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Below are the 20 most recent journal entries recorded in Richard Baker's LiveJournal:

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Wednesday, September 1st, 2010
8:31 pm
So, yeah: if you want to crosspost comments from here to anywhere else, go right ahead. You can also reuse anything I say under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. If you ask nicely, I’ll probably grant you even more permissive licensing.
Monday, May 17th, 2010
7:55 pm
I'm not dead yet.
Monday, May 11th, 2009
11:48 pm
Postcards from string theory, part 0

As it seems somewhat remiss to be at least nominally a physicist but to know nothing much about superstrings, I've decided to learn a bit of string theory during my lunch breaks. As the theory becomes clearer and I put the pieces together I'll write about it here. This series will be a little different to my other articles on physics: usually I only write about things that I understand quite thoroughly but here I'm writing about things that I don't understand very well. I'll try not to say anything too incorrect but you should consider these articles to be provisional and subject to revision as I learn more. (This series will have at least one thing in common with my other series: it's likely to peter out...)

When people talk about "string theory" they usually mean "superstring theory", the quantum theory of relativistic, supersymmetric, interacting strings. The defining characteristic of string theories is that the fundamental objects are not pointlike particles but extended one-dimensional objects. Unlike the more familiar strings of everyday live, these strings have no internal structure. They're supposed to be fundamental entities in just that same way that quarks or leptons are supposed to be fundamental in the standard model of particle physics. It's my intention to sneak up on the full superstring theory by starting out with non-quantum, relativistic, non-supersymmetric, non-interacting strings and progressively adding more complexity. (This is the approach in the excellent A First Course in String Theory by Barton Zwiebach, which I'm using as my guide for the first part of the journey.)

There are deep analogies between the theory of non-quantum relativistic strings, classical field theory and the theory of classical particles. Each of these theories can be cast in a "Lagrangian" form, which is all about a quantity called the "action". Before I describe how this applies to strings (in Part 1) I'd like to spend this installment talking about the two simpler cases. Let's start by considering the simplest case, that of a classical particle. Consider all the possible paths in spacetime along which such a particle can travel between two fixed events. Associated with the particle is a mathematical gadget called the Lagrangian, which depends on the position and speed of the particle at each event along its path (and potentially on the event itself). The Lagrangian can be added up along the path — remember it's a path through space and time — to give a quantity called the action. The simplest case is that of a non-relativistic particle, for which the Lagrangian is just the difference between the particle's kinetic and potential energies.

Given that we can work out the action for any path, the obvious question is: which path does the particle actually follow? The answer is quite delightfully elegant. Consider a path between the initial and final events and an arbitrary but very small "variation" of that path, which takes the original path to another nearby path that has the same starting and ending points. We can work out how much the variation in the path causes the associated action to vary. The actual physical path is one for which an arbitrary very small variation leaves the action unchanged (to first order). From this condition we can deduce so-called "Euler-Lagrange equations", which are the equations of motion for the particle. (For a non-relativistic particle we find that the equations of motion are just Newton's laws of motion.)

As well as variations we also care about symmetries. For a physical path, any small variation gives no first-order change in the action. A symmetry, on the other hand, is a transformation that we can apply to the whole system that leaves the action unchanged for any path (and so in particular transforms any physical solution into another physical solution). A particular beautiful theorem called Noether's theorem links symmetries to conserved quantities. For example, if a system is symmetrical under translations in time then energy is conserved. If it's symmetrical under translations in space then momentum is conserved. If it has a rotational symmetry then angular momentum is conserved.

Next, let's consider a classical field theory. Whereas a configuration for a particle is a path from one event to another, a configuration for a field is a value for the field at each event in spacetime. Instead of a Lagrangian, we have a Lagrangian density, which is a quantity that depends on the values of the field and its rate of change in each direction in spacetime at each event, and which we can add up over the whole spacetime to get the action. For a field, a variation changes the field's value in an arbitrary but small way at each event in the spacetime (or a region of the spacetime subject to some boundary conditions). A physical field configuration is one which is left unchanged to first order by small variations. This condition gives us the "field equations" for the field. Instead of giving a globally conserved quantity, symmetries in field theories give rise to "conserved currents", which is a technical way to say that there's some quantity that can flow around in spacetime but can't be created or destroyed.

The simplest example of this is electromagnetism. In this theory the fundamental field is the Faraday tensor, which contains the more familiar electric and magnetic fields. The Lagrangian density is a sort of inner product of the Faraday tensor with itself. The field equations derived from the condition that the action be unchanged by small changes in the field are the famous Maxwell equations. There's a local "gauge" symmetry in the theory that leads to a conserved current that describes the local conservation of electric charge. This is all fairly neat and beautiful.

Let's summarise everything so far in a table:

Classical particles Classical fields
Parameters Time t Spacetime events x
Configuration Path x(t) Field φ(x)
Integrated quantity Lagrangian L(x, ∂tx; t) Lagrangian density L(φ, ∂μ&phi ;x)
Action S[x(t)] = ∫ L dt S[φ(x)] = ∫ L d4x
Euler-Lagrange equations Newton's laws Field equations
Symmetries give... Conserved quantities Conserved currents

In the next part, I'll actually get to strings!

Thursday, March 5th, 2009
12:07 am
More on relativity and causality

Someone called Teemu commented on my earlier article on "Relativity, FTL and Causality" and my answer was so long that I thought it should be a post in its own right. Among other things, Teemu said:

You say: "For any event P (where P is a label for something happening at a given place at a given time), the events within P's future light cone make up its absolute future and those within its past light cone make up its absolute past: the former are the events that P can influence and the latter are the events that can influence P." So as I understood this, it means every two events that are causally connected, must lie in each others light cones (if event A causes event B, then B is in A's future cone and A int B's past cone).

Yes, I may have been a little sloppy there. The idea that light cones are about the causal structure of spacetime is deeply engrained in physicists. Let me have another try being more careful. We're really interested in five sets of events related to a given event P:

  1. Events which occur before P according to all observers.
  2. Events which occur at the same time as P according to all observers.
  3. Events which occur after P according to all observers.
  4. Events which can influence P.
  5. Events which P can influence.

In classical, Newtonian physics the situation is easy and intuitive. Sets 1 and 4 are the same, and are the past of P. Sets 3 and 5 are the same, and are the future of P. There's a non-empty set 2, which is the "present" of P. All events other than P fall into one of these three classes. Signals that are as fast as you like don't change this.

In special relativity without faster-than-light signals things are a little more complicated. Sets 1 and 4 are the same, and are the absolute past of P. Sets 3 and 5 are the same, and are the absolute future of P. (People sometimes talk about the "chronological" and "causal" pasts and futures of an event but the use of the word "causal" used in that way would make things even more confusing!) Set 2, though, is empty: there are no other events that all observers agree happen at the same time as P. There is, instead, a large region of spacetime which is not in any of the five sets: events that can't influence or be influenced by P, and don't take place absolutely before, at the same time as or later than P.

In special relativity with faster-than-light signals, sets 1 and 4 are no longer the same, and nor are 3 and 5. Sets 1, 2 and 3 are still the same as in the case without faster-than-light signals. The Lorentz transformations only rely on the principle of relativity and the invariance of the speed of light and so faster-than-light signaling doesn't change the temporal ordering of pairs of events within each others' light cones. However, it's fairly easy to see that with FTL signals the sets 4 and 5 become the whole of spacetime! Events in P's absolute past can influence P anyway. Events outside P's absolute past or future can influence P via superluminal signals in appropriately chosen frames. Events in P's absolute future can influence P through the construction shown in figure 5 (although there it's an event in R's absolute future affecting R.) Causality is quite hard to define at the best of times[1] but if any other event can influence an event P then clearly we're very far away from being able to give a conventional description of causal relationships between events.

A causality violation
Figure 5 from earlier article The white and blue lines are space and time axes in two inertial frames. The yellow lines are light rays. The red lines P-Q and Q-R are two superluminal transissions.

This is the thing that has always confused me and still keeps on doing so. What I would like to see, is the second half of this example: This first half makes assumption that light speed cannot be exceeded (light cones themselves make that assumption), so if this assumption is false, outcome is not reliable. So if someone could prove that FTL implies time travel with assumption that FTL is possible, then we could safely assume that FTL implies time travel.

I don't think it's strictly true that special relativity assumes that light speed cannot be exceeded. Instead it postulates that the speed of light is invariant. Relativistic dynamics then prevent any object that is moving more slowly than light being accelerated to the speed of light or faster but we can still use special relativity in a consistent way to analyse what would happen if we had faster-than-light signals. (I've been deliberately avoiding the phrase "faster-than-light travel" as special relativity doesn't make sense, so far as I can see, for observers in superluminal frames.) As I've shown, if we allow FTL signals in special relativity then we can generate causal loops without a great deal of difficulty. I've said before that you can pick at most two of {special relativity, FTL, causality}. That doesn't stop you picking, in principle at least, {special relativity, FTL}, but that doesn't appear to have been the choice of the real universe. (The real universe appears to have picked neither special relativity nor FTL!)

And now little OT. When you (or anyone else) says that "in special relativity faster-than-light travel is not possible.", do people mean that any kind of movement that appears to exceed speed of light is impossible, or just the kind of movement where you follow certain path, with length s, and it takes time t so that s/t > c? Because I do not understand how causality is broken in case of wormholes. If I had an instant means to get to Alpha Centauri from earth, so that my spaceships "real" speed (traveled distance per time) is slow, even tough it seemed to travel much longer distance, how could I cause problems with causality? I do not think it can be explained with accelerating inertial frames, because I don't need to accelerate at all, I just pass through a hole with constant speed.

Well, in special relativity wormholes don't exist. To discuss wormholes we really need to get into general relativity, which is a much deeper and more sophisticated theory and one which I don't currently have time to try to explain. However, in general relativity the universe looks more and more special-relativistic as you look at ever smaller regions, and this means that material objects like spaceships can't travel faster than light in a general-relativistic universe any more than they can in a special-relativistic universe. There are, though, even more strange aspects of time and causality in general relativity. For example, it's possible for the sets 1 and 3 in my list above to overlap. This happens for spacetimes that contain closed timelike curves, which is a fancy name for paths along which objects can travel slower-than-light and find themselves in their own pasts.

It's quite easy to see how this works with a pair of wormholes in the approximation in which the wormholes are small so most of spacetime looks special-relativisitic. The key idea is that it's possible to use time dilation to "age" one mouth of a wormhole relative to the other. Suppose we have two wormholes, each with a mouth at Earth and a mouth at Alpha Centauri. We can then create a situation just like my figure 5. Suppose one wormhole is such that if you enter the Earth mouth at event P you emerge at Alpha Centauri at event Q. We can use time dilation to arrange for the second wormhole to be such that if you enter the Earth mouth at event R you emerge at Alpha Centauri at event Q. So then if you travel through the first wormhole from P to Q you can then travel through the second wormhole from Q to R (i.e. into the past). The system consisting of the pair of wormholes thus contains curves that are both timelike and closed and so collectively make up a time machine.

In fact it's possible to do pretty much the same thing with a single wormhole. Keep one mouth at Earth and send the other out on a long journey at close to the speed of light to some place far away. If you have a clock attached to the mouth that stays at home and another clock attached to the mouth that goes away then the two clocks will remain synchronised if you look through the wormhole. Suppose the journey starts in 2010AD, takes one year of proper time for the travelling mouth and finishes at an event with coordinates 2020AD and somewhere-far-away in Earth's inertial frame. In 2011 you could then step from the Earth mouth through the wormhole into 2020 in some faraway place. This is quite strange but not much of a danger to causality. However, suppose the travelling mouth makes a similar journey back to Earth. Another year of proper time elapses for the travelling mouth and it gets back to Earth in 2030. However, you could now step from Earth in 2012 to Earth in 2030, or if you're already in 2030 you could step through the wormhole in the opposite direction to get to 2012. Once again there are closed timelike curves and traditional ideas of causality must be thrown away.

[1] Philosophers would probably say that "event A causes event B" is a statement about all possible worlds in which event A and/or event B occur and would get into the concepts of causal necessity and causal sufficiency and the like. Here I'm really talking about a weaker notion of "possible cause", where "event A is a possible cause of event B" simply means that what happens at event A could influence what happens at event B.

Tuesday, January 6th, 2009
6:42 pm
Sharp Blue
If Livejournal should disappear unexpected, my real weblog, Sharp Blue, will continue to offer the same content. Also, if anyone would like to add me to their Facebook friends and hasn't done so, I have a Facebook profile too.
Thursday, October 30th, 2008
8:07 pm
Tweaking ReadyNAS Bonjour settings

I've been very happy with my ReadyNAS NV+ except for small two things. Firstly, it advertises its AFP shares over Bonjour using the name "AFP on Whatever" where "Whatever" is the name of the ReadyNAS, which looks ugly when it appears in a list of other devices with AFP shares. Secondly, it appears in the Finder sidebar with the generic Cinema Display icon so it looks very similar to my iMac. I've just managed to fix both issues and as it wasn't the most obvious process I thought I'd record it here for the benefit of Google. The key part of the solution was finding Simon Wheatley's article on specifying Finder icons with Avahi and then learning that the ReadyNAS uses Avahi for Bonjour. Here are the required steps:

  • Download and install the ToggleSSH and EnableRootSSH RAIDiator addons. You'll need to use the "Local" tab of System->Upate in ReadyNAS Frontview.
  • Connect to the NAS using SSH.
  • Use VI to edit /etc/avahi/services/afp.service to look like:
    <?xml version="1.0" standalone="no"?><!--*-nxml-*-->
      <name replace-wildcards="yes">%h</name>
  • Update the running configuration of Avahi on the ReadyNAS using the command avahi-daemon --reload

Here's the result:

Friday, September 5th, 2008
11:36 pm
Unity, disunity and continuity

This will be a much more rambling post than is usual. On the Brin List, the conversation has turned to the fundamental nature of ethics, and from there, essentially, to whether "might makes right", or at least whether ideologies that endure are de facto the most effective and so most moral. During this discussion, one of the more erudite contributors said:

Historically, empires can last a long time. The eastern part of the Roman Empire, which was split by Constantine in the 300s, lasted roughly 1500 years, and was defeated by another empire. IIRC, the Chinese empire lasted about the same length until it was overtook by the Ghengas Kahn...who's rule ended up merging into that empire.

In reply I wrote quite a long, tangential message on the inaccuracies of these statements, and various other ideas that they brought to mind. I thought that perhaps some of my regular readers might like to read my reply too, even though it's not especially well structured and doesn't really present a proper argument. It is, however, the longest thing I've written for some months...

To begin with, Constantine reunified rather than splitting the administration of the Roman state. The history of the separation between West and East bears closer examination. Under the Republic, the Romans had a long history of the division of the supreme magistracy, first between two consuls and later into first an ad-hoc and later a formalised "triumvirate". This tendency briefly re-emerged during the second century with the co-imperium of Marcus Aurelius Antoninus and Lucius Aurelius Verus, which enabled the presence of emperors at several trouble-spots concurrently.

During the troubled third century this need for divided absolute authority became even more pressing and was formalised by the emperor Diocletian's institution of the "tetrarchy", in which there were two senior emperors ("Augusti") and two junior emperors ("Caesars"). It was Diocletian's intention that the Augusti should periodically abdicate in favour of their junior colleagues who would in turn appoint two new Caesars from the best men of the state. The succession of the emperors would thus be regularised, putting an end to the cycle of rebellion and civil war that had plagued the empire for fifty years. Unfortunately, it didn't work like that, as sons of the Augusti who had been passed over in favour of new, unrelated emperors, asserted their supposed hereditary rights, alternative centres of power crystallised and a new phase of civil wars began. The ultimate victor was Constantine, who became sole ruler of the Roman empire in 324.

Before Constantine, there had been many temporary Roman capitals - for many decades the capital had effectively not been Rome but wherever the emperor was. Under the tetrarchy, for example, the capitals of the Augusti had been Nicomedia in Asia Minor, Mediolanum in northern Italy, Sirmium in what's now Serbia and Augusta Treverorum (modern Trier). One of Constantine's several innovations was the establishment of a permanent new capital at Constantinople. Rather than this city being the capital of an "Eastern Roman Empire", it was the capital of the whole empire. Even during periods of division of the imperial authority, the empire itself was seen as a unitary whole and the usual procedure was for edicts to be issued in the name of all the current emperors and to be enforced across the Roman world.

It's commonly held that the final division of the Roman empire occurred in 395 at the death of Theodosius I, at which Honorius became emperor in the west and Arcadius in the East. From then until the extinction of the western dynasty in 476 there was always an emperor in Constantinople and another usually in Ravenna. However, even as these two centres of power solidified, the Roman world formally remained whole. The two emperors provided each other with military assistance even as late as a major joint naval expedition against the Vandals in 468. Even the man sometimes seen as the last fully legitimate western emperor, Julius Nepos, was appointed by the eastern emperor Leo I. Furthermore, following the overthrow of the last western emperor, Romulus Augustulus, many of the Germanic successor rulers claimed to be ruling not as independent kings but as representatives of the emperor at Constantinople.

As for when the Eastern remnant of the Roman empire fell, I think there were two very clear periods during which large swathes of territory were lost and the character of the empire deeply changed. The first was during the lightning conquests of the Muslim armies in the seventh century, which cut away from the empire the ancient Roman provinces of Syria, Palestine, Egypt and North Africa. Augustus might well have recognised the sixth century empire of Justinian as a successor, however much transformed by the passage of centuries, to his own; but the Byzantine empire of Heraclius and his successors was a different world. The second major collapse occurred with the defeat of Romanus Diogenes by the Seljuk Turkish sultan Alp Arslan at Manzikert in 1071. (The Seljuk sultanate was a successor to the Arab Caliphates that had inflicted the earlier defeats on the Byzantines.)

In any case, much of this is a distraction from the central questions: what endured for those 1500 or more years, and was it totalitarian. In my view the main continuity was that of the administrative bureaucracy created by the Romans, despite the changes at the highest levels of power, the shifts of culture and even the change of religion. During the first few centuries of the Empire, the military and civil leaders were essentially talented amateurs drawn from the senatorial class. A major development during the third century was the replacement of these aristocratic leaders by middle class, professional leaders, first in the military sphere under Gallienus and then in the civil administration under Diocletian and Constantine. Alongside this shift, the administrative bureaucracy expanded dramatically in size as the troubled empire sought to organise its still massive economic resources to meet its ever more desperate military needs. It's striking that the empire of the second century was run by an imperial staff of a few hundred bureaucrats but more striking that by the fourth century this had increased to tens of thousands.

It was this vast administrative machinery - and the parallel hierarchy of the Christian Church, with which it became increasingly entangled - that endured through so many changes of dynasty, provincial structure, prevailing religious orthodoxy and military organisation. Indeed, it even survived the collapse of Roman political authority in both East and West. The Germanic rulers of post-Roman Europe attempted to preserve the Roman administration and the Roman laws, but both fragmented and decayed during the first few centuries of the German states. Under Islam, however, the bureaucracy flourished, becoming the administration of the Ummayyad and Abbasid Caliphates. The civilisation of classical Islam fused the Arab religion with Roman administration and Persian elite culture.

(I think that this kind of continuity through administrative bureaucracy, or at least continuity of scribal and bureaucratic standards, pratice and culture, is typical of ancient civilisations, whether Roman, Egyptian, Mesopotamian or Chinese.)

As for totalitarianism, I think it's clear that it's a product of modern states. Even when the Roman rulers might have aspired to totalitarianism, such as during Diocletian's attempts to control the economy through edicts, or the exasperated attempts by Christian emperors to impose some kind of religious orthodoxy, the tools to do so - mass media, mass surveillance and so forth - simply were not available. Likewise, republicanism or democracy on scales larger than that of city-states are products of modern times. It's not clear to me that the endurance or otherwise of pre-modern empires has much to say about the prospects for democracy or dictatorship in the modern world.

I could say as much about China, but I'll spare you the details. However, it's incorrect both that Genghis Khan conquered China and that the empire the Mongols conquered had endured for 1500 years. Since the fall of the Tang dynasty in 907, China had been divided into a number of smaller states. During the period from 906 to 960, five dynasties rapidly succeeded one another in the north of China and the south was divided into ten or so small states. China was briefly reunified by the Song dynasty but by 1127 the northern part of the country had fallen under the rule of the non-Chinese Jin and Xia dynasties in the east and west respectively. These two northern dynasties were defeated by Genghis but the conqueror of China proper was his grandson Kublia, founder of the increasingly sinicised Yuan dynasty. The Mongols ruled China for a century until the Yuan were overthrown by the native Chinese Ming dynasty.

As with Rome, China passed through succeeding periods of political unity and disunity. Indeed, the normal state of affairs might have been a division into smaller states ruled by independent dynasties. From the first unification of China by the Qin dynasty in 221BC to the Mongol conquest in AD1271, China was only inarguably a single state from 221BC to AD220 under the Qin and Han, from 581 to 907 under the Sui and Tang and from 960 to 1127 under the Northern Song, or about 60% of that period. It was only during the Yuan, Ming and Qing that the idea of China as a coextensive political and cultural zone achieved an enduring reality. (Which is not to denigrate the earlier achievements of the Chinese. For example, at the time of the Mongol conquest the Song capital, Hangzhou, may have been the most populous, wealthy and sophisticated city in the world.)

I'll say even less about another civilisation that I know something about - ancient Egypt - but that one also wasn't a single "Egyptian Empire". Instead, four periods of unity (the Old Kingdom, Middle Kingdom, New Kingdom and Late Period) were separated by periods of political decentralisation or foreign domination, and I seem to recall counting something like fifteen distinct periods of ancient Egyptian imperialistic expansion. In this case too, the continuities across vast periods of time are not so much political as cultural and administrative.

Thursday, May 15th, 2008
11:09 pm
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.

Tuesday, April 15th, 2008
10:32 pm
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:

Causal structure of Minkowski spacetime
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.

Sunday, July 15th, 2007
9:44 pm
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.

Monday, April 30th, 2007
8:31 pm
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.

Wednesday, April 25th, 2007
8:09 pm
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.


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.

Sunday, April 1st, 2007
10:46 pm
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.)

The relative future in the white frame
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.

The relative future in the blue frame
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.

The relative future in the green frame
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.

Absolute past and absolute future
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.

Minkowski spacetime
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" >>

Wednesday, March 21st, 2007
10:12 pm
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.

Alice&quot;s simultaneity
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.

Bob&quot;s coordinates
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).

Simultaneity according to Bob
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.

Alice&quot;s and Bob&quot;s frames
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" >>

Sunday, March 18th, 2007
12:16 pm
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.)

Two observers at rest relative to each other
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.

Using a clock and light rays to assign coordinates to events
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.

Thursday, March 15th, 2007
8:33 pm
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!

Sunday, February 11th, 2007
8:13 pm
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.

Wednesday, January 17th, 2007
10:09 pm

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.

Saturday, January 13th, 2007
2:38 pm
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?

Saturday, January 6th, 2007
11:08 pm
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.

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