This is a work in progress, and today is a busy day. This is just for fun and for you to play with.
The more complex the field of study, the more likely that any result, finding, or theory in that field is wrong. I am only considering science, i.e. that which explains and is subject to empirical verification. I exclude fields such as ethics, morality, philosophy which are fields that tell us “that empirical verification is a good”, and other statements which are not subject to verification.
There are three broad areas, or groupings, of complexity in science. Not uncoincidentally, this laddering also correlates with the fields’ dependence on statistics for evidence, from most to least. The groups are also, from least to most, though somewhat more loosely, ordered by connections with observation via prediction.
- Behavioral: Education, Sociology, Politics, Psychology.
- Biological: Economics, Evolutionary Psychology, Psychiatry, Neurology, Medicine (doctoring), Genetics
- Physical: Climatology, Meteorology, Chemistry, Physics, Engineering, Mathematics
The demarcations between these areas are not abrupt, nor is the ordering within each group anything more than a crude, but still somewhat useful, guide.
Some explanation is needed. Why is Physics, the mother of all sciences, the field requiring the biggest brains, listed near the end and is therefore one of the least complex fields? Because Physics is not complicated in the sense I mean complex.
Physicists study the fundamental properties of the universe, it’s true, but it’s also so that these basics are not complex. They are amazingly difficult to comprehend, yes, but not convoluted. If under your consideration is just the interaction between two electrons, themselves encased in forces that are as precisely defined as possible, then your world view is narrow, constrained, and quite simple. It might be true, and usually is, that this simplicity is difficult to express and to understand, and that to reach this bare pinnacle requires years dedicated to its singular purpose, but that does not render the process under consideration complex in the sense we use that word here. We are only talking about what electron A and electron B will do in strikingly limited terms.
Too, the physicist has ample opportunity to verify his theories. If, under the circumstances he explicated, electron A goes where he predicted it to go, and electron B behaves as he expected, then the physicist has learned that the theory he entertained is probably right—but only probably. But if the particles go their own way, then the physicist must also venture down a new path and toss out or modify his theory. This deep, lasting, and intimate connection with observation is what keep physics honest.
Engineering tops physics because this field is defined as all sciences exposed completely and continuously to reality. It is less complex in the sense that the rules which govern the field are more worked out in advance, but it is also more complex in that engineering implies building something for human use, and human behavior is the most difficult thing of all to predict. More on that in a moment.
I cheated by putting Mathematics as the field which gives us our most certain beliefs, because math is not a science. Mathematics more properly belongs to philosophy. If you think not, and since science is that which is testable, try empirically verifying that, say, a triangle’s interior angles sum to 180o or that, in reality, (if I may abuse the notation) alpeh0 < aleph1, which is to say one kind of infinity is larger than another kind of infinity. Report back to me when you reach aleph0. Math is used in science and openly, but so are the other areas of philosophy and ethics, etc. It is just that these other branches more typically remain unacknowledged.
Now, a chemist can tell us with great precision what will happen when Na hits H2O, but his, or any other scientist’s, ability to predict what John Smith (43) of Cleveland, OH will have for lunch next week Thursday is no better than any unschooled layman. The conceit of the sociologist is to abandon the question and substitute for it one which he believes he can answer: what will the “average person” will eat for lunch in OH. Enter statistics, through which, perhaps (but only perhaps), the sociologist can build a model which will do slightly better than just guessing. And only do better if the prediction is not too far out into the future. Or where the circumstances do not change, it being more of less a mystery what those circumstances are.
Plus the sociologist probably won’t bother to verify his model: won’t use it to make actual predictions. And neither will most of the educationists, psychologists, and so forth. Of course I do not mean all sociologists etc. nor do I claim the fields are sterile.
It is just that the probability of speaking nonsense is greater the more complex the field and the further that field is from empirical verification. Which is why climatology, which is simpler than meteorology, ranks below that field because climatology is further from empirical verification.
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Note: I tried everything I could think of to get the HTML to properly render the Hebrew letter aleph: render it it would, but it would put it in strange places, nowhere near where I put it, and super- or sub-scripted at random.
Hmmm…. you speak as if you know all of those areas well. Don’t you think one would need to know an area to appreciate it? An engineering colleague would tell me that statistics or mathematics is very complex, and I think the opposite.
> I tried everything I could think of to get the HTML to properly render the Hebrew letter aleph: render it it would, but it would put it in strange places, nowhere near where I put it
Recently I was playing with Unicode (in text files, not HTML), and had similar problems with all Hebrew letters. It took me a while to realize it’s probably something “helpfully” rendering Hebrew (and Arbabic) right-to-left and my other characters left-to-right. I suspect HTML does something similar.
I think the complexity issue would be better served by starting with the Comtean Pyramid and working from there. No need to re-invent the wheel.
The further one advances up the Science Pyramid (Comte’s as modified), the more dependent one becomes on the lower tiers being ‘sound’ and the less amiable to observation phenomena become. That last is the important part, it is not that verification is itself more complex per se but that observation to perform verification is difficult and becomes complex. The result is that at a certain point verification becomes less about determining if the theory is correct and more about determining if the observations are correct.
There are more rules to remember in chemistry than in math.. Math is, potentially, self evident whereas the periodic table of elements is not. In that sense I agree with your assessment of complexity.
I think there may be too many “sciences” though. Climate science, as it is practiced, is one application of predictive analytics.. Much of sociology is as well. Unfortunately these fields don’t seem to know this, and so publish results that are missing the most important pieces of information. (forecast skill, for example)
A great sentence:
“Physicists study the fundamental properties of the universe, it’s true, but it’s also so that these basics are not complex. They are amazingly difficult to comprehend, yes, but not convoluted.”
Complexity is not a synonym for “difficult to comprehend.”
I’m thinking it is not the complexity of the knowing, but the complexity of the known. That is why to the physicist, the criterion of beauty is an elegant simplicity: when many things are explained by a few things. But this means that the objects of physics are simple: inanimate objects acting under determinate laws. Hence, the motions of falling bodies, of electricity in a circuit, of light through a lens, and so on. It is the object being studied that is simple, not the methods used to study it.
Chemistry’s objects are a little less simple and a full knowledge of chemistry is not exhausted by a knowledge of the underlying physics. There are things emergent on the molecular level that cannot be predicated at the atomic or subatomic levels. This is what we used to call “formal causation.” But the objects of chemistry are still inanimate and still behave in predictable ways. Na+Cl gives you table salt. It never gives you nuclear fusion.
Biology’s objects are more complex still and knowledge of them is not exhausted by knowledge of chemistry and physics. Living organisms are animate and have inner drives that move them in ways not strictly predicated on external physics. That is, a petunia is a bag of chemicals; but it is not only a bag of chemicals. At the higher reaches, biology begins to deal with objects who are subjects; that is, with motives and purposes: to locate prey, to build a nest, etc.
The objects of the social sciences are the most complex of all; viz., human beings. People are biological organisms (and bags of chemicals, and physical objects), but they are not only these things. You may drop a sack of potatoes from an airplane or a human being from an airplane, and both will follow the same laws of falling bodies. The difference is that the sack of potatoes will not object to the experience.
But physics envy leads social science practitioners to suppose they are looking for the same kinds of laws as those uncovered by Ampere and Maxwell. Foiled of this for the obvious reasons, their resort to [often bad] statistics leads to confusion: That members of a group measure out to a certain average because they are members of the group; whereas in reality, the group presents such an average because of the qualities of those individuals who are assigned membership in it.
I love the way that economists have tried to convince themselve that they are a hard science and not a social science. They have math! Social sciences don’t have math.
But then they get lost in their math. Frequently the income (or output or price…) is dependent on some parameter that cannot be observed (e.g. the Keynsian multiplyer) and a generation of economists can argue over the size (or sign) of the perameter and never question the assumptions the theory is built upon.
First principles:
The fundamental theorem of arithmetic: Every natural number greater than 1 can be written as a unique product of prime numbers
The fundamental theorem of algebra: Every polynomial equation of degree n with complex number coefficients has n complex roots.
The theorem of calculus: If f is continuous on the closed interval [a,b] and F is the antiderivative of f on [a,b], then the definite integral of f(x) from a to b is F(b) – F(a).
Fundamental Theorem of Finance: Security prices exclude arbitrage if and only if there exists a strictly positive value functional, under the technical restrictions that the space of portfolios and the space of contingent claims are locally convex topological vector spaces and the positive cone of the space of contingent claims is compactly generated, that is, there exists a compact set K of X (not containing the null element of X ) such that C = {x ? X : x ? 0} = U ?K for ?>= 0
Mr. Doug M, what was that last sentence again?
I don’t see how this can be a useful notion of the term “complex.”
Just like the number line is everywhere dense, nature is everywhere complex. There are always an infinite number of theories that will fit the experimental data. Some more complex than others. Our use of Occam’s Razor to decide between theories is a convention–an assumption. Occam’s Razor places no restriction on nature herself, only on how we have agreed that we will try and describe her to each other. That predictions can be made using simple concepts is fortunate, but we (should) make no pretense about our simple theories actually being true. Nature can still be as complex as she wants to be. Another way of saying this is that: All scientific theories are wrong, but some are useful. (With apologies to George Box.)
George: it’s much easier to test a predictive model for acceleration of a Titan rocket than to test a predictive model for “happiness”.
Take standardized test scores: are they a measure of intelligence? Are they a measure of good teaching? Are they a measure of social conformity? Are they a measure of institutional aptitude?
I almost failed a high school typing class. At the time I could type over 100 WPM, having been in front of a keyboard since the age of 4 (she was a dumb terminal, and I tried seducing her with the word “beer”). I received a 50%, the lowest passable grade, for that class. What was it my grade measured? What force, or collection of forces, are represented by my miserable grade 12 typing grade? The “true” answer is that I preferred to do other things during typing class, and so expended the minimal effort required to obtain a credit.
The key issue is that in the softer sciences a number may be used in such a way that 1 + 1 != 2. My 50% typing grade is not neccesarily equivalent to someone else’s 50% typing grade (I could type, the other could not).
The rot sets in when those claiming to be scholars in behavioral fields (particularly education) set forth to verify their conjectures by using statistics.
Anyone can collect and analyze numbers. Managing the collection in such a way that the data which represents some activity is reproducible is not so easy.
In my reading, educational researchers tend to make short work of their establishment of protocols and controls for unobserved variables. There seems to be an assumption that any experiment will provide valid results. Protocols change during the experiment; questionable assumptions are made; the Dearborn effect is not provided for; the research tends not to be reproducible. Double blind studies are exceedingly difficult to set up and administer. Other objections also apply to many education research papers.
What ends up being published is worse than useless.
And Doug M: you have the fundamental theorem of Algebra wrong. Every polynomial of degree n with complex coefficients has a root. Look at any proof. It is a corollary that you can factor the roots out, one at a time.
For the apeph (alef) characters, try this:
ℵ₀ and ℵ₁
In case the above gets rendered, the aleph is character 8501 in UTF-8 and the subscripted 0 and 1 characters are 8320 and 8321. For all three of them, precede the number by an ampersand and a number-sign, and follow it by a semi-colon.
/dr.bill
After reading through the postings, I can only laugh at myself for the way my engineering brain insists on reducing everything to an overly simple underlying principle. In this case, I find the underlying principle to be “people do what they are paid to do”.
All the fields of science being categorized in complexity have one thing in common – they are all occupied by humans. Most of the humans seriously engaged in these fields are paid to do so. The payment may be from a salary, book sales, commissions, grants, etc. The form of payment is the largest determinator of results.
For example, suppose you are interested in understanding a certain aspect of human behavior. This human behavior has important consequences. You find three professionals very seriously engaged in studying and understanding this behavior: a researcher with a government grant, an author writing a book, and an actuary. Do you think these three people will uncover the same truth?
Engineering complexity comes out of the need to remain conscious of the magnitude of uncertainties and other “unknowns”. Engineering “codes” attempt to simplify the inclusion of those things into design, construction and operation; in a very general way.
However, one cannot Engineer properly from those codes alone. Stuff will work and it may be deemed “sufficient” (aka “mediocre”). But it is necessary to understand the origins and nature of the “safety factors” (which are frequently non-obvious) incorporated into design or one becomes imprisoned by the codes; unable to improve products or production, resulting in inefficiency and uncompetitiveness against those who do understand and can make things without compromise in integrity or utility, by addressing relevance and the ability to reduce the magnitude of uncertainties as well as exposure to unknowns.
Paramount to Engineering is that stuff must work. It must work reliably. It must be reasonably safe to use. It must be affordable.
None of those paramount objectives seem applicable in the “virtual sciences” of e.g. climatology.
Dear Briggs, it appears that you only learned classical physics (you know, the type where apples fall on heads and someone invents gravity). While it is true that things like the Special Theory of Relativity are based on a very few basic assumptions, there is a new branch called QED (Quantum Electro-Dynamics) that gets very strange and causes arguments about how statistically alive or dead cats are among us physicists. Your example of electrons and their interactions fits right into this branch. In this case, physics is more related to philosophy than the older classical views. Is light (or an electron) a particle or a wave? You will only know when you measure it! (There’s that pesky human observer getting into the picture again.)
Now when you take chaotic equations of physical states, combine them with numerical methods and program them into a computer, you get the field of climatology. Oh, and I forgot to mention you need to add plenty of tuning factors. After all, the measurements you are trying to replicate have errors that need adjustments to make them agree with the original physics, not the other way around.