The Metaphysics of Quality
#1
Posted 23 July 2007 - 06:05 AM
Full essay here - http://moq.org/
QUALITY WITH A HUMAN FACE
by John Beasley
19/2/00.
Metaphysics can be viewed as the attempt to define what is real. Yet any conceivable basis for this attempt can be attacked as itself unreliable, partial or biased. Just as Godel showed that there can be in principle no unassailable mathematical system, so generations of philosophers have undermined any naive consensus for a value neutral basis for understanding what is. In recent times science has come closest to offering the illusion of such understanding, but the twentieth century romance with science seems to have done little to advance wisdom. If there is a way forward for human understanding, though, it will need to take account of the real, if limited, achievements of science; achievements which balance abstract and analytical thinking against messy practical experimentation. In this essay I intend to range over some of the territory of metaphysics, and in particular to critique the work of Robert M. Pirsig, whose thought offers a partial alternative to much of what is on offer in current academic disciplines.
A metaphysics is a human artifact. When Robert M. Pirsig wrote 'Zen and the Art of Motorcycle Maintenance" (ZMM) he established the fundamental significance of what he termed quality in speaking about a range of issues of crucial importance to human beings. In particular, he attacked the false dichotomies that arise from what he saw as the dominant subject/object metaphysical world view, and showed that establishing quality as the primary 'stuff' of the universe, as we encounter it in experience, can resolve many of the difficulties that spring from the subject/object model. Of most significance, he was able to locate value in a central place in his new paradigm, offering an escape from the increasingly sterile debate about the place of values in a world dominated by the supposedly 'value-free' ethos of science.
With his second novel, 'Lila', Pirsig reformulated his earlier thinking about quality to create a structured metaphysics. He postulates that quality is encountered in two forms: dynamic quality, able to be encountered in experience, but necessarily indefinable since definition draws upon the past, and the past can never adequately encompass the potential in each new moment; and static quality, the residue of experiences of the dynamic which is preserved in memory and language, and which can be further categorised into four discrete levels. These four levels, the inorganic, biological, social and intellectual, can accommodate everything in human experience except dynamic quality itself.
Pirsig's metaphysics of quality has been generally ignored or treated with contempt by professional philosophers. At the same time, it has struck a chord with many people who are searching for an intellectually credible way of understanding our existence that can encompass values as well as 'facts'. By postulating that each level of static values is an advance on the level beneath, he also suggests a potential meta-ethics which might provide guidance in situations where the value systems of the varied levels clash. Indeed, in his understanding, such clashes are inevitable since the emergence of a new level, seen as occurring within an evolutionary process, invariably sets up a conflict between the newly emerging higher values and the static hierarchy of values that has previously been dominant. He views the history of the twentieth century as the struggle for control of social values, which dominated the world of the Victorians, by the emerging intellectual values which guide thinkers, planners and specialists of all types. He also vaguely acknowledges the values of art, though it is not clear how they fit with the values of ideas, which appeal to him as an intellectual.
Like all attempts at metaphysics, the metaphysics of quality has its strengths and weaknesses. It does offer a subtle and convincing understanding of just what it is that we can be said to know, similar in broad outline to that developed by William James. It avoids the narcissism which has destroyed traditional concepts of meaning in late structuralism (the deconstructionists) and offers, in Edward Pols apt phrase, "a restorative access to reality". Yet Pirsig is surprisingly dismissive of people, focussing on the "patterns of patterns" which in his view make a nonsense of the 'self'. As a result, there is a strong sense of isolation and loneliness in his books, together with a somewhat stifled appeal to mystic values. He has great trouble explaining just how his metaphysics will actually make a difference to people, particularly when it comes to discriminating those ideas with 'quality' from the dross. Perhaps inevitably, his ideas seem to appeal to intellectuals and those who relish systems and structures; yet they seem equally attractive to those of a mystic bent. Unfortunately, this broad appeal is based on an understanding of "Quality" (Pirsig almost always uses capitals for this term) which seems to mean all things to all men. It would be possible to insert the word "God" in the place of "Quality" in many of his statements without significantly altering the meaning. This is a pity as he has explored enough of the terrain of quality to recognise the real strength of the term, and he has experienced enough to know that we do not require another theological system.
Briefly, his failure has been twofold. First, he loses the value of his core term, 'quality', by equating it with too many other terms, and ultimately reifying it; while at the same time asserting that quality cannot be defined, and ignoring the resulting paradox. Secondly, and more importantly, he subtly devalues people by focussing on patterns of patterns of value, in which people become the necessary carriers of information in an evolutionary process, rather than holistic agents with the potential for contact and encounter.
LANGUAGE AND INTELLIGENCE
Before exploring what might be done to correct these faults, it is necessary to explore the location of our metaphysics. I began by saying a metaphysics is a human artifact. It is an intellectual construct, an attempt to put in words our best understanding of how things are. As Pirsig himself was acutely aware, insofar as he adopts a mystic standpoint, a metaphysics is an offence, given it is an attempt to explore dynamic reality with static tools. It seemingly cannot be done. But this is to ignore the structure of intelligence, which as the physicist David Bohm reminds us in a conversation with Krishnamurti, means quite literally 'to read between the lines'. In Zen terms, a metaphysics is 'a finger pointing at the moon'. If we focus too narrowly on the words, the terms, the definitions, we miss the moon. But if no-one points, we may also miss the moon. It is a fact of our experience that at some point in an explanation of something new, the penny drops, and we, like Archimedes, can suddenly exclaim "Eureka, I have it". The 'Aha' experience! This is intelligence, as it is encountered in experience.
And this is why Pirsig is so wrong when he states that quality cannot be defined. Certainly, definition in dictionary terms cannot encompass the encountered reality of dynamic quality. But we have all experienced such encounter, and the words need not be a straightjacket which limit and constrict the reality; rather, they must become the finger that points, and then, Aha, we see it. Yes, there is a valid point that Pirsig wants to make, that any new encounter may be different in quality from any previous experience we have encountered. But this is simply a proviso, something we bear in mind, and we know that this is true of our experience of new things in the past. It simply does not prevent us using language to explore, to point to something other than the words we use. Indeed, all language is just this, a coded metaphor for something else. If we reflect on how a language grows, or how we as children learnt a dozen or so new words each day for years on end, we face this mystery afresh. And without intelligence, we could never move forward: new words could not be invented, new words learnt. But we do learn, we do make sense of the new term, as intelligence reads between the lines and connection, even contact, occurs. At a physiological level we may speak of traces programmed in our brains, perhaps through some form of self sustaining feedback loops, and we rightly regard memory as a diminished residue of what was in the experiencing a vital event. But this mechanical device is only the hardware that makes possible the miracle of intelligent comprehension. We must not mistake the floppy disc for the novel, with its plot and characterization, that is inscribed there.
Much more could be said about language, its subtleties and the self recursive nature of talking about talking, but ultimately this is irrelevant to our issues in constructing a metaphysics. If our language is 'good enough', then it can trigger the intelligent comprehension of another person, and we do not not require more. Intelligence makes the connection between our words about experience and an intuitive comprehension. This in itself is an encounter with one species of what Pirsig calls quality, and so is directly accessed by us. The encounter with meaning is just as real as the encounter with a hot stove, though in a different realm.
THE REALMS OF ENCOUNTER
And it is those different realms we need now to discuss. Pirsig talks about the inorganic, biological, social and intellectual realms, each with its own system of values, often in conflict with the values of the realm above or below. This is helpful as far as it goes, but we need to reflect more on the human dimension of this arrangement. Intellectual and artistic realms seem predominantly confined to the human species, while the social realm is encountered in a broader group which certainly includes our primate relatives. The biological realm by definition encompasses all living things.
We alone appear to have the consciousness that allows us awareness of self, and the ability to plan for a future fantasised from the remembered experience of the past. And, yes, only humans construct metaphysics, so far as we know. Consciousness of our 'selves' also gives rise to the particular anguish and poignancy of human suffering - animals experience the suffering of what is, while for humans the greatest suffering seems often to arise from what could have been. And lest it be assumed that such suffering is 'merely' emotional, consider the strange fact that the pain we feel in attempting to hold our arms above our heads for a long period disappears under hypnosis. Fatigue is at least in part a creation of consciousness.
Pirsig introduces these realms in the context of evolutionary theory, which in his hands risks becoming a sort of scientism; a teleology at times. Evolution has become the strongest explanatory myth of our culture, and this is in part because it appeals to our intelligence. But it also appeals because it shares the values of the mythos we inhabit, and ultimately it is a conceptual scheme for making sense of the world of experience, much like a metaphysics. It is a useful myth, provided we do not lose sight of its limitations.
I want to propose an alternative, person centred way of viewing these realms. I think it was Darwin who explained that in exploring the natural world, we must perforce start from the middle, the realm of our habitation, which is the natural world seen at the human scale. This, it seems to me, is a necessary truth, consistent with Pirsig's subtle understanding of what and how we know. We do not have any privileged access to the universe. In evolutionary terms, we are creatures whose senses have evolved in response to our situation. Our senses are value laden from the beginning. They provide us with information that increases our chances of survival and reproduction, but we have no way of knowing objectively what 'is'. All that is necessary is that our senses, and the nervous system that links and coordinates them, provide input which minimises our risks of harm and maximises our opportunities for help, in the environment we inhabit. If our evolutionary understanding is somewhere near correct, our survival as a species is dependant upon a good fit between our perception, as organisms, and what 'is'.
We are so used to the scientific explanation of this environment and its functioning that we tend to take for granted that this scientific model of the world is somehow real. One of the great virtues of Pirsig's view of the world is that he neither denies nor worships the scientific understanding of a world 'out there' that functions according to laws we seem increasingly to comprehend. What he makes clear is that all this understanding is second-order, static knowledge. Our primary experience, the bedrock for all the superstructure of knowledge that becomes our mythos; this primary experience is an encounter, a value laden encounter, dynamic when it is in the moment. It becomes static when it is preserved in memory. However, just to complicate things, our memories are routinely projected as fantasy into the maelstrom of encounter, in such a way that what is derived from our past experience, and what is objectively present, are indistinguishable in the moment.
We do not and cannot 'know' what is in our world with any objectivity. Even science, the nearest thing we have to 'value-free' knowledge, performs a strange oscillation between intuitive theorising and pragmatic experimentation. Each keeps the other on the rails, and the results seem to indicate that the process has been remarkably successful, yet there is actually only a tension that is surely in the realm of values and intelligence that indicates when it is appropriate to jump from one modality to the other. Paradigm shifts are rarely obvious at the time they occur, and the best scientists have made stupendous errors. It seems unlikely that there will ever come a time when there can be only one view of reality. There are a multiplicity of competing views on almost any facet of 'knowledge', with more invented daily. Some will be effectively disproved by their incompatibility with the tests of experiment, but even the most successful are merely our best current knowledge, and a new paradigm is always possible. There is also the very real likelihood that our minds, wondrous though they are, are simply inadequate to comprehend what is beyond a horizon which is defined by their sophistication.
So human experience is embedded in a world which we can usefully assume exists independant of us, though it is not possible to prove this. The realms Pirsig postulates are supposed to encompass all our categories of experience, other than the dynamic encounter itself. However I would rather examine these realms, from the human perspective, as nested or interpenetrating 'universes', each utterly unpredictable in terms of the substrate on which they are built. Each level is a new revelation. Pirsig acknowledges that each level carries a new set of values, which re-order and often clash with the values of the level below. What he seems less able to comprehend is that each new level of values is embedded in an understanding of quality different in kind from the quality infusing the values it builds upon. To do this would mean sacrificing the implied unity of quality in his scheme. He faces this most overtly in ZMM Ch 19, where he starts to explore differing forms or dimensions of quality, which he calls "just seeing" and "overall understanding", then withdraws from this enterprise because his shiny new 'Quality' is getting complex. A great pity, for had he gone further in this direction he may have arrived at a more satisfactory, though complex, outcome.
In a sense he returns to this classic/romantic split with his new categories of dynamic and static quality in Lila, which are similarly linked to immediate experience and experience remembered or reflected upon later. But in an effort to construct an elegant model of reality, he chooses to ignore the diversity of types of quality which he touches upon, and pretend that there is just one "Quality", indefinable but overarching. So artistic and intellectual quality are uncomfortably lumped together in one realm, the intellectual, though his unease shows, and he vaguely suggests a "level of art" at one point, but fails to take this further.
VARIATIONS IN QUALITY IN DIFFERENT REALMS
THE BIOLOGICAL REALM
While Pirsig often seems to equate quality with the good, his example of the organism's encounter with quality, sitting on a hot stove, shows an encounter with what is harmful, not good. At the biological level, value can be positive or negative, insofar as it represents help or harm to the individual organism. Survival and propagation are imperatives for living things. At the level of the organism, then, value is defined in terms of individual survival and propagation. What is significant to the organism is contact with those aspects of the environment which can potentially hurt or help it. Everything else, with the exception of reproduction, can be safely ignored. Our ability to attend to what is outside the contact boundary that defines us as organisms is built upon these biological imperatives. This inbuilt bias is the basis of value. Our brains and sense organs are as much concerned with eliminating unnecessary data as they are with gathering data. It is the quality of the data, its value for survival, that is selected for in terms of evolutionary pressures. Those organisms that survive are those better equipped to avoid predators and find sustenance, and these qualities, together with those that offer reproductive success, define those individuals which will tend to pass on their genes to a new generation. (The attributes which increase reproductive success, such as the peacock's tail, may come at some expense to its ability to survive. In one sense this can be viewed as a fundamental value clash within the biological realm: alternatively, the reproductive dynamic may be seen as a basis to the value schism between biological and social realms that Pirsig explores. That this issue does not seem to be cleanly resolvable by Pirsig's metaphysics indicates that his categories are not as absolute and discrete as he would like to believe.)
It is very likely that our brains are 'hard-wired' for the qualities which confer survival benefits upon us. It is plausible that the so-called 'reptilian brain' largely located in the brain stem provides this rapid appraisal of and response to threats and opportunities in the environment. (Derryberry & Tucker, 1990, for example, show how the locus ceruleus (noradrenergic) system in the brain stem is activated by the perception of unexpected, intense or aversive stimuli, and facilitates rapid attention and response outcomes.)
We see that the values that rule the biological domain necessitate a view of quality that is spread along a spectrum from positive to negative, insofar as the quality of any experience is intimately related to the survival value, positive or negative, that is communicated by the experience to the individual organism. Where there is no such value, or it is unable to be apprehended, there is for the organism no 'experience'. (It follows that the mid range of the spectrum is without quality and is not experienced by most living things, though we human beings form a notable exception.) Madame Curie's death from cancer could have been avoided if humans had a sense capable of assessing the negative effects of strong radiation, such as was given off by the radium she carried in her pocket. But such strong radioactivity was previously unknown, so no such sense had evolved, and consequently she did not 'experience' what was in fact a harmful exposure to radiation. Ambient temperature is a good example of the bi-polar nature of the biological quality spectrum. Very low and very high temperatures are noticed and the organism takes what action it can to minimise the damage that temperature extremes can cause it. For humans a temperature of about twenty five degrees Celsius is simply ignored, though it is possible for us to attend to it if this is required of us. [As a hypothetical example, a temperature guessing competition at a party would stimulate attention to something in the environment which would be otherwise ignored. The social reward of winning the competition provides the necessary stimulus in this case.]
#2
Posted 23 July 2007 - 10:08 AM
bodi, on Jul 22 2007, 11:05 PM, said:
Full essay here - http://moq.org/
QUALITY WITH A HUMAN FACE
by John Beasley
19/2/00.
Metaphysics can be viewed as the attempt to define what is real. Yet any conceivable basis for this attempt can be attacked as itself unreliable, partial or biased.
If I disagree with this premise, do I have to argue about the rest of it?
bodi, on Jul 22 2007, 11:05 PM, said:
But only as a magic show. They confuse and switch hands so as to fool the audience - has nothing to do with "real" Reality".
#3
Posted 23 July 2007 - 02:02 PM
Siau, on Jul 23 2007, 11:08 AM, said:
My favourite magic show are those that astound you first and then show you how it's done. Show us how it's done Siau.
Ocelot.
A myth is a fixed way of looking at the world which cannot be destroyed because, looked at through the myth, all evidence supports the myth.
-Edward De Bono, consultant, writer, and speaker (1933- )
#4
Posted 23 July 2007 - 02:40 PM
Ocelot, on Jul 23 2007, 07:02 AM, said:
Well I wish a had a better memory for names and dates...
A woman revealed that if you always guess at a different door in the game of "Let's make a deal", you have a better chance of winning. Many, many mathematicians tried to argue. She had a convincing story as to why it must be true. She wrote a book on it. She was proclaimed as the genius that out witted the mathematicians of the world. The media greatly published her astounding genius. One woman against the entire world of male mathematicians. One problem...
Her reasoning very subtly left out a concern. It is hard to find. The mathematical proof to the contrary is pretty obvious and simple. But with the distraction and selected focus of the media helping out, very many were convinced that she was right (and still are). I looked at her "logical proof" (years ago). It took me a while to find exactly where she slipped the alteration into play. It was all a scam on the public. Perhaps purposely on her part, perhaps not. It was a demonstration that the magic of keeping focus away from the facts can motivate people, sell products, cause belief, and generally toy with the minds of others.
Her claim was that Science is just a mind game and no more right than any other belief system. She gained “followers”. The truth hasn't been revealed to the general public to this day.
#5
Posted 23 July 2007 - 02:59 PM
2) Keep people distracted and busy with other issues to make sure they don't think too much about the details.
3) Employ emotions to keep the sides willingly accepting their side of the issue - the desire to believe.
It is happening all around you everyday. The religions used it for very many years.
"Test all things, keep what works." It works. And makes a handy political tool when the media has no concern for being honest. In a pinch, do what works, even if it "ain't right".
Do you have faith in the media?
#6
Posted 23 July 2007 - 04:58 PM
Siau, on Jul 23 2007, 03:40 PM, said:
A woman revealed that if you always guess at a different door in the game of "Let's make a deal", you have a better chance of winning. Many, many mathematicians tried to argue. She had a convincing story as to why it must be true. She wrote a book on it. She was proclaimed as the genius that out witted the mathematicians of the world. The media greatly published her astounding genius. One woman against the entire world of male mathematicians. One problem...
Her reasoning very subtly left out a concern. It is hard to find. The mathematical proof to the contrary is pretty obvious and simple. But with the distraction and selected focus of the media helping out, very many were convinced that she was right (and still are). I looked at her "logical proof" (years ago). It took me a while to find exactly where she slipped the alteration into play. It was all a scam on the public. Perhaps purposely on her part, perhaps not. It was a demonstration that the magic of keeping focus away from the facts can motivate people, sell products, cause belief, and generally toy with the minds of others.
Her claim was that Science is just a mind game and no more right than any other belief system. She gained “followers”. The truth hasn't been revealed to the general public to this day.
It sounds to me that you're describing the Monty Hall Problem
I have follwed her logic and she convinced me. I din't believe this at first and it took drawing a probability tree for me to twig where there was a constraint I hadn't factored in.
I have run simulations and found that she was correct.
Tell me what flaw you think you found.
Ocelot.
A myth is a fixed way of looking at the world which cannot be destroyed because, looked at through the myth, all evidence supports the myth.
-Edward De Bono, consultant, writer, and speaker (1933- )
#7 Guest_Truth Warrior_*
Posted 23 July 2007 - 06:22 PM
#8
Posted 23 July 2007 - 07:27 PM
As some have said in the past, "reality" just "is".
IMO, metaphysics tends to be just another human constraint on the realm of overall "understanding". Yes, there are systems that seem to help humanity understand, but are any of these systems 100% accurate? Also, to have a better understanding of the universe we should not tie ourselves down to just one form of thinking. So not just critical, spiritual, scientific, metaphysical, physical, philosophical, artistical, skeptical, psychological, sociological, economical, mathematical, rational, political and so on.
Just my thoughts on the subject.
Andrew
#9
Posted 23 July 2007 - 07:38 PM
Quote
Yep. Exactly. (Well, not 'exactly', but you know...)
The complete book Zen and the Art of Motorcycle Maintenance is online here -
http://www.virtualsc...lity/PirsigZen/
#10
Posted 23 July 2007 - 08:07 PM
Ocelot, on Jul 23 2007, 09:58 AM, said:
I have follwed her logic and she convinced me. I din't believe this at first and it took drawing a probability tree for me to twig where there was a constraint I hadn't factored in.
I have run simulations and found that she was correct.
Tell me what flaw you think you found.
Well forgive the confindence in this particular realm, but there is no "think I found" involved.
If you can find that logic tree she created, I can point it out. It has been years since I saw it, and that was from a book a student of mine had bought. The error is very subtle, but definate.
So now look at what you are saying, 100's of mathematicians are wrong in MATH (not about vague things like where the universe came from). You are basically denying the rules that all statistics are based on, because those are what the mathematicians used. Don't you think that situation is a bit odd in the midst of you trying to convince me that psychologists (notebly emotional and irrational people) have accurate measurements of intelligence and have used STATISTICS (the same rules you are denying) to "prove" that intelligence is rising.
The only reason you gave her enough credit for you to even read her proposal came from the media coverage. "The good guys are all talking about it so it must have some truth in it. I'm skeptical so I will walk into the trap myself and become one of the good guys too."
===================
Oh, nevermind, I didn't realize that your reference was a link into Wiki. Give me a little time to sort out the flaw again and I'll try to explain it.
#11
Posted 23 July 2007 - 08:45 PM
In the Wiki write up (and note that Wiki believed the deception too), there are 3 steps revealed as the composition of the game;
1) The player picks the car (this is where the error has already been slipped in under your radar)
2) The player is shown a goat in another door (door 2).
3) The player is shown a goat in door 3.
The explanation continues to point out that given those options, the probability is that the player has a 2 out of 3 chance of picking the car if on his second guess, he changes his choice.
Now the flaw;
The premise of the explanation was that the player "chose the car". At that point, the reader is accepting the premise so as to continue the scenario expecting a full explanation. But the reader generally fails to go back to re-examine that premise. What if the player had chosen incorrectly with his first guess?
If you add that possibility that the players first choice could have been wrong (in holding with the rules of the game), the probabilities calculate out to be even, just as the mathematicians stated.
You are shown only an explanation that shows what you are to believe - that the probability is 2/3. You are not shown what you are not to believe - that the player was wrong to begin with in which case the probability is 1/3.
Isn't magic fun. It's all about controlling your Focus - what "the media" does for their living.
#12
Posted 23 July 2007 - 10:43 PM
Siau, on Jul 23 2007, 09:45 PM, said:
In the Wiki write up (and note that Wiki believed the deception too), there are 3 steps revealed as the composition of the game;
1) The player picks the car (this is where the error has already been slipped in under your radar)
2) The player is shown a goat in another door (door 2).
3) The player is shown a goat in door 3.
The explanation continues to point out that given those options, the probability is that the player has a 2 out of 3 chance of picking the car if on his second guess, he changes his choice.
Now the flaw;
The premise of the explanation was that the player "chose the car". At that point, the reader is accepting the premise so as to continue the scenario expecting a full explanation. But the reader generally fails to go back to re-examine that premise. What if the player had chosen incorrectly with his first guess?
I think you need to read it again. That the player picks the car on the first guess is not the premise. If it were then changing their mind for their second guess would result in a zero probability of getting the car.
Siau, on Jul 23 2007, 09:45 PM, said:
No you don't, as the mathematicians realised when it was explained to them.
If we state that the player will change their mind then.
The probability that they chose the car first go is 1/3
The probability that they get a goat first go is 2/3
One goat is then revealed. Leaving two doors.
If they had first chosen the car (probability 1/3) and they change their choice then they will definitely get a goat.
If they had first chosen a goat (probability 2/3) and they change their choice then they will definitely get a car.
Siau, on Jul 23 2007, 09:45 PM, said:
Did you read the link provided. The decision tree clearly lists all posibilities for the first choice. The chance of being wrong first go in 2/3.
Siau, on Jul 23 2007, 09:45 PM, said:
Ocelot.
A myth is a fixed way of looking at the world which cannot be destroyed because, looked at through the myth, all evidence supports the myth.
-Edward De Bono, consultant, writer, and speaker (1933- )
#13
Posted 24 July 2007 - 12:07 AM
Originally I only had the diagram, not the pics and I misunderstood what the pics were meaning.
So, on to the REAL flaw;
This is very difficult for me to put into words...
In that decision tree you posted, it shows what choices the player had in the beginning. 1 of 3
The second level shows the choices that Monty had (actually irrelevant to the problem).
The decision tree distinguishes Monty choosing either goat A or goat B in the players last option. But this confuses the issues because the players options are the only significant concerns. In the players last option of picking a car, the math related to the players concerns is divided due to Monty having 2 options. But how many options Monty had does not affect the number of outcome possibilities for winning the car, thus the math should not have been divided. Both of those options of goat A or Goat B should be represented in the decision tree as a single option of "a goat", not a decision of goat A or goat B.
The issue is that Monty will always show a goat next. He could be told to always show goat B and that decision tree would change, but the real options to the player would not. The player in each and every case is shown one door where there is a goat, always leaving him with a 1 of 2 remaining risk, not 1 of 3.
So the decision tree should be;
First level; Player chooses 1 of 3
Second layer; Monty opens a "goat door".
Third layer; Player has 2 options remaining (never choosing the opened door) - always 2 out of the original 3.
Monty's decision is irrelevant to the decisions of the player because he will always open a remaining door and always reveal a goat. The decision tree is for the player, not Monty and certainly not a mix of both in one tree.
In the end, the mathematics shows that the player had the following probabilities;
1) 1/3 that he chose goat A from door 2
2) 1/3 that he chose goat B from door 3
3) 1/6 that he chose the car from door 1 by avoiding goat A
4) 1/6 that he chose the car from door 1 by avoiding goat B
Which goat he avoided is irrelevant because the contest is to choose the car, not the car while seeing a particular of the other 2 goats. This means that in reality there were only 3 cases of relevance, not 4. Regardless of whch goat he was shown, he still has a 50/50 chance of getting the car.
Or it could be shown as;
1) 1/3 that he chose the car
2) 1/2 that he chose the car
The choices involving the car or not are the only concern, not which goat or which door.
Her tree mixes permutations involving 2 decision concerns into one tree. Which goat is the irrelevant issue being cast into the picture by the fact that Monty can choose which door the player has left.
Properly, the decision tree should look more like this;
1) 1/3 chance he chose goat A
2) 1/3 chance he chose goat B
3) 1/3 chance he chose the car avoiding either of the goats.
The second level would simply be;
1) goat B is revealed
2) goat A is revealed
3) either A or B is revealed (which door or goat does not change the probabilities involving the player's chance).
Her tree is showing you the probabilities of choosing the car from a particular door after a goat has been shown.
The proposed simulation on that Wiki page does the same thing by deciding who wins by looking not at the players choice, but by looking at the dealers decision and deciding that the play has won or not from there. Why not play the game by letting the player go ahead and finish his choices and win for real. The player will statistically end up winning the same number of times whether the dealer revealed a red 2 card or not.
Imagine what that kind of tree would look like if Monty was instructed to shake the players hand if the remaining goat was white rather than black. The fact that the color of the goat is irrelevant would be ignored and the tree would have to include as further branches whether he shook the players hand or not. That would make the statistics appear to say that the person had a much greater chance by changing choices when Monty shook his hand. You could add 100 irrelevant actions into the picture so as to get a result of 99% probability of winning the car by changing your choice after the first level.
I still feel like I haven't worded it all well enough to make it obvious. As I said, it is a subtle thing. So let me work on the wording. The confusion is because of counting Monty's choices in with the players choices when Monty's was not relevant to actual winning statistics.
#14
Posted 24 July 2007 - 01:20 AM
Quote
When calculating probability, you divide the number of winning choices by the total number of choices available. All else is irrelevant.
In the first level of the game, there are 3 total choice options and one winning option – 1/3 chance of winning with the first guess, IF the player can choose to not go to the second level.
After one of the doors is opened, there are only 2 options available with one always remaining as the winning option – 1/2 chance the second time.
Because there is always a second level to the game and the probability of winning that time will always be the same 1 of 2, the players chances of winning are always 50/50 regardless of what else Monty does.
It is ONLY the number of doors that is relevant, not which door (or goat). So showing goat A is no different than showing goat B. In a decision tree both of those Monty choices should be counting as merely “showing a goat” and leaving 2 unknown doors.
The trick is to focus on the number of options and avoid confusing your mind with other concerns that do not alter the total number of options.
If the game was "choose the car while seeing goat A" then her version of the tree would be relevant. But the game is actually merely to choose the car regardless of what is seen in the other doors.
#15
Posted 24 July 2007 - 01:57 AM
Siau, on Jul 24 2007, 01:07 AM, said:
Originally I only had the diagram, not the pics and I misunderstood what the pics were meaning.
So, on to the REAL flaw;
This is very difficult for me to put into words...
<snip>
I still feel like I haven't worded it all well enough to make it obvious. As I said, it is a subtle thing. So let me work on the wording. The confusion is because of counting Monty's choices in with the players choices when Monty's was not relevant to actual winning statistics.
Fair enough I'll allow you to reword it and restrict myself to noting where we seem to differ. Monty's choice IS relevant to the problem. They players final choice is constrained by monty's choice. The player will not pick Door 3 if Monty has already revealed a goat behind door 3. As such The player cannot predetermine their final choice. Similarly Monty's choice is constrained by the players first choice. Monty will not reveal a goat that is behind a door that the player has chosen. As such Monty cannot predetermine which goat he will reveal. This si how new information enters the system.
Were it not for these constraints then the player's second choice would be as if they started with two doors with a 50:50 chance of a car behind either one. It was the failure to acknowledge these constraints that mislead all those thousands of people who wrote in.
Ocelot.
A myth is a fixed way of looking at the world which cannot be destroyed because, looked at through the myth, all evidence supports the myth.
-Edward De Bono, consultant, writer, and speaker (1933- )
#16
Posted 24 July 2007 - 02:41 AM
#17
Posted 24 July 2007 - 03:40 AM
Siau, on Jul 24 2007, 03:41 AM, said:
Yes that's the typical mistake.
Consider this then. Lets take somebody who is definitely going to switch. (after all why not you say it makes no difference and I say it improves their odds, no-one suggests it'll do any harm.)
Lets also change the scenario a little. Theres now 100 doors, 1 car and 99 goats. After he makes his first choice Monty will reveal 98 goats and the player will switch their choice.
Their initial choice has a 99% chance of being a goat.
If it is then the player will switch doors and win a car.
If they're unlucky their initial choice will be the car 1% chance.
They'll then switch doors and win a goat.
Ocelot.
A myth is a fixed way of looking at the world which cannot be destroyed because, looked at through the myth, all evidence supports the myth.
-Edward De Bono, consultant, writer, and speaker (1933- )
#18
Posted 24 July 2007 - 07:12 AM
In your proposed 100 door scenario, the player begins with 1/100 probability. But then Monty removes 98 choices making the second level back to only 1/2 again just as in the original.
If the player changes to the door that Monty did not choose, then there was originally a 1/100 chance that one was the car. But since Monty did not choose that one, then it either wasn't the car or it is the car. This leaves it all right where the original game was.
The door that he didn't choose had a 1/100 chance of being the car to begin with just as the one the player chose. All Monty did was remove all of the others that he knew were not the car. Monty provided nothing to say that the remaining unchosen door has any more chance of being the car than the one the player chose.
The end result, is that Monty changed the number of doors to only 2 in both scenarios.
What you seem to be thinking is that the unchosen door has a higher probability of being the car. It never gains any higher probability than the players choice had. In the original scenario, the unchosen had a 1/3 chance of being the right one until Monty removed the one door leaving it with a 1/2 chance. In the new scenario, the unchosen had a 1/100 chance until monty removed all 98 others. In the end, you have exactly the same choice 1 out of 2, both stayed equal probability the entire time in both scenarios.
#19
Posted 24 July 2007 - 08:31 AM
Siau, on Jul 24 2007, 08:12 AM, said:
In your proposed 100 door scenario, the player begins with 1/100 probability. But then Monty removes 98 choices making the second level back to only 1/2 again just as in the original.
If the player changes to the door that Monty did not choose, then there was originally a 1/100 chance that one was the car. But since Monty did not choose that one, then it either wasn't the car or it is the car. This leaves it all right where the original game was.
The door that he didn't choose had a 1/100 chance of being the car to begin with just as the one the player chose. All Monty did was remove all of the others that he knew were not the car. Monty provided nothing to say that the remaining unchosen door has any more chance of being the car than the one the player chose.
The end result, is that Monty changed the number of doors to only 2 in both scenarios.
What you seem to be thinking is that the unchosen door has a higher probability of being the car. It never gains any higher probability than the players choice had. In the original scenario, the unchosen had a 1/3 chance of being the right one until Monty removed the one door leaving it with a 1/2 chance. In the new scenario, the unchosen had a 1/100 chance until monty removed all 98 others. In the end, you have exactly the same choice 1 out of 2, both stayed equal probability the entire time in both scenarios.
OK so what you're saying is that his initial choice has a 1 in 100 chance of being the car. Monty removes 98 doors which are constrained to be (a) not the door that the player chose (b) not the door with the car behind it.
I say that the door that he chose still has a 1/100 chance of having the car behind it. You say that the chance that his initial choice was correct. Has suddenly jumped to 50%
And yet at the same time you're saying that Monty's choice has no effect.
Ocelot.
A myth is a fixed way of looking at the world which cannot be destroyed because, looked at through the myth, all evidence supports the myth.
-Edward De Bono, consultant, writer, and speaker (1933- )
#20
Posted 24 July 2007 - 09:52 AM
1) Initially the player had a 1/100 chance.
2) The door that Monty is going to NOT pick also has a 1/100 chance of being the car (from the view of the player).
3) Monty removed 98 doors leaving only one unchosen plus the player's door = 2 doors remaining.
4) Monty either knew that the unchosen door was the car or that the player had the car. So that means that unchosen door, from the view of the player, has a 1/2 chance of being the car even though Monty already knows where the car is.
5) The player is left with only two doors to choose from. He knows that one of the 2 is indeed the car. That means right there, regardless of how it got to that state, the player now has 2 doors available each with equal chance of being the car. The odds change as the number of choices change, but the odds for ALL doors change equally.
The effect that Monty has is only that of reducing the number of doors. Monty is not affecting the probability of any door having the car versus any other. Which door is never an issue when it comes to the odds. The one that he did not choose will have the same odds as the one the player chose during both step 1 and step 2. The odds change equally for ALL doors remaining. The fact that Monty knew where the car was doesn't change the information that the player has (the only information used to calculate the odds). The player never gets any more information other than how many doors might have the car. That number changes from 100 down to 2. But the player has nothing at all to tell him that his chosen door is any different than the one that Monty didn't choose.

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