Induction "debate"
Posted on: November 16, 2010 - 5:54pm
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Induction "debate"
Just wondered how many here, if any have been following my 'debate' with some strange person, obsessed with the "problem of induction", here, in thread
http://www.rationalresponders.com/why_the_problem_of_induction_really_isnt_a_problem_and_why_theists_dont_even_get_it_right
I have seen no others commenting...
I would be interested in some other opinions.
Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality
"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings." - Sam Harris
The path to Truth lies via careful study of reality, not the dreams of our fallible minds - me
From the sublime to the ridiculous: Science -> Philosophy -> Theology
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I think less people are commenting because it is on a blog post. I read some of it.
This is a formal fallacy in deductive reasoning. It tries to show that the conclusion (Christina is a man) necessarily follows from assumed premises. This has virtually nothing to do with the scientific method. There is no hypothesis. There is no experimentation.
Looks like a bunch of strawmen.
Our revels now are ended. These our actors, | As I foretold you, were all spirits, and | Are melted into air, into thin air; | And, like the baseless fabric of this vision, | The cloud-capped towers, the gorgeous palaces, | The solemn temples, the great globe itself, - Yea, all which it inherit, shall dissolve, | And, like this insubstantial pageant faded, | Leave not a rack behind. We are such stuff | As dreams are made on, and our little life | Is rounded with a sleep. - Shakespeare
Yeah, I figured, which is why I thought I'd start this thread to give a link from the 'regular' forums.
Yeah, seems to keep missing the whole point of science and induction, no matter how plainly I lay it out.
Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality
"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings." - Sam Harris
The path to Truth lies via careful study of reality, not the dreams of our fallible minds - me
From the sublime to the ridiculous: Science -> Philosophy -> Theology
I've been following, but as we have seen all too often, here is someone who has a lot to learn before they can start an intelligent conversation, and is apparently unwilling to learn. He (she?) has this idea stuck in their head and they ain't going to let go for love, money, or real facts.
I am a little put off by the font and a lot put off by the sheer inertia of deliberate ignorance.
-- I feel so much better since I stopped trying to believe.
"We are entitled to our own opinions. We're not entitled to our own facts"- Al Franken
"If death isn't sweet oblivion, I will be severely disappointed" - Ruth M.
and it looks a real head banger. Attention, Blake. Please visit the thread Bob pasted in the OP. It will be of interest to you.
"Experiments are the only means of knowledge at our disposal. The rest is poetry, imagination." Max Planck
It looks like Bob is probably doing as good a job of it as can be done. It's a public service, but I think he's mostly banging his head against a wall here.
I'm mostly just good for swooping in for a few snarky remarks in these situations; I doubt I would be of much help- like most of these people, this guy thinks he knows what he knows, and he's probably just on a crusade to convince others of that fact rather than have a dialogue.
This kind of situation is pretty frustrating- when people choose to be dense, it's very off putting.
This is why I like Chinese better- some of them are *very* ignorant (generally by no fault of their own), and some are even genuinely dim (likewise, bad luck of genetic draw), but very rarely are they ever deliberately dense- a sincere effort to explain something (with patience for the language barrier) yields slow but steady results because no matter how ignorant they started out in the discussion, that ignorance wasn't willful and they almost always try to understand and learn.
Seriously, Chinese have probably ruined me with regards to ever seriously debating with Western fundies again. I'm too used to people trying to learn and understand to tolerate people who are only trying to mindlessly proselytize and justify their own beliefs to themselves through rationalizations that only they can convince themselves to buy.
I *do* miss some of the challenge that I had when I was a kid in the good old fashioned four-against-one apologetic debates in university, but I've ceased to find any theist arguments challenging anymore having learned most of their tricks... now it's just redundant and sad.
I've done about as much as I can in laying out straightforward scenarios showing just how induction+empiricism is used to reach reasonable assumptions about what most probably is the 'truth', and asking just what is wrong with this process, and I get dodging, irrelevant references to acknowledged gaps in our knowledge, and the classic thing about lack of proof implying that we cannot 'know' anything.
And crude straw-man caricatures of what science is and does.
If I reply again, I might concentrate on pointing out that any alternative is subject to even more problems, and has no ability to grow our understanding beyond whatever basic assumptions/axioms we start with.
IOW challenging this person to justify their position - I think I've shown the " d'uh " reasonableness of induction as actually applied in science, as clearly as I can. You can lead a fool to reason but you can't make them think.
It only occurred to me in that thread to introduce the idea of 'extrapolation' as another way of describing what we are doing in 'induction'.
Maybe it shows a problem of the God concept itself, esp. monotheistic, supreme, all-powerful ones, in the way the meme captures the imagination of so many people.
My understanding and observation is that many asian cultures, while certainly superstitious, seem to go more for demons and evil spirits and 'bad luck', with charms and symbols and lucky colors, etc, to ward of the bad ones and appeal to the good ones. Or many 'gods', more like the old Greco-roman pantheons, which also usually accompanied somewhat more rational and tolerant societies.
Not even requiring 'faith', just a matter of "there might be these demons around, so we better stick a magic symbol up on the wall just in case".
Maybe the ideas of demons and charms reflects an approach which is more open to "whatever works".
If you can show them an approach which seems to demonstrably work better, 'makes more sense', they are more prepared to go with it.
No super being ready to punish them for rejecting Him, just, at most, some possible critters with very limited powers who might get upset, but can potentially be frightened away themselves.
Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality
"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings." - Sam Harris
The path to Truth lies via careful study of reality, not the dreams of our fallible minds - me
From the sublime to the ridiculous: Science -> Philosophy -> Theology
Yah, I was reading that thread yesterday. He certainly has some strange ideas going on. I did not get to the end before I had to go to work though.
It was probably a good thing that I was not drinking my morning coffee when I got to the part about us only having known about gravity for a couple of centuries though. Wow! How dense can one be?
=
I think Bob has been remarkably patient, considering the above quote is what he has to deal with...
Xaos was a theist who was attempting to get us to defend induction furiously in order to admit support for the bedrock thinking behind inductive god arguments like first cause. He uses the phrase "on faith if you will" to describe an acceptance of induction as a valid scientific method. Of course, I suffer from an oversupply of suspicion when it comes to many posters.
It's an interesting area to consider. I have James Robert Brown's Smoke and Mirrors in my Amazon wish list and would buy the damn thing if it weren't a million dollars. He addresses a range of scientific philosophy issues including the 'problem of induction'. There are unknowns in science that attract people who have a strong sense of skepticism. I was arguing recently with some one who insisted nothing could be known on the basis of particle theory. It was a major pain in the arse, I can tell you.
"Experiments are the only means of knowledge at our disposal. The rest is poetry, imagination." Max Planck
The Problem of Induction.
Induction is a type of reasoning that draws a general rule from a finite number of experiences. For example: I speak Spanish. My wife speaks Spanish. My children speak Spanish. My in-laws speak Spanish. My neighbors speak Spanish. Therefore everyone speaks Spanish.
Induction can result in a false output even when all inputs are true.
The first person to logically address the problem of induction was the Scottish philosopher David Hume. Although he didn't use that terminology, he concluded that there was no logical reason to use induction. Nevertheless, he reasoned, humans use induction so there's just no way around it.
In modern terms one could talk about dopamine generated in the brain when a person eats food, which results in him craving food when he is hungry (or, in some people, addiction to food). However, I reject this argument because it assumes that because we have observed some brains and their relationship to dopamine that all brains work that way. This is an inductive assumption, and that's the very point we're trying to address.
One might wonder why induction can lead to a false outcome even when all inputs are true. The reason is that induction is based on the logical fallacy known as "affirming the consequent." Using my example above, after realizing that I speak Spanish, as does my wife, and my children I postulate that everyone speaks Spanish. After seeing that my in-laws and neighbors speak Spanish too, I think I have confirmation. In reality, I do not.
Now just because it is a logical fallacy does not mean that it couldn't result in true output some of the time. This is, however, just a matter of luck - not due to good technique.
Many rationales have been offered trying to justify induction. The so-called "naive" justification for induction. Someone may think, "Well, I've used induction with success several times recently. Accordingly, induction works." This is, however, using induction to justify induction.
This is not the only attempt made to justify induction. Whole books have been filled with potential justifications. To the best of my knowledge, all of them have been refuted. I believe all of them can be refuted because (as I have pointed out above) induction seems (to me at least) to be based on a logical fallacy.
Karl Popper was one of the most influential scientific philosophers of the 20th century. His article "Science as falsification" is located at http://www.stephenjaygould.org/ctrl/popper_falsification.html
Quoting him would be tedious, so I'll just paraphrase his contentions. He became disturbed by Marx, Freud, and Alder's theories. True believers in these philosophies found confirmation for them on every page of the newspaper and in every experience of life. To their way of thinking the theories were constantly being verified by almost every aspect of life. Popper writes, "It was precisely this fact—that they always fitted, that they were always confirmed—which in the eyes of their admirers constituted the strongest argument in favor of these theories. It began to dawn on me that this apparent strength was in fact their weakness."
From this point Popper outlined his theory of falsification - that science works not by induction, but rather by deduction. Details can be found at http://dieoff.org/page126.htm but again (since quoting him would be tedious) I will paraphrase.
There are no examples of a valid inductive inference.
All knowledge (scientific or otherwise) is basically conjectural.
Science progresses, inasmuch as it is possible, by falsifying theories.
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"The church at the time of Galileo was much more faithful to reason than Galileo himself, and also took into consideration the ethical and social consequences of Galileo's doctrine. Its verdict against Galileo was rational and just, and revisionism can be legitimized solely for motives of political opportunism." -Paul Feyerabend
"Let me just anticipate that nobody to date has found a demarcation criteria according to which Darwin can be described as scientific, but this is exactly what we are looking for." -Imre Lakatos
Eeew... you guys need to wipe your shoes better; you're tracking shit in all over the house ^
You can lead a theist to rationality, but you can't make him think- I like that. This fellow has not interest in thinking- isn't there a point where we should ignore him? Copy and paste arguments as responses to his canned bullshit work well for that without risking other people thinking we can't contest it.
It captures the imagination, and perhaps the emotions as well somehow.
Part of it might be the carrot and stick approach in the same being, and part of it might be the sense of gratitude or "look how special I am" that comes from this concept of revelation in scripture. Like they have some great secret nobody else has- it makes them feel superior and -crucially- it becomes part of their identities (and that's the hardest thing to sever sometimes).
I'm not sure how tolerant some Romans were, though I think you could draw a correlation between number of gods actually worshiped and tolerance. Many Romans tended to focus on one god in particular, and build up cults around them almost as insidious as the Abrahamic cults. I think this is where they made that particular aspect a part of the identity (rather than just acknowledging all of the gods as some others did)- the act of identifying with something or as something has a kind of cling to the character, and sometimes it can be something as trivial as a sports team.
Right- I would say in these cases it's done out of fear/superstition. And while they may have a very strong tendency to follow the superstition, they might rather not have to deal with the demons at all. Most of these creatures don't seem to constitute a form of theism because the people aren't so much in a relationship of worship with them, as one of pest control; I don't think they identify themselves with the belief so much as it just being something they do.
Even beyond that context and into the occasional cases where somebody generally believes in some "king of heaven" deity or even the "Christian god", it's relatively easy to talk them down from it. Even the 'Christians', delightfully rare as they are, will accept logic when presented clearly and instead squish and meld their concepts of this deity until it can still fit within the realm of possibility- perhaps the only ones in the world who will do so- though as much as they'll allow their beliefs to mutate and yield to logic, they don't like to let go of the identity as "Christian". Perhaps it is that they are identifying more with the title than with a specific concept; it's general enough to permit a god-of-the gaps, and perhaps simply because they aren't as surrounded and forced to narrow their identity down that much.
It may be because Chinese live in a more collective culture and so put more emphasis on mutual understanding than the typical Westerner does- it may be because they still identify primarily as Chinese and because they're not isolated enough to become sufficiently foaming-at-the-mouth-dogmatic to manage to reject such clear logic in favor of a more minor quality. I haven't worked it out yet.
Omg, the fundy followed you. Should I respond to his strawmen?
Our revels now are ended. These our actors, | As I foretold you, were all spirits, and | Are melted into air, into thin air; | And, like the baseless fabric of this vision, | The cloud-capped towers, the gorgeous palaces, | The solemn temples, the great globe itself, - Yea, all which it inherit, shall dissolve, | And, like this insubstantial pageant faded, | Leave not a rack behind. We are such stuff | As dreams are made on, and our little life | Is rounded with a sleep. - Shakespeare
My suggestion is to do the responsible equivalent of ignoring the fundie- that is, copy and paste a simple canned response with links to further reading for anybody else who might read this and who is capable of thinking.
My only concern with not responding is always that somebody who is "on the fence" about this stuff might get the wrong idea if he or she only finds fundamentalist bullshit arguments (being unable to smell the bullshit) without rebuttal.
However, responding in full gives the fundamentalists some kind of satisfaction of being in a "debate" (which they don't deserve)- they get something out of it, apparently. Maybe it's that they feel people are engaging with them, and it validates their ideas further to support them under fire? If the fundie knows that it's a canned response, he or she will eventually get bored and go home.
Sure - you've caught me out! My dastardly plan was to convince you all of the correctness of Popperian falsification on the way to convincing you of the truth of the statement: Allah Akbar.
On a more serious note, I was on the bus today and I invented a story as I bumped along. I should like to share it with you.
Once upon a time there was an atheist who bumped into a childhood friend in a pub. Renewing the friendship they sat and talked for awhile about life and the atheist let on to his friend that he was having trouble finding employment.
Unknown to him the friend was now a fundamentalist Pentacostal. Determined to help his friend he organized prayer groups for a week begging Gawd (or do you prefer god or just g-d) to provide his friend with a job.
As chance would have it, the friend obtained a fine new job and a few months later purchased a laptop for himself. One of his first online actions was to look up his friend's Facebook/Twitter/what-have-you page and add him as a friend. A few days later they started chatting and his friend told him about the prayer groups he had organized on his behalf. While he initially tried to be polite, the discussion grew heated as the typed words flew back and forth.
The argument ended when the Pentacostal removed him from his Facebook page and swore never to have him as a friend again. Turning to his wife, he remarked, "There he is, sitting on the computer he bought thanks to money from his job, using electricity paid for with the proceeds of his job, and Internet that he is paying for with his salary and he has the nerve to question the power of prayer."
Like Aesop's fables, there's a moral to the story.
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"The church at the time of Galileo was much more faithful to reason than Galileo himself, and also took into consideration the ethical and social consequences of Galileo's doctrine. Its verdict against Galileo was rational and just, and revisionism can be legitimized solely for motives of political opportunism." -Paul Feyerabend
"Let me just anticipate that nobody to date has found a demarcation criteria according to which Darwin can be described as scientific, but this is exactly what we are looking for." -Imre Lakatos
XaosPeru, please read my sig. I think that you will like it.
As far as the rest of the stuff in the other thread goes, as you said of yourself, I find myself drawn to a degree of nihilism. Do we know anything? How do we know what we think that we know?
Fine questions those, for the start of a discussion. However, if the discussion is to ever progress past a certain point, we need to take some idea that understanding may be obtained, even if only in a contingent form subject to modification later on when new information is uncovered.
I suppose that if you want to hold firmly to nihilism, you could then question the new information as possibly invalid. Fair enough but then why bother looking for it in the first place?
Past that, I also note that a fair number of your arguments on induction refer to work done prior to the development of Bayesian statistics. That work is going to, of some need, be somewhat different from the later body of inductive thought.
As an example, you noted that heliocentric thought was in trouble due to the lack of apparent stellar parallax. Well, not really. You seem to be confused as to dates, names and so on.
Sure, Kepler worked out the equations that finally put heliocentrism on a solid footing. He did so using the (what back then passed for a) mountain of data which had been compiled by his mentor, Tycho Brahe. Tycho's data clearly showed no measurable stellar parallax. Since none was needed for Kepler's work, he ignored the matter for the irrelevant detail that it clearly was.
Past that, there was a good reason for Tycho to be looking for the matter. At the time, the belief that the heavens were unchanging was still widely held. However, in 1572, Tycho observed the supernova now cataloged as SN1572. Well, if the heavens never change, then this had to be in between the Earth and the Moon. Certainly, it should move through the sky with a daily parallax greater than that of the moon. Or not as the data clearly showed.
Now, since you also seem to like relating stories about what the early astronomers were involved with outside of astronomy itself, I would observe that Tycho had a pet elk. By pet, I mean in the same sense that we give cats and dogs the run of the house, the elk had the run of Uraniborg castle. Apparently, the elk was an alcoholic as one night, it drank so much beer that it fell down a flight of stairs to it's death.
What does that have to do with the topic at hand? About as much as some of the other irrelevant details that you have dragged into the other thread.
=
As chance would have it? What was god/s/dess doing? Rolling dice?
The argument ended when the Atheist removed him from his Facebook page and swore never to have him as a friend again. Turning to his wife, he remarked, "There he is, sitting on the computer he bought thanks to money from his job, using electricity paid for with the proceeds of his job, and Internet that he is paying for with his salary and he has the nerve to question chemistry, physics, and the power of induced theories of electromagnetism."
So what did the atheist do? Sit on his butt waiting for god/s/dess to plunk a job in his lap? His work searching the job boards, networking, having his resume reviewed by a professional, preparing carefully for the interview, have nothing to do with finding a job?
As one of the passengers said, it wasn't god who brought that plane down safely on the Hudson River, it was Captain Sully.
-- I feel so much better since I stopped trying to believe.
"We are entitled to our own opinions. We're not entitled to our own facts"- Al Franken
"If death isn't sweet oblivion, I will be severely disappointed" - Ruth M.
Ok, yes, you're right... I tend towards nihilism but a particular form of nihilism and I'm not absolute about it. After all statements like "Truth doesn't exist" are self-falsifying. Similarly claimng that truth cannot be known results in the question: How do you know truth cannot be known? As such nihilists often end up, like Nietzsche, with a "God is dead" kind of attitude, but not like the militant atheists here in a triumphant way as though the problems were solved. On the contrary, it's with a "What do we do now?" air.
Now really the real point of the topic that interests me is the Bayesian part, as that's what drew me here in the first place, but I want to take a moment to nuke your sig, since you brought it up.
Postulate a Christian on this board with a sig that says: So dude, you are sitting on a chair made out of wood, that was grown over a course of years thanks to the sun shining down on us, that grew the way it did thanks to the DNA code in it, along with all the natural elements making up the computer you're using in order to tell me that you don't believe in God?
Now, I think you can easily see the fallacy of the logical process there. The unmentioned assumption is that trees, the sun, and DNA all exist because God created them. Similarly in your sig the unmentioned assumption is that the computer, electricity, and nuclear plant all exist because of science.
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Now as for Bayes, I have been looking into the situation for a long time - and I still am. Recently I discovered this information...
Imagine you want to know who the best teacher is of a group of 30 teachers. You have a procedure that has been shown previously to identify the best teacher from similar groups of teachers with 95% accuracy (both false negatives and false positives have been only 5%). If we use this test to identify the best teacher out of the 30, what is the probability that the person selected really is the best teacher?
The answer is:
(1/30)(0.95)
--------------------------------
(0.95)(1/30) + (29/30)(0.05)
Or basically 39.6%
Less than 50% - 50% chance of being right. And this calculation assumes that all the starting assumptions of the math are 100% accurate.
==============================
I was also surprised to hear the claim that the theory that all cats are black is more likely to be true - calculated Bayesian style - if I find a green apple.
Strangely enough the green apple also makes it more likely that all cats are white.
So finding 1 million green apples might be enough to make it much more likely that all cats are white AND that all cats are black SIMULTANEOUSLY?! Apparently so.
This is the solution to the problem of induction? I think I need a little more explanation before I'm willing to sign on.
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"The church at the time of Galileo was much more faithful to reason than Galileo himself, and also took into consideration the ethical and social consequences of Galileo's doctrine. Its verdict against Galileo was rational and just, and revisionism can be legitimized solely for motives of political opportunism." -Paul Feyerabend
"Let me just anticipate that nobody to date has found a demarcation criteria according to which Darwin can be described as scientific, but this is exactly what we are looking for." -Imre Lakatos
Yes, as CHANCE would have it. Did I stutter? Did I claim that the job was the result of God? No, I did not. I said CHANCE. In NO WAY did I state or imply that God had anything to do with it. So with that in mind, read the story again and maybe you'll understand it.
-----
"The church at the time of Galileo was much more faithful to reason than Galileo himself, and also took into consideration the ethical and social consequences of Galileo's doctrine. Its verdict against Galileo was rational and just, and revisionism can be legitimized solely for motives of political opportunism." -Paul Feyerabend
"Let me just anticipate that nobody to date has found a demarcation criteria according to which Darwin can be described as scientific, but this is exactly what we are looking for." -Imre Lakatos
Wow! You're mathematically illiterate! Congratulations!!!
Oh, wait- congratulations are for good things. My bad.
(If anybody actually needs it explained why this guy is an idiot, let me know)
I've been reading it... I think you're doing a fine job. Me adding to it wouldn't qualitatively add to the discussion because it would only be restating what you've said already.
“Hokey religions and ancient weapons are no match for a good blaster at your side, kid.”
I double-checked and I did copy the math verbatim. Other than personal attacks and ridicule, perhaps you could explain to us where the person who made the example went wrong. I'd be interested in knowing why you think it's wrong.
P.S. I also typed it into an Excel sheet and the number came out as 39.583333 percent so the calculation isn't wrong. Your complaint must be with the underlying assumptions.-----
"The church at the time of Galileo was much more faithful to reason than Galileo himself, and also took into consideration the ethical and social consequences of Galileo's doctrine. Its verdict against Galileo was rational and just, and revisionism can be legitimized solely for motives of political opportunism." -Paul Feyerabend
"Let me just anticipate that nobody to date has found a demarcation criteria according to which Darwin can be described as scientific, but this is exactly what we are looking for." -Imre Lakatos
Looks to me as if he explained his own stupidity for you.
=
I might need an explanation, Blake. This is supposed to be Bayes Theorem? What is he doing?
If the procedure identifies the best teacher from a group with 95% accuracy, then the probability that the person selected is the best teacher is......95%, isn't it?
Why does he solve (0.95)(1/30) + (29/30)(0.05)? This makes no sense.
Where did he get 39.6%? (0.95)(1/30) is 3.2%. (0.95)(1/30) + (29/30)(0.05) is 8%.
Edit: Oh, that's supposed to be a division sign. Okay, that's about 39.6%, but I still don't understand why he did that.
Our revels now are ended. These our actors, | As I foretold you, were all spirits, and | Are melted into air, into thin air; | And, like the baseless fabric of this vision, | The cloud-capped towers, the gorgeous palaces, | The solemn temples, the great globe itself, - Yea, all which it inherit, shall dissolve, | And, like this insubstantial pageant faded, | Leave not a rack behind. We are such stuff | As dreams are made on, and our little life | Is rounded with a sleep. - Shakespeare
Bayes is actually *really* cool.
I found the paper he ripped/plagiarized that from (citation fail). Their example is a little bit strange- that is in the paper itself, they used a rather poor example, but they do explain it (which is probably why he didn't want to link- because then he couldn't take meaningless quotes out of context).
It's not the algebra that's the problem- any idiot with a thumb can work a calculator- that he thought that was the problem and double checked his "math" is funny. It's the set-up and the 'explanation' that's problematic.
As I said, at first the paper itself used a bad example.
Then this guy misappropriated their explanation (less than 50%) in a way similar to that creationists use to "disprove" evolution by misquoting biologists about "gaps" in the fossil records, etc.
He wants to imply that a scientific experiment with 95% accuracy is worse than tossing a coin. It doesn't work like that.
First lets dispense with the bad example by replacing it with something more coherent.
In the case of a best teacher: Not only is "best" some kind of nebulous and undefined property, with access to all participants, only one should come out as the "best", with any other result being inconclusive in the test (that's when we test again).
The chances of a "perfect" correct result are:
.95^30 = 21.5%
That's pretty low indeed, but if you randomly choose a teacher as the "best", you'd have a 1/30 chance of being correct
1/30 = 3.3%
Let's compare again:
The test = 21.5% chance of being right with that sample. Random: 3.3% chance- not 50%
However, there's another difference between the test and a random selection- a VERY important difference. The test gives a 21.5% chance of being right, but if it's not right, it's probably inconclusive (it's not wrong either- you just need to run the test again). The chances of the test being wrong are actually very small:
(.95^28)*(.05^2)= 0.059% (yes, about once in 2,000 times it will be wrong).
The ratio between the two is important, assuming you run the test until you get a conclusive answer.
That ratio (wrong/right: ((.95^28)*(.05^2))/(.95^30) ) gives you 0.28% chance of being wrong before you're right.
Compare this with the chances of the random selection being wrong:
29/30 = 96.67%
Just to put it into perspective, the random test is 350 times more likely to be wrong than the actual test.
Of course, the idea that a 50%-50% coin toss is at all relevant here is just bizarre.
If you used a 50-50% coin toss for each teacher, you'd get more than one "best" out of your test group- it ignores the nature of the experiment, and the additional information that we have-- that is, we *know* that there is only one best.
A better example is the more common disease example. If you have a group of 30, you don't know how many of them have the disease- even if you know it has a prevalence of an average of one in 30 people.
So, that was a bad example of Bayes in that paper. The idiocy of our poster was in selecting that example because he thought it proved his point. However, compounding his idiocy, is that the paper goes on to explain what's actually going on (that it really isn't a coin toss), and this poster completely ignored the extensive explanation which completely contradicts his argument.
His idiocy is carrying on with this "it's all a coin toss" nonsense and finding anything he thinks supports it.
I'll quote the actual paper here to demonstrate.
Here's the paper: http://www.electric-cosmos.org/Bayes.pdf
Scroll down a bit past half way.
(EDIT: spaced some punctuation in the quote above to avoid the weird smiley face)
It goes on to explain quite a bit more in opposition to the poster's bullshit, but I'll leave that.
He's mathematically illiterate because he doesn't understand what the math is saying (and particularly because he chose this very poor example), and instead quote mines from papers he either doesn't read, or chooses not to understand.
He seems to think if the chances are less than 50% then a coin toss has a better chance of being right- which, in itself is again bizarre- and thinks he is supported on this stance when he finds some reference to Bayes.
Well, I can explain that, but I'll do it with a better example.
Lets say there is a disease which causes the person afflicted with it to lose all capacity for reason and become a Christian. This disease has a prevalence of one thirtieth of the population. There is a test for this disease which is 95% accurate (giving a false negative or positive 5% of the time).
What are the chances that somebody has this disease?
Based on pure random chance, without the information from the test, the chances are 3.33%
What are the chances of the person having the disease if the test says he or she does NOT have the disease?
(.95 * (29/30) ) / (( (.05 * (1/30))+(.95 * (29/30) )) = 99.82% ; 100% - 99.82% = 0.18%
This is important: After the information of the test, the chances of having the disease have been statistically reduced. How much?
3.33% - 0.18% = 3.15% ; 3.15% / 3.33% = 95% reduction ; That is, the chances have been *reduced* by about 95%
Instead, lets say somebody flips a coin, and the coin says that he or she doesn't have the disease- now what are the chances the person has it?
(.5 * (29/30) ) / (( (.5 * (1/30))+(.5 * (29/30) )) = 96.67% ; 100%- 96.67% = 3.33%
This is important: After this awesome new information from that super scientific random test, how have the chances changed? Do we have new information? Has it told us something important? Well, lets check!
3.33% - 3.33% = 0% ; 0% / 3.33% = 0% reduction ; Amazing! the chances of having the disease have been changed by... oh, wait. They're exactly the same as they were before the meaningless coin toss.
What are the chances of the person having the disease if the test says the person DOES have the disease?
(.95 * (1/30) ) / (( (.95 * (1/30))+(.05 * (29/30) )) = 39.58% (don't need to subtract from 100% because this is testing for positive)
This is important: After the information of the test, the chances of having the disease have been statistically increased. How much?
39.58% - 3.33% = 36.25%. 36.25% / 3.33% = 10.88, which is 1,088%
More than ten times more likely to have the disease!
Again, instead, lets say somebody flips a coin, and the coin says that the person DOES have the disease- now what are the chances that he or she has it?
(.5 * (29/30) ) / (( (.5 * (1/30))+(.5 * (29/30) )) = 96.67% ; 100%- 96.67% = 3.33%
This is important: After this astounding revelation of 'new information' from that super scientific random test, how have the chances changed? Maybe this time we have new information? Has it told us something important, anything at all? Well, lets check!
3.33% / 3.33% = 100% ; 100% - 100% = 0% ; Amazing! yet again the chances of having the disease have been changed by precisely jack shit. They're exactly the same as they were before the meaningless coin toss because the coin toss tells us nothing.
However, there is one way the coin toss can tell us something:
Lets say we're testing to see if somebody has this disease, and we do a coin toss, and the person actually thinks the coin toss changes the chances of him or her having the disease in the same way an actual test does- the fact that the person is that much of an irrational mathematically illiterate boob increases the chance of him or her having this idiot disease substantially- not from the result of the coin toss, but from the reaction of the subject giving us more information.
I'd say it's nearly a sure thing.
Every legitimate test you do provides more information, and increases or decreases the chances- no matter the circumstances. Every random coin toss you do does precisely nothing, no matter how many times you do it.
That's the difference between science and pseudoscience- that's the difference between objective empirical information and bullshit superstition and this kind of anti-information fideism.
The poster's faith is random- he was born into it, or bumbled into it in his incompetence and randomly accepted it- it is not valid, and has been repeatedly invalidated. Despite the poster's protestations that science, by controlled empirical analysis, is the same as chance, it simply isn't so.
Well Blake, I would nominate the above for post of the month if we had such an award. Whatever.
The thing is that having seen that paper, I suspect that while it may have been the ultimate source for the example, Xaos was probably drawing from some other source that was intermediate. Really, the paper is only six pages of quite tight prose. Really well done compared to what you would see in the average text book or the relevant page on wikipedia. That and the subtitle is very clear “The application and misapplication of Bayes’ theorem”
How one could extract the bit that they need from that work and yet miss so much that is really obvious? It seems more likely that he found another bit of work that contained that material but which was itself a snow job. Then because he does not really understand the material, he did not trip his personal BS alarm.
I could well be wrong here. I have been in the past and I will be in the future. Even so, I get the impression that Xaos want's to understand the matter at hand but he is just barking up the wrong tree.
That much being said, what tripped my BS alarm was the idea of getting a 95% confidence level from a sample of 30 people. The fact is that I did not even bother to work the equation. Either it was right or it was wrong (we now know it to be right but misapplied). Whichever, we really would still know pretty much nothing.
Had whatever the hidden assessment tool been used at a hundred schools previously and each report filed individually with no larger analysis, then the method might as well have been consulting goat entrails. A confidence level of 95% would amount to a naked assertion.
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Response composed off-line.
As I'm sure you're aware I asked for an example of Bayes theory several times without success. Accordingly, if you feel that the one I stumbled upon is a bad one, then you really have no one to blame but yourself for failing to provide a better one.
I assumed, as I think most people do, that a method that has a 95% confidence interval works 95 percent of the time. I don't mind telling you that I was pretty shocked at the idea that a 95% test comes up with a 39.58% chance of being right. Certainly I was never taught anything like that in my science courses at school.
So thanks for confirming the math for me, and for explaining it a little, but shame on you for being an a-hole about it.
Now I want to address my real concern. The starting point of this mathematical equation states that we have a test that "has been previously shown to identify the best teacher from a similar sized group with 95% accuracy." Now that's when my BS detector went off. For the sake of simplicity I'm going to assume that the test was run at 20 schools and screwed up once giving the supposed 95% confidence level. My real question is: How can we know whether the person identified as the "best" teacher really is the best? As far as I can imagine the only way that this can be done is that some undisclosed test "X" exists that can identify the best teacher with 100% accuracy (against which the new test will be checked). This leads me to ask two questions: 1) If such a test exists, then why in the world are we screwing around with the new test that's only 95 percent? Secondly, I wonder how we can know that test "X" really is 100% accurate? This leads me to believe that it was compared against test "W" and that test "W" that was confirmed 100% by test "V" which was in turn verified by test "U", which was verified by "T", etc., with an infinite regress problem.
After some further thought I realized that it might be possible that it was a rabies test we were talking about and that the test which is believed to be 100% is to destroy the animal and perform a necropsy. While I might see the validity of the 95% test under these circumstances, I imagine that in the world of physics this example is the exception, not the rule. After all, we cannot determine the "true" speed of light by killing a photon and performing a necropsy.
I look forward to receiving your response.
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"The church at the time of Galileo was much more faithful to reason than Galileo himself, and also took into consideration the ethical and social consequences of Galileo's doctrine. Its verdict against Galileo was rational and just, and revisionism can be legitimized solely for motives of political opportunism." -Paul Feyerabend
"Let me just anticipate that nobody to date has found a demarcation criteria according to which Darwin can be described as scientific, but this is exactly what we are looking for." -Imre Lakatos
Thanks Blake.
Ah, so we have a 95% probability of correctly identifying whether any individual is the 'best' teacher. Then, the probability of correctly identifying 30 individuals is .95^30.
XaosPeru confused me by writing, "You have a procedure that has been shown previously to identify the best teacher from similar groups of teachers with 95% accuracy," implying that the probability of identifying the best teacher from a group of 30 people is 95%.
Right.
Okay, so if the test identifies more than one individual as the best teacher, the test is inconclusive. It's wrong when it identifies only one teacher as the best teacher that is not actually the best teacher?
I'm not sure I understand this equation. *I'm noob*
How does this equation get you the probability of being wrong?
This is the probability of correctly identifying 28 people and incorrectly identifying 2 people?
Our revels now are ended. These our actors, | As I foretold you, were all spirits, and | Are melted into air, into thin air; | And, like the baseless fabric of this vision, | The cloud-capped towers, the gorgeous palaces, | The solemn temples, the great globe itself, - Yea, all which it inherit, shall dissolve, | And, like this insubstantial pageant faded, | Leave not a rack behind. We are such stuff | As dreams are made on, and our little life | Is rounded with a sleep. - Shakespeare
edit: deleted - wrong post got posted
The rest of your post is irrelevant as you don't understand what a confidence interval is.
Let's say you are collecting data. It doesn't matter what your data is or why you are collecting it. What does matter is how you analyze the type of data you are collecting and how much you collect. There are different methods of computing a confidence interval depending on the type of data and how your data is analyzed. In my textbook (that I have moved around with me for 20 years now), Statistics for Experimenters by Box, Hunter and Hunter, copyright 1978, chapter 5 covers confidence intervals.
Emphasis is the author's.
*The effect is in the context of making an experiment. If we give patients drug y will it improve condition x. Can we make a reduction in average time to manufacture widgets by changing <number of people (labor)>, <number of machines>, <type of machines>, <type or source of materials> and so on. If we give teachers a test, does the test tell us which teacher has or will have the highest success rate <in graduation rate>, <in student test scores>, <in continuing education rate> and therefore is the "best" of a group?
Briefly, what a confidence interval is telling you is that x% of the time, when you gather y amount of data, you will get an answer that is statistically the same as z. A 95% confidence interval is the goal of every experimenter and so a lot of people throw that percentage around without understanding what they are claiming. We would all like to be 95% confident that the answer is <this particular teacher is best>, <this much time to produce widgets on average>, <this test result is accurate>. What is left over from 100% is your expected error rate. 5% of the time, we will pick the wrong teacher, take way too long to produce a functioning widget, or we thought your test was positive but you really don't have the disease.
So, one of the problems with your example, is that the statement "the test predicts the "best" teacher with a confidence interval of 95%" is truncated. What would make better sense (to a person with some statistics knowledge) is "the test predicts the "best" teacher 100% of the time with a 95% confidence interval". That is, 95% of the time, the test will select the "best" teacher with absolute certainty and 5% of the time the results will not be certain. You may have other just as valid numbers - 75% of the time the test predicts the "best" teacher with 80% confidence interval. That makes just as much sense but it means the test is less accurate.
Of course, there is no such test, and people continue to argue over what constitutes "best teacher" let alone how to determine who is that person.
A side note on statistically significant: this means that your experimental results are not due to pure chance, but are due to some other factor. It does not mean a causes b. It means the two events or situations or objects occur at the same time in the same place more often than random chance would indicate.
I have not participated in the conversation previously as I know I am not an expert on statistics, probabilities or any related subjects. My professor insisted we knew just enough statistics after one college level course to make us dangerous but not expert. Unfortunately, with the increased use of computer software that does the statistics for you, too many people are using it incorrectly. But confidence intervals are something I feel comfortable discussing.
-- I feel so much better since I stopped trying to believe.
"We are entitled to our own opinions. We're not entitled to our own facts"- Al Franken
"If death isn't sweet oblivion, I will be severely disappointed" - Ruth M.
Thanks Answers (and cj), also good reasons why the teacher thing was a bad example. I had to do some guess work as to what they were trying to say based on the disease bit.
Right, that's why the setup is really weird- the way they treated it, that's what they were saying, but that's not what they said. Saying it will be 95% accurate with a group like this is just... well, wrong (like what cj said, it doesn't make much sense). That's from the original paper that the poster plagiarized, though- it's not exactly his mistake, but his failure to understand it and choice to quote mine it was.
You're right, it doesn't make much sense in the context of the problem. It was a bad example to use; it took me a good while to sort out what it was on about. If I didn't find the original article he plagiarized, I probably wouldn't have been able to figure out what it was saying out of context like that.
Exactly, and that's what this equation (partially) does:
28 were identified correctly as not the best teacher, one was identified incorrectly as not the best teacher (false negative), and one was identified incorrectly as the best teacher (false positive). That is, two false results, and 28 true ones exactly.
Actually, though, that's a far larger number than it would be- because there are more than one way to have two wrong results.
You have to divide that number by the solution to the "handshake problem"- how many possible ways are there for it to be wrong about two of them? Most are inconclusive (with three positive results).
There are 29 ways for it to be wrong with a conclusive false result (the actual best teacher has to be wrong, but any one of the other 29 could be wrong)
Totally, though, there are ( 30 * 29 / 2 = 435), so only 29 out of 435 of these cases (two incorrect) are actually falsely conclusive.
(.95^28)*(.05^2)*(29/(30*29/2)) = 0.00396378142%
I did this originally when I did some of the math the prior day, but failed to repeat it in the post (oops).
So yeah, in my post it was an estimate (that equation gets you in the ball park), but I was off by a bit more than a factor of ten (meaning the wrong results are more rare than I suggested)- I wrote my post too quickly and forgot that important bit of information. Sorry about that, if it caused any confusion.
At last, though, it's even more staggeringly accurate than I posted. So, only one in about 25,000 tests will be conclusively wrong.
So, that ratio (wrong/right: ((.95^28)*(.05^2)*(29/(30*29/2)))/(.95^30) ) actually gives you 0.0184672207% chance of being wrong before you're right.
Comparing this with the chances of the random selection being wrong:
29/30 = 96.67%
96.67% / 0.018% = 5,235
So yeah, the random test is actually 5,235 more times more likely to be wrong, and not a mere 350 times more likely wrong. Thanks for pointing that out.
P.S.
I think the mathematically illiterate theist made a post somewhere above in response to my post (I saw he quoted me anyway- maybe he thinks I was talking to him?). I did not read it. If anybody read it and he said anything worth replying to (very unlikely), please just let me know and I'll respond to it.
OK, first, I am breaking your wall of text down a bit to make it easier to read. If I am breaking it in places that you would not, well, the breaks are where they seem to make sense to me. Let me take the fake paragraphs in order.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
First, you really are not helping matters to get abrasive and call people assholes. But let's pretend that that never happened and deal with your real question here.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
OK, that sounds like an honest mistake. I would agree that most people do not understand this stuff and just make assumptions which may turn out to be wrong.
That much being said, the issue at hand is largely the sample size. When you try to do statistics and probabilities on a very small population, the results will be all over the place. In this case, the issue is that the calculation involve the rather small fraction of 1/30. So that will distort the results fairly badly.
Sure, the calculation is valid but the result really doesn't tell you much of any usefulness.
In all honesty, I suspect that the example provided may have been constructed specifically to show how a serious error can be made without even trying.
Well, in all truth, even twenty schools of similar size is on the small side of getting this right. That is going to be about 600 teachers in total. Even then, if the reports on each school are filed individually, the calculations will still be subject to the distortion of there only being about 30 teachers in the sample population.
In order to get to the heart of the matter, one really ought to test a few thousand teachers and take the aggregate results to check if there is a pattern in a much larger population. In fact, if it were possible, it would be desirable to test a hundred thousand teachers.
OK, that is a great question. The fact is that there really can't be a test that is 100% certain. To get there, you would have to test an infinite number of teachers. On the other hand, if you were to test a hundred thousand teachers AND (pay attention because this a very big “and&rdquo
your testing method is actually valid, then you might eventually get to, say, 99.9% confidence.
Take that level as the gold standard for this work. Now we have something that we can work with. However, testing that many teachers is complicated and expensive. That and it is only valid for the gigantic population. The tiny population of a mere 30 teachers is still going to be subject to the effect of the small sample.
OK, as noted above, an astoundingly accurate test requires a huge and very expensive effort. That and the small sample size is going to be an issue.
Let's look at a different but related question.
Say you have two six sided dice. There is actually a standard table for showing the probable outcomes. For brevity, I will not go into detail on this.
As it happens, there are six ways to roll a 7 but only one way to roll a double 1. Now, if you roll the dice thousands of times and record the results in a spreadsheet, you will see the expected statistical distribution. However, if you roll the dice 30 times, then there is basically no way that you will see the same distribution. Heck, there are 36 possible outcomes and if you roll them only 30 times, you can't help but miss some of the possible outcomes.
OK, I have no clue where that one is coming from. We have many ways of measuring the speed of light. I could go into great length on a good number of these but that would have no bearing on bayes theorem.
Perhaps you should start a new thread for that one and we can explain that to you separately?
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It is doubtful that you, BobSpence1 (or anyone else for that matter), would find my opinion any more enlightening or interesting than usual: it looks like a bunch of inane jibberish about the doctrines of logic.
As usual, I have little interest in such subject matter as I consider it little more than "reinventing the wheel", but even at that... it's almost impossible to determine what specifically you and Xaos are debating.
Todangst's OP isn't much help either, with all the latin loanwords used. It would have helped had he dumbed the post down to 'somewhat common English' for us meager plebs.
ugh, note to self: next time, use quote button
“A meritocratic society is one in which inequalities of wealth and social position solely reflect the unequal distribution of merit or skills amongst human beings, or are based upon factors beyond human control, for example luck or chance. Such a society is socially just because individuals are judged not by their gender, the colour of their skin or their religion, but according to their talents and willingness to work, or on what Martin Luther King called 'the content of their character'. By extension, social equality is unjust because it treats unequal individuals equally.” "Political Ideologies" by Andrew Heywood (2003)
Well, I think that I may have post ninja'd you because I just filed a response to that.
On a side note: Do I remember correctly that you are doing some research on gravitation on the cosmological scale?
On a seconds side note: Last Friday, I got two new ultra wide field 2 inch eyepieces for my 120mm refractor. The only thing that was worth looking at that night was the moon (which was a few hours from full at the time). The leading edge of the terminator was way cool. Also, I saw stuff that I only remember from NASA photos from the early 70's.
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Oooohhh, right.
In order to get a conclusive wrong answer, we need one false positive and the only possible false negative.
But, multiplying by just (.05^2) includes all possible combinations of two incorrect results; it includes all of the two false positives. Those are inconclusive, not wrong, so we need to multiply this by the fraction of two false results that is actually the one false negative and one false positive. That's 1/15.
Our revels now are ended. These our actors, | As I foretold you, were all spirits, and | Are melted into air, into thin air; | And, like the baseless fabric of this vision, | The cloud-capped towers, the gorgeous palaces, | The solemn temples, the great globe itself, - Yea, all which it inherit, shall dissolve, | And, like this insubstantial pageant faded, | Leave not a rack behind. We are such stuff | As dreams are made on, and our little life | Is rounded with a sleep. - Shakespeare
Sort of, but I don't have the proper equipment to do the necessary tests, so I was, but I can't proceed until such a time as I come into the situation where I can actually test.
I need some very accurate and precise clocks and gravitometers.
Gravitometers are no problem- I could easily buy a material one (hundreds of dollars or less), or construct one using lasers to measure the local vertical time dilation gradient off the top of a building or something.
Clocks are a pretty big problem, though.
Based on my rough calculations, the magnitude of time dilation difference in my predictions from Einstein's predictions is extremely small, but just within the significant precision of cutting edge atomic clocks- stuff out of research laboratories.
Instead of a clock, I could possibly make my own super-accurate time measuring device using a couple extremely large and radioactive radiation sources for a statistical equivalent to a clock... though the precision would be pretty questionable, and that brings in a number of other variables.
...Or an obscenely powerful laser and a satellite to receive the pulses. I don't have either of those, though.
If I could get a hold of an uninterrupted fiberoptic line that was long enough, I might be able to pulse a laser through it and analyze the frequency at the other end (conquering the curvature of the Earth and getting more distance).
All of those seem more unlikely than getting use of a clock, though.
In other words, I did enough research to find out that it's possible to test, but far too expensive for me to do so right now.
My options are:
1. Find and enroll in a university that has access to clocks like these or meet somebody who has the connections to make it happen
2. Become obscenely wealthy and buy/build some clocks and/or super laser and satellite
3. Collect underwear -> ??? -> Profit! -> Atomic clocks.
4. Give up until they are cheaper and more prevalent, or some research lab somewhere notices the consistent anomaly and figures it out before I have a chance to test it.
Or think of another, cheaper way to test it. Gravitational lensing of light is popular- I could do a meta-analysis of NASA's studies of refraction from "dark matter" to demonstrate it consistent with my theory. I'd need to do quite a bit of software development to accomplish that, though. I don't know if I have patience for that much data analysis.
Anybody like to program tedious data analysis software and want to help me solve gravity? Hah...
I think it's left to #1 or #4 for me.
OK, that was actually a bit more than I was hoping for. Simply confirming that you are actually doing science was what I was after. The fact is that when an actual scientist tells me that I am on the right track gives me that warm fuzzy feeling.
Past that, I get the impression that what you are after will refine general relativity. Well if I had been having a similar discussion a century ago with some guy from Germany that nobody had ever heard of, I would probably go along the lines of: “So you want to refine Newton and Maxwell? Perhaps you should get a job in some government office where you will have the free time to think about stuff. I hope that works out for you.”.
Well, history shows that that did. Today, I have a cell phone where the time is accurate to astounding levels because it uses the GPS time base. The Rolex company can eat it.
Seriously though, I would suggest that you go for option #1. I assume that you know that much already but yah, for those who might not:
Go to school. Most nations that have an economy of reasonable size have programs in place to make sure that anyone who wants to can have an education for free or as close as possible to free. They mostly don't worry about the cost up front because they know that having educated people is a good thing.
Let me use Texas A&M as the example here. The original plan was to make sure that farmers could grow more crops and that there would be railroads to move the crops. Today, it is a huge and well respected university that does a whole lot of stuff.
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To (perhaps) demonstrate the importance of sample size in a real world situation, I will relate an example that truly happened to me. I even submitted it to Scott Adams, and he used it in a Dilbert cartoon.
I started work for a company that was part of a very large international company, but had just become a subsidiary of another company. They were a manufacturing facility for the large international company and all of a sudden they became totally independent as a separate entity of the new company. That means they had to make up or reuse policies and procedures. Since the management of this manufacturing facility now a manufacturing company did not change, they mostly chose to continue with the old policies and procedures. What could be wrong with that?
One of the policies of the original international company was that for any job description, all employee performance evaluations had to add up to a normal ( "bell" ) curve. Employees had written portions of their evaluations, but were given an over all grade - 1, 2, 3a, 3b, 3c, 4, 5. With 1 being fantastic and 5 being 1/2 step from being fired. If you plotted all of the numbers given to all the employees, it was supposed to look like this for each different job description:
edit: hit the post button too soon
Image is from http://en.wikipedia.org/wiki/Normal_distribution
The middle where the graph is highest should be all the employees who made a 3a, 3b, or 3c on their evaluations.
But, the new company, as a stand alone, did not have tens of thousands of employees, it had about 300. There were 6 people in the computer department, and I was one of those. Our 6 employees were required to form a normal curve with only 6 data points. Guess what, we got one 3a, one 3c and every one else got a 3b. Did not matter how good or bad we all were, we had to fit that stupid curve with only six people.
-- I feel so much better since I stopped trying to believe.
"We are entitled to our own opinions. We're not entitled to our own facts"- Al Franken
"If death isn't sweet oblivion, I will be severely disappointed" - Ruth M.
It more redefines the causality relationships between gravity and time- comparing the change from Newtonian to Relativity isn't off bat; it completes gravity as an emergent effect from known quantum phenomena, allows for modeling the early moments of the big bang and explains dark matter and the behavior of condensates.
The problem is that the effect is almost identical in measuring and for practical applications and... well... it's a lot of work that I don't stand to gain much from- even if I manage to prove it before anybody else does (it tends to be the case, in science, that you're in a race without even knowing it).
The biggest thing I have to gain is satisfying my own curiosity, which, once I figured it out, has been pretty much satisfied. I'd be genuinely surprised if I were wrong (I could be).
If this were profitable, I'd be all over it, but considering how many revolutionary scientists barely get along by teaching, well... even if I won that race, unless I won the nobel prize, I would be very lucky to break even (and perhaps even if I won the prize I might not break even). This is not so much a road to wealth as one to poverty, particularly if I come in second place- which is almost completely worthless- I can't spend much valuable time or money on it.
I went ahead and wrote out most of my theory and filed a copyright (so it would be on record), so if somebody else does figure out the same thing (and there are a few people who are on the same track, but none that I've seen who are quite there- it might be a few more months or years), I can point at it and say "See, I knew that already"- good parlor trick anyway. It's the equivalent of notes on a cocktail napkin as far as the writing goes (probably spelling errors and all), but it got my mind off of it.
If I could find a commercial application for the difference- perhaps use the theory to develop a functional model for quantum computation- then I could get the funding to really make it happen, and make some serious cash from patents. As it stands, I just have the foundations- and while I know some of the basics of quantum computation, I'm not sure I could really do that on my own, even just on paper (which is the only way I'd have a good enough head-start on it to get funding for the patent race)- that would be quite a bit of work, if it's even possible.
So, really, I'm leaning towards the "give up and wait" option. In the mean time, I do what I do.
Yeah, that threw me for a loop. I was Googling to see the cost of atomic clocks and research the accuracy. I thought "WOW, these are surprisingly cheap!" then "Oh, shit, these are just remotely updating. Useless." -- that is, because I need to measure local time dilation, not the dilation wherever these clocks are, and I need corresponding gravitometric readings.
Actual clocks, at even close to the accuracy and precision I need, are absurdly expensive.
I'll see if I can visit a university in Mexico City while I'm there and ask around- maybe I can find some faculty who would be interested. I've had half a mind to do that in Shanghai, and I might when I get back, but I don't want to spend any money enrolling in one- crazy expensive for out-of-state/country tuition.
As a matter of policy, I can't justify spending so much money on something that can't return.
I could probably enroll and get in state tuition in California, though. They have a law that gives illegal aliens in-state tuition if they have resided in state for the accepted time, despite mandate that any alien can not receive a tuition benefit that a national is denied (I'm a US citizen). They don't let people from other states have in-state tuition because they argue that nationals have the ability to get in-state tuition in their own states, but I've been largely out of the country for years so am not eligible for residency in any state, so they'd either have to give me in-state tuition, or they'd have to strike down the law granting alien residents in-state tuition (that is, if they denied me, I could sue for it).
I might consider that if it's seriously cheap.
Here's hoping you all had a great Thanksgiving. I didn't respond right away because I wanted to take some time to seriously think about it.
Since we've been using the "best teacher" example and although everyone seems to agree that it's not a very good one, I've decided to continue with it since (other than the virus making you Christian example) there are no others.
So the first thing we need to decide is: How can we determine who the best teacher is? I've decided that for this hypothetical example it should simply be the result of student satisfaction surveys. The goal of the test is to determine which teacher will get the highest average score on the student surveys.
So now we want to design a test that we think will predict that. In my example, I am postulating that the teachers are all English teachers living in Latin America (because that's something I know a bit about). I am also postulating that they're all not native.
So we will start by putting in factors about their education. If they have a bachelor's degree in education, or English, they get some points. If they have international certifications like FCE, CAE, etc., that gives them points. As for teaching methodology, certificates like CELTA, DELTA, or TKT get them points. Points could also be awarded for their on-the-job performance (punctuality, lesson preparedness, etc.) and then on-going education. They would be awarded points for attending workshops during the past 6 months and perhaps the schools offer a "tourist outreach programme" in which they contact English-speaking tourists in order to get continuous exposure to real English in real situations.
So now with this situation in mind, we postulate that the scores have been applied to 100 schools in Latin America (each with 30 teachers) and that they successfully predicted the best teacher 95 percent of the time - that is, that the people who scored highest on the predictive test also got the highest mean score on the student satisfaction surveys.
So now I don't see how such a test can be "inconclusive." Either the person who scored highest on the predictive test got the highest score on the surveys, or they didn't. In the event of a tie on the predictive test, I would expect that the student surveys would also be a tie (or close enough that the difference isn't statistically significant). How could such a test be inconclusive?
Secondly, it was suggested that the test could be run again. How would that work? The teacher's basic underlying data won't have changed. They'll still have the same bachelor's degree, still have attended the same workshops over the last 6 months, etc. The test results would be the same.
It's entirely possible that some portion of the test has a flaw that is difficult to fix. For example, some teachers may not participate in the tourist outreach programme - for example, maybe the teacher is married to an Australian and figures there's no reason for her to waste her weekends talking to people in English when she does it every night at home. Or maybe one of the teachers is looking to marry a gringo to move to the USA or UK and so spends all her weekends in touristy bars chatting up white guys and trying to sleep her way into a fiancée visa. Or maybe one of the teachers is so cash strapped that she works at nights doing telemarketing or inbound customer service and so doesn't need more contact with English to maintain/improve her level.
In conclusion, I generally deny that:
Most or all tests can have an inconclusive result.
That this inconclusive result can be eliminated by redoing the test.
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"The church at the time of Galileo was much more faithful to reason than Galileo himself, and also took into consideration the ethical and social consequences of Galileo's doctrine. Its verdict against Galileo was rational and just, and revisionism can be legitimized solely for motives of political opportunism." -Paul Feyerabend
"Let me just anticipate that nobody to date has found a demarcation criteria according to which Darwin can be described as scientific, but this is exactly what we are looking for." -Imre Lakatos
Okay. This is a reasonable start.
My sister-in-law teaches in the public schools in the north west US. They have a similar system of evaluating teachers for promotions using education and certifications. Though they don't compare with student surveys. I've only found student surveys at the university level or with private schools like the IT specialty certifications. At university, the surveys are intended for the professor/instructor's personal information. As university professors are promoted and retained based on research accomplishments, not on how well they teach. Combining the two may be done at private institutions, I wouldn't know about that.
Okay, when you do a test like this, you want to know which parts of your test are significant. That is, is it educational level that best predicts receiving good student survey scores? Or one of the other factors. You repeat the test comparison the next term/quarter/semester/year/session. That is, with a new batch of students, you give the surveys and see if factor A is still a good predictor of good survey scores.
Maybe you can adjust the criteria in the test portion - interaction with native English speakers not just in a particular program but maybe number of hours a week speaking with anyone. This would have to rely on self reporting - that is, you would have to ask the teacher and s/he would tell you and you would have to take their word for it. But this is done frequently in life style and health studies. It seems to work well enough. People aren't always totally truthful, but they tend to be the same not truthful. For example, total calorie intake. People generally underestimate the number of calories they eat during a meal. But it is fairly consistent, as people tend to underestimate calories on average the same percentage. So you can allow for that in your test with a little investigation.
Maybe one factor in the test - the requirement for certifications in the IT world drives me nuts. Certifications in IT mean doodly squat. You can pass the test, big deal, can you fix a real system? Maybe it turns out that certifications do have a significant influence on survey scores. Maybe they don't. You look for patterns and you can adjust the test. You continue to repeat student surveys and test criteria until they approach 100% predictive.
You will probably never get 100% predictive, but you continue to examine test results and survey results. You can repeat the survey part every time you run a class. This will gain you more information about the reliability of your test. You can also refine your survey. Do the questions reflect what the students want to tell you? Usually there is an open ended question on surveys - is there anything else you want to say? And you examine this to see if there is another question you should put on the test or if you should rephrase one of the questions. And so on.
100 schools, 30 teachers, for a total of 3000 teachers. How many students on average? The numbers approach being able to have a confidence interval of 95%.
So your results would be expressed as: 95% with a confidence interval of 95%. That is, 95% of the time, your test will predict the teacher with the best survey scores, and you expect this result with a confidence interval of 95%. That means 95% +/- 5%. The +/- (plus or minus) 5% is your uncertainty. Sometimes your test will be 90% accurate, sometimes 100% accurate, sometimes somewhere in between. But most often 95% of the time, your test will predict the teacher with the best surveys.
Perfection is never attainable, but we can always strive and improve.
-- I feel so much better since I stopped trying to believe.
"We are entitled to our own opinions. We're not entitled to our own facts"- Al Franken
"If death isn't sweet oblivion, I will be severely disappointed" - Ruth M.
XaosPeru, your continuing error is in equating 'lack of certainty' to 'totally inconclusive', of 'less that 100% certainty' to 'no knowledge whatever'.
I partly blame philosophers for this, with their dumbass circular definition of 'knowledge' as "justified true belief". For that to be applied, you have to have a way to 'know' whether something is 'true' in the first place....
Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality
"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings." - Sam Harris
The path to Truth lies via careful study of reality, not the dreams of our fallible minds - me
From the sublime to the ridiculous: Science -> Philosophy -> Theology
This last post was almost intelligent, so I'll grace you with a response in hope that you'll realize what you just did there:
That definition itself -- There is your 100% certainty. You have defined "best teacher" by the student surveys, and so by definition, that means of testing (student surveys) IS 100% certain. It doesn't matter what those surveys say- that is the best teacher; they could elect a dog and it would still be fact, because it is ontologically so. The other test, which uses other factors, is 95% compared to that.
Bayes does not apply here, because the sample size was specified for that certainty in the example (similarly sized school). 95% is 95%, simple. If you want 100%, then do the student surveys.
For a better example- such as using cancer tests, those approaching 100% certainty come in the form of a biopsy and extensive sequencing of the genes to identify the cells as cancerous. A simpler cancer test would try to identify the presence of a protein or other chemical that might indicate cancer, or would be a simpler genetic analysis rather than complete sequencing- thus slight imperfection.
You seem to have some serious problems understanding the concept of probabilistic knowledge beyond the notion of a coin toss, which is itself not any probabilistic knowledge. Probabilistic knowledge is that which is beyond pure chance- in excess of chance, even if slight excess; I coin toss is precisely chance. That's why ALL legitimate studies are compared, statistically, to random chance and placebos to ensure that the results are confidently in excess of chance or other non-effects, and generally report regarding what the confidence level there is.
Thank you.
Saint Will: no gyration without funkstification.
fabulae! nil satis firmi video quam ob rem accipere hunc mi expediat metum. - Terence
As I'm sure you know, I still blame Plato. Well, Plato and his minions tilting at phantom windmills.
Saint Will: no gyration without funkstification.
fabulae! nil satis firmi video quam ob rem accipere hunc mi expediat metum. - Terence
I very much agree.
Aristotle wasn't much better. Flies have four legs. Nitwit.
Both of them attacked the ideas of Democritus about 'atoms', which were actually closer to truth than any of their ideas.
Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality
"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings." - Sam Harris
The path to Truth lies via careful study of reality, not the dreams of our fallible minds - me
From the sublime to the ridiculous: Science -> Philosophy -> Theology
That might make yet another point in favour of refined testing. It's all well and good to stand around yammering in your toga, but unless you actually count the legs, how much truth can we actually get from the process?
Saint Will: no gyration without funkstification.
fabulae! nil satis firmi video quam ob rem accipere hunc mi expediat metum. - Terence
Wait, how did that happen? Something smells fishy here. Rarely is somebody that wrong about something one can catch in one's palm and count.
EDIT: A Google search has informed me that he was referring to the mayfly, which he was studying, which walks on four legs (four points of contact) and flies with four wings; two legs are largely unused for locomotion, but in grappling during mating.
He was apparently very wrong about the number of teeth in men and women (having apparently not controlled well in his observations for lost teeth biases between sexes), and -of course- about the brain being a cooling organ (reasonably good guess without any other information, though).
Actually, that sounds like it might explain it. When I first heard it, I too did a bit of Googling, but didn't come across the mayfly thing.
Aristotle actually puzzles me, he seems to be a mix - some stuff he seems to make an effort to actually study empirically, then he comes out with outlandish purely intuitive claims.
I think probably, for whatever reason, his approach to empirically investigation was very sloppy, which he unconsciously covered by intuitive ideas, this leading to his very mixed record on accurate claims.
Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality
"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings." - Sam Harris
The path to Truth lies via careful study of reality, not the dreams of our fallible minds - me
From the sublime to the ridiculous: Science -> Philosophy -> Theology
That is pretty close to my point. Those guys, even Aristotle, didn't take testing seriously enough.
I suspect that they weren't necessarily the smartest guys around at the time, but they either had the best charisma, or PR, or whatever, so they are the ones we remember.
Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality
"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings." - Sam Harris
The path to Truth lies via careful study of reality, not the dreams of our fallible minds - me
From the sublime to the ridiculous: Science -> Philosophy -> Theology
I think he generally made an attempt to study everything he could, but this was well before modern scientific method and statistics. He was biasing his results terribly, and didn't realize it, or have the methodology to prevent it through blind studies or correct it through statistical normalization.