considered that end users might react so strongly to shared library names!

mamcx contributed two entries to the Carnival - Velocidad turbo ("Información sobre las nuevas versiones Turbo de Delphi. Delphi para .NET y C++ Builder.") and El extraño mundo de Mamcx: Pa'afuera y no pa'adentro! ("Como afrontar correctamente el desarrollo de una aplicacion.") - but I must admit that my linguistic talents and BabelFish's translation algorithms are not good enough to allow me to add any further comment to either.

In Problems with learning through code reuse posted at A C# Coder's World, Simple Guru argues that becoming too reliant on reuse of other developers' code might speed up development in the short term but it also gets in the way of truly learning new skills. I think that it's probably true that many programmers don't ever acquire an understanding of what their code actually does at anything other than a superficial level, and that this can lead to serious problems with efficiency. For example, I'd imagine that many developers could get through their whole careers without delving deeply enough into the machine to understand endianess. Which brings me to the first of OpenAsthra's contributions to the Carnival: Little, Big endianess explained.

(OpenAsthra's other two entries are Pelt: Posix Wrapper for Windows Threads and PoTerm - A Serial Terminal Shell. The former is about an implementation of POSIX threads that uses native Windows threads. The latter is an open-source shell for sending commands over serial ports.)

Moving away from the development of software itself to the broader issue of the development of software products, another regular, Pawel Brodzinski, tells us a story about Logo and Website Design. I found his earlier article on logo design interesting too. Pawel's articles aren't directly about this problem, but balancing aesthetics and usability in web applications is an interesting challenge.

(There were several entries only tangentially related to software development. In the first, Corey muses about Web 2.0 and its effects of communication. I still pretty much think that Web 2.0 is just an attempt to hype Bubble 2.0 so those of us who missed out on zillionairedom the first time around can have another shot. The second only tenuously on-topic article was Why you should use google from Exchange Ingredients. Is there anyone who doesn't use Google?)

And finally, Avant News reports the amusing news that Windows Vista Startup Music Was Designed on Macs: "The first time a PC ever got close to the Windows Vista ditty was when the first prototype was booted up, and even then it crashed before we could hear the final chime."

That concludes this edition. If you'd like to submit an article to the next edition of the Carnival of Software Development, please use the carnival submission form.

Hatchepsut

One of the most intriguing figures in Egyptian history is Hatchepsut[1], a woman who became pharaoh during the Eighteenth Dynasty. Too little material has survived the three and a half millennia that separate us from Hatchepsut to allow the writing of a conventional biography. We have, for example, no diaries, no letters, and not even palace archives from which to discern clues to her personality. Nevertheless, in her Hatchepsut: The Female Pharaoh Joyce Tyldesley has written as full a biography as the extant evidence allows, and has managed to paint an engaging portrait of her life and times.

Hatchepsut was born a princess of the Tuthmosid royal house towards the beginning of the Eighteenth Dynasty. This was an age of warrior pharaohs. At the time of Hatchepsut's birth, around a century had elapsed since the kings of Thebes, the great religious and political centre in Upper Egypt, had expelled the foreign Hyksos kings from Lower Egypt and reunified the Egyptian state. The pharaohs Ahmose I, Amenhotep I and Thutmose I, Hatchepsut's father, had then pushed the borders of Egypt far north into Asia and south into Nubia. The empire they founded, the New Kingdom, would endure for five centuries and be seen, both then and later, as one of the glorious peaks of Egyptian civilisation. On the death of Tuthmose I, Hatchepsut's half-brother and husband became the pharaoh Tuthmose II and she became queen of Egypt. Tuthmose II seems to have been quite a weak man and may well have been dominated by his sister-wife (the political history of the New Kingdom was full of strong-willed women as well as warrior pharaohs), but the despite this Hatchepsut was portrayed as an exemplary wife and queen. So far, so conventional. Tuthmose II died young and Hatchepsut soon found herself regent for the child Tuthmose III, a son of Tuthmose II by a secondary wife. This too was far from unusual - there had already been two very successful queen regents in the Eighteenth Dynasty - but it provided the opportunity that Hatchepsut's extraordinary ambition needed.

By the seventh year of the regency, this ambition had fully flowered and the young Tuthmose had been pushed into the background. Egypt had seen queens regent and a queen regnant - Sobekneferu, last monarch of the Twelfth Dynasty - before but Hatchepsut then went one step further and assumed the titulary and powers of a pharaoh. This was a development of quite astonishing audacity - the pharaoh was not merely the ruler of Egypt but an incarnation of the god Horus and so a being who existed on a higher level than the rest of humanity - and it says something for Hatchepsut's strength of personality and political skills that she managed this transformation seemingly without serious opposition and held onto power for two decades. She certainly maintained the loyalty of key members of her father's and brother's regime throughout her rule. Foremost amongst these was the steward Senenmut, who probably entered the royal service under Tuthmose II and became the most powerful figure in Hatchepsut's regime. Tyldesley devotes a whole chapter to the career of Senenmut and his enigmatic relationship to the pharaoh.

The throne name chosen by Hatchepsut, Maatkare ("Maat is the soul of Re"), provides one clue to her political strategy. The concept of maat, which is often translated as "truth"[2] but means something closer to "correct-orderedness", was a central one to the ancient Egyptians. Pharaohs and everyone else were supposed to act in conformance to this timeless correct way of organising the affairs of Egypt. The surviving monuments of Hatchepsut, including her sublime mortuary temple Djeser-Djeseru ("Holiest of the Holy") at Deir el-Bahri, are "propaganda in stone" emphatically presenting the vision of Hatchepsut as the ideal pharaoh. So far as we can tell Hatchepsut's reign was as stunningly successful as that of most of the other Tuthmosid pharaohs. (To some it has seemed disappointing lacking in military glory - as was that of Tuthmose II - but it made up for this through a spectacular expedition to the exotic land of Punt in eastern Africa.)

Tyldesley also tells the story of the modern rediscovery of Hatchepsut and the varying attitudes of Egyptologists towards her. Until comparatively recently the most popular interpretation of Hatchepsut's career revolved around a power struggle at the heart of the Tuthmosid family. Hatchepsut was supposedly an "evil stepmother" who usurped Tuthmose III's rightful place for two decades and whose monuments were systematically defaced by Tuthmose is a fit of righteous anger when he became pharaoh. The book demolishes this interpretation quite thoroughly. Hatchepsut would clearly have had many opportunities to quietly dispose of the young Tuthmose III but failed to take advantage of any of them. Indeed, she even allowed him to lead important military expeditions, a development that would have been recklessly dangerous and entirely out of character if she hadn't entirely trusted him. Nor is it easy to paint the young Tuthmose as a weakling dominated by his older relative, as he went on to become one of Egypt's greatest conquerors. He must surely have seen her as a respected elder rather than the target of brooding resentment. Against this, however, must be weighed Tuthmose III's attempts to erase the reign of Hatchepsut from history through a campaign of extensive (although incomplete) vandalisation and destruction of her monuments. However, the evidence suggests that this occurred late in his reign and Tyldesley interprets it as targeted not at Hatchepsut herself but at younger royal women who might try to emulate her and further complicate dynastic succession. She points out the significant fact that it was only representations of Hatchepsut as king that were destroyed, not those of her as queen consort.

Hatchepsut is a book that I thoroughly enjoyed reading. As with Tyldesley's other "New Kingdom biographies" (of Nefertiti and Ramesses (II, the Great) it's pleasantly concise, conveys a surprisingly vivid sense of its subjects life and times, and it taught me a lot of new things about ancient Egypt. I hope she writes more such biographies.

[1] Or sometimes "Hatshepsut".

[2] In a similar sense to the ancient Persian asha.

Interacting causes and the collapse of states

Margaret and I have been discussing the possible causes of the collapse of the Old Kingdom in the comments to my article "Ancient Egypt in Ten Paragraphs. I've just posted a long comment, which I thought was probably worth bringing to the attention of my readers:

I think that I first read about the role of climate change towards the end of the Old Kingdom in New Scientist, but now I can't find the article so I may be wrong. I suspect that the role of climate in the history of most civilisations has been underestimated. I seem to recall, for example, that an earlier change in climate across the eastern parts of northern Africa might have been responsible for concentrating pastoral populations in the Nile valley and so putting in place the conditions for the formation of states in the first place.

Having said that, I think most of the major transformations in the histories of states and civilisations have been caused by the interaction between multiple intrinsic and extrinsic factors. Arguments are then really about the relative weights accorded to these factors and their distribution along the spectrum from proximate to ultimate causes. In centralised, autocratic states the competence of the ruler is certainly a key factor in the effectiveness of response to perturbations. Long, weak reigns followed by succession crises are clearly not conducive to effective responses to internal or external problems. So I think we might both be right: the political difficulties caused by Pepi II's ineffectual dotage and the subsequent successional difficulties would have weakened the ability of the Old Kingdom state to deal with the issues caused by the changing climate, and if the nomarchs were more able to provide security to the people during the time of crisis then the state would have been torn apart.

The collapse of other states can be analysed along similar lines. The New Kingdom, for example, was subject to external pressures from the collapses of its neighbours and to global climate changes brought on by volcanic eruptions in Iceland. It's unfortunate that these stresses coincided with internal political developments that saw a series of old men come to power between the long reigns of Ramesses III, IX and XI (none of whom save the first were particularly effective). The troubles of the western Roman Empire under the hopeless Honorius provide another obvious example: would the western Empire have collapsed so rapidly if its emperor had been of the calibre of Augustus or Diocletian?

Simple "solutions", complex failures

In physics it's often that case that if you find the right way to view a difficult problem then its solution becomes almost obvious. When I started writing this weblog, one of my intentions was to try to share with non-physicists some of these ways of viewing physical theories. The weblog's subtitle - "making the complex simple" - and its title are both references to this intention[1]. However, as Einstein said, things should be made as simple as possible but no simpler. This is especially true of the political realm, where there's a widespread, deplorable and dangerous tendency towards vastly oversimplifying problems and applying unsubtle "solutions" which make the situation worse and increase human suffering. The debate about the best way to deal with the problem of international terrorism - as well as the actions actually taken to do so - is full of such oversimplifications. For example, after I recently criticised the absurd view that Allied forces are in Iraq to fight against an international terrorist network controlled by Iran, someone commented:

Are you all claiming there is NOT a world wide terrorist network, or that we are just going after the wrong people?

The idea that there's a single world-wide terrorist network is clearly a gross misunderstanding of the situation. In fact there are a number of terrorist organisations, some of which have links to others and some of which receive various kinds of support from one or more states. The specifically Islamist terrorist organisations clearly divide into one class which are Sunni and another class which is Shia. These two classes of organisations are generally hostile towards each other even though they have a number of enemies (foremost amongst them the United States and Israel) in common. Some, but not all, of the latter groups receive backing from Iran.

Out of all of these various terrorist groups, it's my belief that we should primarily be targetting the ones affiliated with al-Qaeda, which is a network of Sunni terrorist organisations. (This is not to say that Iranian-backed terrorist organisations such as Hezbollah should not also be considered our enemies, but I think that the defeat of al-Qaeda should be our primary aim.) This is clearly not the reason that Allied forces attacked Iraq, as al-Qaeda and the former [secular, semi-socialist] Iraqi regime were hostile towards each other. Until the invasion, Al-Qaeda was only active on Iraqi soil in the Kurdish regions in the north of the country, which were more or less out of the control of the Baathist regime. Following the invasion, groups affiliated with al-Qaeda have been busy fighting in Iraq against Shia terrorist groups backed by Iran. Regardless of whether the primary enemy is al-Qaeda or the Shia groups, the situation is a total mess and it's likely to become worse before it gets better.

However, the real problem with Allied strategy is much larger than operational difficulties or confused objectives in Iraq. The Islamic world is a vast and varied place, and its problems are many, deep and very complex. The current American and British governments, however, seem to view it as a homogeneous region with a simple problem - lack of democracy - that can be solved using a simple means - the application of military force to overthrow governments. This doesn't seem to me to be a particularly sensible approach, no matter how much its supports claim that they are "morally serious" and any dissenters are not. As I've argued previously, terrorism is a symptom of failure and defeat. The core regions of the Islamic world have failed to provide an effective social and economic model that can support a modern industrial society, or to borrow one from elsewhere. It's this failure, especially when contrasted with the past glories of the Islamic world, that has provided the breeding ground for terrorism, and the obviously successful western states (which during the 19th and 20th century almost casually dismembered and colonised the last of the great Islamic empires) have provided its clearest target.[2] Further military humiliation is unlikely to ameliorate this seething resentment.

Furthermore, even if it could be imposed by force, democracy is not a panacea nor is it something that can be separated from the whole fabric of a society. I don't doubt that democracy could in principle thrive across the whole Middle East but for it to do so the people there will have to build a whole supporting infrastructure: ubiquitous respect for the rule of law and for individual rights, a much greater degree of freedom of expression, an educated populace, newpapers and television stations representing a plurality of positions (which are free of the taint of propaganda), a citizenry that shares some minimal feeling of fraternity, a sufficiently egalitarian distribution of wealth, and so forth. This will take many, many years to put into place by the cumulative effect of a myriad small steps. Any realistic Allied strategy to help the peoples of the Middle East to achieve this democratisation and modernisation will have to take a very long view (decades to a century) and use the full spectrum of resources available to western states. There will be a place for intelligence work, covert action and military strikes against specifically terrorist targets. But softer power will play the key roles, engaging with, encouraging and supporting the progressive elements within the region. In the end, the western Allies must be the junior partners in the building of a brighter, more hopeful, freer and more peaceful Middle East, a development that will benefit everyone.

Cooking up an exit strategy for the forces deployed to Iraq is an almost trivially simple problem in comparison to these real challenges.

[1] In Iain Banks' Culture books, citizens of the Culture can secrete a chemical called Sharp Blue that acts as an "abstraction modifier", making complex problems appear simple.

[2] It's also the reason that fundamentalist Islam doesn't even remotely pose an "existential threat" to the West, regardless of the hysterical commentary in the blogosphere and elsewhere. If the Islamic fundamentalists posed an existential threat then we'd currently be worrying about, say, dozens of Islamic armoured divisions flooding across Russia in the direction of Europe or Islamist ballistic missile submarines incinerating the key cities of the western states with a rain of thermonuclear fire.

The Eloquent Peasant

The weblogs that I like most seem to combine two elements. Firstly, the writer is an expert on some field and the weblog is focused to some degree on that field. Secondly, the factual content is leavened with personality and opinion. (I suppose by these criteria I must dislike my own weblog, as I'm not an expert on anything much and I've been trying to stay away from personal posts for no reason other than that I think that my readers aren't particularly interested.) Most of my interests are well served by weblogs that meet these two criteria, but when I started to become very interested in ancient Egypt a year or two ago I looked around for a weblog on Egyptology that I thought I'd enjoy reading and couldn't find any. Now Margaret Maitland has filled this gap with her new and very interesting weblog, The Eloquent Peasant. I'd advise anybody who enjoys my posts on history to take a look.

Now, is there a good weblog on Sumer, Akkad, Babylon and Assyria out there?

Rome and Assyria: Contrasting Imperialisms

Over at Gene Expression there's a discussion about ancient Rome, one aspect of which is a sub-thread on Roman imperialism. Someone towards the beginning of the thread asserted that the Romans dominated the ancient Mediterranean because they eschewed diplomacy or "realism" in favour of brutal military subjugation and extortion of resources. I'd like to take a few moments to try to refute that claim by comparing the imperialistic policies of Rome and the earlier Neo-Assyrian empire (the dominant empire in the Middle East in the first centuries of the first millennium BC and a state which much more closely approximated to the picture of military subjugation and extortion).

The earliest phase of Roman imperialism outside Italy was the gradual conquest of the Mediterranean coastal regions. The Romans, at least until the later phase of the Republic, expanded considerably more slowly than they might have done and generally only annexed territory as provinces when it was necessary to secure Italy itself. Even Italy was, as late as the first century BC, not a Roman province but a network of theoretically independent allies (socii) bound to Rome by treaties. During the last decades of the Republic this changed as military conquest became the main method used by ambitious men of the senatorial class to gain prestige and political power at Rome. This later phase of more aggressive imperialism saw the Romans expand not just into the civilised world of the Near East but also into the less developed territories of what became the Empire's frontiers along the Rhine and Danube.

On both the eastern and northern borders of the Empire, the Romans used more subtle methods alongside naked force. Beyond the eastern frontiers of the Empire proper extended a range of client states that were neither provinces nor independent states. The situation in the north was similar, with substantial use of subsidies for friendly tribes called foederati (from feodus, "treaty", hence our "federation") as well as punitive expeditions against hostile ones. The frontiers were highly permeable to trade too, to the benefit of Romans and non-Romans alike. Until the crises of the third century, the Romans controlled an extremely long frontier with a quite modest number of troops, essentially by ensuring that none of the minor kings in the east or tribal groupings in the north became powerful enough to mount a serious challenge to Roman power.

While all empires ultimately depend on military force, most of the successful ones have a balanced policy reminiscent of that of Rome. The Assyrians, in their later imperialist phase, provide an interesting contrast. The Assyrian Empire was an intensely militarised and more than usually ruthless state, prone to deporting entire populations and ruling largely through terror. The Neo-Assyrian regime was much more willing than the Romans to openly use its military power to subjugate other peoples, and much more dependent on their army as an instrument of internal social control. This militarism was attested not just by historical records from outside the Assyrian Empire but even by the Assyrians themselves. Indeed, it seems to me that the Neo-Assyrian kings were rather proud of how widely they were feared. For several centuries, the Assyrian army was almost always at war, and plunder and tribute poured into the great Assyrian cities of Ashur and Nineveh. Unlike the earlier kings of the Middle Assyrian period, the Neo-Assyrian monarchs channeled the vast majority of their resources through a highly efficient bureaucracy into the service of the military. The Assyrian Empire became the largest and most powerful empire that the Middle East had yet seen.

However, the true strength of the greatest and most enduring empires is never military but the ability to make other peoples (and especially their elites) support the imperial system. The Romans were masters of this strategy. Indeed, many subject cities were allowed to retain their native political and cultural institutions for the whole period of the Principate, and these institutions became part of the Roman imperial tapestry. It was to almost everyone's advantage to become Roman. The semi-autonomous local systems only withered after the massive reorganisation and expansion of the bureaucracy (in the service of the equally expanded military) during the early Dominate. In this period the Empire was faced such serious threats that it became necessary to channel talented people directly into the imperial service rather than into more local career paths. By then, however, the distinction between Romans and their subject populations had been almost entirely erased, which was not something that ever happened in Assyria.

I think that it was this alignment of the interests of the conquered people with the interests of the Roman state that gave the Empire its great resilience and reserves of stength and endurance sufficient to weather the crises of the third and (more or less...) fifth centuries. In contrast, as soon as the Assyrian Empire faced a serious crisis its economic and military reserves were rapidly depleted and the whole awesome edifice rapidly crumbled: in 627BC Assyria was a mighty power feared through the Near East but by 612BC it had been entirely swept away by the Babylonians and Medes. Ultimately, military force alone - no matter how awesomely powerful and seemingly dominant - is not enough to sustain an empire.

The Prehistory of Sharp Blue, part two

Here is another batch of posts I made to the Culture Mailing List that would have been Sharp Blue articles if I'd had a weblog back then:

"Newtonian Spacetime", Part 1 of my old Very Brief History of Time. This is about the structure of space and time in classical physics, which closely conforms to our intuitive notions of absolute space and time.
"Coordinate and Proper Time", the second part of the VBHT. This one seems to make some very pedantic observations about different types of "time" in classical physics, but these distinctions will become very important when I talk about the theories of relativity.
"The Subjective Horizon" a discussion of the future effects of technological progress on our sense of the size of the universe.

I hope that my readers are happy with this rate of recycling of old content. If not, I could go more slowly.

The Carnival of Software Development, number 1

As this is the first edition of the Carnival of Software Development and I didn't give much notice to allow time for submissions, there were only two entries. To pad the Carnival out to a less dismal length, I'll add a little bit more commentary than usual and conclude with a round-up of other articles on software development that I've found interesting recently.

Mark Levison presents Scrum in a Nutshell or 5 minutes to learn scrum, a primer on a lightweight project management process. Having read the article, it's suddenly struck me that although such things are generally viewed as lightweight software project management processes they might be of broader applicability. Scrum, for one, seems to have little to do with software and much to do with incremental product refinement and the handling of shifting requirements. Does anyone know about similar methods being used in other fields?

Pawel Brodzinski explains his views on Context Switching, which disrupts the flow of software development but is often a necessary evil for larger business reasons. I think there's a distinction to be made between context switching and needless interruption: I sometimes get plagued by phone calls that completely disrupt my ability to program but which aren't really about pressing issues that need to be resolved immediately. Asynchronous communication is the developer's friend.

There's an interesting article On Haskell, Intuition And Expressive Power over at defmacro. The thesis is that even though Haskell is more productive than most other languages, and results in cleaner, clearer code that's easier to maintain, it feels less productive. Programming in Haskell requires just as much thinking as programming in other languages, but less typing, and developers have become accustomed to only feeling productive when they're typing. I suppose using lines of code as a metric for productivity - something that I have been known to do in my sloppier moments - is to blame for this. Metrics can be dangerous!

Joel Spolsky has been thinking more than usual about Elegance and Simplicity. As usual, these articles are well worth reading and I have very little to add. However, I feel that I must defend the Clifton Suspension Bridge, which is just around the corner from where I work. Maillart's bridge might be more elegant and beautiful than Brunel's, but Maillart also had another seventy years of technological progress to work with. Given the material and economic limits within which Brunel was working, his bridge had a certain sublimity too and it's preserved much of that lustre to this day. Some people like to link technological progress with ugliness, but the truth is that technology opens up new territories in the space of designs and thus allows new kinds of beauty and elegance.

The debate about the possibility (or existence!) of "silver bullets" in software development rumbles on. Larry O'Brien's More on Functional Languages and Silver Bullets is one of the more interesting recent contributions. Despite the benefits of expressive density and ease of parallelisation, Larry isn't convinced that functional languages attack the "essential" (as opposed to "accidental") problems inherent to the the development of large software systems. As someone who has recently become interested in learning a wider range of languages, I think this is interesting stuff.

That's it for now. The next edition will be on January 21. To enter an article please email me with the names and URLs of the article itself and your weblog, and a short description of the article's contents. You can also use the automated submission system if you'd prefer.

The prehistory of Sharp Blue, part one

Before Sharp Blue existed as a weblog, I used to write many more long posts for the Culture Mailing List on similar topics to the ones I write about here. I've decided that I really ought to fill in the "prehistory" of Sharp Blue by adding these posts retroactively to my archive. I'll move them over in small batches so as not to swamp anybody who might be interested in reading them, and interleave them with new articles. The first batch consists of:

2002: A Snail's Odyssey, a very short and whimsical piece.
Yet another attempt to explain quantum mechanics, which is mostly about the differences between states and observables in classical and quantum mechanics.
Quantum mechanics and measurements, which goes into a bit more detail about the two ways in which a state can evolve in quantum mechanics.
Free will and explanatory levels, a brief note on the relationship between the world of moral agents and the world of neural events. I must expand on these comments one day.
Argument against an afterlife from the correlation between neural and conscious events.

I've re-redecorated a bit too!

Population filters; or The Wine Bar Drake Equation

A post by Razib on the weblog Gene Expression about meeting a pretty sf fan[1] who was working in a wine bar seems to have created quite a storm in the science blogosphere in the last day or so. Shelley Batts, Suzanne Franks, Jennifer Ouellette, Tara Smith and PZ Myers all have interesting comments threads that are worth reading. However, I think that almost everyone is missing a key point.

We can consider the predicates is intelligent, is physically attractive and likes sf as filters on populations. Given a group of people we can pass them through the is intelligent filter and select out the intelligent subset, and similarly for the is attractive and likes sf filters. Each of the filters is a little bit subjective, because there are no absolutely agreed upon standards for how intelligent or attractive someone is or what counts as sf. For the sake of argument, let's say someone passes the is intelligent filter if they're in the top 10% of the general population ranked in intelligence as discerned by Razib[2], that they pass the is physically attractive filter if they're in the top 10% of the general population ranked in hotness by him, and that 10% of the general population like what he or I would consider science fiction. Furthermore, let's suppose that the three filters act independently[3]. (If you have more stringent filters then any degree of surprise will, of course, be greater.)

Razib's surprise at meeting an attractive, intelligent[4] sf fan working in a wine is the surprise of a person who's met someone who passes through three quite stringent filters. If only one in ten people get through each then a mere one in a thousand will get through all three. If we assume that people working in wine bars are an accurate reflection of the general population with respect to these three filters then you'd have to visit an awful lot of bars to find an attractive, intelligent sf fan working in one. Hence his post.

Most of the commenters seem to be implying that it shouldn't be a surprise. Many of the examples given are along the lines of "I work in a science department and there are plenty of hot, smart people here!" But, of course, that's working from a biased population. People found in a science department - excluding many support staff - have already passed the is intelligent filter. (If they work in your science department they've also most likely passed the is interesting filter that I haven't mentioned until now.) This means that around one in ten people in the department will pass the joint is intelligent and is attractive filters, rather than one in a hundred in the general population. Hanging around science departments is a much better idea than hanging around bars if you want to meet smart, attractive people!

Furthermore, I think that many people are confusing making observations with perpetuating stereotypes. This is clearly very easy to do, and it's also very easy for people to read comments like Razib's as attempts to push stereotypes even if the comments are not intended to do so. I think I'm willing to give Razib the benefit of the doubt on this front, even though his choice of words would make it very easy to take what he's said the other way. But I'm not going to wade into that debate as last time I made some reasonable, rational comments on the subject I was accused of being a brain-damaged purveyor of "pseudo-intellectual bullshit"[5].

The argument I've been making above can be seen in less charged ways too. For example, suppose I posted that I was quite surprised to meet someone on the bus-stop who was well-read in both history and science. I think that would be quite surprising as perhaps 1% of the general population is what I'd consider well-read in history and similarly for science. I'd have to talk to ten thousand people at the bus-stop - assuming people riding the bus from my suburb are representative of the general population - before meeting such a person. (Actually, probably quite a lot fewer than that as in this case I don't think the two filters are anywhere near independent.) Given that I've only spoken to perhaps a dozen people on the bus-stop, it would be a surprise indeed! I don't think anyone would find me making such a post objectionable[6] because it stays far from stereotypes of groups of people.

[1] Not quite his choice of words...

[2] Of course, I'm really the ultimate arbiter of such things but I'm feeling magnanimous today.

[3] Which they probably don't, but I think any correlations are likely to be fairly small.

[4] Okay, so he did specify that she was intelligent, but she clearly likes not just sf but good sf and I can read between the lines as well as any other blogger.

[5] I think my critic might have a point with that last part ;)

[6] Dull, perhaps, but not objectionable.

Heraclius, Persia and the Arab Conquests

In my recent articles "Fundamentalist Islam's Cargo Cult" and "Conversions", I mentioned the devastation caused by the final war between Rome and Persia as the key precondition that enabled the explosive military expansion of Islam. In a discussion that followed on Brin-L, somebody expressed the opinion that it was bureaucracy and religious divisions that caused to the decline and fall of the Byzantine Empire and not the devastation caused by war with Persia. I think that the characterisation of the period as one of "decline and fall" is false - Byzantium endured for almost another thousand years and saw periods of renewed power - and also that bureaucracy and religious divisions were largely irrelevant to the conditions in the seventh century when the major Arabic conquests took place[1]. I'd like to say a little more about the reign of Heraclius, which in my view forms the natural break between "Roman" and "Byzantine" (although there were, of course, many continuities across that period too). Whereas Justinian's empire in the mid sixth century was manifestly Roman, and Justinian saw himself as the heir of Augustus and Diocletian, Heraclius clearly didn't. The near terminal crisis of the empire during his reign changed the entire character of the state. Furthermore, that era was one of the key turning points in world history.

For the whole period of the Dominate, from the end of the troubled third century until the final war between Rome and Persia, the military strategy of the Romans was dominated by the Persian frontier. Even during the period of the fall of the western part of the Empire, the bulk of Roman forces were tied up in the east. (Indeed, if not for this the western provinces would almost certainly not have fallen, and if the threat of Persia had receded then the recovery of the west by Justinian's generals Belisarius and Narses would probably have been much more complete, plague or no plague.) For much of this period the massive Roman forces and fortifications along the frontier preserved the peace although there were limited wars in the buffer regions.

During the century and a half between the fall of the west and the final war, there were relatively small wars during 502-6, 526-32 and 540-57 (a more serious pair of overlapping wars on different fronts during which Antioch fell to the Persians). Then in 602, the apocalypse that the balance of military might between the two powers had postponed for centuries finally broke out. The Romans had been weakened by another bout of civil war, military unrest and the invasion of the Balkans by the Avars. The Persian king Khosrau II took advantage of this weakness and invaded Roman Mesopotamia. In 608, Heraclius, the son of the Exarch of Africa, rebelled against the emperor Phocas, whose rule had been generally disastrous, and took Constantinople in 610. The renewed civil war in the Roman Empire further strengthened the position of the Persians, who invaded Syria, taking Damascus in 613 and Jerusalem in 614 and then conquering Egypt in 616 (it remained under Persian control for a decade). At the low point for the Romans, the territory not under enemy occupation in the east was reduced almost to the city of Constantinople itself: the Avars controlled the Balkans and the campfires of the Persians were visible just across the Bosphorus. The imperial government came within a whisker of abandoning the city and moving the capital to the safety of Carthage in Africa.

I don't think anybody at the time can have expected anything except the imminent dissolution of the Roman Empire. Remarkably, that's not what happened, largely because of Heraclius himself. Unlike most of the later Roman emperors his charisma could inspire immense loyalty and courage in his troops and he turned out to be something of an organisational and military genius. He totally reformed the administrative and military structure of the Empire (and along the way replaced Latin with Greek as the official language of the imperial government). His reorganisation largely endured for eight centuries, which is why I consider him the first Byzantine emperor. Heraclius was also the first emperor to lead his troops in person for over two hundred years, and his campaigns between 621 and 627 were spectacular indeed. A combination of strategic and tactical brilliance and skillful exploitation of weaknesses in the Persian political system brought the Persian empire to its knees, plunging it into a series of crises that fatally weakened it. By the end of the war, the Romans had recovered all the territory they'd lost to Persia, but they were territories ravaged by a quarter of a century of foreign occupation and war.

It was only seven years after the end of this last war between Rome and Persia that the armies of Islam erupted from Arabia. By that time Heraclius had fallen into terminal illness, and his generals failed him. Syria fell to the Arabs in 634, the Persian army was defeated in 636, Armenia and Egypt were conquered in 639, Africa in 642, Persia itself in 651...

[1] However, religious divisions amongst Christians in the Middle East were certainly important after the Islamic expansion. Many Monophysite Christians found their new Muslim rulers much more agreeable than the Byzantine emperors who viewed them as heretics.