Monday, December 31, 2007

Trey Smith

Trey Smith, who was CTO of Cable and Wireless International back in 2001-2, and my boss there, died of lung cancer in September. I have only recently discovered this as we had not remained in touch.

Trey Smith

Here is the obituary notice from the Rappahannock Times.

"Died September 27, 2007

Theoren P. "Trey" Smith III, 53, of Great Falls, a physicist, died at home Sept. 27. He had lung cancer. Friends may call Oct. 5, from 7 to 9 p.m., at the family home.

Services will be held Oct. 6 at 11 a.m. at Reston Bible Church in Reston. Burial will be in East Aurora, N.Y. Dr. Smith was born Sept. 1, 1954, in Denver, Colo., to Kitty Smith and the late Theoren P.L. Smith. He held a Ph.D. and worked for a science and technology company.

Survivors include his wife, Kathy Smith; three daughters, Kristen, Julia and Kimberly Smith; a son, Theoren Smith; two brothers, Mark Smith and Nate Smith; and a sister, Susan S. Kranz.

Memorials may be sent to Johns Hopkins Medicine, Trey and Kathy Smith Lung Cancer Research Endowment, The Harry and Jeanette Weinberg Building, 401 N. Broadway, #121, Baltimore, MD 21231 or online at www.hopkinskimmelcancercenter.org/contributions.

Arrangements are by Adams-Green Funeral Home of Herndon."


Trey had been headhunted into C&W from the US Internet company Roadrunner, where he had been CTO. His style was avuncular and 'presidential' in the US executive sense. His public persona was extravert, gregarious and 'in charge' and he looked a million dollars in a smart suit. He was Republican through and through, and had been a navy submariner, of which he was very proud.

What Trey was not good at was the kind of machiavellian corporate politics which some English companies excel in, including C&W. Although appointed CTO, the job in reality was to fix the IT which had been outsourced - in a mess - to IBM. Trey could never accept his de facto role as CIO and fought continuously to acquire the network technology organisation. This was never going to happen.

I was VP for systems architecture reporting into Trey during this period, and along with my colleagues found it was not easy trying to do our jobs against the background of such a bitter turf war. And then as C&W International turned into a slow-motion train wreck, we got to spend most of our time downsizing the Office of Technology from around 2,000 people to less than 300. Not the most pleasant experience of any of our lives.

Trey left C&W before it collapsed into Chapter 11 in 2003, the Office of Technology being abolished. He moved on to various senior roles in the US R&D organisation SAIC, from whence this recent interview (here).

He was a very generous man, and both Clare and myself were shocked to hear of his death.

Sunday, December 30, 2007

Stow-on-the-Wold

We're just back from a three-day break in the Cotswolds, staying at the Grapevine in Stow-on-the-Wold. Not entirely clear what a "Wold" is.

The hotel was classy - featured in Signpost - and the restaurant was excellent, as was our room. What rather let it down was the bed: I still have the outline of bedsprings imprinted upon my body.

Yesterday we struck out to Warwick to visit the castle. Both Clare and myself had spent years as students in the area, and of course neither of us had ever visited the place. The castle has been completely 'touristified', with proper historical tableux and very lifelike models, plus the funfair in the courtyard which you see below.


Warwick Castle - within the walls

In the grounds there is an ice rink and a conservatory, near which peacocks brave the chill air. They appear to subsist on crisps and there is a never a shortage of (human) feeders.


Clare and the Peacock

Inside the castle, the rooms are furnished in the manner of a stately home of the 17th century - the banqueting hall shown below.



Nigel in the Banqueting Hall

Now we're back and the next job this afternoon is to put the Christmas decorations back in their boxes for another year. And to let the roomba out to play.

Wednesday, December 26, 2007

Roomba's first outing

It was the day after Christmas. I should be upstairs, practising my piano, but the Roomba got there first. Even as I write this, it's working away, vacuuming under the bed, hopefully not getting stuck.

We did this video of its very first outing, as we tried to figure out how to turn it on, and then how to have it not run over us!



Our other geeky toy is a pair of BT Freeway walkie-talkies. I could, perhaps, just justify these as a business expense - experience in push-to-talk. They operate in the 400 MHz band and have a 3 km operating range, apparently. They certainly work in the house!

Mostly they function as FM radios. Then you press "talk" and we're into "over", "roger", "wilco" and the other accoutrements of 1940s war movies. Great!

Update: the Roomba has finished upstairs, and has now been set to zoom around the downstairs. It's buzzing away in the background as Clare stares at it, fascinated.

Further update: after an hour's hard work, the power indicator went from green to red and we've had to put it on feed.

Monday, December 24, 2007

Carols at Salisbury Cathedral

Yesterday evening, Alex, Clare and myself motored down to Salisbury - through the sporadic fog - to attend the Christmas Carol Service. You get to queue in the quadrangle (there's probably a better name for it) outside the main Cathedral, from whence this picture was taken.


Inside the cathedral it was pretty cold, and we were forbidden to take pictures, so the snap below was covert. It shows the altar and crib with an angel suspended from the ceiling.


The carols were mostly traditional, except for an atonal "Deep Midwinter" by Judith Bingham (b. 1952). The choristers, girls and men, were of course, superb.

We returned to hot crumpets and Top Gear's Richard Hammond doing a programme on Evel Knievel.

Friday, December 21, 2007

The 'Chavtivity' or 'The Xmas Reindeer'

Very amused to see this modern nativity scene, known as the 'Chavtivity' or the 'Chav Xmas Card' (see story here).




From The Argus:
"In the picture Mary and Joseph are a pair of tracksuit wearing teenagers slumped in a battered bus shelter with their baby in a pushchair and a Staffordshire bull terrier on a chain. They are being greeted by three wise chavs, who are presenting them with gifts of booze, cigarettes and a stolen car stereo. Mary is chain-smoking and there is a Crimestoppers' poster of Joseph behind his head."
We also had our chav moments back in the US in 2001. Impressed by our neighbours' luminous displays, we went to WalMart to pick up some front-garden accessories of our own. As I pushed the huge boxes around on an outsized trolley, I heard a storeman exclaim 'Oh my gawd, it's the reindeer family!' - and so it was.

Our first problem was that it was self-assembly. I naturally delegated this problem to Clare, who was unamused.




However, she performed miracles and was delighted by the result.




We duly installed our two reindeer in the front garden. They were not just pretty lights - they had little motors so that their heads went up and down, and turned around in an attentive way. We were utterly pleased with this aesthetic effect, as Clare showed posing with the reindeer family in the gloom.



However, they only truly came alive after dark.




After a while, the motors failed so they remained stuck in one position, like sufferers from an obscure medical disease. We have never risen to such heights of Christmas exuberance since.

Wednesday, December 19, 2007

SA: hell in a handcart?

The Scotsman has an article today "Chaos on way as ANC hands Zuma top job" (here). The depressing prognosis for South Africa is illustrated by reader comments following the article. One, by "Media 1 - capetown", reads as follows (link here).

"Prior to 1994 South Africa was one of the safest nations on Earth. The suburbs were clean, the roads were good, the electricity never went out, the water always flowed from the taps, violent crime was something you saw on a movie screen, sanctions inspired innovation, invention and growth, school children were safe, the laws on the roads were strict and people adhered to them, ministers were held accountable for their actions, problems were solved and people both black and white were divided by a racist government.
Today: South Africa is the most violent nation on Earth, 52 000 rapes per annum, almost 40,000 murders, the lights are beginning to go off more than once per week, which leads to millions lost in business and chaos on the roads.
The rivers and dams are becoming contaminated, the municipalites are incapable of managing the problems, and the budget money is always stolen. The roads are chaos, and the metro police who are supposed to manage them are corrupt and inept. There can be a traffic jam consisting of hundreds of cars due to a power outage, and the metro police, instead of assisting the situation, will hand out fines to motorists who edge over a white line without completely coming to a standstill. It has become so bad that local business has had to train pointsmen to alleviate the problems on the roads.
The head of the metro police is up on drunk driving charges, he rolled his car on the motorway and even had his blood samples stolen from the hospital. He may never be charged (incidently, he was a former ANC activist who blew up McGoos bar, killing many during apartheid).
The Chief of the South African Police, Mr Selebi, is up on corruption charges, although he probably won't be forced to stand trial.
The Chief Whip Tony Yengeni defrauded parliament, got 5 years and was out in 4 months.
The Health Minister is an alcoholic who was given a liver transplant before others on the list. She is still drinking, never in parliament and drawing a massive salary
."

South Africa is a kind of laboratory for African abilities to run a complex modern, capitalist economy and state. The black majority inherited a functioning entity. And like Zimbabwe, it appears to be falling apart.

James Watson, referencing empirical research by a number of authors, identified the issue as IQ. I am not so sure: a functioning, scalable capitalist economy seems to additionally require personality attributes in the mass of the population such as:

  • high empathy (contra impulses to random violence against strangers - team player),
  • high conscientiousness (maintain essential processes even without immediate reward)
  • low neuroticism (maintain a level-headed reaction to interpersonal & other issues).
These, of course, are particular values of three of the factors from the famous five-factor model of personality (Agreeableness, Conscientiousness, Neuroticism). They are also the qualities employers tend to look for when recruiting. The other two factors are 'Openness to Experience' - positively correlated with IQ, and Extraversion.

Richard Lynn, Professor Emeritus of Psychology at the University of Ulster, wrote an article here about racial differences in personality, which makes depressing reading.

I hope it doesn't all end in tears.

Sunday, December 16, 2007

The 'Now' Calculator

One of the strangest results from special relativity is that a distant spacecraft moving away from or towards the earth at the present moment will consider that what is happening 'right now' on earth (according to the spacecraft crew) are events which to us are either in our past, or perhaps more surprisingly, in our future. For example:

1. A spacecraft in the Andromeda Galaxy moving away at 300 km/sec, at a time 'right now' according to us, considers the birth of Jesus to be happening 'right now'.

2. A missile at the distance of the moon (~400,000 km) and travelling towards us at 225 km/sec considers 'now' on earth to be one millisecond ahead of when we do.

3. An alien in a very distant galaxy, ten billion light years away, can move its 'now' for the earth plus or minus a human lifetime (70 years) simply by walking away from or towards the earth at 2 metres per second (4 mph). And we can do the same for it.

I have put together a small (25 kB) Excel online calculator here.

Input the event in the future (or past) you want to think about (the next election?) and the distance of the assumed spacecraft - typically some number of light-years. The calculator will then tell you how fast the spacecraft would be moving so that its crew - right now! - think that your event is happening 'right now', from their point of view.

Sobering for any of us who still think the future 'doesn't exist' because it 'hasn't happened yet'.

Piano diary #4: intervals key to sight-reading

Sight-reading! Tell me about it ... ! I've got three months (until the Grade 1 exam in April) to get it right.

I started by trying to learn the notes under each finger. Put your right-hand thumb on D, and then the fingers touch E, F, G, A. If the sight-reading test starts on D, and you are asked to put your thumb on D, then you can read the next note on the score and, if you know which finger is above that note, just play it. (You don't have to move your hands at Grade 1).

Two things subvert this approach. Forgetting the sharps and flats of the black notes, there are seven possible positions for the thumb to be placed, A-G: the pattern of notes under the fingers obviously varies with each. That’s 7 * 5 = 35 patterns to learn.

But of course you can’t ignore the sharps and flats - because they’re everywhere. And of course, they are built into the key signatures themselves.

And in non-test music, as bar follows bar, you are frequently told to move your hand position, which throws everything off. I’m not saying it’s impossible, but the procedure is utterly ponderous:

- see the next note on the score - suppose it’s “a”
- name it to yourself (A)
- recall where your thumb (“1”) currently is (D)
- recall that in that position, A is under the little finger (“5”)
- depress the little finger.

There is a better way.

A few months back, the book I was studying made a big fuss about intervals (2nds, 3rds, 4ths, 5ths, etc). You were meant to look at adjacent notes and “by inspection” say what interval encompassed them. For example, a “D” followed by an “A” is the interval of a fifth. At the time, I had little idea of the point of this. But ...

With a little practice, it is possible to read the pattern of intervals straight off the score. We all spontaneously do it for 2nds, where the notes follow each other up or down the scale. If you can internalise the fingering of an interval (thumb to little finger typically spans a fifth, for example) then playing intervals is pretty direct. The new algorithm is simply this:

- identify the interval between current note and next note
- shape the fingers to encompass that interval and play it.

Much faster and permits controlled look-ahead.

In a certain sense, you have to know everything - including which note your finger is currently depressing. But moving to an interval-based approach to sight-reading really unlocks it for me.

The obvious metaphor is differential calculus. With intervals, playing the score is really like computing:

f(x + dx) = f(x) + f’(x)dx*,

so that next-note = current-note + interval.

* Or more correctly, difference equations. The key point is that the interval approach is invariant as regards differences in key (subject to managing accidentals - sharps and flats - correctly), pun unintended.

Wednesday, December 12, 2007

World's funniest joke

Can't resist it.

Two hunters are out in the woods in New Jersey when one of them collapses. He doesn't seem to be breathing and his eyes are glazed.

The other guy whips out his phone and calls the emergency services. He gasps 'My friend is dead! What can I do?' The operator says: 'Calm down, I can help. First, let's make sure he's dead.'

There is a silence, then a shot is heard. Back on the phone, the guy says 'OK, now what?'

More funniest jokes here.

'Electromagnetism' with the Open University

Two days before the end of course registration, I finally made up my mind and enrolled with the OU for SMT359 - Electromagnetism (course description here). I quote:

"This course is concerned with the electromagnetic fields and electromagnetic radiation that pervade the world around you. It shows how the main ideas of electromagnetism can be encapsulated in the famous Maxwell’s equations."

Maxwell's equations constitute one of the pinnacles of classical physics. I see the course as a rehearsal, mathematically speaking, for the OU's course on quantum mechanics (SM358 - here) which is not available until 2009.

I am mindful that even that is two steps away from the frontier. After basic quantum mechanics comes quantum field theory, and beyond that (for most researchers), string theory. Both seem inaccessible to mere mortals, but I recently discovered books covering each at advanced undergraduate level.

I have ordered "Quantum Field Theory in a Nutshell" by A. Zee for Christmas (thanks, Alex!) and have my eye on "A First Course in String Theory" by Barton Zwiebach, for later. They both get pretty good reviews on Amazon.

Tuesday, December 11, 2007

LL7

Just back from the dentist, where I had an old filling removed and replaced - lower left seven, as you ask.

As I lay on the fully-reclined couch, with two masked operatives advancing with instruments towards my face, I thought of a BBC website report I had read earlier today (here). I quote:

A retired CIA agent has said a top al-Qaeda suspect was interrogated using a simulated drowning technique, but that he believes it was justified. John Kiriakou told US broadcaster ABC that "water-boarding" was used when his CIA team questioned suspected al-Qaeda chief recruiter Abu Zubaydah. He said it might be torture but that it "broke" the detainee in seconds.

Mr Kiriakou said the day after water-boarding was used on Abu Zubaydah, the detainee told his interrogator that Allah had visited him in his cell during the night and told him to co-operate. "From that day on, he answered every question," the retired agent said. "The threat information he provided disrupted a number of attacks, maybe dozens of attacks."


I don't know about Allah, but as the high-speed drill whined ever-closer, I also felt a strong desire to co-operate!

Saturday, December 08, 2007

Ofcom's 2.6 GHz auction

Come mid-2008, Ofcom plans to auction thirty eight lots of 5 MHz spectrum between 2500 and 2690 MHz. (There will also be an auction of 15 MHz of spectrum between 2010 and 2025 MHz, which will not be further discussed in this note).
In the CEPT band plan for the 2.6 GHz spectrum block, twenty eight blocks (14 x 2) are reserved for 3G operators using WCDMA in paired slots (FDD - frequency division duplex). The remaining ten slots are intended for TDD services (time division duplex), most likely for mobile WiMAX - see figure 1 (click on picture to enlarge it).

Figure 1: The CEPT band plan for 2.6 GHz

To launch a national WiMAX service would probably require a minimum of two adjoining 5 MHz slots - the ten TDD slots could support five WiMAX operators in this way. A WiMAX channel could use up to 20 MHz for higher bandwidth, and an operator could deploy multiple WiMAX frequency bands. For example, three WiMAX ‘channels’, each of 20 MHz, would require 60 MHz or twelve 5 MHz slots. Adding in competing WiMAX operators might require even more TDD slots. To accommodate this, the Ofcom plan is to auction generic lots, which can be assigned later to 3G/FDD or WiMAX/TDD usage depending upon the winning bidders’ desires.

Value for Money?

Ofcom are experts in the area of spectrum auctions and in the broader issues of the telecoms industry. They are unlikely to have made obvious errors in either the objectives of the auction or its design, particularly when their work is carried out in public and is under the scrutiny of the industry as a whole. So any assessment of the auction and its possible outcomes should focus on more subtle effects.

a. The ‘market’
Ofcom has made much of the inherent lack of knowledge of the regulator, and how the ‘market’ will know more about the utility of this spectrum. While this is certainly correct, we should look more closely at the market structure which obtains here. In textbook discussion of the superiority of markets over, say, centrally-planned economies, there is a presumption of competitive markets, maximally-responsive to customer needs.
However, in mobile wireless, for well-understood reasons, the market structure is oligopolistic. Perhaps the most likely outcome of the 2.6 GHz auction is the existing five 3G operators (O2 - Telefónica; Orange - France Telecom; T-Mobile - Deutsche Telekom; Vodafone; 3 - Hutchison Whampoa) owning some of the spectrum, who will then square up to one or more WiMAX operators (perhaps BT, Craig Wireless Systems, Inquam Broadband). The ‘knowledge of the market’ then reduces to the vector sum of the interests of these players, whatever that may be.

b. Post-auction market structure
How many providers can there be in a mobile wireless market? Consider a very simple model where the cost of rolling out and operating a significant (quasi-national) network is C and the total revenues available in the market are R. Then there can be no more than (R/C) distinct operators, as the revenues are not great enough to support any more.
Since mobile wireless voice networks already exist in the current GSM and 3G networks, we are talking about residual revenues in a distinctive wireless broadband data market. These are hard to predict and unlikely to be large, at least in the early years. The result is to raise some questions.

(i) If too many bidders acquire WiMAX spectrum, is this likely to inhibit all or most of them from investing, on the grounds that the cake will have to be split too many ways?


(ii) As Ofcom has proposed no requirements either as regards timescales to deploy or extent of geographical coverage, wouldn’t successful WiMAX bidders without deep pockets simple cherry-pick the centres of large cities and other high-valued locales? Doesn’t this then undermine the business case for more extensive deployment from operators with more capital resources?


There are probably good answers to these questions, but the issues seem under-discussed in the Ofcom discussion document (here).

c. Uncertainties in spectrum utilisation via new services
Ofcom seems unsure about the uses to which the 2.6 GHz spectrum could be put. Their report simply reiterates a list of services commonly used by consumers on their fixed broadband links, via PC.
In fact the business case for public wireless broadband services today looks fragile. Engaging with likely revenue possibilities requires a detailed review of location-based services, the specific needs of early adopters such as emergency services, councils and governments - as well as consumer requirements (which are heavily device-dependent).

High-bandwidth services such as mobile CCTV will surely be additional early drivers for these services. Ofcom could argue that it is not their concern to do such analysis - this is down to the bidders. However, taking an accurate, forensic view of likely services roadmaps, relevant vertical markets and early adopter requirements might help both in shaping the process and in estimating the likely benefits of various outcomes.

Tuesday, December 04, 2007

How many ancestors? (Part 3)

I guess I'm finally able to have a stab at this - how many ancestors did I have living in the mid-sixteenth century? I expect the answer will work for most people in England, of English ancestry. To save working through the stuff below, the answer I come up with is around 30,000, which is about 1% of the English population of the time (see note below).

My parents are from Bristol, which has had a large population for a considerable period. According to the Wikipedia article, Bristol had a population of 66,000 in 1801, and around 12,000 in the sixteenth century. Other provincial cities such as Manchester were probably similar. Pushing the family tree exponentially backwards, these numbers set upper limits.

In a city, out-marriage from the extended family is likely so I am comfortable that there isn't complete coalescence of the family tree back to, say 1700. Since that's ten generations, and factoring in some coalescence (50%), let's say around 500 ancestors in the tree in the oldest cohort.

From 1700 back to 1550 is another six generations. In this period, many people lived in rural villages, with significant inbreeding. On the male side, this is shown by localisation of surnames and also by genetic analyses.

Probably my 500 ancestors in 1700 can be traced back to villages surrounding Bristol and Oldham (Lancs), where my father's side came from. However, 500 ancestors will certainly include many emigres to Bristol (or Oldham/Manchester) who had come from all over the place. Let's guess the 500 ancestors came from 200 different villages, so each village gets on average 2.5 people.

In the six generations from 1700 to 1550, each villager will have 64 ancestors of the oldest generation. Assume a village size of around 128. Suppose several of my 1700 ancestors came from any particular village: they certainly won't each have a different set of 64 ancestors in that village; in fact the overlap will be extreme (see the paper referenced in the previous post here). Let's say they will share the same 80 ancestors of the oldest generation in 1550. In fact, let's use the figure 80 anyway, taking account of villagers who had come to the city and entered my family tree subsequently (post 1700).

So in 1550, over 200 villages, there would be 200 * 80 = 16,000 ancestors.

Now, we need to move this up a bit, as some of my ancestors would have stayed in the cities, which even in the sixteenth and seventeenth centuries were a lot larger than villages and where inbreeding would be less. It's hard to estimate how many we're talking about here, as outside of London, most people - prior to the enclosures - lived off the land. The result, however, would be less inbreeding, so let's move the oldest cohort of ancestors up from 16,000 to 20,000, as a rough estimate.

Then the total number of ancesters alive in 1550 would be no more than 20,000 + 10,000 + 5,000 = 35,000. Say 30,000 allowing for more double-counting due to family tree branch coalescence. This compares with the figure of 458,752 computed from simple backwards doubling over 16 generations - see the first post on the subject here.

According to the human genome project, the total number of genes in the human genome is around 30,000. Some of these are not variant, being highly conserved because they do something essential. However, genes are long sequences of nucleotides and typically differ between people at a number of different sites. So you could argue that each of my 1550 ancestors probably contributed on average less than one gene (allele) to me!

Finally, a graph showing the population of England in the mediaeval period. Click on the picture to read the text.

Note: Based on the paper (which assumes random mating) referenced in the previous post, How many ancestors? (Part 2), there are 14 generations between an ancestral tree covering 1% of the population and one covering 99%. On this basis, everyone who lived in 1200 AD in England and who has descendants today is an ancestor of everyone of English ancestry living today. Or using another result from the paper, my family tree includes 80% of everyone living in England in 1200 (the remaining 20% did not leave any descendants alive today).

Monday, December 03, 2007

How many ancestors? (Part 2)

It appears the statistical physicists got there ahead of me, I quote:

"On the genealogy of a population of biparental individuals

Authors: B. Derrida, S.C. Manrubia, D.H. Zanette

(Submitted on 7 Mar 2000)

Abstract: If one goes backward in time, the number of ancestors of an individual doubles at each generation. This exponential growth very quickly exceeds the population size, when this size is finite. As a consequence, the ancestors of a given individual cannot be all different and most remote ancestors are repeated many times in any genealogical tree.

The statistical properties of these repetitions in genealogical trees of individuals for a panmictic closed population of constant size N can be calculated. We show that the distribution of the repetitions of ancestors reaches a stationary shape after a small number Gc ~ log N of generations in the past, that only about 80% of the ancestral population belongs to the tree (due to coalescence of branches), and that two trees for individuals in the same population become identical after Gc generations have elapsed.

Our analysis is easy to extend to the case of exponentially growing population."

Read the entire paper (PDF, 15 pages) here.

Note: Here's another really interesting paper on the most recent common ancestor to humans living today - here.

Sunday, December 02, 2007

How many ancestors? (Part 1)

I was thinking some more about computing how many ancestors I, or anyone else, might have had in 1559 - see the "Fight between Carnival and Lent" post here.

The obvious, simplistic approach is to double the number each generation back, say every 25 years. Two parents, four grandparents, etc. Then assuming a three generation overlap, add the last three answers together to get a total ancestor population.

1951: me + 2 parents + 4 grandparents = 7
1925: 2 parents + 4 grandparents + 8 great-grandparents = 14
1900: 4 + 8 + 16 = 28
1800: 64 + 128 + 256 = 448
1700: 1024 + 2048 +4096 = 7,168
1600: 16,384 + 32,768 + 65,536 = 114,688
1550: 65,536 + 131,072 + 262,144 = 458,752.

Call it half a million. A simple Google search indicates that the population of England during the 16th century was around 3 million. Surely my ancestors (or anyone else's) wouldn't have been one sixth of the entire population?

It appears that rural populations were pretty static until comparatively recently. This probably means that villages were pretty inbred. If we assume that a village was constituted of 100-150 people (the hypothesised upper limit of organic human communities) then for a number of generations, this was probably the limit to the number of ancestors as we push the family tree backwards.

The arrival of a stranger in the village would introduce new genes into the local gene pool, but it would take a number of generations for that person's genes to propagate throughout the village.

Working out a revised (and lower) number of ancestors, I think it's difficult to estimate plausible parameters and solve this analytically. I therefore decided to write a simulation. To do this would involve my favourite programming language, LISP.

To my surprise, it has proved quite hard to find a free download which would work on Windows XP and Vista. Eventually I found "LispWorks Personal Edition" with a download site here.

Nest step is to install the system (not tonight!).