It's just a difference of degree. There are hard physical limits on information processing that cannot be exceeded: https://en.wikipedia.org/wiki/...
NB that these limits directly imply that any finite region of space can be fully simulated by a sufficiently large, (non-deterministic) linear bounded automaton--an abstract computational machine less powerful than a Turing machine.
QM by itself is not enough. It's only once you mix it with thermodynamics that you can derive the Bekenstein bound (the result that the maximum information in a region of space is the entropy of a black hole of the same surface area) and thus put an ultimate limit on information density. There are also hard physical limits on minimum energy per unit of computation, and minimum time per unit of computation (Margolus–Levitin theorem, Bremermann's limit, etc.).
>>If math was really modeling the universe well, we would have whole numbers for constants: e, c, k, pi.
You're wrong in your implication. Quantum mechanics and quantum field theory are fully computable theories. Moreover, in the physical universe there are no arbitrary precision real numbers, because that would allow you to encode infinite information in a single quantity, which would violate the Bekenstein bound--a fundamental limit on the number of distinguishable quantum states in a finite region of space (which is equivalent to limiting the information that can be stored in a finite region): https://en.wikipedia.org/wiki/...
The other issue to address is physical security. However, there have been cheap ICs for years that store a key and securely wipe it nearly instantaneously if signaled on a given pin--this allows you to hook it up to physical interlocks on a computer case, alarm system, remote control, or whatever (or OR-gate a few of those). Due to low power draw, these could easily run off a battery, preventing the security being defeated by the attacker shutting off power.
In the long run, it may actually bring on an extinction event, so I see no reason for it to be excluded. It's probably more likely than wide-scale nuclear war over the coming decades, and in the worst case, potentially more thorough than it as well (after all, even in the case of global nuclear winter, there would still be survivors).
Took me a moment to see your link it to the nanotech "grey goo" disaster scenario. Given Google's ventures in various new areas, such as their recent involvement in robotics, I wouldn't be surprised if that comes from there too, eventually.
The article discusses at length the detailed concerns, but just to demonstrate that this is taken seriously far beyond the doomsday clock group, I quote here an excerpt related to that specific point:
Challenging the assumption of the inevitability of autonomous weapons and building on the work of earlier activists, the Campaign to Stop Killer Robots, a coalition of nongovernmental organizations, was launched in April 2013. This effort has made remarkable progress in its first year. In May, the United Nations Special Rapporteur on extrajudicial killings, Christof Heyns, recommended that nations immediately declare moratoriums on their own development of lethal autonomous robotics (Heyns, 2013). Heyns also called for a high-level study of the issue, a recommendation seconded in July by the UN Advisory Board on Disarmament Matters. At the UN General Assemblyâ(TM)s First Committee meeting in October, a flood of countries began to express interest or concern, including China, Russia, Japan, the United Kingdom, and the United States. France called for a mandate to discuss the issue under the Convention on Certain Conventional Weapons, a global treaty that restricts excessively injurious or indiscriminate weapons. Meeting in Geneva in November, the state parties to the Convention agreed to formal discussions on autonomous weapons, with a first round in May 2014. The issue has been placed firmly on the global public and diplomatic agenda.
It's hard to take normative positivism seriously when it's premier proponent rejects the principle of judicial review--something not merely incidental to the former.
The second annoyance is that a more socialist system is a panacea. Europe is suffering most of the problems we are.
Europe's problems are due to the euro, as having a monetary union without economic and fiscal union allowed Germany to use exploitative mercantilist practices to beggar their neighbors. The problems in the eurozone were predicted by MMT pretty much spot on.
Joe Nocera, by the way, is a "business" columnist/commentator who has a penchant for taking a reasonable position to silly extremes, so I guess this isn't such a surprise.
On the other hand, his primary source is Jaron Lanier, the guy who pioneered virtual reality in the 80s.
So what Dawkins pointed out over three decades ago and has been considered as generally accepted and uncontroversial for most of that time is all wrong? Ah, the things one learns from random slahdotters!
>The "audio" in question is most likely all below 24 kHz, that being the Nyquist limit for the 48 kHz sampling hardware, unless it happens that some phones can actually sample faster, and have microphones that can respond to higher frequencies. The instruction rate of the CPUs in question is many times that frequency. It doesn't sound likely.
Your objection was directly addressed in the article:
"Cryptanalytic side-channel attacks typically require measurements with temporal resolution similar to the time scale of the target operation, but here the target cryptographic computation is many orders of magnitude faster....the key extraction attack relies on crafting chosen ciphertexts that cause numerical cancellations deep inside GnuPG's modular exponentiation algorithm. This causes the special value zero to appear frequently in the innermost loop of the algorithm, where it affects control flow. A single iteration of that loop is much too fast for direct acoustic observation, but the effect is repeated and amplified over many thousands of iterations, resulting in a gross leakage effect that is discernible in the acoustic spectrum over hundreds of milliseconds
I dare suggest that sometimes even the experts need to RTFA.:)
>So if there's a limited set out possible outcomes, a non-deterministic system can simulate them? I'm not sure that follows.
Finiteness and non-determinism are completely separate issues. Let me elaborate on these two for a bit.
I specified a non-deterministic LBA because what's known as "The First LBA problem" is still outstanding--that is, whether the class of problems solvable by a non-deterministic LBA is the same as its deterministic counterpart. It may be possible that the non-deterministic LBA is more powerful. And, as QM is non-deterministic, if they are indeed different in power, it may take a non-deterministic LBA to be able to simulate any possible finite physical system in a universe that is quantum in nature, such as ours.
The finiteness issue is not addressed by non-determinism; it's addressed by using an abstract model of computation that is strictly more powerful than LBAs: Turing machines. They are just like LBAs, except that they have unlimited memory. It's worth noting here that for TMs it's been shown that non-deterministic TMs are exactly as powerful as deterministic ones. All that non-determinism adds for TMs is an increase in efficiency for some classes of problems.
To physically realize a universal TM, you'd need to make sure it can have an arbitrarily large amount of memory, to cover all possible information processing that a TM can do. This is not possible in our universe, since due to quantum uncertainty, as your TM's extent in either time or space goes to infinity, the probability that a quantum fluctuation will screw up its processing goes to 1 (certainty). Not to mention other issues such as running out of reachable usable energy gradient to power arbitrarily long information processing due to accelerating expansion of the universe (which limits the matter-energy that can ever be within our Hubble volume).
The infinity of a TM's infinite memory is countable infinity; i.e. akin to the set of integers, or other countable sets. However, another type of infinity is uncountable, such as the set of real numbers. In a finite interval, such as from 0 to 1, there are still infinitely many real numbers. Uncountable infinites were proved to be strictly larger in a mathematical sense than countable ones, by Cantor's famous diagonalization argument. If real numbers were physically realizable, you could have an entity that is super-Turing in information processing power. But this is exactly what the Bekenstein bound rules out, by limiting the number of states in a finite expanse.
Penrose is one of the most prominent respected scientists to propose noncomputable physics (see his "The Emperor's New Mind" and "Shadows of the Mind"), but his arguments were refuted by various experts, from physicists to logicians (see, for example, "A Refutation of Penrose's Godelian Case Against Artificial Intelligence"). He seemed to do it without any evidence, really, and claimed that quantum mechanics must be wrong since it's computable (as is, by the way, quantum field theory).
There were other related arguments around the same time bearing upon this. One had to do with things such as a proposal that artificial neural networks can be super-turing if the weights at nodes could be arbitrary precision real numbers--something clearly excluded by the Bekenstein bound. Yet another one was the observation that a turing machine modified to have continued interaction with its environment, rather than just starting with input and ending with output, can be super-turing. However, this argument is akin to a slight of hand, because it's based on a misleading definition of what the information processing system is, by excluding part of it--the interacting environment in question. If that environment is finite (and it is limited by the system's light cone, unless you believe superluminal communication speed is possible), then the combined system is still sub-turing: a non-deterministic LBA.
So are human minds subject to the same theoretical limits that apply to finite computers? It certainly appears that way, according to our current understanding of physics. Of course, it may be that this will be upturned in the future by the discovery of new, noncomputational physics, and, of course, not all philosophical worldviews align with physicalism.
As for your comment on how powerful quantum computer algorithms can be, we already have a pretty good idea that they're not all that powerful--they're just more efficient (and, specifically, polynomially more efficient); see the computational complexity classes defined for them, like BQP etc. http://arxiv.org/abs/0804.3401
>That there is a maximum possible information needed to completely describe a volume of space. Surprisingly that limit grows with surface area, not volume.
This is equivalent to the Bekenstein bound, where the maximum entropy/information density is proportional to the radius and mass/energy. In the extreme case, for the latter substitute the Schwarszchild radius for that mass/energy, giving a formula proportional to the square of the radius--i.e. surface area, as you wrote.
> It's best not to read too much into that because the limit here is really quite high....[11D to 10D reduction] much more interesting result that the black hole result
I suggest otherwise. A finite maximum number of quantum states in any finitely bounded region of space implies that any physical system with a finite extent can always be simulated by a nondeterministic linearly bounded automaton, an abstract model of computation that is strictly less powerful than a Turing machine. So no super-Turing machines, no noncomputable information processing/thinking, no arbitraty precision real numbers--all of these things are unphysical. Unless you're a dualist and don't believe that mind is what the brain does, this physical constraint means that our minds are ultimately computational, because their physical implementation is computational, and that any finite brain can ultimately have only a finite number of different thoughts. It also means that halting problems and Godelian limits exist for our minds just as they exist for our electronic computers.
I think my own bias seeped in when I posted that, as I'm partial to "melting pot" integration and cautious of multiculturalism. I think it's arguable what all the critical pieces you allude to are, and so, at what stage sufficient knowledge has accumulated but cultural indoctrination has not yet completely set in.
Actually, any physical system, be it brain or computer, is more limited than the universal Turing machine abstraction. By the Bekenstein bound result from QM+thermodynamics, there is a finite upper bound on the maximum number of distinguishable quantum states that are possible within a region of space with a finite extent. From this it follows that any physical system's processing of information, whether that is an algorithm on a computer or thoughts in the brain, can always be simulated by a sufficiently large non-deterministic LBA (linearly bounded automaton), which is less powerful than a TM. It also bears remembering that QM and QFT are both computable, implying that, if they really are appropriate models of reality (which almost no physicist will disagree with), reality is computable as well.
It's not that I don't find your argument persuasive. I certainly agree that, in principle, it is important to teach the "why" (and, by extension, the "how" of discovering the "why"/"what"). However, I can't ignore tlambert's more pragmatic concerns, which he reaffirms in http://slashdot.org/comments.pl?sid=4536685&cid=45648383 It bears remembering that humans are boundedly rational, and in kids that's exacerbated by their initial ignorance. We don't know whether, if given the formal tools of critical thinking before foundational knowledge and some experience has been laid, they would necessarily be applied without significant bias in a way that affects further learning in a negative manner. And yes, as you wrote, they would otherwise create their own answers as to the "why" with bias as well, but this can be countered by teaching some of the "why" in a subject-targeted manner, which can be done in a way that has less of the potential downside that tlambert is worried about. I don't think anyone here is actually advocating "brow beating and rote memorization", but tlambert, please comment here if I've misrepresented your position.
As an aside, I want to point out that even "hardcore" memorization has its place. In a recent discussion on organic chemistry here, http://slashdot.org/story/13/11/03/1537247/why-organic-chemistry-is-so-difficult-for-pre-med-students , many derided the difficulty brought on by the tremendous amount of special cases and exceptions to the rules one has to remember. However, a couple of posts there noted with insight that it is through that very process that one begins to learn to recognize the patterns underlying all the exceptions and when to apply them, patterns generally too complex to be expressed formally and distilled into a textbook.
I don't think you can really blame academics. It seems to be, rather, that universities have succumbed to the same general trend that made MBAs and other business/management types infuse institutions beyond just the corporate world with a management style and optimization strategies that look only at narrowly defined metrics (usually revolving around financials, PR, etc.). Academic institutions seem to be run more like businesses these days than places of learning and research, and this is reflected in their employment distribution: in just one example, "employment of administrators jumped 60 percent from 1993 to 2009, 10 times the growth rate for tenured faculty" (source: http://www.businessweek.com/articles/2012-11-21/the-troubling-dean-to-professor-ratio ). I remember reading about this trend of falling faculty-to-administrator ratio quite a few years ago, along with the claim that it's been going on since at least the 1970s; it really struck home, however, when I noticed it affecting very schools I had attended. With the falling powers of faculty associations (like unions in general), I doubt that researchers and instructors could have stemmed this.
> For an upper bound, I would point to the medical data concerning when a person is statistically likely to have completed the mylenation process, and the body of data concerning the strong correllation between dendrite formation and migration and the curve that corresponds to mylenation.
I'm sorry anon, but I don't see any justification as to why this should be an upper bound. I was not referring to neurological maturation, but psychological. They're not the same, nor do they coincide; though the first has an undeniably critical impact on the second, the second also depends on many other factors, including acquired knowledge and experience. Teaching something during a developmental stage with high dendrite formation may make learning more efficient, but this efficiency does not by itself define what is the most appropriate timing. (Plus, dendride plasticity remains an aspect of the human brain throughout life: http://onlinelibrary.wiley.com/doi/10.1002/dneu.20951/full )
Slashdot Mirror
It's just a difference of degree. There are hard physical limits on information processing that cannot be exceeded: https://en.wikipedia.org/wiki/...
NB that these limits directly imply that any finite region of space can be fully simulated by a sufficiently large, (non-deterministic) linear bounded automaton--an abstract computational machine less powerful than a Turing machine.
QM by itself is not enough. It's only once you mix it with thermodynamics that you can derive the Bekenstein bound (the result that the maximum information in a region of space is the entropy of a black hole of the same surface area) and thus put an ultimate limit on information density. There are also hard physical limits on minimum energy per unit of computation, and minimum time per unit of computation (Margolus–Levitin theorem, Bremermann's limit, etc.).
>>If math was really modeling the universe well, we would have whole numbers for constants: e, c, k, pi.
You're wrong in your implication. Quantum mechanics and quantum field theory are fully computable theories. Moreover, in the physical universe there are no arbitrary precision real numbers, because that would allow you to encode infinite information in a single quantity, which would violate the Bekenstein bound--a fundamental limit on the number of distinguishable quantum states in a finite region of space (which is equivalent to limiting the information that can be stored in a finite region): https://en.wikipedia.org/wiki/...
If you're using TrueCrypt but without full disk encryption, encrypt your pagefile: http://www.sevenforums.com/tutorials/143662-page-file-encryption-enable-disable.html
You can easily encrypt your pagefile on Windows by at least three methods: http://www.sevenforums.com/tutorials/143662-page-file-encryption-enable-disable.html
The other issue to address is physical security. However, there have been cheap ICs for years that store a key and securely wipe it nearly instantaneously if signaled on a given pin--this allows you to hook it up to physical interlocks on a computer case, alarm system, remote control, or whatever (or OR-gate a few of those). Due to low power draw, these could easily run off a battery, preventing the security being defeated by the attacker shutting off power.
In the long run, it may actually bring on an extinction event, so I see no reason for it to be excluded. It's probably more likely than wide-scale nuclear war over the coming decades, and in the worst case, potentially more thorough than it as well (after all, even in the case of global nuclear winter, there would still be survivors).
> Grey Google
Took me a moment to see your link it to the nanotech "grey goo" disaster scenario. Given Google's ventures in various new areas, such as their recent involvement in robotics, I wouldn't be surprised if that comes from there too, eventually.
This was covered on Slashdot less than a week ago, link inlcuded: http://bos.sagepub.com/content/70/1/32.full
The article discusses at length the detailed concerns, but just to demonstrate that this is taken seriously far beyond the doomsday clock group, I quote here an excerpt related to that specific point:
Challenging the assumption of the inevitability of autonomous weapons and building on the work of earlier activists, the Campaign to Stop Killer Robots, a coalition of nongovernmental organizations, was launched in April 2013. This effort has made remarkable progress in its first year. In May, the United Nations Special Rapporteur on extrajudicial killings, Christof Heyns, recommended that nations immediately declare moratoriums on their own development of lethal autonomous robotics (Heyns, 2013). Heyns also called for a high-level study of the issue, a recommendation seconded in July by the UN Advisory Board on Disarmament Matters. At the UN General Assemblyâ(TM)s First Committee meeting in October, a flood of countries began to express interest or concern, including China, Russia, Japan, the United Kingdom, and the United States. France called for a mandate to discuss the issue under the Convention on Certain Conventional Weapons, a global treaty that restricts excessively injurious or indiscriminate weapons. Meeting in Geneva in November, the state parties to the Convention agreed to formal discussions on autonomous weapons, with a first round in May 2014. The issue has been placed firmly on the global public and diplomatic agenda.
It's hard to take normative positivism seriously when it's premier proponent rejects the principle of judicial review--something not merely incidental to the former.
Mod parent up!
The second annoyance is that a more socialist system is a panacea. Europe is suffering most of the problems we are.
Europe's problems are due to the euro, as having a monetary union without economic and fiscal union allowed Germany to use exploitative mercantilist practices to beggar their neighbors. The problems in the eurozone were predicted by MMT pretty much spot on.
Joe Nocera, by the way, is a "business" columnist/commentator who has a penchant for taking a reasonable position to silly extremes, so I guess this isn't such a surprise.
On the other hand, his primary source is Jaron Lanier, the guy who pioneered virtual reality in the 80s.
I wish I had mod points. Please mod parent up.
So what Dawkins pointed out over three decades ago and has been considered as generally accepted and uncontroversial for most of that time is all wrong? Ah, the things one learns from random slahdotters!
Their attack is based on spectral analysis, not time series analysis, so this sort of obfuscation would not work well. Please RTFA.
>The "audio" in question is most likely all below 24 kHz, that being the Nyquist limit for the 48 kHz sampling hardware, unless it happens that some phones can actually sample faster, and have microphones that can respond to higher frequencies. The instruction rate of the CPUs in question is many times that frequency. It doesn't sound likely.
:)
Your objection was directly addressed in the article:
"Cryptanalytic side-channel attacks typically require measurements with temporal resolution similar to the time scale of the target operation, but here the target cryptographic computation is many orders of magnitude faster....the key extraction attack relies on crafting chosen ciphertexts that cause numerical cancellations deep inside GnuPG's modular exponentiation algorithm. This causes the special value zero to appear frequently in the innermost loop of the algorithm, where it affects control flow. A single iteration of that loop is much too fast for direct acoustic observation, but the effect is repeated and amplified over many thousands of iterations, resulting in a gross leakage effect that is discernible in the acoustic spectrum over hundreds of milliseconds
I dare suggest that sometimes even the experts need to RTFA.
>So if there's a limited set out possible outcomes, a non-deterministic system can simulate them? I'm not sure that follows.
Finiteness and non-determinism are completely separate issues. Let me elaborate on these two for a bit.
I specified a non-deterministic LBA because what's known as "The First LBA problem" is still outstanding--that is, whether the class of problems solvable by a non-deterministic LBA is the same as its deterministic counterpart. It may be possible that the non-deterministic LBA is more powerful. And, as QM is non-deterministic, if they are indeed different in power, it may take a non-deterministic LBA to be able to simulate any possible finite physical system in a universe that is quantum in nature, such as ours.
The finiteness issue is not addressed by non-determinism; it's addressed by using an abstract model of computation that is strictly more powerful than LBAs: Turing machines. They are just like LBAs, except that they have unlimited memory. It's worth noting here that for TMs it's been shown that non-deterministic TMs are exactly as powerful as deterministic ones. All that non-determinism adds for TMs is an increase in efficiency for some classes of problems.
To physically realize a universal TM, you'd need to make sure it can have an arbitrarily large amount of memory, to cover all possible information processing that a TM can do. This is not possible in our universe, since due to quantum uncertainty, as your TM's extent in either time or space goes to infinity, the probability that a quantum fluctuation will screw up its processing goes to 1 (certainty). Not to mention other issues such as running out of reachable usable energy gradient to power arbitrarily long information processing due to accelerating expansion of the universe (which limits the matter-energy that can ever be within our Hubble volume).
The infinity of a TM's infinite memory is countable infinity; i.e. akin to the set of integers, or other countable sets. However, another type of infinity is uncountable, such as the set of real numbers. In a finite interval, such as from 0 to 1, there are still infinitely many real numbers. Uncountable infinites were proved to be strictly larger in a mathematical sense than countable ones, by Cantor's famous diagonalization argument. If real numbers were physically realizable, you could have an entity that is super-Turing in information processing power. But this is exactly what the Bekenstein bound rules out, by limiting the number of states in a finite expanse.
Penrose is one of the most prominent respected scientists to propose noncomputable physics (see his "The Emperor's New Mind" and "Shadows of the Mind"), but his arguments were refuted by various experts, from physicists to logicians (see, for example, "A Refutation of Penrose's Godelian Case Against Artificial Intelligence"). He seemed to do it without any evidence, really, and claimed that quantum mechanics must be wrong since it's computable (as is, by the way, quantum field theory).
There were other related arguments around the same time bearing upon this. One had to do with things such as a proposal that artificial neural networks can be super-turing if the weights at nodes could be arbitrary precision real numbers--something clearly excluded by the Bekenstein bound. Yet another one was the observation that a turing machine modified to have continued interaction with its environment, rather than just starting with input and ending with output, can be super-turing. However, this argument is akin to a slight of hand, because it's based on a misleading definition of what the information processing system is, by excluding part of it--the interacting environment in question. If that environment is finite (and it is limited by the system's light cone, unless you believe superluminal communication speed is possible), then the combined system is still sub-turing: a non-deterministic LBA.
So are human minds subject to the same theoretical limits that apply to finite computers? It certainly appears that way, according to our current understanding of physics. Of course, it may be that this will be upturned in the future by the discovery of new, noncomputational physics, and, of course, not all philosophical worldviews align with physicalism.
As for your comment on how powerful quantum computer algorithms can be, we already have a pretty good idea that they're not all that powerful--they're just more efficient (and, specifically, polynomially more efficient); see the computational complexity classes defined for them, like BQP etc. http://arxiv.org/abs/0804.3401
>That there is a maximum possible information needed to completely describe a volume of space. Surprisingly that limit grows with surface area, not volume.
This is equivalent to the Bekenstein bound, where the maximum entropy/information density is proportional to the radius and mass/energy. In the extreme case, for the latter substitute the Schwarszchild radius for that mass/energy, giving a formula proportional to the square of the radius--i.e. surface area, as you wrote.
> It's best not to read too much into that because the limit here is really quite high....[11D to 10D reduction] much more interesting result that the black hole result
I suggest otherwise. A finite maximum number of quantum states in any finitely bounded region of space implies that any physical system with a finite extent can always be simulated by a nondeterministic linearly bounded automaton, an abstract model of computation that is strictly less powerful than a Turing machine. So no super-Turing machines, no noncomputable information processing/thinking, no arbitraty precision real numbers--all of these things are unphysical. Unless you're a dualist and don't believe that mind is what the brain does, this physical constraint means that our minds are ultimately computational, because their physical implementation is computational, and that any finite brain can ultimately have only a finite number of different thoughts. It also means that halting problems and Godelian limits exist for our minds just as they exist for our electronic computers.
I think my own bias seeped in when I posted that, as I'm partial to "melting pot" integration and cautious of multiculturalism. I think it's arguable what all the critical pieces you allude to are, and so, at what stage sufficient knowledge has accumulated but cultural indoctrination has not yet completely set in.
Actually, any physical system, be it brain or computer, is more limited than the universal Turing machine abstraction. By the Bekenstein bound result from QM+thermodynamics, there is a finite upper bound on the maximum number of distinguishable quantum states that are possible within a region of space with a finite extent. From this it follows that any physical system's processing of information, whether that is an algorithm on a computer or thoughts in the brain, can always be simulated by a sufficiently large non-deterministic LBA (linearly bounded automaton), which is less powerful than a TM. It also bears remembering that QM and QFT are both computable, implying that, if they really are appropriate models of reality (which almost no physicist will disagree with), reality is computable as well.
It's not that I don't find your argument persuasive. I certainly agree that, in principle, it is important to teach the "why" (and, by extension, the "how" of discovering the "why"/"what"). However, I can't ignore tlambert's more pragmatic concerns, which he reaffirms in http://slashdot.org/comments.pl?sid=4536685&cid=45648383 It bears remembering that humans are boundedly rational, and in kids that's exacerbated by their initial ignorance. We don't know whether, if given the formal tools of critical thinking before foundational knowledge and some experience has been laid, they would necessarily be applied without significant bias in a way that affects further learning in a negative manner. And yes, as you wrote, they would otherwise create their own answers as to the "why" with bias as well, but this can be countered by teaching some of the "why" in a subject-targeted manner, which can be done in a way that has less of the potential downside that tlambert is worried about. I don't think anyone here is actually advocating "brow beating and rote memorization", but tlambert, please comment here if I've misrepresented your position.
As an aside, I want to point out that even "hardcore" memorization has its place. In a recent discussion on organic chemistry here, http://slashdot.org/story/13/11/03/1537247/why-organic-chemistry-is-so-difficult-for-pre-med-students , many derided the difficulty brought on by the tremendous amount of special cases and exceptions to the rules one has to remember. However, a couple of posts there noted with insight that it is through that very process that one begins to learn to recognize the patterns underlying all the exceptions and when to apply them, patterns generally too complex to be expressed formally and distilled into a textbook.
I don't think you can really blame academics. It seems to be, rather, that universities have succumbed to the same general trend that made MBAs and other business/management types infuse institutions beyond just the corporate world with a management style and optimization strategies that look only at narrowly defined metrics (usually revolving around financials, PR, etc.). Academic institutions seem to be run more like businesses these days than places of learning and research, and this is reflected in their employment distribution: in just one example, "employment of administrators jumped 60 percent from 1993 to 2009, 10 times the growth rate for tenured faculty" (source: http://www.businessweek.com/articles/2012-11-21/the-troubling-dean-to-professor-ratio ). I remember reading about this trend of falling faculty-to-administrator ratio quite a few years ago, along with the claim that it's been going on since at least the 1970s; it really struck home, however, when I noticed it affecting very schools I had attended. With the falling powers of faculty associations (like unions in general), I doubt that researchers and instructors could have stemmed this.
> For an upper bound, I would point to the medical data concerning when a person is statistically likely to have completed the mylenation process, and the body of data concerning the strong correllation between dendrite formation and migration and the curve that corresponds to mylenation.
I'm sorry anon, but I don't see any justification as to why this should be an upper bound. I was not referring to neurological maturation, but psychological. They're not the same, nor do they coincide; though the first has an undeniably critical impact on the second, the second also depends on many other factors, including acquired knowledge and experience. Teaching something during a developmental stage with high dendrite formation may make learning more efficient, but this efficiency does not by itself define what is the most appropriate timing. (Plus, dendride plasticity remains an aspect of the human brain throughout life: http://onlinelibrary.wiley.com/doi/10.1002/dneu.20951/full )