This week's thought experiment, titled Bursting the Soap Bubble, is a modernised adaptation of perhaps the most famous parable in the history of philosophy -- Plato's Allegory of the Cave. Let's read the update quickly and then compare it to the original before considering the usefulness of this kind of story.

-------------------------------------------------
     Members of the bizarre Weatherfield sect lived a very secluded life at St Hilda Hogden House. All but the leaders were forbidden any contact with the outside world and were taught that reality was the world portrayed on soap operas - the only television programmes they were allowed to watch. For the Weatherfieldians, as they were known, Coronation Street, The Bold and the Beautiful, EastEnders, and Neighbours were not works of fiction but fly-on-the-wall documentaries. And since most of the members had been born in the commune, the pretence was not hard to maintain.
     One day, however, disciple Kenneth, who had always been a touch rebellious, decided to leave Hogden's and visit the places he had seen so often on the altar box. This was, of course, strictly prohibited. But Kenneth managed to escape.
     What he found amazed him. The biggest shock came when he managed to get to Coronation Street and discovered it wasn't in Weatherfield at all, but was a set in the Granada Studios.
     But when he furtively returned to Hogden's and told his fellow disciples what he had discovered, he was dismissed as a lunatic. 'You should never have left,' they told him. 'It's not safe out there. The mind plays tricks on you!' And with that they chased him from the commune and forbade him to enter again.

Baggini, J., The Pig That Wants to Be Eaten, 2005, p. 55.
-------------------------------------------------

The original Allegory of the Cave takes up only four pages in my edition of The Republic, but rather than type that all in here, it'd be easier for you to click over and read a pdf version online from Stanford. Or, if you prefer, you can just watch this 3-minute summary made with clay puppets.

From this, the parallels to the Weatherfield sect being forced to watch soap operas all their lives should be obvious. But regardless of what limited version of reality the subjects are viewing, the most common scholarly interpretation of this story is an epistemological one that "interprets the allegory of the cave as one about human ignorance and a people who are unable or unwilling to seek truth and wisdom."

Plato used this story to describe the feelings a philosopher has when he tries to speak to the common man after going off to contemplate the "higher truths of reality." But the widespread and lasting power of this story is a testament to just how many groups and individuals have felt this way about others being chained to their views. Take this final passage for example:

Now imagine what would happen if he went down again to take his former seat in the Cave. Coming suddenly out of the sunlight, his eyes would be filled with darkness. He might be required once more to deliver his opinion on those shadows, in competition with the prisoners who had never been released, while his eyesight was still dim and unsteady; and it might take some time to become used to the darkness. They would laugh at him and say that he had gone up only to come back with his sight ruined; it was worth no one's while even to attempt the ascent. If they could lay hands on the man who was trying to set them free and lead them up, they would kill him.

How many people throughout history can identify with these feelings of righteousness as well as these fears of hostile incomprehension? Religious zealots, nationalist citizens, meditated yogis, drugged-out hippies, political warriors, scientific practitioners, evolutionary philosophers.....  Any group of "us" has the potential to see a group of "them" as chained fools. But each of us are also susceptible to committing logical fallacies (a list of which I detailed in my response to thought experiment number three), which blind us to our own blindspots. But, as Plato said,

Knowledge is justified true belief.

And as David Hume said,

A wise man proportions his belief to the evidence.

When we can keep these definitions of fallacies and knowledge and wisdom in mind, we are much less likely to find ourselves staring at shadows or soap operas, or believing that others are the ones that are doing so. We've all come out of caves at some point in our personal and evolutionary history, so it would be far better to recognise that shared fact and discuss the light that we each see rather than comforting ourselves with stories of how others are mired in darkness.

Did you watch anything good this weekend? Time to consider it in the context of this week's thought experiment.

-------------------------------------------------
     Members of the bizarre Weatherfield sect lived a very secluded life at St Hilda Hogden House. All but the leaders were forbidden any contact with the outside world and were taught that reality was the world portrayed on soap operas - the only television programmes they were allowed to watch. For the Weatherfieldians, as they were known, Coronation Street, The Bold and the Beautiful, EastEnders, and Neighbours were not works of fiction but fly-on-the-wall documentaries. And since most of the members had been born in the commune, the pretence was not hard to maintain.
     One day, however, disciple Kenneth, who had always been a touch rebellious, decided to leave Hogden's and visit the places he had seen so often on the altar box. This was, of course, strictly prohibited. But Kenneth managed to escape.
     What he found amazed him. The biggest shock came when he managed to get to Coronation Street and discovered it wasn't in Weatherfield at all, but was a set in the Granada Studios.
     But when he furtively returned to Hogden's and told his fellow disciples what he had discovered, he was dismissed as a lunatic. 'You should never have left,' they told him. 'It's not safe out there. The mind plays tricks on you!' And with that they chased him from the commune and forbade him to enter again.

Baggini, J., The Pig That Wants to Be Eaten, 2005, p. 55.
-------------------------------------------------

Crazy right? But what ideas have you swallowed from society? What truths are out there waiting to be discovered or have already been rejected? More on Friday.

Remember when I shared this picture during my discussion of the mind vs. the body? I said it was a shame our brains didn't get pumped up like this when we use them a lot so that we would be sure ideas didn't reside in some other dualist plane of existence. We'll need to remember this as we dive into this week's thought experiment, but before I go too deep, let's remind ourselves what's being considered.

-------------------------------------------------
     Sophia Maximus has always prided herself on her rationality. She would never knowingly act contrary to the dictates of reason. Of course, she understands that some of the basic motivations to action are not rational - such as love, taste, and character. But not being rational is not the same as being irrational. It is neither rational nor irrational to prefer strawberries to raspberries. But, given the preference, it is irrational to buy raspberries when strawberries are just as cheap.
     Right now, however, she is in something of a fix. A very intelligent friend persuaded her that it would be perfectly rational to set off a bomb which will kill many innocent people without any obvious benefit, such as saving other lives. She feels sure that there must be something wrong with her friend's argument. But rationally, she cannot see it. What it worse, the argument suggests she should set off the bomb as soon as possible, so thinking longer is not an option.
     In the past she has always thought it wrong to reject good rational arguments in favour of hunches and intuitions. Yet if she follows reason in this case, she can't help but feel she will be doing a terrible wrong. Should she knowingly follow the less rational path, or trust reason over feeling and detonate the bomb?

Baggini, J., The Pig That Wants to Be Eaten, 2005, p. 52.
-------------------------------------------------

Just as the mind and body aren't separate, neither are their products: reason and feeling. Each are highly related to the other with bidirectional feedback between them, all occurring inside a single organism. Sophia has set up a false dichotomy by insisting she should follow one at the expense of another. She should instead recognise that the conflict between her reason and feelings are a warning sign that one of them needs to change. In my post, What's Causing These Emotions, I pointed out how our emotions are in fact a product of our thoughts:

An influential theory of emotion is that of Lazarus: emotion is a disturbance that occurs in the following order: 1) cognitive appraisal - the individual assesses the event cognitively, which cues the emotion; 2) physiological changes - the cognitive reaction starts biological changes such as increased heart rate or pituitary adrenal response; 3) action - the individual feels the emotion and chooses how to react. Lazarus stressed that the quality and intensity of emotions are controlled through cognitive processes.

These thoughts that drive our emotions aren't always driven with words though. When I wrote later about how we are Learning to Tame Your Elephant, I noted that:

We also have unconscious cognitive appraisals - cognitive appraisals without words. This is how all animals think. The rise of language and an inner voice provides a loud layer of consciousness that allows us to “talk over” our emotions, but that should not be used as an excuse to ignore them. It is easy to lose touch with our emotions when we do not listen to our bodies by noticing all the subtle sensations we feel. We can learn to focus our attention though and hold an internal (or external) dialogue to figure out our unspoken cognitive appraisals. We must do so if we want to regulate them and change them.

Using these ideas, we see in this week's thought experiment that Sophia is experiencing a disequilibrium between the new rational argument to bomb people and the unconscious cognitive appraisal that is driving her feelings to reject such a bombing. She is momentarily stuck in the delay between her two systems of thought that need some time to catch up to one another. What are these two systems? As I also reported in Learning to Tame Your Elephant, "in Daniel Kahneman's latest book, Thinking Fast and Slow, Kahneman describes the two different ways the brain forms thoughts:

• System 1: fast, automatic, frequent, emotional, stereotypic, subconscious
  
• System 2: slow, effortful, infrequent, logical, calculating, conscious
  

System 1 - the Elephant. System 2 - the Rider. We can't get rid of the Elephant because a) that's not the way evolution works, but more importantly b) it enables us to take instantaneous action whenever the situation requires it - when we touch a hot stove, when a car swerves towards us, when an assailant attacks us. Our system 1 quickly gets us out of harm's way. It is easy to rely on, and it would be impossible to let slow, calculating system 2 tackle all our questions. We would be wracked with doubt and inefficiency. We need to appreciate our Elephant. It seems to have a few innate or universal judgments already programmed into it at birth, but we also feed it with new rules of thumb from our experiences and we let our system 2's create new intuitive judgments that can be passed on to system 1 for faster action (such as when professional speakers go from fearing a crowd to loving the sight of one after a bit of practice). This is a highly efficient design, but one that can be used inefficiently when we don't take the time to let our system 2 evaluate what it has wrought in our system 1. When our youthful experiences leave our system 1 full of cognitive biases such as anchoring, loss-aversion, confirmation bias, framing issues, or the fundamental attribution error, we end up making faulty decisions based on poor emotional clues."

In Sophia's case, her system 1 emotional clues are trying to lead her away from making a decision based on a system 2 argument that may or may not be right. We aren't told the elements of her friend's argument that make it "perfectly rational to set off a bomb which will kill many innocent people without any obvious benefit," but from that description alone it seems obvious that the argument must be false. If it's not, then with time Sophia's feelings will come around to be aligned with a new cognitive appraisal. Until her feelings and thoughts are aligned, however, she would be rash to act on either one of them. If forced to act NOW, she would do better to rely on her system 1 feelings, which have been built up over her lifetime of thoughtful judgment. That's the actual rational thing to do.

What about you? What are you feeling about this rational argument of mine? Or do you need to sleep on it to know for sure?

This week's thought experiment is frustratingly vague, although it's meant to be so. Try not to get too annoyed as you read this and think about it until Friday.

-------------------------------------------------
     Sophia Maximus has always prided herself on her rationality. She would never knowingly act contrary to the dictates of reason. Of course, she understands that some of the basic motivations to action are not rational - such as love, taste, and character. But not being rational is not the same as being irrational. It is neither rational nor irrational to prefer strawberries to raspberries. But, given the preference, it is irrational to buy raspberries when strawberries are just as cheap.
     Right now, however, she is in something of a fix. A very intelligent friend persuaded her that it would be perfectly rational to set off a bomb which will kill many innocent people without any obvious benefit, such as saving other lives. She feels sure that there must be something wrong with her friend's argument. But rationally, she cannot see it. What it worse, the argument suggests she should set off the bomb as soon as possible, so thinking longer is not an option.
     In the past she has always thought it wrong to reject good rational arguments in favour of hunches and intuitions. Yet if she follows reason in this case, she can't help but feel she will be doing a terrible wrong. Should she knowingly follow the less rational path, or trust reason over feeling and detonate the bomb?

Baggini, J., The Pig That Wants to Be Eaten, 2005, p. 52.
-------------------------------------------------

Thoughts? Feelings? How will you choose between the two before it's time for Friday's answer?

Let's jump right into this week's thought experiment with a reminder of the subject matter.

-------------------------------------------------
     Hadi's captives looked resolute, but he was sure he could break them, as long as he followed through on his threat. The father, Brad, was the real villain. It was he who had planted the huge bomb that he promised would kill hundreds, perhaps thousands, of innocent civilians. Only he knew where the bomb was, and he wasn't telling.
     His son, Wesley, had nothing to do with it. But Hadi's intelligence told him that, though Brad would not break under torture, he almost certainly would if he were to see his son tortured in front of him. Not immediately, but soon enough.
     Hadi was torn. He had always opposed torture and would probably have to leave the room while it was carried out. Wesley's innocence was not the only reason for his qualms, but it certainly exacerbated them. But he also knew this was the only way to save hundreds of people from death and mutilation. If he didn't order the torture, would he be condemning people to death, just because of his own squeamishness and lack of moral courage?

Baggini, J., The Pig That Wants to Be Eaten, 2005, p. 49.
-------------------------------------------------

Sometime's these thought experiments seem remote and theoretical, totally detached from our daily lives. Unfortunately, that is not the case with this one. Just this week, on July 10th, the New York Times reported how Outside Psychologists Supported the U.S. Torture Program. The article stated how:

"The Central Intelligence Agency’s health professionals repeatedly criticized the agency’s post-Sept. 11 interrogation program, but their protests were rebuffed by prominent outside psychologists who lent credibility to the program, according to a new report. The 542-page report, which examines the involvement of the nation’s psychologists and their largest professional organization, the American Psychological Association, with the harsh interrogation programs of the Bush era, raises repeated questions about the collaboration between psychologists and officials at both the C.I.A. and the Pentagon. The report, completed this month, concludes that some of the association’s top officials, including its ethics director, sought to curry favor with Pentagon officials by seeking to keep the association’s ethics policies in line with the Defense Department’s interrogation policies, while several prominent outside psychologists took actions that aided the C.I.A.’s interrogation program and helped protect it from growing dissent inside the agency."

It's a sordid affair that has led to three senior officials losing their jobs at the APA, and perhaps more shakeups to come. The involvement of psychologists in the interrogation programs was "a source of contention within the profession for years," and something which clearly contradicted with the APA's stated Position on Ethics and Interrogations:

The American Psychological Association's (APA) position on torture is clear and unequivocal: Any direct or indirect participation in any act of torture or other forms of cruel, degrading or inhuman treatment or punishment by psychologists is strictly prohibited. There are no exceptions. Clear violations of APA's no torture/no abuse policy include acts such as: Waterboarding. Sexual humiliation. Stress positions. Exploitation of phobias.

These interrogation programs from the CIA and Pentagon also clearly contravened the third article of the Geneva Convention:

"Persons taking no active part in the hostilities, including members of armed forces who have laid down their arms and those placed hors de combat [outside of combat] by sickness, wounds, detention, or any other cause, shall in all circumstances be treated humanely, without any adverse distinction founded on race, colour, religion or faith, sex, birth or wealth, or any other similar criteria. To this end, the following acts are and shall remain prohibited at any time and in any place whatsoever with respect to the above-mentioned persons: violence to life and person, in particular murder of all kinds, mutilation, cruel treatment and torture; taking of hostages; outrages upon dignity, in particular humiliating and degrading treatment; and the passing of sentences and the carrying out of executions without previous judgment pronounced by a regularly constituted court, affording all the judicial guarantees which are recognized as indispensable by civilized peoples." (underlined emphasis added)

These international agreements, signed on to by 196 countries, were developed largely in response to the horrors of the second World War, but 50 years later, some people seem to be forgetting the reasons these limits to intraspecies competition were put in place. When cheaters don't play by our rules and they plot to bomb innocent civilians, it can certainly be tempting to strike back at them using tit-for-tat rationales. Utilitarian ethics promoting actions that provide "the greatest good for the greatest number" even seems to offer mathematical justification for hurting one guilty person in an effort to save hundreds or thousands of innocent lives. I'll have much more to say about this utilitarian mathematics when we get to the inevitable trolley problems that are coming down the track, but let's stay focused on this particular version of this thought experiment where the punishment of one guilty person is traded for the punishment of his innocent son. Evolutionary philosophy agrees with the prohibitions of torture on the grounds that it destroys possibilities for long term cooperation. Pragmatically, torture doesn't work either. (Psst. That's a great article I just linked to that really settles this question. Go read it.) Two of the reasons we've become as successful a species as we have, is 1) our ability to create our own internal motivations which override any circumstances, and 2) our ability to deceive other competitors about our intentions. Take these two characteristics together and there's no way Hadi could know that Brad "almost certainly would [confess] if he were to see his son tortured in front of him." Nor could Hadi know that torture "was the only way to save hundreds of people from death and mutilation." Realistically, Hadi was already too late, and torture would only add to the likelihood that he would be too late another time in the future as well. Better to stop and simply detain Brad until you can stop him or rehabilitate him from ever doing this again.

Sorry for the brief interruption to my blogging schedule (I'll still post my answer this this week's thought experiment on Friday), but I found out yesterday that a former philosophy professor reviewed my journal article on his website Reason and Meaning (which was later reprinted at the Institute for Ethics and Emerging Technologies). The review came from Dr. John Messerly who, according to his bio, "was a member of the faculty of both the philosophy and computer science departments for many years at the University of Texas at Austin. He is the author of books on ethical theory, evolutionary philosophy, and the meaning of life, as well as dozens of articles on philosophical and transhumanist themes. His recent work has appeared in Salon, Scientia Salon, the Institute for Ethics & Emerging Technologies, and Humanity+." John's short review can be seen in full here:

http://reasonandmeaning.com/2015/07/14/evolution-and-ethics/

but he and I have also had some brief email conversations since this came out. He's generally sympathetic to my point of view and agrees with much of what I have to say, but he did point out how other stubborn philosophers might be apt to object to my arguments in two specific ways. I felt I ought to address those points in a short post. So, here goes.

1) Messerly wrote:

"Philosophers would object to a number of issue in the paper, including Gibney’s basic syllogism:

p exists
p wants to continue to exist
thus p ought to act in aid its continued existence. 

First, they might object that “just because p is doesn’t mean that p ought to be.” By simply stating this, Gibney is begging the question."

I admit this is true. In my paper, I agree with this by saying nothing in this universe says we *have* to follow these imperatives, but it’s clear that we *ought* to. I suppose someone could argue, for example, that there would be a lot less suffering in the universe if life didn’t exist, so we all ought to just wink out into extinction, but if that’s the opposing argument, I’m pretty confident the jury will come down on continuing this project of life. I'll try to state this assumption more clearly in the future to make sure people know I’m making it and trying to get them to agree to it.

2) Messerly also wrote:

"Second, they might say, “if p wants to exist it should act so in ways that help it to continue to exist, but this is a survival imperative and not a moral imperative. And those aren’t the same thing.” In other words Gibney is confusing what behaviors help us survive with moral behaviors. While the two sometimes coincide, often they don’t. (Killing you quickly before you kill me might aid my survival but not be moral.) I agree that there are more to moral imperatives than survival imperatives; nonetheless survival imperatives are a prerequisite for moral imperatives. In other words, oughts that aid survival are necessary but not sufficient conditions for morality."

I don't yet believe this is true. It seems to me that moral urges are entirely about the well-being of “others”, as measured objectively by their long term survival. Emotional urges that protect the self are just considered selfish survival instincts, and it’s my contention that the identity of the “self” could be expanded out to be the protection of *my* organism / family / tribe / society / species / or ecosystem—all of which could be selfishly cared for if their protection came at the expense of life in general over evolutionary timelines. The moral emotions (for example, Haidt’s foundations of 1) Care/Harm; 2) Fairness/Cheating; 3) Liberty/Oppression; 4) Loyalty/Betrayal; 5) Authority/Subversion; 6) Sanctity/Degradation) are all felt during attempts to navigate this choice between “self” and “others”. Emotional choices that don’t deal with this issue (ice cream preference, computer operating system choice, favourite impressionist painter, etc.) fall to the realm of aesthetics rather than ethics. At least, I think so. Messerly gave the example: "Killing you quickly before you kill me might aid my survival but not be moral.”, but I don’t claim that morality depends on an individual’s survival. That moral judgement of an act is tied to wether or not it promotes "life in general over the long term." Shooting an innocent person before they are about to defend themselves is immoral, but killing Nazis quickly vs. being killed by Nazi aggressors is an easy example of when such a killing action is moral. Both of these judgements are made because of how the outcomes lead towards or away from cooperative, surviving societies. I haven't yet found a moral issue that does not, at its roots, eventually revolve around the question of cooperating or competing for survival over the long term. I’m glad Messerly sees the survival question is necessary (the primary question that needs to be answered), but I’m not yet sure why other philosophers don't see it as sufficient.

Thanks to John for his considered remarks and generous correspondence! I'm happy to meet him and start following his blog.

Happy Monday! Sorry to do this to you, but let's think about torture this week.

-------------------------------------------------
     Hadi's captives looked resolute, but he was sure he could break them, as long as he followed through on his threat. The father, Brad, was the real villain. It was he who had planted the huge bomb that he promised would kill hundreds, perhaps thousands, of innocent civilians. Only he knew where the bomb was, and he wasn't telling.
     His son, Wesley, had nothing to do with it. But Hadi's intelligence told him that, though Brad would not break under torture, he almost certainly would if he were to see his son tortured in front of him. Not immediately, but soon enough.
     Hadi was torn. He had always opposed torture and would probably have to leave the room while it was carried out. Wesley's innocence was not the only reason for his qualms, but it certainly exacerbated them. But he also knew this was the only way to save hundreds of people from death and mutilation. If he didn't order the torture, would he be condemning people to death, just because of his own squeamishness and lack of moral courage?

Baggini, J., The Pig That Wants to Be Eaten, 2005, p. 49.
-------------------------------------------------


What do you think of the scenario in this week's thought experiment? You'd torture Wesley if you watched enough Jack Bauer wouldn't you?

Ah, Zeno's paradox. This week's thought experiment is an oldie but goodie, created around 450 BC with the intention of showing  that "motion is nothing but an illusion." To an evolutionary philosopher, this is nonsense of course. The universe we study has been moving for as long as we can observe it and all the particles of matter, light, energy, and life have been moving in this universe as well. It's kind of an essential feature of existence. But still, Zeno's paradox is tricky so we can't just dismiss it out of hand. Any problem that provides an excuse to break out a spreadsheet though is fine by me so let's do that! Before I get into the details, let's remind ourselves of the problem first.

-------------------------------------------------
     Welcome to the Great Athenian Man-Tortoise Run-off. My name's Zeno and I'll be your commentator for the big race. I have to say, however, that the result is a foregone conclusion. Achilles has made the terrible mistake of giving Tarquin the tortoise a 100-yard head start. Let me explain.
     Tarquin's tactic is to keep constantly moving, however slowly. If Achilles is to overtake Tarquin, first he must get to where Tarquin is when the race starts. That will take him several seconds. In that time, Tarquin will have moved on a little and will then be a short distance ahead of Achilles. Now if Achilles is to overtake Tarquin, he must again get to where Tarquin is first. But in the time it takes Achilles to do that, Tarquin will again have moved forward slightly. So, Achilles once more needs to get to where Tarquin is now, in order to overtake him, in which time Tarquin would have moved forward. And so on. You get the picture. It's logically and mathematically impossible for Achilles to overtake the beast.
     Still, it's too late to place your bets on the tortoise now, because they're under starter's orders, and...they're off! Achilles is closing...closing...closing...Achilles has overtaken the tortoise! I can't believe it! It's impossible!

Baggini, J., The Pig That Wants to Be Eaten, 2005, p. 46.
-------------------------------------------------

We know this isn't impossible, but what's going on here? First, like a good engineer, let's set up all the facts and assumptions and do some basic math. The fastest human speed ever recorded is 27.78 miles per hour (during Usain Bolt's 100-meter dash), so let's say Achilles can run 25 mph. The fastest recorded speed for a tortoise is 5 mph, so let's use that nice round figure for Tarquin. We'll ignore the short period of acceleration during the start of the race just to make the math much easier. So since rate x time = distance, we can calculate that Achilles (running at 12.22 yards/sec) would overtake Tarquin (running at 2.44 yards/sec) in 10.2272 seconds when they would both have gone 125 yards. After that, Achilles would steadily pull away until the end of the race. This is the straightforward way of looking at this problem. But what about Zeno's way?

Zeno's method of describing Achilles as always having to catch up to Tarquin relies on looking at a series of ever smaller steps and claiming you can't get over them all. To see just how small these steps get though, let's run the math. Using the same rates of speed described above, we get:

• Step 1: Achilles goes 100 yards in 8.18 seconds, while Tarquin makes it 20 yards.
• Step 2: Achilles goes 20 yards in 1.64 seconds, while Tarquin makes it 4.0 yards.
• Step 3: Achilles goes 4.0 yards in 0.33 seconds, while Tarquin makes it 0.8 yards.
• Step 4: Achilles goes 0.8 yards in 0.07 seconds, while Tarquin makes it 0.16 yards.
• Step 5: Achilles goes 0.16 yards in 0.01 seconds, while Tarquin makes it  0.032 yards.
• ......
• Step 10: Achilles goes 0.0000512 yards in 0.00000419 seconds, while Tarquin makes it 0.0000102 yards.

In just 5 steps, we get to the kind of time gap seen in an Olympic photo finish. In 10 steps we get to a gap that is 4 millionths of a second -- far beyond anything we are capable of seeing with the naked eye. Even with our best tools, the current world record for the shortest unit of measured time is 12 attoseconds (1.2 × 10−17 seconds). Zeno crosses that threshold in just 27 steps. What about the next million steps?

Some philosophers have attacked Zeno's paradox this way by saying the universe isn't actually infinitely divisible. At some point in this process, you get to a step that must be the size of the fundamental grain of space-time that makes up the fabric of the universe. After that, Achilles and Tarquin must cross these steps at differing rates until Tarquin is passed. But we don't actually know if the universe is infinite or finite (see Planck lengths for a brief discussion), so this doesn't conclusively refute Zeno.

What all this math makes clear to me, however, is the way that Zeno is actually refuted. We see quickly how Zeno is relying on slowing down time to make smaller and smaller observations during the moments when Achilles is about to overtake Tarquin. As long as we give Zeno this power, his paradox holds true. But time waits for no man. During the one-hundredth of a second between 10.22 and 10.23 seconds, Achilles will pass Tarquin, and no amount of thinking about this will make that time stand still. Achilles moves independently of Tarquin and his location in the universe will be farther along the path of the race. The concept of infinity is only a mathematical abstraction so there is no real-world power in saying someone must overcome "an infinite number of obstacles." The barriers are always numbered and we see they can be surmounted.

That's 16 thought experiments passed for me. Only 84 more to go...

I'm back! And I'm still blogging about Julian Baggini's 100 thought experiments to see how well my evolutionary philosophy can cope with these historically difficult problems. Let's ease back in at a nice slow pace...

-------------------------------------------------
     Welcome to the Great Athenian Man-Tortoise Run-off. My name's Zeno and I'll be your commentator for the big race. I have to say, however, that the result is a foregone conclusion. Achilles has made the terrible mistake of giving Tarquin the tortoise a 100-yard head start. Let me explain.
     Tarquin's tactic is to keep constantly moving, however slowly. If Achilles is to overtake Tarquin, first he must get to where Tarquin is when the race starts. That will take him several seconds. In that time, Tarquin will have moved on a little and will then be a short distance ahead of Achilles. Now if Achilles is to overtake Tarquin, he must again get to where Tarquin is first. But in the time it takes Achilles to do that, Tarquin will again have moved forward slightly. So, Achilles once more needs to get to where Tarquin is now, in order to overtake him, in which time Tarquin would have moved forward. And so on. You get the picture. It's logically and mathematically impossible for Achilles to overtake the beast.
     Still, it's too late to place your bets on the tortoise now, because they're under starter's orders, and...they're off! Achilles is closing...closing...closing...Achilles has overtaken the tortoise! I can't believe it! It's impossible!

Baggini, J., The Pig That Wants to Be Eaten, 2005, p. 46.
-------------------------------------------------

So what do think about this paradox? Can you overtake my thoughts on it? I'll be back on Friday to see where you've gotten to.