Outside the Laboratory

But when it comes to the actual meat of the religion, prophets and priests follow the ancient human practice of making everything up as they go along. And they make up one rule for women under twelve, another rule for men over thirteen; one rule for the Sabbath and another rule for weekdays; one rule for science and another rule for sorcery...

???

I thought those rules were the outcome of competition between different factions. The factions with the better rules were more likely to win. For example, a century or two ago, part of the Jewish community decided to try ignoring the requirement to not eat shrimp etc. It looks like that isn't working very well. As far as Jews are concerned, God really does hate shrimp.

Joseph, how did they get these "competing rules" in the first place? By making them up as they went along. So, in accordance with human psychology, they make up lots of different rules for different occasions that "feel different". Both sides (or all sides) of any religious battle do this, and it doesn't matter who wins, they still won't come up with a unified answer.

Hmmm...

Q) Why do I believe that special relativity is true? A) Because scientists have told me their standards of evidence, and that the evidence for special relativity meets those standards.

I haven't seen anything contract when moving close to the speed of light. I haven't measured the speed of light in a vacuum and found that it is independent of the non-accelerating motion of the observer. I haven't measured a change in mass during nuclear reactions. I simply hear what people tell me, and decide to believe it.

George Orwell put it far more elegantly, and you can read what he wrote at http://www.newenglishreview.org/blog_direct_link.cfm?blog_id=4274

I can try to apply filters to determine who I can regard as a legitimate authority on various topics. Anyone whose arguments are logically inconsistent is obviously right out. I can check credentials. I can ask people why they accept a claim, and if I disapprove of their standard of evidence, I can give their claims less credence. I can see if the topic is controversial among those whose standards of evidence I respect, and if it is, I can refrain from judgment on the grounds that if there were strong evidence either way, there would be no controversy.

Many things tend to be such that we have to act without anywhere near the amount of evidence that even the social sciences demand. How should I invest my money? What will make me more attractive to potential mates? Who should I vote for? Is (insert enemy here) really a dire threat that my country needs to fight and defeat? What career should I pursue? Which person should I hire? It's really hard to design and perform experiments to answer questions like this. Heck, we still don't even know what kind of food is best to eat!

Yes, academics largely train people to follow various standard procedures as social conventions, instead of getting people to really understand the reasons for those conventions. Apparently it is very hard to teach and test regarding the underlying reasons. That is the fact that really gives me pause.

"Now suppose we discover that a Ph.D. economist buys a lottery ticket every week. We have to ask ourselves: Does this person really understand expected utility, on a gut level?"

Tricky question. It we look purely at the financial return, the odds, then no. If we look at the return in utility, possibly yes.

Is $1 too much to pay for a couple of days of pleasurable dreams about what one would do if one won? Don't we think that such fleeing from reality has some value to the one entering such a fantasy, a suspension of the rules of the real world?

If we don't agree that that has some value then it's going to be terribly difficult to explain why people spend $8 to do to the movies for 90 minutes.

"g = -g" as Voltaire said. Oh, wait, that would put him a bit ahead of his time.

Doesn't Goedel's theorem propose that the set of truths is larger than the set of provable truths? And that the set of falsehoods is larger than the set of provable falsehoods?

If our best logical reasoning concludes there are truths outside the boundaries of rationality, why should we not assign them to the spirit world?

In sum, I agree, but one small issue I take is when you argue that someone acts contrary to their learning it demonstrates that they don't really understand it. I'm sure this is often the case, but sometimes it's a matter of akrasia: the person knows what they should do and why, even deep down inside, yet finds themselves unable to do it.

Humans suffer heavily from their biases. I recall at in middle school I came to the conclusion that no deities existed, yet it took me a long while to act on it because of social pressures, so I continued to behave contrary to my beliefs out of fear. It was only later in life that I gained the self-confidence and bravery to act upon my beliefs, no matter how contrary to the social norm.

You might say that I didn't really understand and that if I did I would have acted differently, but I find this contrary to my own experience, and this is only one such example. The human brain is a mine field, and even when we understand, we may still fail to act correctly.

Tao was described (I wouldn't say invented...) long before Isaac Newton, and yet expresses Feynman's sentiments almost exactly. But then it isn't a religion, either.

Apparently it is very hard to teach and test regarding the underlying reasons.

Does "apparently" (in general) mean you aren't using additional sources of information? In this case, are you concluding that it's difficult simply from the fact that it isn't done? That only seems to me like evidence that it's not worth it. Unfortunately, the value driving the system is getting published, not advancing science.

Douglas, I have found it hard to teach when I have tried, but I'm sure another reason it is rarely done is that academic rewards for it tend to be small relative to the costs.

Tim Worstall, if a PhD economist has pleasurable dreams about winning the lottery, that is exactly what I would call "failing to understand probability on a gut level". Look at the water! A calculated probability of 0.0000001 should diminish the emotional strength of any anticipation, positive or negative, by a factor of ten million. Otherwise you've understood the probability as little symbols on paper but not what it means in real life.

Also, a good economist should be aware that winning the lottery often does not make people happy - though one must take into account that they were the sort of people who bought lottery tickets to begin with.

A calculated probability of 0.0000001 should diminish the emotional strength of any anticipation, positive or negative, by a factor of ten million.

I don't play the lottery, but I sometimes have pleasurable daydreams about what I'd do if I were some great success - found the cure for cancer, proved P=NP, won a Nobel prize... objectively speaking, the probability is extremely low, but it doesn't scale my pleasure down by a million times.

A calculated probability of 0.0000001 should diminish the emotional strength of any anticipation, positive or negative, by a factor of ten million.

And there goes Walter Mitty and Calvin, then. If it is justifiable to enjoy art or sport, why is it not justifiable to enjoy gambling for its own sake?

if the results are significant at the 0.05 confidence level. Now this is not just a ritualized tradition. This is not a point of arbitrary etiquette like using the correct fork for salad.

The use of the 0.05 confidence level is itself a point of arbitrary etiquette. The idea that results close to identical, yet one barely meeting the arbitrary 0.05 confidence level and the other not, can be separated into two categories of "significant" and "not significant" is a ritualized tradition indeed perhaps not understood by many scientists. There are important reasons for having an arbitrary point to mark significance, and of having that custom be the same throughout science (and not chosen by the experimenter). But the actual point is arbitrary etiquette.

The commonality of utensils or traffic signals in a culture is important, even though the specific forms that they take are arbitrary. The exact confidence level used is arbitrary; it's important that there is a standard.

Nor is Bayes's Theorem different from one place to another.

No, but the statistical concept of "confidence" depends on how an experimenter thinks that a study was designed. See for example this discussion of the likelihood principle.

If Alice conducts 12 trials with 3 successes and 9 failures, do we reject the null hypothesis p = .5 versus p < .5 at the 0.05 confidence level? It turns out that the answer depends in the classical frequentist sense on whether Alice decided ahead of time to conduct 12 trials or decided to conduct trials until 3 successes were achieved. What if Alice drops dead after recording the results of the trials but not the setup? Then Bob and Chuck, finding the notebook, may disagree about significance. The "significance" depends on the design of the experiment rather than the results alone, according to classical methods.

How many scientists understand that?

The vast majority of scientist, by your standard, don't really understand science. Humans have certain built-in biases and consistently make certain kinds of bad judgements. Even statisticians and mathematicians make common errors of judgement. The fact is that people are often not rational and are driven by emotion, biases, and other non-rational factors.

While it's useful to study and understand these biases and it's healthy to try to avoid commoon errors of judgement, it's not accurate to declare that anyone who acts irrationally is not truly a scientist or doesn't actually understand science. You are merely observing that they are human.

Probability theory still applies.

Ah, but which probability theory? Bayesian or frequentist? Or the ideas of Fisher?

How do you feel about the likelihood principle? The Behrens-Fisher problem, particularly when the variances are unknown and not assumed to be equal? The test of a sharp (or point) null hypothesis?

It does no good to assume that one's statistics and probability theory are not built on axioms themselves. I have rarely met a probabilist or statistician whose answer about whether he or she believes in the likelihood principle or in the logically contradicted significance tests (or in various solutions of the Behrens-Fisher problem) does not depend on some sort of axiom or idea of what simply "seems right." Of course, there are plenty of scientists who use mutually contradictory statistical tests, depending on what they're doing.

John, I consider myself a 'Bayesian wannabe' and my favorite author thereon is E. T. Jaynes. As such, I follow Jaynes in vehemently denying that the posterior probability following an experiment should depend on "whether Alice decided ahead of time to conduct 12 trials or decided to conduct trials until 3 successes were achieved". See Jaynes's Probability Theory: The Logic of Science.

The 0.05 significance level is not just "arbitrary", it is demonstrably too high - in some fields the actual majority of "statistically significant" results fail to replicate, but the failures to replicate don't get into the prestigious journals, and are not talked about and remembered.

 from random import random

p_success = 0.10

def twelve_trials(p_success = 0.25):
>>>># Runs twelve trials, counts the successes
>>>>success_count = 0
>>>>num_trials = 0
>>>>for i in range(12):
>>>>>>>>if random() < p_success:
>>>>>>>>>>>>success_count += 1
>>>>>>>>num_trials += 1
>>>>return success_count

def trials_until_3(p_success = 0.25):
>>>># Runs trials until it hits three successes, counts the trials
>>>>success_count = 0
>>>>num_trials = 0
>>>>while success_count < 3:
>>>>>>>>if random() < p_success:
>>>>>>>>>>>>success_count += 1
>>>>>>>>num_trials += 1
>>>>return num_trials

for i in range(100):
>>>>num_tests = 10000
>>>>twelve_trials_successes = 0
>>>>for i in range(num_tests):
>>>>>>>># See how often there are at least 3 successes in 12 trials
>>>>>>>>twelve_trials_successes += (twelve_trials(p_success) >= 3)
>>>>
>>>>trials_until_3_successes = 0
>>>>for i in range(num_tests):
>>>>>>>># See how often 3 successes happen in 12 trials or less
>>>>>>>>trials_until_3_successes += (trials_until_3(p_success) <= 12)
>>>>print '{0}\t{1}'.format(twelve_trials_successes, trials_until_3_successes)

I don't follow this. If we meet a scientist who is a Marxist, or a Democrat, or a libertarian, or a Republican, or whatever, we don't point out that there is no empirical proof that any of those political programs would achieve its desired aims, and that no true scientist would hold political beliefs. We accept that political decisions are made on different (some would say weaker) evidence that scientific decisions. More generally, there are many questions that the methods of science can't be used to answer.

I consider myself a 'Bayesian wannabe' and my favorite author thereon is E. T. Jaynes.

Ah, well then I agree with you. However, I'm interested in how you reconcile your philosophical belief as a subjectivist when it comes to probability with the remainder of this post. Of course, as a mathematician, arguments based on the idea of rejecting arbitrary axioms are inherently less impressive than to some other scientists. After all, most of us believe in the Axiom of Choice for some reason like that the proofs needing it are too beautiful and must be true; this is despite the Banach-Tarski paradox and knowing that it is logically independent of the other axioms of Zermelo-Fraenkel set theory.

it is demonstrably too high

Hmm. I lean towards agreeing that it may be too high, but at the same time there would be problems introduced from a lower standard as well. In particular, one such silly problem is that from testing many relationships at the same time, and one then inevitably finding that (from random chance) one is "significant," another thing that many scientists are not aware of, particularly when doing demographic studies. I shudder at the idea of ridiculous demographic data dredging and multiple comparisons being even more widespread.

That said, I, being largely a Bayesian, question the entire concept of null hypotheses. If you are truly "vehemently denying that the posterior probability following an experiment should depend on whether Alice decided ahead of time to conduct 12 trials or decided to conduct trials until 3 successes were achieved," then you must logically reject the entire concept of point hypothesis testing, not merely believe that it's arbitrary or too high, and favor something like Bayes factor.

Of course, it's hard for any of us to be completely consistent in our statistical tests or even understand them all or understand all the completely arbitrary axioms that go into our reasoning.

Sorry, ambiguous wording. 0.05 is too weak, and should be replaced with, say, 0.005. It would be a better scientific investment to do fewer studies with twice as many subjects and have nearly all the reported results be replicable. Unfortunately, this change has to be standardized within a field, because otherwise you're deliberately handicapping yourself in an arms race. This probably deserves its own post.

In my head, I always translate so-called "statistically significant" results into (an often poorly-computed approximation to) a likelihood ratio of 0.05 over the null hypothesis. I believe that experiments should report likelihood ratios.

I am an infinite set atheist - have you ever actually seen an infinite set?

I am a "subjective/objective" Bayesian. If we are ignorant about a phenomenon, this is a fact about our state of mind, not a fact about the phenomenon. Probabilities are in the mind, not in the environment. Nonetheless I follow a correspondence, rather than a coherentist, theory of truth: we are trying to concentrate as much subjective probability mass as possible into (the mental representation that corresponds to) the real state of affairs. See my "The Simple Truth" and "A Technical Explanation of Technical Explanation".

"And there goes Walter Mitty and Calvin, then. If it is justifiable to enjoy art or sport, why is it not justifiable to enjoy gambling for its own sake?"

You don't have to believe (at any level) that there's a higher chance of you winning than there actually is to enjoy gambling. You just have to consider that the "thrill" payoff inherent in the uncertainty itself is high enough to justify the money that will be statistically spent. I think exactly the same argument could be made about sport.

OT: Eliezer, what do you think about null hypotheses? E.g. what's the correct null hypothesis regarding the probability distribution of the size of (cubic) boxes produced by the box factory, where a flat distribution over the length would produce a polynomial distribution over surface area and volume, for instance?

pdf, that gets into the issue of ignorance priors which is a whole bagful o' worms in its own right. I tend to believe that we should choose more fundamental and earlier elements of a causal model. The factory was probably built by someone who had in mind a box of a particular volume, and so that, in the real world, is probably the earliest element of the causal model we should be ignorant about. If the factory poofed into existence as a random collection of machinery that happened to manufacture cubic boxes, it would be appropriate to be ignorant about the side length.

Sorry, ambiguous wording. 0.05 is too weak, and should be replaced with, say, 0.005. It would be a better scientific investment to do fewer studies with twice as many subjects and have nearly all the reported results be replicable. Unfortunately, this change has to be standardized within a field, because otherwise you're deliberately handicapping yourself in an arms race.

Ah, yes, I see. I understand and lean instinctively towards agreeing. Certainly I agree about the standardization problem. I think it's rather difficult to determine what is the best number, though. 0.005 is as equally pulled out of a hat as Fisher's 0.05.

From your "A Technical Explanation of Technical Explanation":

Similarly, I wonder how many betters on horse races realize that you don't win by betting on the horse you think will win the race, but by betting on horses whose payoffs exceed what you think are the odds. But then, statistical thinkers that sophisticated would probably not bet on horse races.

Now I know that you aren't familiar with gambling. The latter is precisely what the professional gamblers do, and some of them do bet on horse races, or sports. Professional gamblers, unlike the amateurs, are sophisticated statistical thinkers. (And horse races are acceptable for sophisticated gamblers because there's only the small vigorish involved, and there's plenty of area for specialized knowledge.)

I think you've made a common statistical fallacy. Perhaps "someone who bets on horse races is probably not a sophisticated statistical thinker." But it does not necessarily follow that "someone who is a sophisticated statistical thinker probably does not bet on horse races." Bayes's Theorem, my man. :)

I know plenty of math Ph.D.s and grad students who do gamble online and look for arbitrage in a variety on ways. Whether they're representative I don't know.

To add to the comment about gambling-- professional gamblers are well aware of the term Dutch book, if not necessarily with arbitrage (though arbitrage is becoming more commonly used).

Heh. Fair enough, John, I suppose that someone has to arbitrage the books. I'll add it to Jane Galt's observation regarding the genuine usefulness of salad forks.

I agree that 0.005 is equally pulled out of a hat. But I also agree on your earlier observation regarding there being some necessity for standardization here.

Personally, I would prefer to standardize "small", "medium", and "large" effect sizes, then report likelihood ratios over the point null hypothesis. A very strong advantage of this approach is that it lets someone do a large study and report a startling likelihood advantage of 1000 for "no effect" over "small effect", rather than just the boring old phrase "not statistically significant". This is probably worth its own post, but I may not get around to writing it.

"Outside the laboratory, scientists are no wiser than anyone else."

My doctor can't program his VCR. My accountant can barely dress himself. My mechanic can't operate a computer. This may seem like a problem to some people, but I recognize that specialization is a good thing. I am not surprised when Nobel winners wear mis-matched socks. The degree of specialization required to excel at that level requires sacrifices in other areas of life. Said another way, a generalist who is equally good at everything will never win a Nobel, or bat .300 in the majors, or release a platinum record.

That's not an excuse for ignoring basic logic outside of laboratory. But I'm not going to ask you, mister scientist, to babysit my kids or do my taxes. I'm going to hire specialists in those fields when I need those services.

I must admit that I did not follow all of the comments about the application of this experiment standard or that mathematical hypothesis of probability. I'm a BA, not a BS, for a reason. I understand that there is a place for the rigors of scientific investigation. I am pleased that you folks know that stuff, and I'm glad that you openly debate when and where it is applicable. But that is not how I want to spend my time.

Do you recognize that you are an animal? You have emotions and drives that are not subject to logical argument. Some people have more logical control than others. You are arguing in favor of total logical control--no emotions, no whims, no taste, no fun for it's own sake, no mistakes.

But a goal of 100% logical control is not desirable. Such a person would be less than a robot. They would have no vices, except unbridled selfishness. But they would have no real virtues either. They would have no compassion that wasn't clearly calculated to benefit themselves. They would be the ultimate free-rider, using all available resources to please only themselves.

Don't tell me that you choose to recycle based upon logical reasons alone. You can't possibly believe that the ecological damage caused by your household waste will generate greater than zero impact on your appreciation of nature throughout your life.

Outside of the laboratory humans live in community. We interact with and effect each other. We don't get to make perfect decisions designed for our own optimal outcomes because there are other people involved. People have needs and wants that just aren't easily quantifiable. The group often has needs that the individual should accept as overriding, for the sake of living in community. And there is no accounting for taste. These things are a large part of what makes us human.

Having said all of that, I'm not going to bother arguing the value of spirituality or the possibility of the existence of God. I may be a touchy-feely-type, but I recognize when I would be wasting my time.

So how do you account for Newton's faith? And--perhaps--Einstein's?

Eliezer,

You're ignoring the logic of evolution. When Feynman looked at the wine glass and saw the whole universe implied therein, he was of course looking through the lens of physics. Further, he was, I think, making two distinct observations.

First, the greater part of what we actually know about the universe is reflected in the behavior of that glass and its content. That is you take all the concise formula of which we so far know then some part of the behavior of the wine glass will show evidence of most of those formula either directly or by artifact.

Second, there are still a great many things about the behavior or the nature of that wine glass that we do not understand. If we understood all the mysteries, extracted all the formula, then a major hunk of the rest of the universe would suddenly become clear.

It's that second point that is at the root of my queaziness about your judgement of others for their irrational beliefs. For the reality is that logic and the scientific method will only take one so far. Most of the world we live in we do not understand. Most of it. Most of the things -- unfactored by even a proper name -- that affect you and me and determine the quality or even the existence of our lives are not understood and certainly show no immediate prospect of becoming comprehensible.

So what do we do with all this vast darkness that figuratively surrounds us on all sides? Naturally we focus on what we do understand: the fire. But the darkness is still there and we have to somehow deal with it.

We deal with it by guessing. Or by believing what we prefer to believe. Or by believing the same things that our parents believed. The virtue in these things is not that they are correct; because they are almost certainly not, but instead that people believing similar things have repeatedly survived. The only logical screening here is the evolutionary one. Some beliefs are fatally wrong. This is not to say that people don't continually rediscover fatally wrong ideas but the tendency is simply because we are the descendents of the survivors to not adopt beliefs that leave no children behind.

Thus you are looking at these irrational beliefs through the wrong lens. They are not really about truth. They are about beliefs that help people to survive.

Why not let scientists believe whatever they want? Why worship the scientist as a perfect unbiased hero dredging against the sins of falseness? Seems too much to ask from a single human. And not very accurate: science is a social institution. It relies on convincing others that not only your interpretation of the data is correct but that your technique for getting the data is kosher and that you aren't outright making things up. There are checks and balances (even if fallible in the short-term) in science - but no scientist is an island of truth. That notion doesn't begin to make sense. There really wasn't much science until people wrote back and forth to each other asking "Can you confirm this?" and "Does this make sense?".

Mentioning Isaac Newton should itself disprove the current post's hypothesis - 90% of his writing was about alchemy and conspiracy theories and other beliefs even his contemporaries didn't bother with. We can only trust his good ideas because the good ideas were confirmed by others. That's the best we can ask scientists to do. Have ideas, throw them on the fire of like-minded folks, see what sticks. Likewise when Dawkins goes off about the psychology of religion - well, it's really opinion that wouldn't get (or hasn't been) published in a peer-reviewed journal. That's how we know not to take it too seriously. But we can still take his work on molecular biology seriously enough.

To expect a scientist to be statistically perfect in any sphere their mind wanders -- politics, religion, relationship with their spouse, child-rearing, literature,music, art -- is to ask them to be very, very quiet.

The point is not that scientists should be perfect in all spheres of human endeavor. But neither should anyone who really understands science, deliberately start believing things without evidence. It's not a moral question, merely a gross and indefensible error of cognition. It's the equivalent of being trained to say that 2 + 2 = 4 on math tests, but when it comes time to add up a pile of candy bars you decide that 2 + 2 ought to equal 5 because you want 5 candy bars. You may do well on math tests, when you apply the rules that have been trained into you, but you don't understand numbers. Similarly, if you deliberately believe without evidence, you don't understand cognition or probability theory. You may understand quarks, or cells, but not science.

Newton may have been a hotshot physicist by the standards of the 17th century, but he wasn't a hotshot rationalist by the standards of this one. (Laplace, on the other hand, was explicitly a probability theorist as well as a physicist, and he was an outstanding rationalist by the standards of that era.)

Yes, there have been many great scientists who believed in utter crap - though fewer of them and weaker belief, as you move toward modern times.

And there have also been many great jugglers who didn't understand gravity, differential equations, or how their cerebellar cortex learned realtime motor skills. The vast majority of historical geniuses had no idea how their own brains worked, however brainy they may have been.

You can make an amazing discovery, and go down in the historical list of great scientists, without ever understanding what makes Science work. Though you couldn't build a scientist, just like you couldn't build a juggler without knowing all that stuff about gravity and differential equations and error correction in realtime motor skills.

I still wouldn't trust the one's opinion about a controversial issue in which they had an emotional stake. I couldn't rely on them to know the difference between evidence versus a wish to believe. If they can compartmentalize their brains for a spirit world, maybe they compartmentalize their brains for scientific controversies too - who knows? If they gave into temptation once, why not again? I'll find someone else to ask for their summary of the issues.

Great example, Eliezer. 2 + 2 = 4. This is one of those rituals that scientists go through every time the analyze data. Do they sit down and prove 2 + 2 = 4? No, they don't. They stand on the shoulders of greater men (to use Newton's phrase I believe), and use their computers to move on. Requiring every working scientist to reexamine every assumption - is well, philosophical (which is fine) and uneconomical (which is less so).

I'm beginning to think that the blogger at hand doesn't understand science. Was there anything we could call science before peer review? Isn't science not only the repeatablility of the experiment but also the validity of its method? How do you know your experiment's method is valid? Isn't the majority of the method based on tried and true techniques learned in school, ie, tradition? Whenever a chemist uses a pipet load a chemical to into a test tube, how does he know it's the correct quantity? Etc, etc.

The criterion is too high. Too many of today's scientists -- personally, I bet, all of them -- would have to pack up their bags and go home if they couldn't hold any unprovable beliefs (as last year's Edge.org essays demonstrated, most people believe something they cannot prove). Certainly we'd have to discard Newton, Einstein, Godel from the pantheon for their metaphysics.

So what if a scientist has the "wrong" mentality towards lotteries? So what if he believes in the "spirit world?"

Why should anyone care what a scientist believes in as long as he comes up with results? When scientists peer-review another, they ask questions like: "did you follow the correct procedure?" or "Did you interpret the data correctly?" They do not ask silly questions like "Do you know what the experimental method is?" and rightly so. Publishing scientists are pragmatic people who care about results more than anything else. It shouldn't matter what a scientists believe in; as long as he gets results and he publishes, then he's a "good scientist." This is the only criteria we should judge scientists by.

If 'spirituality' is a catch-all dumpster for 'a common explanation toward things I cannot show empirically at this very moment,' then the criticism is correct: this is a useless discarding of knowledge.

On the other hand, if you don't start with an assumption of first principles, you have no science at your disposal. Certainly, new knowledge can build upon established knowledge; but what did that knowledge build upon? Sooner or later, we must come up with a blank. No question can be asked, and tested, unless it starts with something to build upon. The scientist who says "I believe God did it; so how is it put together, and what can cause its condition to change?", is hardly incapable of making honest and useful observations about what s/he finds, nor -- at that broad of a level -- is s/he particularly different from the scientist who says "I have no God; so I'll investigate it, and ascribe its origin and operation to a chain of mechanisms that I was not around to observe, and which must ultimately go backwards to infinity."

It is also worth reiterating, as others have noted, that no man on earth has empirically proven everything he believes to be accurate (unless, perhaps, he is of an extraordinarily shallow and uncurious intellect). Time is on no-one's side; sooner or later, you must take someone else's word for it. The moment you are clutching your chest in agony is not the time to go enroll in a medical school's cardiology program, for example. You have a good-faith reason to trust in the surgeon's knowledge. Nor is the surgeon obligated to explain all of his knowledge and proofs to you at that moment, and you won't get past the mortuary by demanding otherwise. You can accept or decline the offered help on the basis of what you do know about your predicament; the wise man simply accepts the help and sets aside all other questions until a better time.

Which could be extended into a very interesting discussion of 'religious' faith, or more correctly who or whom you place your faith in (Jesus Christ? Buhdda? Mohammad? Someone else?), and what that person's credentials are to require it of you. Even better, it would be a discussion that does not plead to the rationality of being willfully ignorant of things that one cannot personally, empirically prove right now. No human really lives that way, nor can anyone do so. Death will come first.

What has not been mentioned yet here is that there is an extraordinary amount of evidence FOR phenomena that Eliezer dismisses as a "spirit world".

Those not willing to examine this evidence are following in the footsteps of Cardinal Bellarmine with his refusal to look through Galileo's telescope. And the refusal is for the same essential reasons: sociology and arrogance.

For those who do not wish to seal themselves off from all evidence that contradicts their assumptions on the nature of reality, I offer the following:

Rupert Sheldrake's research papers, both conventional work published in magazines like Nature and Scientific American, and his more controversial research on telepathy:

http://www.sheldrake.org/Articles&Papers/papers/

Dean Radin's popular book summarizing psi research, Entangled Minds:

http://www.amazon.com/Entangled-Minds-Extrasensory-Experiences-Quantum/dp/1416516778/sr=8-1/qid=1169561660/ref=pd_bbs_sr_1/104-1724254-3375900?ie=UTF8&s=books

The Gift, a collection of anectdotes from the Rhine Research Center files, describing psi phenomena "in the field"

http://www.amazon.com/Gift-Extraordinary-Experiences-Ordinary-People/dp/0312997760/sr=8-1/qid=1169561821/ref=sr_1_1/104-1724254-3375900?ie=UTF8&s=books

That's just a scratch on the surface of the evidence for these kinds of phenomena. . . For those who have not actually read the research on this subject, I invite you to get out of your sociological fishbowl and read something new. There are dozens more peer-reviewed, published papers on psi-type phenomena available online for free, email me if you want links to them.

have you ever actually seen an infinite set?

Wait, are you an finitist or an intuitionist when it comes to the philosophy of mathematics? I don't think I've ever met one before in person?

Clearly you have to deal with infinite sets in order to apply Bayesian probability theory. So do you deal with mathematics as some sort of dualism where infinite sets are allowed so long as you aren't referring to the real world, or do you use them as a sort of accounting fiction but always assume that you're really dealing with limits of finite things but it makes the math and concepts easier?

Do you believe in the Axiom of Choice? Would the Banach-Tarski paradox make you less likely to?

Does the two envelopes problem make you less likely to believe the Bayesian theory of probability?

Can you justify your acceptance of the Bayesian theory of probability or the other mathematical axioms to which you hold through pure evidence?

Does it bother you that (as shown by Godel) no theory which contains elementary arithmetic (addition and multiplication of the natural numbers) can be both consistent and complete, and that no theory that contains elementary arithmetic and the concepts of formal provability can include a statement about its own consistency without being inconsistent? Does this evidence cause you to reject elementary arithmetic, based on the importance of consistency, rational logic, and the need for all true statements to be proved?

Are you also an empiricist in mathematics, akin to Quine and Putnam?

Sorry, posted too soon. I'm a little confused because you said that you rejected coherentist views of truth, but most mathematical empiricists these days use the idea of coherence to justify mathematics. (Mathematics is necessary for these scientific theories; these theories must be taken as a whole; therefore there is reason to accept mathematics, to grossly simplify.)

Q) Why do I believe that special relativity is true? A) Because scientists have told me their standards of evidence, and that the evidence for special relativity meets those standards.

I also know that GPS satellites work with high precision, and that they wouldn't if they didn't correct for relativity.

GPS? You can do better than that! I believe special relativity because it's implied by Maxwell's equations, which I have experienced. Normal human speeds are enough to detect contraction, if you do it by comparing E&M.

John Thacker:

I consider myself a finitist, but not an ultrafinitist; I believe in the existence of numbers expressed using Conway chained arrow notation. I am also willing to reject finitism iff a physical theory is constructed which requires me to believe in infinite quantities. I tentatively believe in real numbers and differential equations because physics requires (though I also hold out hope that e.g. holographic physics or some other discrete view may enable me to go digital again). However, I don't believe that the real numbers in physics are really made of Dedekind cuts, or any other sort of infinite set. I am willing to relinquish my skepticism if a high-energy supercollider breaks open a real number and we find an infinite number of rational numbers bopping around inside it.

I consider the Axiom of Choice to be a work of literary fiction, like "Lord of the Rings".

Bayesian probability theory works quite well on finite sets. Real-world problems are finite. Why should I need to accept infinity to use Bayes on real-world problems?

The two-envelopes problem shows the necessity of having a finite prior.

Godel's Completeness theorem shows that any first-order statement true in all models of a set of first-order axioms is provable from those axioms. Thus, the failure of Peano Arithmetic to prove itself consistent is because there are many "supernatural" models of PA in which PA itself is not consistent; that is, there exist supernatural numbers corresponding to proofs of P&~P. PA shouldn't prove itself consistent because that assertion does not in fact follow from the axioms of PA. (This view was suggested to me by Steve Omohundro.) Now, I don't believe in these supernatural numbers, but PA hasn't been given enough information to rule them out, and so it is behaving properly in refusing to assert its own consistency.

I have no desperate psychological need for absolute certainty or proof, which, even if PA proved itself sound, I couldn't have in any case, because I would have to believe in PA's soundness before I trusted its proof of soundness. Or maybe I'm in the grips of a Cartesian demon playing with my mathematical abilities.

Correspondence, not coherence, very easily justifies mathematics. Math can make successful predictions, ergo, it's probably true. No one has ever seen an infinite set, ergo, they probably don't exist, and at any rate I have no reason to believe in them.

Eliezer wrote: "Godel's Completeness theorem shows that any first-order statement true in all models of a set of first-order axioms is provable from those axioms. Thus, the failure of Peano Arithmetic to prove itself consistent is because there are many "supernatural" models of PA in which PA itself is not consistent; that is, there exist supernatural numbers corresponding to proofs of P&~P."

This is getting far from the topic but... I really don't see how Completeness entails anything about PA's failure to prove itself consistent (much less how it suggests an explanation in terms of "supernatural models", whatever that is supposed to mean). PA is not expressible as a first-order statement, so Completeness has nothing to say about PA or its limitations.

"PA is not expressible as a first-order statement." Countable sets of first-order statements still count. But, yes, this is getting rather far off-topic.

http://en.wikipedia.org/wiki/G%C3%B6del%27s_completeness_theorem

"Those not willing to examine this evidence are following in the footsteps of Cardinal Bellarmine with his refusal to look through Galileo's telescope. And the refusal is for the same essential reasons: sociology and arrogance."

From the Crackpot Index: "40 points for comparing yourself to Galileo, suggesting that a modern-day Inquisition is hard at work on your case, and so on."

Anyway, based on what I've read, Sheldrake's experiments do return statistically significant results, but there tend to be problems with the experiments themselves that suggest the results are not caused by anything currently unknown to physics. For more details, just check out www.randi.org and search for Sheldrake's name.

Alot of these comments are getting pretty far off topic. Why not create new posts on these interesting topics?

From the Crackpot Index: "40 points for comparing yourself to Galileo, suggesting that a modern-day Inquisition is hard at work on your case, and so on."

Are you seeking truth, or seeking to confirm your current beliefs? Do you deny that the mainstream of the scientific establishment has sociological parameters and taboos, and that these are extremely hostile to the possibility of telepathy and related topics? In that case, you might find this essay by the editor of the Journal of Consciousness Studies, of interest (JCS is a mainstream journal a mainstream journal that publishes material from scholars like Daniel Dennett, in addition to a recent issue discussing some of Sheldrake's research):

http://www.imprint.co.uk/Editorial12_6.pdf

Rather than reading apologia from self-proclaimed guardians like Randi (who is not a scientist, but rather a successful entertainer and propagandist for an official version of truth, the very idea of which is anathema to science), why not read Sheldrake's papers for yourself and come up with your own criticisms? Sheldrake discusses some of Randi's attacks, which turn out to be totally off base or even fabricated. For example:

http://www.sheldrake.org/controversies/randi.html

I can only suggest that you read Sheldrake's published papers with an open mind, not prejudging that their results are "impossible" without reading his research methods and results. The papers are quite accessible, generally clearly written and straightforward, with a general lack of the masses of domain-specific jargon that mars so much journal writing.

I know for a fact that some scientists, even some world-renowned scientists, are morons outside of their own field. I used to manage construction at a Big 10 University, and had many conversations like this one:

BRILLIANT SCIENTIST, looking over my estimate for a remodelling project on his floor: "What the heck is this, $4000 for a door? A door? I just replaced the front door of my house for $500!"

ME: "Sir, your house is made of wood, and the doors don't have to meet any particular fire code. This building is concrete and steel, and the doors have to be 90-minute fire-rated. This means, among other things, that the door slab has to be hollow metal, which means it is heavy, which means that the frame, hinges, latch, and handle all have to be much sturdier than the hardware on wood doors. Also, the carpenter who will install this door is probably getting paid more than carpenters who work residential, and he's going to have to spend more time on it because it is more complicated. Finally, the lock core has to match all the rest of the cores in this building, so as not to mess up the keying system."

BS: "Don't give me that! This is ridiculous!"

I wish I had a dime for every time this happened . . . .

But the proverb does appear true to some degree, and I propose that we should be very disturbed by this fact. We should not sigh, and shake our heads sadly. Rather we should sit bolt upright in alarm. Why? Well, suppose that an apprentice shepherd is laboriously trained to count sheep, as they pass in and out of a fold. Thus the shepherd knows when all the sheep have left, and when all the sheep have returned. Then you give the shepherd a few apples, and say: "How many apples?" But the shepherd stares at you blankly, because they weren't trained to count apples - just sheep. You would probably suspect that the shepherd didn't understand counting very well.

A very, very belated note: there's an interesting scene in the first season of The Wire where one protagonists is running his kid brother through some math homework - some problem with people boarding and getting off buses. The kid brother is completely lost. Then the protagonist restates the problem in terms of the drugs being sold outside, and the kid brother gets the answer perfectly.

Hmm. Personally, as a Christian and a student of science (doing a Bachelor of Aviation Technology), I have to say that my thought processes were entirely different from what you described in your article.

I went with Pascal's Wager, or at least a modified version of it. Any sort of existence is infinitely better than not existing at all; this eliminates atheism, Buddhism, and Hinduism from consideration, along with other reincarnation-oriented religions. Judaism is almost impossible to convert into, so it's out of the running. Of the religions that remain, most of the pagan ones have relatively mediocre afterlives compared to the heavens of Christianity and Islam, and similarly mediocre punishments if I'm wrong as long as I live virtuously. If I do follow a pagan religion, and Christianity or Islam is correct, I'll suffer eternal hellfires. Therefore, I will be either a Christian or a Muslim. Since Christianity doesn't require me to attempt to overthrow Western civilization, has generally easier requirements to attain Heaven, and will probably allow me to avoid Hell if Islam is correct, I chose to be a Christian.

Of course, simply believing something to be true does not neccessarilly make it true, so I plan to put off testing that belief as long as humanly possible. Or, more accurately, as posthumanly possible, considering I plan to become a posthuman robot god and live forever.

"everything is connected to everything else". (Since there is a trivial isomorphism between graphs and their complements, this profound wisdom conveys exactly the same useful information as a graph with no edges.)

This seems like it is somehow connected to the fact that pantheism and solipsism are identical beliefs with different terminology for that which provides sensation.

And yes, that does make me wonder if I can trust that scientist's opinions even in their own field - especially when it comes to any controversial issue, any open question, anything that isn't already nailed down by massive evidence and social convention.

Not all scientists go around tallying up the expectations payed by their beliefs. If they have a freeloading belief they hadn't examined, one that doesn't affect their science, so what of it?

There's something fundamentally different between a gambling economist and a theist scientist: the thinking required for economics constantly forces you to acknowledge that gambling is dumb (although...). The thinking required for most sciences barely ever runs into the problem of God / spirit world / other wacky nonsense.

Most scientific reasoning treats God as a non-agent while never actually claiming atheism. A scientist who's never evicted a freeloading belief isn't necessarily a bad scientist. Theism is a warning flag only when it causes real-life expectations.

In learning we have two drives, to find truth and to avoid error. These rarely do come in conflict, and even more rarely do they come into any major kind of conflict, but there still are times that we have to decide whether we consider it to be more important to find truths or to avoid errors. Religion, for instance.

Let us imagine that a time traveler arrives from some distant point in the future and teaches me five facts which are not currently known to the world. Four of these facts can be explained with current scientific knowledge, and when they are tested they are proven correct. The fifth is as far beyond our current scientific knowledge as quantum mechanics is beyond the state of science as it was in the first dynastic period of Egypt. We not only are unable to understand the explanation or how to test it, but we are unable to understand the information that would let us understand the explanation, and so on and so forth for a great many regressions.

Nevertheless, because I am more concerned with finding truth than I am with avoiding error, and because the time-traveler's first four facts were true, I would conclude that it is reasonable for me to believe the fifth fact until I am proven to be in error or at least have sufficient reason to doubt it.

This same process applies to religion. The concept that there is some kind of higher being or beings is a concept which causes the universe to make more sense to me in several ways. Some of these ways are ones which I cannot even express well if at all, making it even more difficult to find possible alternatives, but I am not very distressed by this situation. There are concepts which you yourself no doubt believe and which similarly fulfill and answer things which I cannot express to my satisfaction.

Where there would be issue is in knowingly believing an error. While certain interpretations of Deity have been proven wrong either by history or mere logic, I do not believe that theism as a whole has been proven utterly incorrect. Perhaps this is straying into the territory of "Religion cannot be proven incorrect and is an entirely different magisterium," but in the end, if your concept of God is flexible enough, God actually can't be proven to not exist. Some hypotheses can't be tested. It makes them utterly useless for scientific purposes, true, but I've never thought that we can prove that God exists or not, only that we can prove that a particular religious concept is incorrect.

Knowing this, I revise my religious beliefs in accordance with scientific knowledge. I consider evolution to be true, and I am well aware of such things as the craziness of our retinas, and so I do not believe that the Divine created everything in six days, or even that the Divine did anything at all to guide evolutionary processes. I am aware that there are studies which raise interesting questions about consciousness, free will, and the relationship between the two, and I have had to redefine my conception of the soul as a result.

I do not believe that there is any issue with a scientist who has religious beliefs. The problem lies with scientists who have religious beliefs which are incompatible with science and basic reason.

Good day, sir. I look forward to continuing my reading of your site and can hope only that, whether you agree or disagree, I have at least managed to state my case in a way that does not, through its ludicrousness, lend support to the idea that some people shouldn't be allowed to reproduce or even talk to other people.

sadfsdf

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This article reminds me of a question one of my favorite teachers asked his classes. Are you learning to enrich your life or to avoid pain? What he wanted us students to question was our motivations for sitting in his class and taking notes and memorizing curriculum. Was it because we wanted to do what society tells us we need to do (get good grades, go to college, make a lot of money) or because we genuinely wanted to learn? Obviously the answer for the vast majority of student is the former. The same could be said of the scientists who operate differently outside the lab. Society tells them the right way to act inside a lab to avoid pain (ie the scientific method, control groups) but when they leave the lab they leave all the scientific stuff behind.

Looks like somewhere along the transition to lesswrong, the trackback to this related OB post appears to have been lost. It's worth digging a step deeper for the context, here.

I'm an athiest but I never particularly liked the assumption that anyone religious is some kind of idiot or isn't really a scientist.

A great many physicists in particular were theists. Half the terms you'd find yourself using in physics are the names of theists. Leaving out lots of people with less well known names:

Antoine Becquerel,

Guglielmo Marconi,

Gustav Hertz,

Werner Heisenberg ("“The first gulp from the glass of natural sciences will turn you into an atheist, but at the bottom of the glass God is waiting for you”"),

Max Planck (was really quite disdainful of atheists),

Victor Hess,

Albert Einstein,

Michael Faraday.

outside of physics even EY's favorite historical figure expressed similar sentiments to Heisenberg.

Francis Bacon ("It is true, that a little philosophy inclineth man's mind to atheism; but depth in philosophy brings about man's mind to religion: for while the mind of man looketh upon second causes scattered, it may sometimes rest in them, and go no further; but when it beholdeth the chain of them confederate and linked together, it must needs fly to Providence and Deity.")

These are not stupid people. These people were real scientists, many with a deep understanding of the fabric of the universe.

This horrible little trope that theists can't also be good scientists is both demonstrably wrong and little more than unpleasant Applause Lights within sections of the atheist community.

Quick q: the above article reminds me of the theory of scientism (i.e. that science is the only source of knowledge). Have I misunderstood the article?

(apologies - I'm a lowly physics student so my Bayesian logic is definitely flawed)

"A witty saying proves nothing." How ironic. I love it.

In modern society there is a prevalent notion that spiritual matters can't be settled by logic or observation, and therefore you can have whatever religious beliefs you like.  If a scientist falls for this, and decides to live their extralaboratorial life accordingly, then this, to me, says that they only understand the experimental principle as a social convention.  They know when they are expected to do experiments and test the results for statistical significance.  But put them in a context where it is socially conventional to make up wacky beliefs without looking, and they just as happily do that instead.

One thing that strikes me about this paragraph is that by and large scientists doing science by conforming to this social convention, seems like it works...I think.

It certainly seems better for scientists to understand what they're doing on a deep level. But I don't know how much better.

And this seems more true beyond science. Civilization is mostly made out of people cargo-culting people who understood what they were doing. And, I speculate, that this is actually better than the world where those people were not cargo-culting. If you're going to have customs and social conventions, it seems like those that are imitating more thoughtful processes are better than ones from other sources.