Your IP address is 220.127.116.11
View Author detected.
view author posts with search matches:
Retrieve source record and display it.
q: SELECT AUTHOR, MEMBER_NAME, IP_ADDR, POST_DATE, TOPIC_ID, t1.FORUM_ID, POST, POST_ID, FORUM_VIEW_THREADS from ib_forum_posts AS t1 LEFT JOIN (ib_member_profiles AS t2, ib_forum_info AS t3) ON (t1.forum_id = t3.forum_id AND t1.author = t2.member_id) WHERE MEMBER_NAME like 'Corkscrew%' and forum_view_threads LIKE '*' ORDER BY POST_DATE ASC
DB_result: Resource id #6
|Date: 2006/01/05 04:05:28, Link|
I'm a mathematician not a scientist, but hey.
1) 5 that they could have appeared by mechanisms that we understand well, 2 that they actually did.
2) 6, unless you include viruses in which case 5
3) 6 that they could have, 4 that they did
4) 6 that it wasn't necessary, 4 that it didn't
8) 4 (you can't disprove a negative, so I'm mostly going by my answer to q9 and knocking a couple of points off. Strictly speaking my answer should be MU, but the 1-7 range of answers was clearly not tailored to the needs of Zen practitioners)
10) 4 (evolutionary sociology always seems a bit fuzzy to me)
|Date: 2006/01/05 04:28:11, Link|
Recently I've been noticing a lot of comments about how evolutionary biology should try to boost its public profile and play to the crowd a little more. I've yet to see any organised discussion of this though. What techniques do people think that evolutionary biology could legitimately use to increase public awareness?
The problem as I see it is that mostly defenses of evolutionary theory are reactions to creationists (for example in the case of Ken Miller's excellent talk the other day). We need to find ways to encourage people to take an interest in their origins and to learn about the scientific approach that's being used to determine the facts. As an additional problem, we have to do this without making non-Fundie religious folk feel excluded.
Sorry if this is already being discussed in another thread, I did check the fifty or so most recent but I might have missed one.
|Date: 2006/01/07 12:55:37, Link|
One thing that I did think seemed quite interesting is this guy over on the ARN boards who's attempting to put together a set of DIY home experiments to demonstrate various parts of how life may have come about, to show that they are in fact probable. Starting with a variant of the Urey-Miller experiment, going via collection of proteins on seashores and ending up with the formation of protocells from basic molecules.
This seems like the sort of thing that could hypothetically help snap people out of thinking of origin-of-life related sciences as not just a scientific ivory tower. Plus, any experiment that includes meat tenderiser can only be cool.
|Date: 2006/04/14 05:40:20, Link|
I'd say that: no scientific evidence => it's not useful to accept existence.
If you can't make valid predictions of any sort about what X will do next, then it's not advantageous to consider X as a factor in your calculations - you'll do just as well on average if you simply ignore X and get on with your life.
This doesn't necessarily mean that X doesn't exist, but it does mean that belief in the existence of X is fairly daft - if nothing else, it's a waste of valuable brain resources, which aren't something that most people are overly blessed with to start with...
|Date: 2006/04/17 14:33:36, Link|
I'm afraid I'm going to go a couple over the five-statement limit - sorry about that
1) We know that artificial selective pressures (with a few random mutations thrown in) can give rise to substantial changes in organisms (e.g. chihuahuas vs great danes).
2) We know that the various natural selective pressures can give rise to similar changes, albeit (usually) more slowly (e.g. finch beaks, moth colour schemes, etc).
3) We have a fossil record in which many quite radical transitions are documented in sufficient detail that the individual steps are quite obviously within the scope of the aformentioned selective pressures (e.g. mesonychids to whales).
4) We can even make and confirm non-trivial predictions based on the premise that life is limited to naturalistic evolutionary processes (e.g. the resemblance between one human chromosome and two chimp chromosomes, haemocyanin in stoneflies, Tiktaalik). In other words, it's extremely useful.
5) There is no direct scientific evidence for the presence of a Designer of any sort.
6) The premise that an unspecified intelligent designer did something unspecified at some unspecified point in the process (which is all that ID claims) hasn't given rise to any testable predictions whatsoever. In other words, it's bloody useless.
7) Hence, it's fairly sensible to affirm evolution as a useful scientific concept, and fairly daft to affirm Intelligent Design as a useful scientific concept.
|Date: 2006/04/18 06:20:31, Link|
The classic example here is the "nylon bug" bacterium, in which a single frame shift mutation has apparently transformed a well-documented gene for digesting sugar into an equally well-documented gene for digesting nylon. The interesting thing here is that the modified gene couldn't have existed before nylon was invented, as it completely destroys the bacterium's sugar-eating capability (which would, of course, be instantly fatal in the absence of nylon).
Disclaimer: I have no interest whatsoever in attacking your religious beliefs. However, the scientific claims of flood geology that are made on the basis of those religious beliefs are, to the best of my understanding, complete mince. The idea is apparently that a massive worldwide flood somehow managed to sort zillions of fossils into exactly the order that would be predicted on the basis of potassium-40 and uranium-235 dating, and no other characteristic. For some unspecified reason, this corresponded very well with the arrangement that would be predicted by species, genus, etc - members of the same species, regardless of age, sex, size or any other factor, always end up in strata that return approximately the same apparent ages when dated.
To the best of my knowledge, there is no physical process that can achieve this. Of course, if you think God was directly involved then that's not a problem - but if you can't make testable hypotheses about how exactly God was involved then your conjectures can't be considered scientific.
Back to the whale evolution. The transition described here looks like:
- Basilosaurus (note especially that it had land-animal-like feet)
The only gap there that's significantly bigger than that between a Great Dane and a Chihuahua is the one between Rodhocetus and Basilosaurus. I'm no palaeontologist, but apparently other similarities (such as inner-ear structure) are sufficient to demonstrate a close relationship.
Obviously I can't really reply to the entire Answers in Genesis article here (although if you have any specific questions I'll go away and do the research), but I'd particularly like to critique one comment they make:
Basilosaurus did have small hind limbs (certainly too small for walking), and Teaching Evolution says ‘they were thought to be non-functional.’ But they were probably used for grasping during copulation, according to even other evolutionists.
The claim here appears to be that the fact that Basilosaurus's legs had some purpose means that they can't be pointed to as being vestigial. This is bonkers. Of all the myriad different forms that such graspers could have taken (pincers, tentacles, hooks, suckers, etc.), Basilosaurus just happened to pick a variant that was massively similar in both appearance and structure to limbs used for a completely different purpose by other animals?
4) We can even make and confirm non-trivial predictions based on the premise that life is limited to naturalistic evolutionary processes (e.g. the resemblance between one human chromosome and two chimp chromosomes, haemocyanin in stoneflies, Tiktaalik). In other words, it's extremely useful.
The hypothesis that species originate only through naturalistic evolutionary processes (rather than divine intervention) can be used to make predictions that can then be tested. Specific examples of these are:
1) It was noted that humans have 23 chromosomes per haploid whereas all our nearest relations have 24. We know from investigation that it's practically impossible to just lose a chromosome's worth of genetic material - that kills the organism quite fast. Thus it was hypothesised that one of the human chromosomes must have resulted from the fusion of two ancestral chromosomes. To test this prediction, a comparison was done of chimpanzee chromosomes and human chromosomes. One human chromosome turned out to be effectively identical to two chimp chromosomes (or, at least, to what they'd look like if they'd fused together)
2) Haemocyanin is used by the majority of non-winged arthropods to transport oxygen around their bodies. Winged arthropods use a different system involving tiny capillaries. Since, on other grounds, stoneflies were considered to be "primitive" in comparison to other winged arthropods, it was proposed that they might have vestigial features - such as haemocyanin. This was checked and found to be correct. IIRC, stoneflies are the only winged arthropods known to possess haemocyanin.
3) The recent discovery of Tiktaalik was a classic example of evolutionary predictivity. Based on their hypotheses about the evolutionary path from fish to amphibians, scientists were able to figure out exactly where they should look (in terms of location and strata) if they wanted to find a transitional fossil. They found a transitional fossil. To quote from Nature:
Tiktaalik retains primitive tetrapodomorph features such as dorsal scale cover, paired fins with lepidotrichia, a generalized lower jaw, and separated entopterygoids in the palate, but also possesses a number of derived features of the skull, pectoral girdle and fin, and ribs that are shared with stem tetrapods such as Acanthostega and Ichthyostega.
(Quote taken from here)
In short, even if a chorus of angels appeared tomorrow and announced that God had indeed created the world in six days and that evolution had nothing to do with it, scientists would probably still keep using the evolutionary premise because it's so darn useful. In science, predictivity is king, and evolution has a heck of a lot of it.
That's fair enough. But, if you don't believe that there's necessarily scientific evidence for a Designer, why support ID? Just to clarify: ID does not just say "there's a Designer"; it says "there's a Designer, and His presence is scientifically detectable". The problem with that is that the vast majority of actual scientists in the relevant fields feel that the ID mob are, uh, not talking via the usual orifice.
Believe whatever you like. Claiming that your beliefs are scientific when they're not, though, is profoundly dishonest, and that's precisely what the DI and co. are doing.
I'm sorry, I didn't go into sufficient detail on what I meant by "useful". When referring to science, this term means "can be used to generate testable predictions". Your belief that the God of the Bible created the world is indeed useful to you, but not in this specific scientific sense. It is not scientifically useful. It makes no testable predictions that have subsequently been confirmed, and as such it can't be evaluated using the scientific method of hypothesis testing and peer review- it's not scientifically tractable.
The reason this is an issue is that this scientific method is specifically tailored so as to home in on highly accurate solutions to scientifically-tractable questions. It homed in on evolutionary biology over 100 years ago, and has since been homing in on increasingly detailed evolutionary descriptions of species' origins. Whether you feel the scientific method is applicable in a given situation is a philosophical question rather than a strictly scientific one, but the fact that science has indeed converged on one solution strongly suggests that this is a scientifically tractable problem - if it weren't, you'd expect the scientific community to be all over the place on this issue, which it manifestly is not.
You might be interested to know that evolutionary processes also function very well as electrical engineers. In particular, genetic algorithms have recently been harnessed to produce highly-efficient chips. This science is still in its infancy, but appears very promising. See this guy's website for more details (I recommend starting with the paper at the bottom of the list).
Evolutionary processes also operate very well at optimising the structure of things like wings and engines, and can be surprisingly good at writing computer programs. Here is a great example - for more, I recommend browsing outwards from the wikipedia page
As I mentioned, it's entirely possible to evolve solutions to quite complex problems - no intelligence required. The reason why this doesn't occur with non-biological machines is that non-biological machines don't reproduce in any meaningful sense, and hence evolutionary effects can't kick in.
You may be pleased to hear that that's not something that science can in any way disprove - one would not expect a sufficiently secretive God to be scientifically detectable. There's even an entire theological position about origins known as theistic evolution that proposes that God used evolution to His own ends. It may interest you to know that C. S. Lewis was (broadly speaking) a theistic evolutionist.
To the best of my knowledge, no geologist has ever come to that conclusion without already having decided that the Bible is literally true. I'm no geologist, but the inference I'd draw from this is that the evidence does not in fact support this viewpoint. I already mentioned one problem (the sorting of fossils); I can look up more if you're interested.
I hope the above verbiage has been vaguely informative for you
|Date: 2006/04/24 12:09:35, Link|
I thought you might think that, which is why I carefully chose examples that referred to actual complete skeletons. To the best of my knowledge, none of the fossils I listed were mere "artists' impressions" - they were all either actual fossils or direct, unmodified drawings of the fossils. No parts were added or altered.
If you can see any linked pictures of which this isn't true, please point them out to me and I'll either find better images or retract my support for that fossil.
Well, technically speaking, according to Darwin every fossil is transitional. It'll take more time than I have at the moment to provide linkey support for this, but I'm given to understand that most of the major transitions are very thoroughly documented. The classic anecdote here is that palaeontologists working on the reptile/mammal transition actually spend hours arguing which of their fossils are reptile-like mammals and which are mammal-like reptiles. This makes no sense unless there's actually a continuum from one to the other.
Now, this is an interesting point for me - in fact, it's actually the one that brought me to this debate in the first place. See, I'm a maths student, and one of my courses is Coding and Cryptography - basically it's Information Theory 101. And the interesting thing about information is that mutations will nearly always increase it. This of course depends on your definition, so I'll run through a couple:
Mathematical definition 1: Shannon information
Shannon information is a measure of the amount of information that a given communication could contain. Say you wander down to breakfast and grunt "good morning" at your wife. That's something you do very often, so it doesn't really tell your wife much about your state of mind.
Now say you wander down, take one look at her and run screaming from the room. Your wife now knows:
a) there's something very unusual happening
b) you're sleeping on the couch
The rarity of this behaviour on your part makes it a high-information communication.
Now, let's say that your behaviour spontaneously mutates - in other words, you pick a random action from your repertoire to perform. There's going to be a half chance that you pick the low-information grunt and a half chance that you pick the high-information scream. Comparing this to your usual behaviour (the grunt), it's easy to see that a random behaviour is going to be higher-information than a "normal" behaviour. This result transfers directly across to study of genetic sequences.
Mathematical definition 2: Kolmogorov complexity
Kolmogorov complexity is, broadly speaking, the length of the shortest program that can generate a given communication. So, for example, the Kolmogorov complexity of "AAAAAAAA" would be very low by comparison to that of "NBCJEDFJLEDLAN". It's fairly easy to see that, going by this definition, most random strings will be higher-information than most non-random strings, since the latter will generally display patterns that can be exploited to reduce the K-complexity.
Layman's definition 1: Data that means something
Since meaning is a purely subjective measure, this is something that is unlikely to be produced by an objective process. One would not expect nature to produce works of Shakespeare, for example. Fortunately for evolution, there's no information of this sort in the genetic code of living creatures. No really. What there is, however, is...
Layman's definition 2: Data that does something
To anyone who isn't a mathematician, this is probably the most interesting definition, and it's undeniable that living systems have it in spades. Fortunately, functionality is a fairly objective measure, so it's entirely possible for objective processes to produce it. In fact, it turns out that this is something evolution is perfectly capable of producing.
In particular, it's fairly hard to deny that information of this sort is produced by genetic algorithms. What's really interesting is the fact that GAs apparently often come up with solutions that humans would never in a million years have considered.
If you can come up with another definition that you believe can't be produced by evolution, I'll happily discuss it.
Well, you could certainly get back something that was Great Dane shaped, although in other, less obvious ways it would probably differ from the original. I'm rather intrigued by your idea that breeding from a wolf to a Chihuahua is possible but breeding from a Chihuahua to a Great Dane isn't - are you suggesting that wild wolves originally had some kind of essence-of-Chihuahua in them alongside the essence-of-Great-Dane?
Not being a geologist I can't speak about the Grand Canyon stuff, but I already discussed problems with hydraulic sorting. Can you please explain roughly what criteria you would expect a flood to sort carcasses by, so we can compare it to the evidence?
I'd note that creationists have been saying this for about the last hundred and fifty years, and yet the overwhelming majority of reputable scientists in relevant fields still support evolution. That suggests that the claim is factually inaccurate.
Just out of interest, could you give a few examples?
|Date: 2006/04/24 12:23:37, Link|
|Regards the tree of life thing, this is the best example at present.|
|Date: 2006/04/25 07:17:51, Link|
Huh, afdave may be right about a couple of my original links. I'd interpreted "reconstruction" as meaning only that the artists drew the bones in an anatomically-correct configuration rather than in exactly the configuration they were found, but on reflection I have no idea if this is correct. Can anyone with more knowledge confirm or refute this?
Afdave: I'd note that your comments about the ambulocetus skeleton are totally irrelevant since the one you discussed was considerably less complete than the one I actually linked to. It'd be good if you'd actually read my points before responding to them, rather than assuming that the AiG page has already covered the material - apart from anything else, this approach presupposes that there haven't been any recent palaeontological finds in the relevant areas.
I'd also prefer it if you left off the poll results. If your position is correct then they're irrelevant. If your position is incorrect then they're rubbing our noses in the fact that large numbers of our fellow human beings are credulous idiots. Either way, they come across as more snarky than helpful.
Any thoughts on my comments about information? I'd be interested to get some feedback on that, since it's something that seems to come up rather a lot.
|Date: 2006/04/30 02:09:10, Link|
afdave: I think you've slightly misunderstood what constitutes a scientific prediction. A valid prediction must answer a yes-or-no question that isn't already known, but that we can go out and check.
For example, using the most up-to-date hypothesis of gravity I can calculate the position that an arbitrary heavenly body will be in at a later date. I can then go out with my telescope and verify or falsify that prediction. If I falsify it, that means that the hypothesis is dodgy.
The reason we use this definition is that any hypothesis that can give rise to this sort of prediction has the potential to increase our ability to manipulate the universe. For example, Einstein's quantum mechanical hypotheses allow us to predict how electrons will behave in semiconductors and thus let us build transistors. Faraday's electromagnetic hypotheses allow us to communicate at great distances. The various chemical hypotheses developed over the centuries allow us to produce materials that our ancestors wouldn't even think to dream of.
Looking at the statements you list as predictions, I can't see any that fulfil this criterion. In particular:
a) "sophisticated stuff exists" is not a prediction as the answer is already known. If you could find a way to anticipate the existence of specific sophisticated stuff that hadn't yet been discovered and that wouldn't be predicted to the same degree of specificity by naturalistic hypotheses, that would constitute a valid prediction.
b) "big, impressive stuff exists" is not a prediction for the same reason. Scientists will only listen if you actually tell them something they didn't know (that they can go out and confirm)
c) To the extent to which this is a prediction, it would also be one that's made by purely naturalistic explanations. In particular, it's notable that the societal behaviours that tend to be conserved across cultures are precisely those that are essential for the survival of a complex society. My experience is that any other "law" will inevitably come with its own little set of counterexamples.
d) Again, this doesn't predict anything that we don't already know. As an aside, I'd note that the same argument could be used to infer the existence of many Gods and other supernatural entities. What is your rationale for applying it solely to the idea of a unitary creator God?
e) Again, the "prediction" here is something that we already know to be true. Actually, we also have some fairly sophisticated ideas about why it's true - for example, out-of-body experiences appear to relate to the deactivation of a specific part of the brain.
f) Again, this doesn't predict; it merely explains. It adds absolutely nothing to the sum total of human knowledge, merely substituting a useless platitude ("Goddidit") for further serious investigation.
g) Again, this is something that we already know. Now, if a number of religious people had been predicting time dilation before its existence was uncovered, that would be a different matter entirely. To get an actual valid prediction going here, you'd need to predict the existence of a novel phenomenon that hasn't yet been observed, and then go out and confirm its existence. If you pull that off, you'll win a Nobel and I'll quite possibly become a Christian.
My background: I'm currently a maths student at Cambridge, UK. I've been an atheist for pretty much as long as I've given the issue any thought. That's probably my parents' fault, but I've done sufficient investigation of religious beliefs to satisfy myself that my position is probably right. The investigation consisted (in part) of 7 years attendance of a mostly-YEC Baptist youth club, where I was always the one who spent hours discussing theology with the leaders whilst all the Christian kids were playing football
|Date: 2006/05/02 05:34:17, Link|
AFDave: again, I think we have a slight confusion of terminology. What you're describing as an hypothesis would, if I understand correctly, be more accurately considered a conjecture.
My understanding is that statements about the universe subdivide into the following categories:
Conjectures - statements that fit all the known data (these are produced by the largely-intuitive process of abduction)
Hypotheses - conjectures that are falsifiable
Data - conjectures that have been verified (there's no term for conjectures that are merely verifiable)
Predictions - conjectures that are both verifiable and falsifiable, and that haven't yet been verified or falsified
Science is concerned primarily with deciding which of the infinite number of possible hypotheses for any given situation is best. It does this by applying three principles: predictivity, parsimony and credibility. Predictivity means that an hypothesis must give us some idea of what we'll find next (otherwise it's scientifically useless), parsimony means that an hypothesis must be efficient in its use of "magic numbers" (so, for example, five dots in a row would be best described by a linear equation not a quintic equation), and credibility means that an hypothesis must have survived attempted falsification. Of these, credibility is the most important, followed by predictivity and then parsimony (this is partly because predictivity is a necessary condition for credibility).
Your conjecture does not, as it stands, make any predictions, so can't be considered an hypothesis. To rectify this, you'll need to:
1) increase its specificity until you can use it to make a prediction of the form described above
2) confirm that the current best-of-breed scientific hypotheses would not also make that prediction (ideally, they shouldn't even leave open the possibility of that prediction being true, but you can't have everything)
3) go out and test the prediction
I repeat: for your conjectures to be scientifically valid, it is not sufficient to present existing evidence in support of each of them. To match the level of current origins science, you must also be able to derive and confirm predictions from them. Otherwise, it really is just a "just so story". Predictivity is what makes the difference.
As an aside:
Because over the centuries scientists have shown an alarming tendency to get sucked into ultimately-unsuccessful research of the paranormal and cease to ever again produce useful scientific results. That's not a tendency that anyone particularly wants to encourage, so it's considered valid to basically tell students: "It's a dead end. Live with it." Plus, of course, a wide array of folks claim erroneously to have scientific support for their religious beliefs, which effectively dilutes science's trademark.
As I understand it, Dawkins merely says that modern science proves that God doesn't necessarily exist, not that He doesn't exist. It's a necessary condition for atheism, not a sufficient condition.
|Date: 2006/05/02 06:04:47, Link|
- Hypothesis: humans evolved from the same lineage as modern apes
- Observation: the modern apes that are most physiologically similar to humans have 24 chromosomes per haploid
- Observation: humans have 23 chromosomes per haploid
- Conclusion: either humans have lost a chromosome or the other apes have all gained a chromosome
- By application of parsimony: humans have lost a chromosome
- Observation: chromosomes are generally "lost" by merging with another chromosome, as destruction of a chromosome's worth of genetic information is generally fatal
- Conclusion: at some point in our ancestry, two human chromosomes merged
- Prediction: one human chromosome will closely resemble two ape chromosomes merged together.
This prediction was subsequently confirmed. I can present other instances of confirmed predictions if you like.
|Date: 2006/05/02 06:14:48, Link|
However, it was still a valid hypothesis because it makes the falsifiable, verifiable prediction that, if he chose to go to the factory, he would see planes being made that were identical in style to his. Likewise, the conjecture that the aerodynamics book was accurate is falsifiable - he could go away and build a bunch of toy aircraft and compare their flight with the book's claims, for example.
In general, the only time we take a statement on trust is when we can reasonably expect that it would have been falsified were it not true. Or when we have absolutely no other option. Abduction is rarely more than half the story, and in science it's generally not even that.
|Date: 2006/05/13 09:18:59, Link|
Well, it appears I've joined the UD shitlist club. The ironic thing is that I wasn't attempting to be nasty or argumentative (or dumb) - I've been actively resisting the urge to post on UD unless and until I felt I could engage in polite conversation on an issue.
Let's see what the effect of attempting to remain polite is...
|Date: 2006/05/26 12:22:52, Link|
We're not perfect. That's why, when attempting to contribute to the sum of human knowledge, we operate via a process that's very good at weeding out daft errors.
Hovind doesn't have that kind of humility, and a direct result of this is that his talks have enough egregious mistakes in to make a serious biologist/palaeontologist/geologist/cosmologist/archaeologist vomit.
What's really really annoying is that his audiences seem not to care.
|Date: 2006/05/28 01:32:01, Link|
|Uh... I suspect that the data in question will be slightly out of copyright. Even in the US.|
|Date: 2006/06/03 03:58:41, Link|
That's correct - as you say, it's possible to build almost any framework round a given set of facts. That's why science requires predictive as well as explanative power.
In the case of common descent, if the chain of thought had been "ooh, fossil record. Hmm, common descent could explain this. Case closed" then the fossil record would indeed not validate common descent. However, the fact that evolutionary biologists then went on to draw further predictions as to what they'd see next, and that these predictions were subsequently confirmed, does validate common descent. Anyone here should be able to rattle off at least three such predictions for you. My favourite examples are:
1) One human chromosome resembling two fused chimp chromosomes
3) Stoneflies possessing haemocyanin
If these evolutionary hypotheses and theories did not bear a close resemblance to the processes that actually give rise to life, they would not consistently give rise to accurate predictions.
|Date: 2006/06/03 06:41:00, Link|
|It's a reductio ad absurdum. As such, it's appropriate for it to be, um, absurd.|
|Date: 2006/06/06 01:10:05, Link|
Well, apparently viewing the results before voting bars you from participation, but I'd like to throw in a vote for Salvador.
Not particularly on the basis of his intellect, I don't know him well enough to come to a conclusion on that, but on the basis of the time he spent the best part of a week explaining Shannon information one slooow step at a time to a maths undergrad, and then more or less burst into tears when the response was "yeah, and your point is?"
|Date: 2006/06/07 02:54:29, Link|
I have noticed a propensity for academically-inclined YECs to focus on more practical, even vocational subjects rather than, say, number theory. I suspect that this is because, if they feel like getting a deep understanding of how things work, they already feel they know where to go. They lack the "theory itch" that drives mathmos and scientists, and as such tend to go into subjects that involve applying knowledge rather than generating it.