Saturday, May 05, 2012
The Avengers
If you like comic book movies, go see it, because it is pretty much everything a comic book movie tries to be. Joss Whedon really knocked this one out of the park. I hadn't realized how long it was going to be -- it's nearly two and a half hours -- but I hardly noticed. It keeps moving, the funny scenes are genuinely funny, and while a comic book can't completely avoid cheesiness, there isn't any part of the movie that is embarrassingly cheesy, and that is an accomplishment in itself.
Friday, May 04, 2012
Music on My Mind
Beastie Boys, "Intergalactic." This video, which was directed by MCA and won awards in 1999, pretty much sums up the whole Beastie Boys approach: not quite coherent, weirdly interesting, and inanely entertaining. And now MCA has died of cancer. He was an interesting character. After converting to Buddhism in the 90s he began to rethink the band's approach, which in the 80s had been to maintain a heavily bawdy and rowdy image:
"I didn't realize how much harm I was doing back then and I think a lot of rap artists probably don't realize it now," the newspaper quoted him as saying. "I said a lot of stuff fooling around back then, and I saw it do a lot of harm. I had kids coming up to me and saying, 'Yo, I listen to your records while I'm smoking dust, man.' And I'd say, 'Hey, man, we're just kidding. I don't smoke dust.' People need to be more aware of how they're affecting people."
Kierkegaard on Confession IV: Commitment
Having discussed common forms of double-mindedness, Kierkegaard continues Purity of Heart Is to Will One Thing by looking at what purity of heart requires, in light of the previous argument. And he boils this down to two things: to do all things for the Good and to endure all things for the Good. While all who are pure of heart will to some extent do both, Kierkegaard holds that the two actions divide the population: some people are so situated as to be primarily doers, active people, and some are so situated as to be primarily endurers, sufferers. He takes the task of each in turn.
(1) To will the Good in truth one must do all for the Good.
We are first hit with the 'all'. It seems that describing the active task of the pure of heart will take forever. What is required to will the Good will be infinitely diverse, because it could require radically different things from different people. But Kierkegaard suggests that there is in fact something in common to all these things, which allows us to say something about the task in general, and that common element is "the act of commitment to will to be and to remain loyal to the Good" (p. 123). Whatever else it may require, it requires commitment to be loyal, and to remain loyal, to the Good. This also has the benefit of avoiding a potential problem. Since different people do different things, there's a temptation to think that the person who does the most things, or the most obvious things, is really the one doing all for the Good. But willing the Good in truth is not a competition like this; someone who does little may be just as committed to the Good as someone who does much. What matters for the individual, and what matters with respect to the Good, is simply commitment to the Good. Also, recognizing that commitment is key allows us to shed light on the task of doing all for the Good by looking at what threatens commitment. And what does threaten commitment? Cleverness.
Cleverness is both a useful ability and a dangerous one. What makes it dangerous is that cleverness is, among other things, both our excuse-making ability and our appearance-manipulating ability. It is that whereby we can deceive ourselves and others, and, as we already have seen, self-deceit is deeply involved in double-mindedness. In the case of the active task, cleverness may work inwardly, in which it seeks out evasions, and it may work outwardly, in which it constructs deceptions.
Cleverness working inwardly is evasive, trying to stall or put off serious decision, and it does so in such a way that the evasion is presented as a good. To flee your post in battle is very shameful; but this can be avoided if you cleverly make sure that you yourself are never in the battle at all. The same cowardice could be operative in both cases, but it's the second one, the one created by cleverness, that is less obvious about the cowardice, even to the person doing it. It is by evasion that cleverness convinces us that true commitment and loyalty is too risky, and the list of excuses it can give to back this up is endless: it's too dangerous, it's beyond our power, what little we can do is not enough, we have obligations to family, we shouldn't put all our eggs in one basket, and so on and so forth. These are the kinds of things that might be perfectly fine if you were talking about minor issues of practical life. But when we are talking about commitment to the Good, in each case these excuses carry a little lie about the Good -- that the Good has no power, that the Good is like any other goal, that any other commitments could have any real value apart from being part of our commitment to the Good, and so forth.
Cleverness also works outwardly, turning appearances to one's advantage:
But there is a lie in all of this, which is that the Good in any way needs human beings for victory, and that the Eternal can ever be fooled. It is, as with evasion, all a way of falsely pretending that the Good itself is not good enough.
In reality, commitment requires that we not try to help ourselves by evasion or by deception, but firmly stick to the Good. Kierkegaard points to Christ as an example here. Surely if he was who he said he was, he could have been more clever about how he brought the truth to people, appearing in glory for all to admire, setting himself up as king, marrying like a good rabbi and becoming a great and famous teacher. This is what clever and intelligent people thought at the time. And when he was dying on the cross, could you have honestly looked around and said that he had accomplished much at all for the Good? If you put all the great teachers of mankind together, is there any one of them who had accomplished so little as Christ had by the time he died, especially in comparison with what people were expecting? How very uncleverly he acted; doing some minor things in a backwards province he failed to avoid being crucified. But at the very same time, he, seeing farther, could say: "It is finished." The work was done. We should keep this in mind in whatever we do.
(2) To will the Good in truth one must endure all for the Good.
The difference between the active task and the passive task is that the active task is the means whereby the Good brings its victory into the world; but the passive task is the means whereby the Good is victorious in the sufferer. As with the active task, we are struck here by the word 'all', and here as well Kierkegaard identifies something in common with all endurance for the Good, which he calls the wish. The wish is not an ordinary wish, that comes and goes. It endures. It is both the sore spot of suffering and the perseverance in it. Kierkegaard is less clear about this suffering commitment than he is about the active commitment, but the basic idea is that we refuse to accept relief from our sorrows except through the Good itself. The great temptation of the one whose primary task is to suffer for the Good is to try to kill the wish with some temporal relief. But the wish, although a wound, is a wound that must be prevented from closing until the Good itself heals it; otherwise it never really heals, but simply makes things worse. The pain of the wish, the longing ache it carries, is living pain, the thing that goes with the flesh not being dead yet. Trying to kill the wish is "a kind of spiritual suicide" (p. 149). And in particular what keeps the wish going, and us spiritually alive, is the longing inherent to faith, hope, and love. Under the pain of the wish, the sufferer remains committed to the Good. And this, it is important to recall, is the one thing that matters. The one whose primary task is to endure has the hardship of being only a burden to others; accomplishments in our usual sense are closed off to such a person. But the highest accomplishment is still possible: commitment to the Good.
The sufferer has the same problem as the doer, though, because cleverness seeks out evasion. The sufferer has one advantage, in that outward-working cleverness is of little use to such a person, and therefore deception is not a major temptation. But evasion remains, because cleverness can still work inwardly. Instead of commitment to the Good, cleverness tries devices of temporal, and temporary relief, holding out earthly hopes that seem more certain but are of less worth. The excuses here are also legion: who knows what may happen, maybe we'll get lucky, commitment to the Good is too hard, etc. A pain-reliever is substituted for the cure; the sufferer is double-minded in wanting to be cured, but not wanting to be cured as well, and therefore grasping at less than the highest consolation, the one consolation that matters.
Kierkegaard wants to avoid a common line people take against these failures due to cleverness, in both the active task and the passive task, which is that cleverness of this sort gets you nothing. On the contrary, says Kierkegaard, we should be quite frank in saying that cleverness does get you something. That's why people keep trying to be clever. And we should always avoid the danger of framing things so that we talk about the Good as if we are to will the Good in order to get something else. Evasion and deception get you plenty; they just don't get you the Good, and thus nothing worth having. The real line we should take is to point to the power of memory. As we often say, you have to live with yourself, have to live with the fact that you are the sort of person who did that. And even if you yourself don't remember -- the Eternal never forgets.
What, then is the best way to avoid misusing cleverness to evade and deceive? Use it to expose our own evasions and deceptions:
Kierkegaard's thoughts on cleverness end up being a generalization of Plato's attacks on sophistry and oratory in the Gorgias and the Republic; in the Gorgias, for instance, Socrates argues that the primary use of oratory is not in getting out of responsibility but in getting punished when you should be punished, and Kierkegaard's argument generalizes this to the kind of sophistry and oratory we use on ourselves.
Knowing what double-mindedness is, and what purity of heart requires, naturally raises the question of what we ourselves should do. And thus Kierkegaard will turn to this in his final chapters.
---
Soren Kierkegaard, Purity of Heart Is to Will One Thing, Steere, tr. Harper (1956).
(1) To will the Good in truth one must do all for the Good.
We are first hit with the 'all'. It seems that describing the active task of the pure of heart will take forever. What is required to will the Good will be infinitely diverse, because it could require radically different things from different people. But Kierkegaard suggests that there is in fact something in common to all these things, which allows us to say something about the task in general, and that common element is "the act of commitment to will to be and to remain loyal to the Good" (p. 123). Whatever else it may require, it requires commitment to be loyal, and to remain loyal, to the Good. This also has the benefit of avoiding a potential problem. Since different people do different things, there's a temptation to think that the person who does the most things, or the most obvious things, is really the one doing all for the Good. But willing the Good in truth is not a competition like this; someone who does little may be just as committed to the Good as someone who does much. What matters for the individual, and what matters with respect to the Good, is simply commitment to the Good. Also, recognizing that commitment is key allows us to shed light on the task of doing all for the Good by looking at what threatens commitment. And what does threaten commitment? Cleverness.
Cleverness is both a useful ability and a dangerous one. What makes it dangerous is that cleverness is, among other things, both our excuse-making ability and our appearance-manipulating ability. It is that whereby we can deceive ourselves and others, and, as we already have seen, self-deceit is deeply involved in double-mindedness. In the case of the active task, cleverness may work inwardly, in which it seeks out evasions, and it may work outwardly, in which it constructs deceptions.
Cleverness working inwardly is evasive, trying to stall or put off serious decision, and it does so in such a way that the evasion is presented as a good. To flee your post in battle is very shameful; but this can be avoided if you cleverly make sure that you yourself are never in the battle at all. The same cowardice could be operative in both cases, but it's the second one, the one created by cleverness, that is less obvious about the cowardice, even to the person doing it. It is by evasion that cleverness convinces us that true commitment and loyalty is too risky, and the list of excuses it can give to back this up is endless: it's too dangerous, it's beyond our power, what little we can do is not enough, we have obligations to family, we shouldn't put all our eggs in one basket, and so on and so forth. These are the kinds of things that might be perfectly fine if you were talking about minor issues of practical life. But when we are talking about commitment to the Good, in each case these excuses carry a little lie about the Good -- that the Good has no power, that the Good is like any other goal, that any other commitments could have any real value apart from being part of our commitment to the Good, and so forth.
Cleverness also works outwardly, turning appearances to one's advantage:
The clever one knows just how the Good must be altered a tiny particle in order to win the world's good will. He knows how much should be added to it and how much should be subtracted. He knows just what ingratiating thing should be whispered in men's ears, what should be entrusted to their hands, and how the hand should be pressed, how it should be swung away from truth's decision, how the turning should be done, and how he himself in suppleness should shift and turn--"in order that he can accomplish all the more for the Good." (p. 132)
But there is a lie in all of this, which is that the Good in any way needs human beings for victory, and that the Eternal can ever be fooled. It is, as with evasion, all a way of falsely pretending that the Good itself is not good enough.
In reality, commitment requires that we not try to help ourselves by evasion or by deception, but firmly stick to the Good. Kierkegaard points to Christ as an example here. Surely if he was who he said he was, he could have been more clever about how he brought the truth to people, appearing in glory for all to admire, setting himself up as king, marrying like a good rabbi and becoming a great and famous teacher. This is what clever and intelligent people thought at the time. And when he was dying on the cross, could you have honestly looked around and said that he had accomplished much at all for the Good? If you put all the great teachers of mankind together, is there any one of them who had accomplished so little as Christ had by the time he died, especially in comparison with what people were expecting? How very uncleverly he acted; doing some minor things in a backwards province he failed to avoid being crucified. But at the very same time, he, seeing farther, could say: "It is finished." The work was done. We should keep this in mind in whatever we do.
(2) To will the Good in truth one must endure all for the Good.
The difference between the active task and the passive task is that the active task is the means whereby the Good brings its victory into the world; but the passive task is the means whereby the Good is victorious in the sufferer. As with the active task, we are struck here by the word 'all', and here as well Kierkegaard identifies something in common with all endurance for the Good, which he calls the wish. The wish is not an ordinary wish, that comes and goes. It endures. It is both the sore spot of suffering and the perseverance in it. Kierkegaard is less clear about this suffering commitment than he is about the active commitment, but the basic idea is that we refuse to accept relief from our sorrows except through the Good itself. The great temptation of the one whose primary task is to suffer for the Good is to try to kill the wish with some temporal relief. But the wish, although a wound, is a wound that must be prevented from closing until the Good itself heals it; otherwise it never really heals, but simply makes things worse. The pain of the wish, the longing ache it carries, is living pain, the thing that goes with the flesh not being dead yet. Trying to kill the wish is "a kind of spiritual suicide" (p. 149). And in particular what keeps the wish going, and us spiritually alive, is the longing inherent to faith, hope, and love. Under the pain of the wish, the sufferer remains committed to the Good. And this, it is important to recall, is the one thing that matters. The one whose primary task is to endure has the hardship of being only a burden to others; accomplishments in our usual sense are closed off to such a person. But the highest accomplishment is still possible: commitment to the Good.
The sufferer has the same problem as the doer, though, because cleverness seeks out evasion. The sufferer has one advantage, in that outward-working cleverness is of little use to such a person, and therefore deception is not a major temptation. But evasion remains, because cleverness can still work inwardly. Instead of commitment to the Good, cleverness tries devices of temporal, and temporary relief, holding out earthly hopes that seem more certain but are of less worth. The excuses here are also legion: who knows what may happen, maybe we'll get lucky, commitment to the Good is too hard, etc. A pain-reliever is substituted for the cure; the sufferer is double-minded in wanting to be cured, but not wanting to be cured as well, and therefore grasping at less than the highest consolation, the one consolation that matters.
Kierkegaard wants to avoid a common line people take against these failures due to cleverness, in both the active task and the passive task, which is that cleverness of this sort gets you nothing. On the contrary, says Kierkegaard, we should be quite frank in saying that cleverness does get you something. That's why people keep trying to be clever. And we should always avoid the danger of framing things so that we talk about the Good as if we are to will the Good in order to get something else. Evasion and deception get you plenty; they just don't get you the Good, and thus nothing worth having. The real line we should take is to point to the power of memory. As we often say, you have to live with yourself, have to live with the fact that you are the sort of person who did that. And even if you yourself don't remember -- the Eternal never forgets.
What, then is the best way to avoid misusing cleverness to evade and deceive? Use it to expose our own evasions and deceptions:
Cleverness is indeed a great power, yet it is greated by him as an insignificant servant, as a shrewd contemptible one. He hears the servant, to be sure, but in action he is not guided by him. He uses cleverness against himself as a spy and informer, which informs him instantly of each evasion, yes, even gives warning at any suspicion of evasion. (p. 140)
Kierkegaard's thoughts on cleverness end up being a generalization of Plato's attacks on sophistry and oratory in the Gorgias and the Republic; in the Gorgias, for instance, Socrates argues that the primary use of oratory is not in getting out of responsibility but in getting punished when you should be punished, and Kierkegaard's argument generalizes this to the kind of sophistry and oratory we use on ourselves.
Knowing what double-mindedness is, and what purity of heart requires, naturally raises the question of what we ourselves should do. And thus Kierkegaard will turn to this in his final chapters.
---
Soren Kierkegaard, Purity of Heart Is to Will One Thing, Steere, tr. Harper (1956).
Thursday, May 03, 2012
Little James
Today is the feast of Ss. Philip and James. We actually know a fair amount about Philip: he was from Bethsaida, and seems to have been a disciple of John the Baptist. When called by Jesus, he went and found Nathanael and brought him, and is the second apostle, after Andrew, to claim that Jesus was the Messiah. He is always listed fifth of the Twelve, after the two pairs of brothers (Peter and Andrew, James and John), which perhaps indicates his importance, and he speaks several times in the gospel of John.
James the Less is somewhat trickier. He is not the brother of John (that James is sometimes called James the Greater, to distinguish him); and his epithet, which is Scriptural (Mk 15:40), should really be "the Little". What we know for sure is that his mother's name was Mary of Cleophas (and that probably means his father's name was Cleophas) and his brother's name was Joses, probably a form of Joseph. But there are three other cases where someone is called James who might be the same James.
(1) James son of Alphaeus, one of the Twelve Apostles;
(2) James the brother of the Lord
(3) James the brother of Jude
By tradition these are all four considered the same. If James the Less is not any of these, then we know next to nothing about him. But Paul in Galatians 1:9 seems to suggest that James the brother of the Lord was counted as an apostle, and it would explain why James the brother of the Lord had such extraordinary importance in the early church. James the brother of the Lord was the leader of the Church in Jerusalem. Because of this he is the Apostle to whom the later Patriarchs of Jerusalem traced their succession. He also seems to have been very Jewish (hence his other name, which, although first attested in the second century or thereabouts may have been widely known: James the Just, i.e., the Righteous, which seems to indicate close observance of the Law), and Eusebius notes that the Patriarchs of Jerusalem continued this, all of them being "of the circumcision" until Hadrian expelled the Jews from Jerusalem. It is interesting to reflect on how the Church might have been different had their been an unbroken succession of Jewish Christian Patriarchs in Jerusalem. In any case, Paul says that he, with Peter and John (James the Greater is martyred in Acts 12:2, and it's not clear what happened to Andrew), are the "pillars of the church", and it is to him that the Epistle of James is attributed. He seems to be explicitly mentioned by Josephus, who says he was stoned to death. Later legends say that he was first thrown off the Temple, but did not die from the fall, so was finished off by stoning.
James the Less is somewhat trickier. He is not the brother of John (that James is sometimes called James the Greater, to distinguish him); and his epithet, which is Scriptural (Mk 15:40), should really be "the Little". What we know for sure is that his mother's name was Mary of Cleophas (and that probably means his father's name was Cleophas) and his brother's name was Joses, probably a form of Joseph. But there are three other cases where someone is called James who might be the same James.
(1) James son of Alphaeus, one of the Twelve Apostles;
(2) James the brother of the Lord
(3) James the brother of Jude
By tradition these are all four considered the same. If James the Less is not any of these, then we know next to nothing about him. But Paul in Galatians 1:9 seems to suggest that James the brother of the Lord was counted as an apostle, and it would explain why James the brother of the Lord had such extraordinary importance in the early church. James the brother of the Lord was the leader of the Church in Jerusalem. Because of this he is the Apostle to whom the later Patriarchs of Jerusalem traced their succession. He also seems to have been very Jewish (hence his other name, which, although first attested in the second century or thereabouts may have been widely known: James the Just, i.e., the Righteous, which seems to indicate close observance of the Law), and Eusebius notes that the Patriarchs of Jerusalem continued this, all of them being "of the circumcision" until Hadrian expelled the Jews from Jerusalem. It is interesting to reflect on how the Church might have been different had their been an unbroken succession of Jewish Christian Patriarchs in Jerusalem. In any case, Paul says that he, with Peter and John (James the Greater is martyred in Acts 12:2, and it's not clear what happened to Andrew), are the "pillars of the church", and it is to him that the Epistle of James is attributed. He seems to be explicitly mentioned by Josephus, who says he was stoned to death. Later legends say that he was first thrown off the Temple, but did not die from the fall, so was finished off by stoning.
Poem Re-Draft and Three New Poem Drafts
Sor Juana's Apologia
Why persecute me, World, behind a thousand faces?
In what do I offend you, when all I am demanding
Is to conform to graces my understanding,
Not to my understanding those graces?
I regard not treasures nor mundane riches;
Thus have I always tranquillity bought
By putting riches into my thought,
Not giving my thought to those riches.
And I do not regard beauties that, taken,
Are imperial spoils for over-long centuries;
Nor can treacherous wealth my pleasure waken;
For I hold it better, in these ckear verities,
To let the vanities of life be shaken
Than vainly to waste my life in vanities.
Man
Alas! I cannot marry;
no merriness for me,
a wolf has seized my lamb,
a pure and show-white lamb.
I weep;
for wolf with vicious eye,
I cry.
And shall man sow sorrow,
seed sadness in the field
when mouse has blighted harvest,
the sweet and golden harvest?
Rise up!
New work awaits the hand,
I reprimand.
River
Love in every way may veer,
may fall away, may fail.
As rivers overflow we err--
borders burden by being there --
waves will war, fight and flail,
for bounds are death: death we fear.
Yet every water must be bound
or, formless, it will forceless move,
creep and seep devoid of rush
like words that waver into hush,
enslaved by furrow and by groove.
This way may never sea be found.
The force of love to rush, to flood,
is force of love to river be,
not pool nor puddle on the plain:
it moves with end and not in vain,
to flow through vale to violet sea,
to find a home in unbound good.
Michael
Hear the lauds of Zion,
hallels in the heights:
sunrise-hosts of angels
raise their swords of light!
Witnessing the Presence,
scattering the night,
singing songs of glory,
Michael leads the fight.
Why persecute me, World, behind a thousand faces?
In what do I offend you, when all I am demanding
Is to conform to graces my understanding,
Not to my understanding those graces?
I regard not treasures nor mundane riches;
Thus have I always tranquillity bought
By putting riches into my thought,
Not giving my thought to those riches.
And I do not regard beauties that, taken,
Are imperial spoils for over-long centuries;
Nor can treacherous wealth my pleasure waken;
For I hold it better, in these ckear verities,
To let the vanities of life be shaken
Than vainly to waste my life in vanities.
Man
Alas! I cannot marry;
no merriness for me,
a wolf has seized my lamb,
a pure and show-white lamb.
I weep;
for wolf with vicious eye,
I cry.
And shall man sow sorrow,
seed sadness in the field
when mouse has blighted harvest,
the sweet and golden harvest?
Rise up!
New work awaits the hand,
I reprimand.
River
Love in every way may veer,
may fall away, may fail.
As rivers overflow we err--
borders burden by being there --
waves will war, fight and flail,
for bounds are death: death we fear.
Yet every water must be bound
or, formless, it will forceless move,
creep and seep devoid of rush
like words that waver into hush,
enslaved by furrow and by groove.
This way may never sea be found.
The force of love to rush, to flood,
is force of love to river be,
not pool nor puddle on the plain:
it moves with end and not in vain,
to flow through vale to violet sea,
to find a home in unbound good.
Michael
Hear the lauds of Zion,
hallels in the heights:
sunrise-hosts of angels
raise their swords of light!
Witnessing the Presence,
scattering the night,
singing songs of glory,
Michael leads the fight.
Let Something Good Be Said
Let Something Good Be Said
by James Whitcomb Riley
When over the fair fame of friend or foe
The shadow of disgrace shall fall; instead
Of words of blame, or proof of thus and so,
Let something good be said.
Forget not that no fellow-being yet
May fall so low but love may lift his head:
Even the cheek of shame with tears is wet,
If something good be said.
No generous heart may vainly turn aside
In ways of sympathy; no soul so dead
But may awaken strong and glorified,
If something good be said.
And so I charge ye, by the thorny crown,
And by the cross on which the Savior bled,
And by your own souls' hope of fair renown,
Let something good be said!
Wednesday, May 02, 2012
Hidden Assumptions
If it takes 5 machines 5 minutes to make 5 widgets, how long would it take 100 machines to make 100 widgets?
This is a common kind of riddle that's put forward as a trick question. Most people will simply jump in and say 100 minutes; the reason almost certainly being simply that it gives you the closest-fitting pattern of numbers. Then people say "Aha! It's only five minutes. In the second case you have twenty times the machines, and thus they would make twenty times the widgets (=100) in the same amount of time!" And that's all right as far as it goes.
However, all such questions presuppose background information. I noted this point some time ago with the Anne-George-Jack puzzle, the 'real' answer of which requires assuming that Anne, George, and Jack are all people and that they each fit clearly into either the class of married people or the class of unmarried people (not both and not neither). I always find this interesting: the hidden assumptions. This is a really good example. In the strictest logical sense the question doesn't give us enough information to answer it without making assumptions. Consider the following logically possible scenarios.
(1) Five machines make five widgets in five minutes. But these machines are each one-shot and can only work in series, not in parallel. That is, they make the five machines by the first machine making a widget (at which point the machine is used up), and then (and only then) the second machine makes the second widget (at which point the second machine is used up), and so on down the lines. Each machine takes one minute to make its widget. All of the hundred machines work in exactly the same way. How long will it take 100 machines to make 100 widgets? 100 minutes, because each machine makes one widget in one minute, and the minutes are not overlapping. What hidden assumption is uncovered by this scenario? That the machines can in some way do their work simultaneously.
(2) Five machines make five widgets in five minutes. But the machines are all very different, just as you would often expect in real life: some are old and creakingly slow, some are very new and fast and efficient. How long will it take 100 machines to make 100 widgets? We don't know, because for all we know our five-minute machines are the very best and it's all down hill from there. What hidden assumption is uncovered by this scenario? That the machines are all the same.
(3) Five machines make five widgets in five minutes. But, you know, the thing about widgets is that they get made faster if you have more machines working on them -- fewer redundant actions, and so forth. So increasing the number of machines always improves the rate at which they make widgets. How long will it take 100 machines to make 100 widgets? Less than five minutes, but we don't know exactly, because we don't know how the increase affects the rate. Or go the other way: the more machines you have, the worse your rate. As the saying goes, too many cooks spoil the broth. They just keep getting in each other's way, or become increasingly hard to organize. (That's often what the result would be if you had five people working on a project and increased it to a 100, after all.) How long will it take 100 machines to make 100 widgets? More than five minutes, although we don't know how much more. What hidden assumption is uncovered by this scenario? That the ability of the machines to produce the effect is not affected by the number of machines.
These are, of course, all entirely reasonable assumptions, at least for practical purposes, in many cases, although how many will vary for each one. In practice assumption (2) could get potentially very worrisome, whereas I suspect assumption (1) is rarely going to be a big issue. In any case, the assumptions are all needed because we don't know how the machines work, and this is a pretty big gap in our knowledge. If Wal-Mart originally has five check out lanes that always check out five people in five minutes, it doesn't, in the real world, following that 100 check out lanes will always check out 100 people in five minutes; indeed, we know it would never happen, because they would only actually use them all at really busy times and in any case the more people you have to check out, the more likely it is that something will go wrong (fights in lane, stupid customers, stupid employees, etc.) , etc., etc. How check out lanes work is relevant to whether 100 check out lanes is a good way to check out 100 people in five minutes; indeed, it may be relevant to whether it's even a good idea to try. Likewise, how machines produce widgets is something that could potentially be relevant here. Since we don't know anything about it, we're expected to make the simplest assumptions: the machines are the same in both cases, that the rates are the same in both cases, that the machines can work in parallel, and so forth. But they are assumptions.
As I said, I suspect that most people who answer 100 minutes to the question are just treating it as a pattern recognition exercise because they don't see any point to the question or any reason to think that getting a right answer is important. I also suspect, however, that some people would give as their reason a scenario similar to (1). It's certainly true that the assumptions will hold quite often; but it's also true that there can be times when those assumptions give you the wrong answers. In general, I find that it's never very interesting to discover that people are getting the wrong answer (or the 'wrong' answer); the really interesting question is why.
This is a common kind of riddle that's put forward as a trick question. Most people will simply jump in and say 100 minutes; the reason almost certainly being simply that it gives you the closest-fitting pattern of numbers. Then people say "Aha! It's only five minutes. In the second case you have twenty times the machines, and thus they would make twenty times the widgets (=100) in the same amount of time!" And that's all right as far as it goes.
However, all such questions presuppose background information. I noted this point some time ago with the Anne-George-Jack puzzle, the 'real' answer of which requires assuming that Anne, George, and Jack are all people and that they each fit clearly into either the class of married people or the class of unmarried people (not both and not neither). I always find this interesting: the hidden assumptions. This is a really good example. In the strictest logical sense the question doesn't give us enough information to answer it without making assumptions. Consider the following logically possible scenarios.
(1) Five machines make five widgets in five minutes. But these machines are each one-shot and can only work in series, not in parallel. That is, they make the five machines by the first machine making a widget (at which point the machine is used up), and then (and only then) the second machine makes the second widget (at which point the second machine is used up), and so on down the lines. Each machine takes one minute to make its widget. All of the hundred machines work in exactly the same way. How long will it take 100 machines to make 100 widgets? 100 minutes, because each machine makes one widget in one minute, and the minutes are not overlapping. What hidden assumption is uncovered by this scenario? That the machines can in some way do their work simultaneously.
(2) Five machines make five widgets in five minutes. But the machines are all very different, just as you would often expect in real life: some are old and creakingly slow, some are very new and fast and efficient. How long will it take 100 machines to make 100 widgets? We don't know, because for all we know our five-minute machines are the very best and it's all down hill from there. What hidden assumption is uncovered by this scenario? That the machines are all the same.
(3) Five machines make five widgets in five minutes. But, you know, the thing about widgets is that they get made faster if you have more machines working on them -- fewer redundant actions, and so forth. So increasing the number of machines always improves the rate at which they make widgets. How long will it take 100 machines to make 100 widgets? Less than five minutes, but we don't know exactly, because we don't know how the increase affects the rate. Or go the other way: the more machines you have, the worse your rate. As the saying goes, too many cooks spoil the broth. They just keep getting in each other's way, or become increasingly hard to organize. (That's often what the result would be if you had five people working on a project and increased it to a 100, after all.) How long will it take 100 machines to make 100 widgets? More than five minutes, although we don't know how much more. What hidden assumption is uncovered by this scenario? That the ability of the machines to produce the effect is not affected by the number of machines.
These are, of course, all entirely reasonable assumptions, at least for practical purposes, in many cases, although how many will vary for each one. In practice assumption (2) could get potentially very worrisome, whereas I suspect assumption (1) is rarely going to be a big issue. In any case, the assumptions are all needed because we don't know how the machines work, and this is a pretty big gap in our knowledge. If Wal-Mart originally has five check out lanes that always check out five people in five minutes, it doesn't, in the real world, following that 100 check out lanes will always check out 100 people in five minutes; indeed, we know it would never happen, because they would only actually use them all at really busy times and in any case the more people you have to check out, the more likely it is that something will go wrong (fights in lane, stupid customers, stupid employees, etc.) , etc., etc. How check out lanes work is relevant to whether 100 check out lanes is a good way to check out 100 people in five minutes; indeed, it may be relevant to whether it's even a good idea to try. Likewise, how machines produce widgets is something that could potentially be relevant here. Since we don't know anything about it, we're expected to make the simplest assumptions: the machines are the same in both cases, that the rates are the same in both cases, that the machines can work in parallel, and so forth. But they are assumptions.
As I said, I suspect that most people who answer 100 minutes to the question are just treating it as a pattern recognition exercise because they don't see any point to the question or any reason to think that getting a right answer is important. I also suspect, however, that some people would give as their reason a scenario similar to (1). It's certainly true that the assumptions will hold quite often; but it's also true that there can be times when those assumptions give you the wrong answers. In general, I find that it's never very interesting to discover that people are getting the wrong answer (or the 'wrong' answer); the really interesting question is why.
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