Scientific Samsara

Samsara, as taught to me at highschool and stated by Wikipedia, refers to the Buddhist belief in a "cycle of reincarnation and ... mundane existence". To a Buddhist, then, all life, riches and success are pointless with the exception of attaining enlightenment.

We scientists should heed this lesson, for this logic applies equally well to our set of axioms. Our Nirvana consists of making the most accurate observations of nature, creating falsifiable hypotheses which best fit this data and developing a technology which is demonstrably better or more useful than all others in some way.

Let this sink in. Publishing countless highly-cited articles in Nature on the most mathematically elegant theory of the luminiferous aether is garbage science, if it fails to describe experiments in photonics better than our current leading theory. Controversially, I would even argue that such work advances science less than the discovery of some beetle by a retired hobby gardener, much as I am indoctrinated as a physicist to believe that my branch of science is superior to biology. Continuing to develop thermionic valves for computation, or - even more controversially - to work on supersymmetry, is Samsara.

Our cousins working in the tech industry, who have short-term profit and loss hanging over their innovation as the Sword of Damocles, have long known about technical debt, whereby it is ill-advised to struggle with something that would yield little benefit today and would in any case be more easily solved tomorrow. Consider that, assuming a Moore's Law with a doubling time of 2 years, delaying the ill-fated National Ignition Campaign from 2009 until now would have allowed scientists a theoretical factor of 16 improvement in computing power to help direct their fusion experiments. On the other hand, the technology to build LIGO, develop diode-pumped solid state lasers or launch a solar orbiter was just as mature back then as it is today. If we are honest, aside from making a quaint story, the work of Charles Babbage to build a steam-powered computer has had little practical impact on modern computer science.

In debates like "those coal miners made unemployed by their mine closure should find other jobs", I have heard the argument that it would be difficult to retrain to another career. I would question how scientists who intellectually cannot change research fields were able to reach the forefront of their profession in the first place.

Let me end with a different theology, the ending of Medea:
Our wishes do not always come to pass,
yet some god will find a way to make unexpected happen.
So with this story.

The challenges of equality: a mathematical perspective

There has been a lot of talk recently of equal representation in various fields. I would like to offer my mathematical opinion on the matter and I will illustrate these thoughts with an example I hope to be totally politically uncharged. I was recently lucky enough to learn - in person - about the formation of a new Overwatch League. For those over 40, Overwatch is a multiplayer videogame and the new OWL is a league of professional teams (each player is likely to be on at least 6 figures) with sponsorship deals and games at live stadiums.

So, let's imagine how statistically likely we are to have equality in this league, specifically that between two groups: professional players with glasses and those without. The examples below are, of course, completely hypothetical.

As a consequence of the Central Limit theorem, any meaningful probability is extremely likely to be Normally distributed. Not guaranteed, but extremely likely. The Normal distribution is characterized by the standard deviation (width) σ and mean μ.

Assume that two groups of precisely equal size play the videogame: those who wear glasses and those who do not. As expected, given that the total number of players is large enough to be statistically significant at 35 million worldwide (and therefore each group, since they're 50% of the total), then their skill is normally distributed. Suppose that the groups' standard deviations are equal, but the "Glasses" group for whatever reason has a small skill advantage in the form of a slightly higher mean:

The grey area represents the overlap of the two distribution functions - perhaps it is accurate to describe them by having more in common than not. That is true for the majority of players, but to qualify for a top-level place on a competitive team, a player must surely be at the highest levels of skill. Let's model this by making the (not very realistic) assumption that only the most skillful players are selected, until spots on every team are filled. 

Statistically, this is represented by taking an integral from infinity down to some threshold skill value T (the skill of worst players on a team). We can expect that the integral is larger for the Glasses population for the example above, but you can see it clearly, equally scaled below:

 

The definite integral of the Gaussian function is the error function (erf). The sum of the two integrals is the total fraction F of the playerbase playing on a team.

The inversion of this equation allows finding the threshold, given a set fraction. This becomes non-analytic for an arbitrary number of distributions, but is straightforwardly done with Brent's algorithm.

Let's imagine that we set a threshold - "the top 1% of all players are on a professional team" - and wish to know the proportion with glasses. The expected percentage is shown for three choices of threshold as a function of the shift in mean below:

The functions are symmetric about the point (50%, 0), because the two groups can effectively be "swapped" if Δμ is reversed in sign.

Similarly, assuming both populations have the same mean, but varying the standard deviation of Glasses compared to No Glasses is shown in the plot below:

So arguably the standard deviation has a greater effect than the mean, because when skimming only the very best off the top, it helps having a lot of statistical spread - having many highly skilled and equally many poorly skilled players - as opposed to having almost everyone "average".

To conclude:

• If there is a true disparity between two populations, then the mathematics is clear: one group will always tend to be over-represented. The solution to achieving parity of representation is to equalize the statistical distributions: perhaps there is a systematic poorer retention of the No Glasses group, which can be eliminated, or the game itself can be changed to be more friendly to both.
• Conversely, if the statistics suggest that 70% of players should have glasses, but the true figure is 95%, then there is some strong bias in the system. The situation is unfair, but also certain to be counter-productive: for the Glasses integral to make up such a large proportion, its threshold must be lower than for No Glasses; this means that the overall skill level of the players could be increased if the latter were represented fairly (making up 30% of professional teams).
• If measuring game skill directly is not possible, one should be very wary of proxy metrics like reaction time, etc. These may be only weakly correlated with the truly interesting parameter and that correlation itself may be poorly known, leading to bias in the analysis itself.

"Westworld"/"Spartacus: Blood and Sand" review

Westworld  

While flying to California recently, I watched the entire first season of Westworld. The premise, taken from the eponymous movie from the seventies, is of an expansive Western-themed adventure park populated by lifelike androids. The human visitors are free to engage with this park world and interact with the androids in any way they like – in practice mostly violently or sexually. The androids are very extensively programmed and respond intelligently and with a range of human emotions, which means it’s inevitable that they become sentient and their treatment becomes immoral. After being shot, mangled and emotionally traumatized, their memories are wiped and they are patched up in a vast futuristic underground complex by staff at the park.

At this point, I would like to discuss the moral or philosophical points of the show, but I can’t. The ideas of robot sentience and what it means to be alive or human, have been explored so often in various media that Westworld brings nothing else to the table. It is just a well-made summary of other fiction works. The story is gripping enough to keep my attention, at least when the viewer is locked with it in an aluminium tube – though I did look out over Iceland and Hudson Bay for a short while.

My biggest gripe with the show is the poor portrayal of logistics*, taking the superlative remake of Battlestar Galactica as a benchmark. Humans are shown on wilderness treks for days, sometimes tied up, without food and with scarce water – how do they comfortably survive? Why do even prepared park technicians set out into the hot “California” sun (that’s where it’s filmed) without taking water or any trail mix with them? How do revolvers and Winchester rifles fire seemingly dozens of shots without reloading? What happens when a human visitor goes on a romantic overnight train ride; the Civil War-era train would cover 200-300 miles in this time, which is larger than the park is expected to be? Is the seemingly single train bringing guests in and out of the park enough to maintain the stated equilibrium population of several hundred visiting humans? These and a great deal many other questions are left unanswered – perhaps they were inside a simulation all along and the humans are really holograms.

Had there been a noteworthy philosophical message, I would have suggested that it is overly mired by the gratuitous violence and nudity – practically every other scene in the park ends with blood and guts, frequently with an entire town of androids being gunned down, while every shot in the sci-fi setting has naked androids (i.e. human actors) awaiting repair in the fore- or background. Speaking of gratuitous violence and nudity...

Spartacus

 

This series ("Blood and Sand"/"Gods of the Arena" ...) charts the historically-inspired paths of Spartacus, a Thracian leader of a gladiatorial uprising, and his fellow rebels. The first point to be made about this series, more so than any others, is that dramatic media invariably play up excitement and downplay the monotony of life; even the most banal soap opera cuts out the characters waiting for a bus or sitting in reception at the dentist's.

For this reason, this show was initially - and perhaps unfairly - labelled as a show purely for teenage boys, due to the copious amounts of sex and gore. But given the setting, this is totally justified: the portrayal of the blood and guts of gladiatorial combat in the late Roman republic is archaeologically sound, if a little embellished - in most arena fights the loser would be allowed to live - while the lewd aspects fit with our view of ancient Rome from the brothels of Pompeii and vulgar poetry.

Overall, I felt the show was very well made. It had the deceit and dirty dealings of any modern political drama and was excellently themed. The most superb touch of the entire show was the way the English script imitated Latin speech - brisker and containing no definite articles. It certainly dipped in the last series, since the format was not really conducive to the massed battles late in Spartacus's campaign, but perhaps no worse than when everyone inevitably turns out to be in The Matrix in future season 36 of Westworld.

---

*It has been said of me that I "can't enjoy anything" because of my pointed questioning of logistical matters in the Terminator film series.

My first play-through of Crusader Kings II

I picked up Crusader Kings II as a bundle in a steam sale last year, having had a nice impression of the publisher Paradox Interactive - renowned for meticulous grand strategies. I tried my best to play it twice before, but couldn't seem to bear out the tutorial. Choosing an ideal spouse to build your medieval dynasty seemed a shuddering jump away from strategically redeploying Siberian divisions to stop an armoured breakthrough, as in Hearts of Iron from the same publisher. This was my first thought as I went into the tutorial - wanting for a slow game which could be paused at will with a crying baby at night - for the third time.

But this time I found it surprisingly enjoyable.  The game is an endless Machiavellian climb to the top, usually on a pile of bodies. Every duke wants to become king, every king desires the emperor's throne and the emperor seeks to keep his vassals in place by dividing and ruling. Actually, these feudal courts were eerily reminiscent of Stalin's 20th century government: he eliminated all his ambitious "vassals" and split the power, so that the remaining loyalists dared not oppose him.

Although the tutorial stated that it would be over when Alfonso of Leon died, after playing to his heir and restarting the game, I still received a prompt to start a tutorial again. So, without the tutorial registering as completed and irked that I couldn't otherwise unlock achievements, I jumped in at the deep end and started an "Ironman" campaign. In this roguelike mode, there is a single computer-controlled savefile: any mistakes are permanent.

I started in 867 (no Charlemagne DLC) as the leader of Wessex, because my wife and I have recently been watching "The Last Kingdom", a period drama set against the backdrop of King Alfred the Great of Wessex stopping the Vikings. Without a full understanding of how wars or combat works, or how the initial Viking "horde" spawns work, I initially launched myself into a series of disastrous counterattacks which quickly depleted our war score and losing Northumbria.

In modern military textbooks, one of the principles of defence is an Offensive Spirit and I was fully committed to use this in the defence of Wessex - and eventually England - from the Vikings. While they consolidated their spoils, and with Mercia as a buffer zone, I immediately set about fabricating claims to take Cornwall, a county in Wales and then counties in Mercia itself. This emboldened me to start taking on some of the weaker Vikings and soon to press forward to form the kingdom of England.

While I was consolidating England, the Vikings had settled and formed a large Scotian block under the Kingdom of Ireland, with a surprisingly strong and independent Wales in the mix. However, when the lords of Scotland briefly rebelled and split the country in two, I seized my chance to fight both individually and take enough counties to form the Empire of Britannia. Now with a dominant position in the British Isles, I was unopposed in taking the rest of the counties de jure, one at a time, but greatly slowed down by the need to have a 10 year truce after every county. This was greatly sped up when I was able to usurp the kingdom of Ireland, fracturing the lands there and allowing me to press multiple wars simultaneously.

By 1066 I had most of the British Isles and set about googling a few things. I had previously attempted to press a courtier's claim to be king, but was exasperated to find that this merely installed him as an independent ruler. But then I read something which said that giving the claimant a landed title would make them your vassal when a claim was pressed. I set about testing this theory by giving out a county and installing a new king of Sweden under my banner. Now I could take whole countries at a time, but the downside was a Threat increase taking 20 years to dissipate.

But there was another alarming find for me online (since I had the Sunset Invasion DLC). In this alternate history, a great North American empire had captured a wayward Viking ship. This had caused a paradigm shift for them, leading eventually to the construction of a vast armada intent on taking Europe. This was in large part a move to balance out the Mongol invasions of the East with a huge (albeit horseless) horde in the West. Now my Stalinist expansion (sometimes called "map painting" online) had a true purpose, as I needed to force enough subjects under my banner to show a united front against these Transatlantic hordes, whose human sacrifice was surely worse than vassalage to me. Finally, my expansion had another unexpected effect: in order to create land holdings to give to claimants, I built cities (which give the highest monetary income) in sparsely populated places such as the Shetland Islands (where construction is cheapest). Cities in Crusader Kings II are miniature republics and the lands taken when their mayor has a claim pressed become republics too. Thus France and parts of Germany under me entered the Renaissance as fledgling democracies.

The "Aztecs" (really a collection of Mesoamericans) arrived very early, first in Muslim Spain and then in Scotland in 1254 (when the expected arrival is usually 1300). In my realm they had a force of over 100 thousand troops, but I now had marginally more and importantly concentrated my forces. This led to a complete rout and subsequent destruction of all their armies before they could capture a single holding. Without bothering to make peace, I immediately sailed to Spain and fractured their armies there too, until I hunted their retreating force deep into France. For the sake of the relevant achievement, I didn't make peace until their army size dropped precisely to zero.

The Mongols, unfortunately, failed to make any progress in this play-through, though I understand the Horse Lords DLC might give them a bit more edge. This was a shame, because I was expecting them to arrive at the gates of Byzantium or somewhere else I would need to face them. My strategy for hiring a retinue, a standing army, was focused on beating the Mongols and their wily mobile horse archers.

I now needed a goal for the final two centuries of gameplay. I chose an overall strategy of restoring the old Roman Empire, for which I would need control of Byzantium and several other counties around the Mediterranean, such as Alexandria and Venice. In between taking France and succeeding in several Crusades, I made a good start on these prerequisites. Taking the title of Emperor of Byzantium, however, would require more slick maneuvering. Since I couldn't vassalize another emperor, I would have to create an heir with a claim to the throne.

I had already passed Agnatic-Cognatic succession in my empire, allowing female rulers. Now I had managed, through several strategic marriages to Greeks, to have a female heir and a grandson with a claim to the throne of Byzantium. All was set for me to recreate the Roman Empire in two generations. But I snatched defeat from the jaws of victory in what would be my Great Mistake for this play-through. When my character's aged wife died, I thoughtlessly remarried the first princess I could find with high stats, so I wouldn't need to reduce my demesne size. But she quickly gave birth to a boy, who would sidestep my carefully planned lines of inheritance. In retrospect, I could have forced him to take the vows of priesthood, thereby disinheriting him. And what's more, I had also married off one of my daughters without thinking, so that the male heirs she had would later challenge me for succession.

From the Great Mistake came the Great Survivor of my dynasty. Pretty soon I found myself as a child on the throne, with the next in line to succeed me outside my dynasty. If I died now, before I had any direct heirs, it would be game over. It was a tense time when little Mærleswegn fell ill at age 8. But he recovered and as soon as he came of age married a buxom Polish princess. He soon had several sons to succeed him, enlarged his empire earning the title "The Hammer" and even knocked off two of the pretenders, though this was now unnecessary. But becoming the Byzantine - and therefore Roman - emperor was now out of the question before the game ended in 1453 and the Renaissance began.

The longest reigning Wessex monarch

It is clear that there is a lot to learn in this game even after a full play-through. Indeed I never once made any tactical military choices, like manually assigning commanders, or giving battle orders. Some things I did purely for the achievements, such as forming Wales for "United the Kingdoms", taking an opportune moment during a Threat cooldown to go on the shortest possible pilgrimage, but also choosing to expand to Arabia for "Protector of the Holy Places" when I had 30 spare years before I could make my next attempt at Byzantium.

Overall a pleasantly challenging and very relevant game.

The Empire of Britannia at greatest extent

Typical empire summary at the end of the game

Achievements obtained during run:

• The Marriage Game // Full House
• Until Death Do Us Part
• Crusader
• United the Kingdoms
• Protector of the Holy Places
• Pilgrim
• Paragon of Virtue // Exalted Among Men // Merchant Prince // Saint // Celebrity
• And Stay Out!
• Persistent Survivor
• Divine Blood // Dragon Blood // Royal Blood
• Turbulent Priest 
• Dwarf Fortress

DLC (as the 5-year anniversary bundle): SoI, LoR, SI, TR, TOG, SoA, RoI

I'm having a kid. Here's why

Albert Einstein's father co-founded an electrical company. Had he decided to focus on his career over having children, his small-time company would likely have gone bankrupt or been bought out anyway; for the sake of that irrelevance, we would have lost one of the greatest minds of the 20th century.

We recently scanned my wife for lifeforms. Specifically this one, due to be born in about a month:

I have seen a fair number of articles in the press or online opinions about people deciding not to have children, perhaps to pursue a career instead. Our Prime Minister got a free ticket to 10 Downing Street because of such a scandal. Others argue that the world is becoming overpopulated and resources ever more strained. Particularly, the link between lower levels of economic development, lower level of education and high birth rate and relatively high infant mortality is well understood. Perhaps it is a good idea to have fewer children in the developed world to offset this effect.

To me, this argument is as if the heating fails in a block of flats, so that each one is freezing cold, setting fire to one of the flats so that the average temperature is acceptable. Having huge variations in the birth rate between countries - or between different social groups in a given country (such as based on level of education) is bound to brew trouble. It would mean, for example, a huge rate of migration (and brain drain etc) or that child-bearers are less represented in government (which has a high rate of university graduates).

What's more, we in economically developed countries should set a precedent for the rest of the world who are industrializing. As increasing GDP leads to higher living standards, countries adopt many "Western" paradigms (such as the internet where you are reading this blog). This applies for demographic trends as well. For example, as Thailand and Korea have become more industrialized, their birth rate has dropped below the rate of replenishment. 

If the entire world were to reach the current Western level of socioeconomic development (which is broadly happening), and this correlates with a below-replenishment birth rate (which is also the case), then the human race would eventually die an anguished death. Anguished, because the exponential drop in numbers would leave a proportionately high ageing population needing care. Saying that "children aren't for me" is like saying "a job in farming isn't for me" - if everyone had that opinion, we would go extinct.

In his farewell speech, Barack Obama talked about his accomplishments: ending recession, giving 20 million Americans access to healthcare, achieving marriage equality - regardless of your personal political viewpoint, things important to him - yet he cited raising his children as his proudest accomplishment.

It is worthwhile to have a large population. Whether there are 1 or 10 billion people on the planet, there will always be (for example) 2% working as farmers just to feed the rest, but the difference in the latter case is that there is a 10-times larger pool of talent to work on the space program or write music. Spending some extracurricular time to do childcare for 20 years and the associated career setback (if there even is any) is well worth the years of accomplishments from the children that result.

For a different viewpoint, here is Doug Stanhope:

Why I prefer "Star Wars" episodes I - III

(Though I must admit - I haven't seen The Force Awakens)

Naturally, contains spoilers

Edit: The US president's battle with judges in early 2017 makes the following line - and stark warning about limiting executive power - from Revenge of the Sith the most meaningful in the entire franchise:
"He controls the senate and all the courts" - Mace Windu's justification for the (morally correct) extra-judicial killing of Chancellor Palpatine

It's a sign that humans either enjoy repetition or lack imagination, that most cultural narratives mostly share common "tropes". I feel that the major shortcoming of the Star Wars series is their egregious use of the "death of millions is a statistic" trope (or nine million, in this case). With a Dunbar number of 150 individuals, humans cannot empathize with millions of others. Most fiction therefore focuses on just a few individual characters.

Unlike a "Trek", the word "Wars" which in this case follows "Star", does not normally conjure images of discovery and self fulfilment, but carries the heavy burden of death, devastation and is not to be taken lightly. Moreover, wars are won by logistics and massive mobilization (corresponding to billions of soldiers in the setting of Star Wars) - not by the action of a few individuals.

That is why I despair at the incestuous Star Wars films and their extended universe. A few members of one family decide the fate of a galaxy of billions; the death of a single character really is given more screen time than the destruction of an entire planet.

Perhaps most laughable of all is the fact that one of the most pervasive and iconic characters is the robot R2-D2, whose entire personality and psyche would have been endlessly copy-pasted on a production line. Think about it - with a naming scheme of two letters and two digits, fewer unique astrometrics droids (shown to be used in single-pilot fighters) could exist in an entire galaxy than the number of ground attack aircraft produced on one planet (Il-2 and related variants). And yet a single such robot participates in all the greatest historical events of its time.

Seen through this prism, I feel that the narrative of Episodes I-III is more robust than the others. The characters feel truly embedded into grandiose events unfolding around them, with the clash of vast armies Rescuing a princess is a fine plot for a fairy tale, but wars are fought and won because of economic needs. (Trade agreements, anyone?) They are best seen by a mature audience, allegoric to the rise of fascism, perhaps also a critique of America in the early G. W. Bush years.

I have a similar problem with the film Pearl Harbor among others, which was a chance to use modern CGI and Hollywood actors to bring history to life. Instead, over half the film isn't even set in the titular military base, but focuses on a mere handful of characters spending most of their screen time in largely unrelated locations. How could a movie about such earth-shattering events have been reduced to the outcome of one love triangle? And, of course, the film cannot conclude with a defeat (at least The Empire Strikes Back may be commended in this regard), so it ends with the militarily irrelevant Doolittle Raid.

I would truly like to know if it's possible to have an alternative to this character-driven form of fiction. Certainly, it dates back at least to Homer, who in the Odyssey gives greater detail of the protagonist's big toe (well, pretty much) than his crew of thirty individuals with their own hopes and dreams.

In the meantime, I would suggest that writers follow the example of Tolstoy in War and Peace - by all means have a character who mans an artillery piece on the flank of a world-changing battle, but do not have them pole vault the entire Grande Armeé to kill Napoleon and single-handedly win a war.