Monthly Archive: October 2015

I had an occasion recently to watch the new science fiction movie called Ex Machina.  While the movie was okay there were some interesting points raised that are worth at least a brief commentary.

The story centers around a genius computer scientist/programmer/inventor (enough… you get the picture) by the name of Nathan.  He’s some sort of strange mix between Elon Musk, Tony Stark, and Sergey Brin, who he most physically resembles and is clearly patterned after in terms of backstory.  It seems that Nathan’s invented an artificially intelligent ‘woman’ by the name of Ava who he wants to subject to a Turing Test.  However, no simply dialog version of the Turing Test is good enough for Nathan and he recruits a bright employee, by name Caleb (no one has a last name in this movie), from his multi-national company to administer a super version of the test.  The problem is that Caleb can’t know the real nature of the test since Nathan wants to see if Ava can elicit a real emotional connection with Caleb. And thus begins a psychological thriller that starts with Nathan manipulating the interactions between Ava and Caleb and ends with the question of just who is manipulating whom.  Overall the movie is mostly telegraphed and predictable, ending with the usual but unspoken admonition that there are certain things man is not meant to mess with – certain genies that once let out of the bottle are impossible to recapture.  Nonetheless, a few ideas stood out as intriguing.

About a third of the way into the movie, Nathan takes to explaining some of the technical details to an eager Caleb – details on just how Nathan was able to model such a human looking Ava.  The two major technical challenges discussed where making her speech natural and making her thinking adaptable.  Nathan says he solved the natural language problem by eavesdropping on every cell-phone conversation and using all those data as a reference (perhaps by training a neural net – the fine points weren’t discussed).  One the thinking front, he claims to have watched how web surfers travel through the World Wide Web.

Most of us expect that our journeys in cyberspace are quietly monitored by big-data marketers, salivating to see what we are interested in and thereby serve up those ‘customers who purchased x also purchased y’ prompts.  What is tantalizing how the discussion in Ex Machina is the idea that Nathan wasn’t interesting in what they users were viewing on the web but how they were viewing the web.  In other words, the patterns of clicks and views reveal more about how we think than what we think.

The discussion reminded me of a game I am fond of playing.  There is no winning or losing.  All that is required is for each participant to say a single word that comes into their min based on the word previously uttered.  Obviously, someone starts with an arbitrary word but from then on it is link by link by link.  Any player is allowed to challenge a word uttered by another player for an explanation on how it links with the previous word.  Most players start reluctantly and soon join in with enthusiasm and I have found it to be a great way to gain insight on how friends and family think.

The technique that Nathan is discussing is like the game described above (it has no formal name) writ large.  Analysis of how people link pages and images together is yet another facet of that ongoing debate over how much does language affect thinking versus how thinking affects language.  Except in this context, the answers are no longing strictly couched in terms of philosophical arguments and mathematical hypotheses.  Suddenly, with this subtle but significant shift in thought, new vistas open where linguistics can truly be tackled in an experimental framework.  The possibilities are staggering.

A couple of weeks ago I wrote about the detective story as a playground for exploring the philosophical question of double effect.  This week I thought I would discuss an excellent example in this category – The Red Box by Rex Stout.

Unfortunately there is no easy way to discuss the ethical dilemma without spoiling the story so beware.

At the center of the story is the Frost family and the vast Frost fortune.  The Frost family consists of two major branches.  On one side is Llewellyn Frost, a shallow young man who produces flop plays on Broadway and his father Dudley, who is a babbling, blowhard.  Neither has much more than their bluster to their name.  On the other side is Helen Frost, Dudley’s niece and the heiress to Dudley’s brother’s immense fortune, and her mother, Calida Frost, Dudley’s sister-in-law.

Caught in the orbit of the Frosts are a wide variety of people, the two keys being Boyden McNair and Perren Gebert.  McNair is a successful designer of women’s clothing and he own a fashionable boutique in lower Manhattan where Helen works as a fashion model.  Perren Gebert is a useless dandy who is an old friend of Calida Frost and a would-be suitor for Helen.  Unlike McNair, Gebert has no visible means of support.

The story starts with Llewellyn Frost bullying the famous literary detective Nero Wolfe into investigating the death of Molly Lauck, a fashion model in McNair’s boutique.  About a week earlier, between runway calls, Molly, Helen, and a third girl by the name of Thelma Mitchell, snuck away to a deserted spot to rest.  Molly produces a box of candy that she ‘swiped’ for them to have a snack.  One poisoned Jordan almond later and Molly is no more.  Llewellyn’s aim is for Wolfe to find Molly’s killer as a way of pulling Helen away from her job at Boden McNair’s shop thus opening a door for Llewellyn to rid himself of a McNair as a perceived rival for Helen’s affection.  It seems that Llewellyn is so smitten with his cousin that he has researched whether it would be licit for them to marry.

As Wolfe investigates he finds that the box of poisoned candy was intended for Boyden McNair.  McNair, recognizing his peril begins to put his affairs in order and even goes so far as to name Wolfe in his will as the executor of his estate.  Shortly afterwards, Boyden McNair visits Wolfe’s office to explain the situation and to ask Wolfe to consent to the arrangement.   Boyden hints that the danger to him is rooted long ago in the past around the time of the birth of his daughter Glenna, who was born a month before Helen Frost.  McNair explains how his wife died during childbirth and how Glenna was lost to him a few months later.  He goes on to tell Wolfe that should he die all the proof Wolfe needs can be found in his red box.  Unfortunately, just before McNair reveals where the box is hidden he also dies from poison, this time expertly put into a bottle of aspirin that he carried around.

With no other obvious recourse, Wolfe sets his agents to the task of finding McNair’s red box.  The New York police are also eager to find the box as are the Frosts.  Indeed, everyone is so anxious to see what truth lies in the red box, that the box itself begins to take on a life of its own.

Meanwhile, Perren Gebbert begins to push hard for the hand of Helen in marriage.  He even goes so far as to try to find the red box for himself, which is quite remarkable considering his layabout status.  He is rewarded for his effort by becoming the third victim of the poisoner.

With three deaths on hand and no red box, Wolfe resorts to a clever plan.  Realizing that the red box has now become an incredibly powerful psychological symbol, he pays an artisan to manufacture a faux red box.  He then gathers the suspects and begins to reveal the truth all the while with the counterfeit red box in plain view.

The truth he reveals is this.  The real Helen frost died those many years ago.  Being penniless and a recent widow, Boyden McNair agrees to allow Calida Frost to raise Glenna as Helen.  Calida is the one who suggests this arrangement because secretly she sees it as a way of keeping control of the vast Frost fortune – a fortune that she was disinherited from due to her marital infidelity years earlier.  Gebbert, who was witness to the switch, offered his silence in return for a monthly stipend from Calida.  Having identified the motive for the murders, Wolfe has revealed Calida as the culprit and convincingly hoodwinked the gathering into believing that all of this is supported by the evidence he found in the red box.

However, Wolfe really has no tangible evidence as he has never been able to locate the red box.  To keep hi gambit alive, he hands the red box to Calida.  Upon opening it, she finds a bottle of oil of the bitter almond, a potent poison.  Believing herself to be trapped, she quickly swallows the poison and kills herself.

And here we have the ethical conundrum of double effect:  was Wolfe justified into cornering Calida Frost into committing suicide?

While there is no easy answer to this question, I would argue that he was.  To support this, let’s look that the four conditions that must be met for the application of double effect, starting with the easiest and progressing to the hardest.

The agent must intend good.  This point is the easiest and most supported of the four.  Wolfe gained in no way, neither financially, personally, nor professionally by the death of Calida Frost. She posed no threat to him physically.  Using the fake red box as a prop actually resulted in less growth in his professional reputation than would have occurred if all concerned knew that he had deduced the story merely by the scattered bits of clues that had emerged since Molly Lauck’s death.

The end must be an immediate consequence and not a means to some other end.  This point is also fairly easy to support.  The end was putting an end to the reign of terror brought on by a murdered.  That end was achieved by the death of the murderer as an immediate consequence of presenting the poison to Calida Frost.

The good must outweigh the bad.  This point is a bit trickier to affirm in Wolfe’s favor.  Clearly taking a murderer off the street, in particular, one so cunning and sneaky as to have killed three people by poison, is a good thing.  And considering that the period in which this story was set also had mandatory capital punishment, it seems that this should be straightforward.  But the people of the city of New York was the only proper authority to administering this type of justice.  By circumventing their proper role and becoming, in essence, a vigilante, Wolfe has visited some bad on the justice as a whole.  Nonetheless, I believe that the good outweighs the bad in this case.

The action must be good or at least morally neutral.  Here is the most difficult point to justify. Is offering poison to anyone with the intention of them drinking and thereby dying ever a good thing.  This point clearly dovetails with the one listed just above but it differs in a subtle way.  In the question about the good outweighing the bad, the central notion was the good and bad done to society.  Here the central question seems to be the intrinsic question about the violence Wolfe may have done to his own soul.  It was a hard choice and while I understand why Wolfe made the choice he did, I still have a hard time becoming comfortable with this way of stopping a killer.  Nonetheless, I think when all things are considered, Wolfe’s actions were supportable by the doctrine of double effect – I just don’t think I could have done it were I in his shoes.

I’ve used the detective story as a model for talking about and modeling epidemiological questions in earlier posts but I was recently inspired to explore a different kind of philosophical exploration using the murder mystery – the question of double effect.

The principle of double effect, introduced by Thomas Aquinas, defines under what conditions it is permissible to perform an action that does good for some but which results in harmful side effects for others.  Hence the term ‘double’ in the name.

Philosophy surrounding double effect is very much an Aristotelian concept in that there is a kind of virtue to this principle.  Aristotle’s point-of-view is that a virtue is achieved when a being performs just the right amount of activity characteristic to that being’s existence.  A soldier has the virtue of soldiering when he is neither too timid nor too foolhardy.  Justice then flows from virtue in that all pieces in the system are working harmoniously by being just in right place that they need to be and by just performing exactly the way they should perform.

Double effect dove tails with the notion of virtue since it seeks to balance the good an action may perform with the bad that may also result.  A popular example of the double effect framework is the classic ethical conundrum about the passengers on a railcar.  While there are many variations that differ in minor details, they all agree on the central notions.  A runaway railcar is heading to certain doom spelling an inevitable death to the five passengers who are sadly aboard.  An innocent bystander finds himself in the position to save the unhappy 5 by switching the train to a safer track but doing so will result in the death of a single passenger who is stuck on the other track.   What does our bystander do?

According to the principle of double effect, our bystander can legitimately pull the switch and kill the single guy to save the 5 if the following conditions are met:

• The action (pulling the switch) has to be good or at least morally neutral
• The agent (the bystander) must intend to do good (i.e. not just taking advantage of the situation)
• The end (saving the 5) must be an immediate consequence and not result from the means (killing of the 1)
• The good (saving the 5) must outweigh the bad (killing the 1)

Of course, the application of these rules to various situations can be quite tricky and their application is hotly debated by philosophers, usually by the construction of hypothetical situations where the agent is placed in different and complicated situations.

And here we come to one of the many uses of the detective story – the construction of realistic and compelling narratives that allow us to explore the possibilities in a way that mere academic constructions lack.  Some of the most interesting questions about justice and double effect come to light in these ‘enjoyable hypotheticals’. Should the detective bring the criminal to justice when the crime has a moral underpinning (e.g. Jean Valjean in Victor Hugo’s Les Misérables).  Or perhaps the moral quandary is whether the detective should shoot a criminal he knows to be guilty of a heinous crime to prevent ‘some lawyer from getting him off on a technicality (Captain Dudley Smith to Officer Edmund Exley in James Ellroy’s LA Confidential).

Well there is plenty of material in the genre to play with, and from time-to-time, this column will explore some of the philosophical questions raised.

Time is a curious thing.  John Wheeler is credited with saying that

Certainly this is a common, if unacknowledged, sentiment that pervades all of the physical sciences.  The very notion of an equation of motion for a dynamical system rests upon the representation of time as a continuous, infinitely divisible parameter.  Time is considered as either the sole independent variable for ordinary differential equations or as the only ‘time-like’ parameter for partial differential equations.  Regardless, the basic equation of the motion for most physical processes takes the form of

\[ \frac{d}{dt} \bar S = \bar f(\bar S; t) \]

where the state $\bar S$ can be just about anything imagined and the generalized force $\bar f$ depends on the state and, possibly, the time.  By its very structure, these generic form implies that we think of time as something that can be as finely divided as we wish – how else can there be any sense made of the $\frac{d}{dt}$ operator.

Even in the more modern implementations of cellular automata, where the time updates occur at discrete instants, we still think of the computational system as representing a continuous process sampled at evenly spaced times.

The very notion of continuous time is inherited from the ideas of motion and here I believe that Wheeler’s aphorism is on target.  The original definition of time is based on the motion of the Earth about its axis with the location of the Sun in the sky moving continuously as the day winds forward. As the invention of timekeeping evolved, items, like the sundial, either abstracted the sun’s apparent motion to something more easily measured, or replaced that motion with something more easily controlled like a clock.  Thus time for most of us takes on the form of the moving hands of the analog clock.

The location of the hands is a continuous function of time, with the angle that the hour and minute (and perhaps second) hands make with respect to high noon going something like $\sin(\omega t)$ where the angular frequency $\omega$ is taken to be negative to get the handedness correct.

But as timekeeping has evolved does this notion continue to be physical?  Specifically, how should we think about the pervasive digital clock

and the underlying concepts of digital timekeeping on a computer.

Originally, many computer systems were designed to inherit this human notion of ‘time as motion’ and time is internally represented in many machines as a double precision floating point number.  But does this make sense – either from the philosophical view or the computing view?

Let’s consider the last point first.  Certainly, the force models $\bar f(\bar S;t)$ used in dynamical systems require a continuous time in the calculus but they clearly cannot get such a time in the finite precision of any computing machine.  At some level, all such models have to settle for a time just above a certain threshold that is tailored for the specific application. So the implementation of a continuous time expressed in terms of a floating point variable should be replaced with one or more integers that count the multiples of this threshold time in a discrete way.

What is meant by one or more integers is best understood in terms of an example.  Astronomical models of the motion of celestial objects are usually expressed in terms of Julian date and fractions therein.  Traditional computing approaches would dictate that the time, call it $JD$ would be given by a floating point number where the integer part is the number of whole days and the fractional parts the numbers of hours, minutes, seconds, milliseconds, and so on, added together appropriately and then divided by 86400 to get the corresponding fraction.  Conceptually, this means that we take a set of integers and then contort them into a single floating point number.  But this approach not only involves a set of unnecessary mental gymnastics but is actually subject to error in the numerical sense.

Consider the following two modified Julian dates, represented by their integer values for days, hours, minutes, seconds, and milliseconds and by their corresponding floating point representations

In an arbitrary-precision computation, the sum of $JD1 = JD2 + deltaT$ would be exact but a quick scan over the last two digits of the three numbers involved shows that the floating point representation doesn’t capture the correct representation exactly.

Of course this should come as no surprise since this is an expected limitation of floating point arithmetic.  The only way to determine if two times are equal using the floating point method is to difference the two times in question, take the absolute value of the result and to declare sameness if the value is less than some tolerance.  Critics will be quick to point out that this fuzziness is the cost of fast performance and that this consideration outweighs exactness, but this is really just a tacit admission of the existence of a threshold time below which one does not need to probe.

Arbitrary precision, in the form of a sufficient set of integers (as used above), circumvents this problem but only to a point.  One cannot have an infinite number of integers to capture the smallest conceivable sliver of time. Practically, both memory and performance considerations limit the list of integers in the set to be relatively small.  And so we again have a threshold time below which we cannot represent a change.

And so we arrive at the contemplation of the first problem.  Is there really any philosophical ground on which we can stand that says that a continuous time is required.  Certainly the calculus requires continuity at the smallest of scales but is the calculus truth or a tool?  Newton’s laws can only be explored to a fairly limited level before the laws of quantum mechanics becomes important.  But are the laws of quantum mechanics really laws in continuous time?  Or is Schrodinger’s equation an approximation to the underlying truth?  The answer to these questions, I suppose, is a matter of time.