## Friday, August 19, 2005

### Common crackpots' errors

Everyone knows John Baez's Crackpot Index that allows you to calculate how obvious crackpot the author of a given article is. While I agree with the general philosophy, let me offer a complementary description of some features that, according to my vast experience and uncountable encounters with most of the crackpots living on this planet, distinguish scientists and those who are viewed as crackpots by the scientific community.

In the most optimistic case, it will help someone to find a more rational approach to the scientific questions and avoid some common mistakes - even mistakes that are usually not emphasized. In the more realistic case, it will at least lead some readers to ask new questions. No doubt, many of the points below overlap with each other but I decided to divide the discussion into these paragraphs anyway. It is also clear that many important points are missing.

Poor estimates of certainty and uncertainty

The crackpots are typically unable to estimate the amount of uncertainty associated with any particular insight. Such an intellectual exercise should often be pretty simple: one should look how many papers or inventions or industries seem to depend on a particular conjecture or theory. And if numerous papers or inventions seem to work, one should be more careful before he questions or replaces the very basic features of the underlying theory. The crackpots may fall on both sides of this divide. There are crackpots who have no problems to question insights that have been tested billions of times; there are also crackpots who seem to be completely certain about a statement that is totally uncertain (or incorrect). Usually these two groups heavily overlap.

Crackpots see no difficulties in assuming that every single statement or equation in every book by the most famous scientists, as accepted and checked by thousands of their readers, is based on a new logical error. Common sense is always less important than the revolutionary message of the crackpot.

Unfocused understanding of scientific terms

Scientific terminology is often a complicated enterprise. It also involves a lot of misnomers that got stuck because of purely historical reasons. But scientists always prefer compact terminology when it leads to no misunderstandings. This implies that more or less every piece of a scientific term plays some role for the whole term; it just can't be omitted. Some crackpots avoid scientific terminology altogether and this paragraph is not about those guys. This paragraph is about the crackpots who like to use scientific terms but they do not understand them. The most typical manifestation of this problem is that a crackpot uses a long scientific term as a compact black box that should not be analyzed or deconstructed. Such a crackpot sees no problem to talk about "twisted sector closed string tachyons" and conjecture that it is the same thing as the "Higgs boson". Of course, for two expressions to be equivalent, all of their features must match. But a crackpot typically does not ask "Why does the word 'twisted' appear in the expression and what it means?" He or she simply uses the whole expression as a single black box and he believes that it is never important to "look inside" in order to verify his ideas.

Inability to falsify conjecture by a comparison with the most elementary data

It is truly simple to rule out some of the silliest theories proposed by crackpots. For example, Mark McCutcheon argues that there exists no universal force of gravity and Newton's unification of the terrestrial gravity with the celestial gravity was a misconception. However, the apparent existence of NASA (something that most kids can see on TV) that is able to calculate and control the trajectory of their shuttles - for whom both terrestrial gravity as well as celestial gravity is important - should be enough for a person with IQ above 55 (and above 4 years of age) to figure out that something must be wrong with McCutcheon's theory. The crackpots often ignore a majority of the phenomena that are clearly relevant for their theories and they don't care.

Reluctance to attempt to verify their hypothesis at least using one example

This paragraph is saying a very similar thing in different words. Cranks often present very general, far-reaching theories that should make them as famous as Albert Einstein or similar people from the history of science. They propose theories of everything but they rarely realize that "everything" essentially means "every thing" and a theory of it should be able to explain every and each thing in a certain class. While we usually don't want to verify a theory on all individual examples, it is obvious that we must make at least some tests. Crackpots usually don't want to do that; they probably think that their hands would get dirty if they broke the beautiful symmetry between all things - a symmetry that says that neither of these things is tested but all of them are subject to the magnificent theory.

Spending a disproportional amount of time with an idea

It's extremely frequent that a discussion between a crackpot and a scientist freezes at one point; a point that should take an intelligent student a few minutes to understand. Nevertheless a crackpot may be missing some wheels and gears in his brain. An implication is that you might need 7 long e-mails to explain him a simple idea that should really take 3 minutes. A crackpot rarely feels that he is wasting time of others; he does not understand that the appropriate speed of understanding should be faster by several orders of magnitude. Because of some dogmatic pre-conceptions, he (and less frequently she) is typically convinced that his (or her) misunderstanding must be very important and everyone should be wasting time with it. Even if you explain a crackpot his error and the correct answer very carefully, you are almost guaranteed that you will have to listen to the same error next time.

This observation may also go in the opposite direction. Crackpots are often convinced that the right amount of time they should spend with learning a theory is a few minutes - and then they can deduce all important answers from their "deep" knowledge. In many cases, crackpots simply can't appreciate that the system of some phenomena and their patterns is pretty complex and it requires correspondingly powerful and complex theories to explain them.

Misunderstanding as a source of pride

The previous paragraph is related to another feature that distinguishes crackpots from scientists. Scientists are often confused, too; in fact, they must live a significant part of their lives in the state of confusion and uncertainty about the questions that are most important for their research - namely the questions at the cutting edge of their research - which is essentially defined to be the research where some questions are not answered today but may find their answers tomorrow. But an important difference is that a scientist is never proud about his state of confusion; confusion is a part of the job but one can only be proud and excited when the fog of confusion disappears and a clearer view of the world emerges. On the other hand, cranks are often proud about their very state of confusion. They tend to believe that the fact that they don't understand a certain theory is extremely important for the world - even if they don't have any working replacement for such a theory. Stupidity is elevated to a virtue.

Linguistic, non-scientific treatment of scientific terms

This point is related to the "unfocused understanding of scientific terms" we mentioned previously. Science is using many words that have existed in the general culture for a long time. There are often very good reasons why scientists start to use the very same words. But if two people are doing the same thing, it is never quite the same thing. The scientific meaning of a term is usually related to the colloquiual meaning but it is rarely identical; moreover, in most cases, the scientific version of a term is much more concrete and well-defined. For example, the word "theory" means a compact set of ideas able to explain a class of facts or phenomena; the laymen often use the word "theory" instead of a "wild speculation", and crackpots also think that it is an insult. Another example: the very appearance of the word "uncertainty" is enough for a crackpot to argue that everything must be uncertain and fuzzy.

Crackpots usually ignore all these subtle differences; they understand words in their vague, non-scientific sense, and derive various conclusions involving these words using non-scientific methods. These methods are often linguistic ones. While an argument in science typically involves a calculation or a less quantitative counterpart of a calculation that is nevertheless based on some terminology-independent rigor and physical relations between the objects, crackpots' arguments tend to be games with words whose meaning is never quite well-defined. One of the implications is that renaming the object does not matter in science, but it often matters for the crackpots (and postmodern lit crits) - a point that was also discussed by Heather Mac Donald. From a physical viewpoint, their statements are often vacuous.

Lack of predictions

A related but more general example of the problems summarized in this category is the lack of actual predictions. A crackpot typically thinks that the most important task for the big thinkers is to find a phrase - a combination of words - that everyone will have to believe. Crackpots can rarely imagine that the right way to apply an important insight is to use it in many particular cases and derive testable predictions. Crackpots behave as scientists even though they could be much better in writing new holy scriptures as long as someone would will to read them.

Strong focus on one number and purely algebraic derivations

Some crackpots - those who enjoy numerology - often believe that the holy grail of physics is to explain the numerical value of one number. For example, a crackpot may think that it is important for the neutron lifetime to be something like 885.2 seconds, and the main task is to develop calculations that lead to this "magic" number. (Note how extremely difficult it is to calculate the lifetime from QCD and how silly it seems today to view this lifetime as a fundamental number or a number that can be obtained from a simple formula like one of those in the comments below.) Crackpots rarely realize that there are thousands of other numbers - such as the nuclear cross sections in this case - that should be explained by their theory if it has any value. Very often, their "calculation" of a single number requires more parameters than the amount of calculable "output".

Also, many crackpots don't understand which quantities depend on the choice of units and which don't; such a crackpot will never understand that because of our complicated history that has led to a definition of one second, it is just not possible for a complex parameter such as the neutron lifetime to equal exactly 885.200000000 seconds.

A related problem is that the crackpots are eager to present derivations of various formulae analogous to "E=mc^2" that are purely algebraic in nature. They either waste no time with a proper definition of their "E" or "m", or they even simply assume that there is one "E" and one "m" in the world. Many of them believe that a simple algebraic manipulation with such simple expressions - manipulation taught at the basic school - represents a significant part of a great physics discovery. Some crackpots have much better mathematical skills but they have no idea how the mathematical structures may be connected with the actual physical phenomena and experiments.

Possession of secret knowledge

This point has been added to the list by Leucipo. Some crackpots may argue that a missing gap in their argument may be filled or a justification of their reasoning or formula may be added, but they can't tell you how it is supposed to be done. It's either because they're convinced that no other human being is capable to understand their deep idea; or it is because they are afraid of losing their priority or an award. Some crackpots only use this story as a part of their tricks; others believe it themselves. At any rate, such hypothetical secret knowledge makes their theories unverifiable - unless they can be easily falsified which happens most of the time.

Sociological, political, and emotional arguments instead of scientific arguments

This is a category of problems that John Baez spends a lot of time with. So let me be brief. A crackpot does not like the idea to study "details" using technical and "boring" manipulations, calculations, or experiments. Instead, he or she wants to use the "powerful weapons" only. The most powerful principle for most crackpots is the postulate that the crackpot is the most important scientist in the history of humankind or something at least comparable to it. Such a principle may be used to "derive" many far-reaching consequences. Even if such a statement were correct, one cannot forget that this argument is purely sociological and can never be the only source of scientific insights.

Against the sociological argument that the crackpot is the best scientist, other people often employ the opposite sociological arguments - for example the fact that most other scientists do not think that the crackpot is a genius. The crackpot typically ends up with conspiratory statements that he or she is being prosecuted because the rest of the scientific community does not want the public to learn the most important truths because it acts like the Inquisition, McCarthy, and so forth. The more manifest crackpot a person is, the higher percentage of his or her "research" is composed of these fairy-tales about the relations of the "genius" with the rest of the scientific community and about the hypothetical future appraisal of the theory. The relation of important scientists to their colleagues may be better or worse, but whatever is the answer, such an observation can't be used instead of a scientific argument to support or reject a theory.

Of course, extreme yet frequent examples of the anti-scientific behavior includes ad hominem attacks against the opponents of crackpot's own theories, comments involving psychiatrists, formulations and spelling that clearly displays the emotional character of the assertion, comments about the importance of the work justified by unusual personal background of the author or the amount of time he has spent with it. Crackpots will often do many typical things - which are unusual among scientists - such as to emphasize that they deserve a Nobel prize; offering money for proving or disproving their theories; naming things after themselves.

Belief that whole fields of science are wrong without being able to identify the error

This observation is related to many previous observations, for example the missing will of crackpots to verify their assertions and their frequent pride about their state of confusion and misunderstanding. But once again, let me use different words. Crackpots often believe that whole scientific fields, including many fields that have been tested for decades or centuries, must be wrong. This is usually derived from the inconsistency of the basic ideas underlying these fields with a basic dogma of the crackpot, or simply from his inability to understand the existing theories. A crackpot will typically focus on the inconsistency between his basic idea and a fundamental idea of the existing science, and he will rarely try to study any further "details".

For example, a crackpot may decide that a theory named in a certain way (e.g. string theory) must be ridiculous and inconsistent based on verbal patterns, but he will always find it unimportant for his final answer to look at any particular quantitative arguments or formulae. A crackpot is always convinced that the whole fields of science can be faithfully summarized in a single over-simplified sentence, and this sentence is a sufficient tool to exclude thousands of papers without any need to study what they exactly say and why they do it.

In this category, one must also mention that there are many particular scientific fields that are simply difficult to understand for most laymen and where the crackpots concentrate: crackpots can rarely understand quantum mechanics, relativity, and sometimes not even the Newtonian physics. Crackpots want to think "big" and therefore they concentrate around these general enough frameworks, instead of trying to study the "details".

Blind belief to preconceptions with no intent to verify them

This characteristic feature is also related to most of the previous ones. At any rate, one of the most important crackpots' defficiencies is their dogmatism. They postulate some important principles - prejudices - that should play the role of their new religion, and then they develop an ideology that is meant to support these principles. A critical error is that they simply don't question their assumptions and they think that a linguistic justification is everything they need; they just believe their starting point and use the agreement or disagreement between their assumptions and any other statement as the primary criterion to decide about the validity of the other statement. For example, a crackpot may decide that the whole world is discrete. But whether or not this assumption leads to realistic and promising predictions and/or agreement with reality is always secondary, to say the least. Let's say a similar thing differently:

Crackpots always find the most important answers first

While it often takes hours, years, or centuries for careful scientists to find truly valuable answers to difficult questions - and such victories often follow long periods of uncertainty as well as boring technical work where all emotions must be forgotten - crackpots usually follow a very different path. They start with their moment of "revelation" in which the most important questions as well as answers are communicated to the future universal genius either by some divine force, by the aliens, or at least by the incredible mental powers hidden in the crackpot's brain. The rest of the work is about filling the details and about promotion of the ideas; everyone is led to believe that nothing can go wrong after the most important insight that has already been done by the crackpot.

At any rate, the basic ideas simply can't be questioned. For example, a crackpot may decide that the whole task of finding a quantum theory of gravity is about finding the right set of variables (a field redefinition) for the regular general relativity - because the phrase "quantum gravity" is verbally a combination of "quantum" and "gravity" and therefore the right answer must only be about combining the usual classical GR with some "quantum stuff" - and everything else follows. (In the context of academia, a similar approach to quantum gravity is called Loop Quantum Gravity and let us avoid debates whether it is qualified to be included as a crackpot theory.) Crackpots will never be affected by an arbitrarily long period of failures to derive any encouraging conclusion - either agreement with reality or a non-trivial internal theoretical consistency check - and they will continue their quest according to the original dogmas much like the cargocultic tribes who are sure that changing the shape of their wooden "earphones" is the only thing they need to make the airplanes land.

More generally, it's hard to communicate with the crackpots because they don't want to learn new things and they don't want to listen. The reason is that they are convinced that they have already found the most important insights.

1. Wow, you surely have irritated a big group of people by calling LQG a crackpot.

Have you ever thought about applying John Baez's index to super string theory, and see how it scores?

In my opinion the John Baez index is un-necessarily too complicated.

Only one criteria is needed: whether a theory has any predictive power or not. If it is unable to predict or calculate any thing, it's crackpot. If it predicted something which turns out wrong, it's a wrong science theory. If it predicts something, and it precisely matches observation, then it is science. You've got to admit it's science if it correctly describes the nature, regardless who did it or whether the community of the establishment gives it a shit or not.

I have had experience dealing with a few crackpots. For example the Nigel on Peter's blog who claimed to have derived G from 233 Ohm vacuum. I showed him how the 233 Ohm is an artificial number of the human's choosing of unit sets, and bears no physics significance whatsoever, and I further show his derivation of G is nothing more than the known relationship between the critical density and hubble constant, and that fact that e^3 happen to be close to 20, which is roughly the inverse of the known baryon density. But he doesn't seem to be capable of thinking logically.

Since predictive power is all one needs to show that a theory is legitimate, one especially needs to pay attention exactly how the predictions are made, whether it could just be a pure numerical coincidence, or whether it will ever be falsifiable by any potential experimental outcome.

My theory leads to a precise calculation of the neutron mass good to 9 or 10 decimanl places. And I correctly associated it to the neutron lifetime of exactly 885.2 seconds. The current known value is 885.7 +- 0.8 seconds. So if they refine the experiments and it does not approach 885.2, I could be sent back to the drawing board. That's the kind of predictive power one should see in science. Now when it comes to the so called Higgs Boson, does any one has any definite idea exactly what it's property will exactly look like? Every one just sits and wait for the LHC data to come out and something to be shown, and then they will try to "predict", with an error bar of one or two orders of magnitude, the mass of Higgs Bosons. What a shame!

Quantoken

2. Dear Quantoken,

the Baez crackpot index of any paper in string theory that is at least a bit respected is surely minus five. Is it so difficult to check?

Best
Lubos

3. Ah Quantoken, I had forgot to tell you, there is a piece of your theory in a preprint of Adler, at fermilab . Check page 3 and references 2 to 4 there.

Aboth predictive power as a measurement of crackpotcity, I call this a GIGO analyis (Garbage In versus Garbage Out). It is very typical to find that there are more arbitrary parameters IN that predicter parameters OUT.

4. I wonder if we could centralise the classification of crackpot / unsolicited material. I mean, someone in the academy could ask the highly exposed people to forward the unsolicited material to a Working Group, which could dissect and classify it. In this way we could have a real corpus to refer to. Yep, we could just collect pointers in the web as crank.dot.net does, but unsolicited mail or email to well known physicists is a better selection criteria; some web pages can be just ego exersices and the author can be really aware of the lack of value except as an scam (ZPEnergisers?).

The corupus could not be useful to physicists (well, who knows?) but it could hace some use for historians and philosophers of science, and even for physicians.

5. Lubos:
I admit there's a bit of linguistic inexactness when I said "And I correctly associated it to the neutron lifetime of exactly 885.2 seconds."
No I never meant to say it is precisely 885.2000000000..., there is certainly always an error to any physical quantity. In this particular case, it should be 885.18 +- 0.04 seconds. Certain the 0.04 seconds uncertainty is virtually nothing comparing with the +-0.8 seconds uncertainly of the best accepted value, 885.7 +-0.8 seconds.

And there is no magic in the particularness of the decimal number 885.18, it just happen to be that value because the particular unit of seconds we choose. But whatever unit you use, it equals to the correct lifetime of free neutron decay.

Based on my theory, the theoretical proton mass is calculated to be
Mp/Me = (ln(2*(1+3x5!+7!))/ln(2))/alpha
= 1836.146836(6)

This is almost the correct value, which is 1836.15267261(85).

However, using this theoretical value. I can derive the exactly precise value of the neutron/electron mass ratio:
Mn/Me = Mp/Me + beta^2
= 1836.146836(6) + beta^2

With
ln(sqrt(PI)*N)
beta = --------------------------
ln(sqrt(2/PI)/PI*(Tau/t0))

Here N is the big N I meantioned many times:
N = PI*exp(2/(3*alpha))
~= 1.5x10^40

Tau is the neutron lifetime, and t0 is the quantum of time, if you set the mass unit M0 so that Me = alpha*M0, and set hbar = C = 1, you could easily derive that
t0 = 9.3996371481x10^-24 seconds.

Another way of deriving t0 is
t0 = alpha^2 * a0 / C,

With Tau = 885.18 seconds you can easily show that the two ln's come to:

93.07442757(31)
Beta = ---------------------
58.43664

Beta = 1.592741

Therefore:
Mn/Me = 1836.146836(6) + beta^2
= 1836.146836(6) + 2.536824
= 1838.683660(7)

This matches the measured value to the precison of the first 10 decimal places:
Measured 1838.6836598(13)
Theory 1838.6836600(70)

And the error bar of my theoretical calculation is purely due to the uncertainty of the exact value of alpha.

This is not numerology. You can NOT get that kind of precision with numerology. There is not a single adjustable parameter in my calculation. And I have the precise procedure of the derivation of the formula but I am not going to publish it until I figure out every thing.

Also see this.

Quantoken

6. Mp/Me = (ln(2*(1+3x5!+7!))/ln(2))/alpha

This is a perfect example. The Garbage In, attributed to some "secret knowledge", contains more information than the Garbage Out. A very similar example is quoted by Adler in the last page of the above mentioned preprint. Also, IJ Good dis a effort to quantify the information added in such kind of formulae, even without account of "folder selection" effect (ie that only positive results are reported)

Your correction term "beta" makes thigs ever worse, because it adds a new lot of GIn, again from "secret knowledge".

N = PI*exp(2/(3*alpha))
This kind of formula (see also Nottale) is mentioned in page 3 of Adler, who gives further references.

To conclude, your excerpt let us to add two characteristics to Lubos ennumeration:

- The possession of secret knowledge.

- The neglect of previous work.

7. Leucipo:

The expression (1+3x5!+7!) do not come out of thin air and I derived it rigorously from an eight folder model which I am not ready to discuss. Should I used something like 49305.546587658854 and with no good reason it would have been numerology.

Sure if you alter any of the integer numbers slightly you get a slightly different output, so there is a certain amount of information embedded in the input, but in no way it explains the 10 decimanl places preciseness of my result, which embeds information of at least 10 decimal digits. If you believe this is numerology, I challenge you to come up with a calculation, use no more and no bigger than the few integers I used, and get a result which is 7 or 8 decimal places accurate.

And certainly you can apply the same GIGO arguments against the standard model, and claim that with up to 17 arbitrarily choosen ad hoc free parameters, there is enough information embedded in the input already that virtually any conceiveable experiment results could be precisely fit to 3 or 4 decimal places accuracy, by adjusting the free parameters. I am not trying to criticize the standard model, but just use it to show how illegitimate your argument is.

And BTW, I looked at what you studied. And after carefully evaluating the input and output, using your GIGO principle, I concluded it's just a numerology conincidence.

8. Quantoken, as you may know (but again, you could have forgot it) we run a whole year quest for precision formulae of the numerological kind. The whole search can be browser in physicsforums and an excerpt of it here. We reported separately in a two interesting ones, namely Koide's and one of Hans.

Besides, my during the last year includes some comparisions of mass of decay widths that while empirical, can not be considered strictly numerology because the coefficients involved are =1, ie we compare two masses or two decay widths and we observe they are equal.

It happens that there are no a good theoretical background to measure the information IN when building a formulae (the OUT is usually a single decimal number). This task was only slightly touched by I.J. Good, and marginally by other researchers in computation theory. So you are right that lacking such measurement we can not decide if Koide square roots are more input that your factorials and sums. Koide has the advantage of an public observation by Foot, who noticed that the condition was just to ask the roots of the masses to form a vector exactly 45 degrees from (1,1,1), and that this relationship was also possible between down-quark masses.
If we only look to the number of operations involved, then numerology as 6 pi^5 for Mp/Me (Phys. Rev. 82, 554 (1951), and Lubos Motl in sci.physics.research) should pass the GIGO tests, and this is a bit troublesome.

As for your factorial, it has the disadventage of having an appearance similar to Wyler formula (ref. 15 of Adler preprint, check esp. the replies in Phys Rev Letters, and/or see also post #33 in the physicsforums thread) for alpha, for which a good bunch of similar formulae were possible. Of course if you can derive it from a model built a priori then you can get some sort of extra security, which again is not easy to quantify.

9. Hmm sorry, it seems that in the previous comment the reference to good was to his CV, not any specific works. The physicsforums thread gives an additional pointer to a relevant postscript file as well as a bit more of bibliography. Googling for IJ Good is a hard task because this author is a well known statistician, so named in diverse tasks. A marginally related article here is his attempt to classify Fallacious Arguments and Interpretations (some points reminder me of Kropotkine charge against Marx: "He believes that every nondecreasing function is linear"). Good uses the word "tricks" in his description, very much as Lubos above. It is no bad to remember the narrow line between crackpottery and plainly salting the mine.

One of the minor computational works I was referring to, also in PF, is Bailey and Ferguson.

Last, there is a missing word above. I intended to say "my during the last year", referring to work from 0312003 to current month. BTW, I dipped into this well while looking some questions on alchemy-- which amazingly does not score in Baez index so I will add "on alchemy, as Newton himself did" to get a +20 bonus :-D

10. aghh, twice: "my research during the last year". It seems that there is a bug in the preview, let me try again:
research. Oh well.

11. Leucipo:
I must say that I am very familiar with your numerology study and I know about your discussions on PhysicsForums, before you even meantion it. They were pretty fascinating and I spent quite a bit of time studying them, trying to determine whether those relationships are mere coincidential, or too coincidential to be coincidential.

You eventually concluded that any conincidences within just a few percentage or even 0.1 percentage could very likely be ruled as pure numerology coincidence, and you need to do much better than that to be not coincidential. I agree with that. But I have a much more rigorous quantitative test on this regard.

Basically, it is numerology coincidence when
I(input) > I(output)

And it is NOT numerology when
I(input) < I(output)

The output information can be evaluated as:
-ln(output precision)*abs(ln(output value in natural units))

Please note, should the output be precisely ONE, then the output information then equals to zero. If you claim to have calculated the correct value of light speed C, then you have an output which is exactly ONE (in natural unit) and that renders yours as numerology, regardless of what you say on the left side!!!

For a practical example, if you claim to have calculated alpha, to within 3x10^-9 precision. The output information is:
-ln(3x10^09)*abs(ln(1/137.036))
= 96.56

That's a pretty high output information.

Now look at the input side. The entropy can be evaluated by sum up information introduced various parameters and math operators, evaluated from how likely these numbers or operators are likely to occur. For example if you used a PI, the odd p(PI) is going to be pretty close to one since this math constant occurs a lot, so -ln(p(PI)) ~= 0, i.e., PI contributes little information.

On the other hand, if you used 3541325. for example, The odd that this particular integer will be choosen rather than the other 3541325 smaller integers, is approximately:
1/(3541325) = 2.82x10^-7
So the information is
-ln(2.82x10^-7) = 15

The point is you try to sum up information of the input, and evaluate information of the output. If the later is bigger, then it is not numerology. Vise versa. It is a pretty accurate way of determination.

Now, for neutron mass, it's value, expressed in natural unit, is 13.41752293, and the precision is 3x10^-9. So the output information is:
-ln(3x10^09)*ln(13.41752293) = 51.

12. Interesting, that one of the Google ads on this very blog takes one to this:

http://www.thefinaltheory.com/pages/1/index.htm

13. Hi Lubos,

I've spend some time today with the Anti-crackspot-"ism" part of your essays and deliberations. I cant say, that i really understand the scientific grounds your standing on, you're delegitimizing the crackpot-positions from (I'm a humble student of the humanities). But I'm preparing a paper about the trouble of demarcation between science (psychophysics) and pseudo-science (spiritism) @1870-80. So the struggle of the crackpots for acknowledgment interests me. I just wanted to say, that I really enjoyed your writing (albeit I don't agree with every point) and to sum up some of my thoughts.

Crackpots don't make science, they feign the parts of science their mind is able to grasp and appreciate. They desperately pursuit the aesthetics of the misunderstood greatness and of the beauty of simplicity (in linguistic and mathematical terms) without the care of understanding the basic: Hobby gardeners drawing flowers instead of growing them. They seem to be deeply in love with The Abstract ignoring the tight bonds of real science to the real world. Maybe this explains their fever, their despair.

One point of critique:
Sometimes you downplay the aspect of suddenness and aesthetics for scientific inspiration to much for my taste (we both know that Maxwell's research had a hard time, because of the perceived "ugliness" of his equations, the "otherness" of the aesthetics of his thinking), but "crackpots" overplay this side and don't get it. They ARE romantics, and you (i think) only PLAY the pure rationalist.
Short: the educated guess trumps the random guess in the end.

But maybe these crackpots are important and not only contaminating the SNR. the buzz they generate in mainstream media might help to interest the young for physics and might help to legitimize the founding of fundamental research for the public. Unfortunately I cant estimate a cost-benefit ratio for crackpots, but appreciate your ire for them all the better.

best wishes,
Daniel.

14. One other element is the idea of winning an argument (as in a debating club, etc) equals scientific proof, when this is not so.

Summed up as Rhetorical Technique substituting for Scientific Evidence. Many logical fallacies fall into this category, where insult, etc serve as substitutes for proof.

Unfortunately, intelligent people can go down the rabbit hole on this one.

A brilliant mind can invent plenty of convincing arguments to shore up a "fixed/fixated idea". A brilliant mind can overwhelm someone with lesser argumentative technique, which does not make the actual basic proposition true.

The absurdity of this is seen in the example of playing a game of checkers to determine if man can fly, or go to the moon.

The absurdity of this is obvious, and yet other scenarios exist where one side does not have an effective response against rhetorical devices.

The differences is between debating for the sake of determining the truth, vs debating for the sake of status (such as trying to prove that one's side is right)