Is science sometimes in danger of getting tunnel vision? Recently published ebook author, Ian Miller, looks at other possible theories arising from data that we think we understand. Can looking problems in a different light give scientists a different perspective?

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In this part of the world, Christmas cards look a little odd with all that snow, etc, but they do remind me why Christmas is at this time of the year: it is the end of the Saturnalia. In Roman times, at the winter solstice the God Saturn would see out the old year, and would promise that shortly the world would be reborn, the days would begin lengthening again, spring would come, crops could be sown, and all would be well. In the short dark interval before there was perceptible lengthening, Romans would feast, play tricks and bow down to the Lord of Misrule! The Christians highlighted the day of rebirth, about three days after the solstice, but I sometimes wonder if the politicians have stolen too much of the preceding concept. Proper rule should be based on logic and clear evidence; misrule by definition, on anything else.
 
Just recently New Zealand seems to have been struck by torrential floods, the effects of which appear to have been magnified as a consequence of theories by "authorities" of where to build and how much forest can be cut from where. As another example, the kiwifruit industry has been hit by a fungal disease that, while it cannot be absolutely proven, appears to have been introduced with imported pollen. The Head of the agricultural authority that approved the importation was reported, as an excuse, as saying there was no scientific evidence published that the fungus could come with pollen. My gripe with that is one of logic: absence of evidence is not evidence of absence.
 
My point is, science has a lot to offer the community, but only if the community understands the basis of it. People who make decisions, and the average citizen who must either accept such decisions or protest, must do so on proper grounds. The average citizen most certainly should not be asked to sit down and do piles of calculus, but it would be extremely beneficial if they could at least assess the arguments given as likely to be correct or not, based on an understanding of what a scientific argument should look like. The experts should provide the analysis, but more people should be able to tell whether the analysis looks sound or is just plain lazy. The most important point of all lies in what is not there, how many assumptions are made and whether they look realistic. That is not impossible for the non-specialist to do.
 
So, how do we bring about such a transformation? We can preach, but I rather feel that will only work with a select few. My personal view is that we can do more. At this time of the year, we give each other gifts, and books are common gifts. While thinking about that, I thought, science fiction might help, then with a little more thought, I had to ask, does it really? Does it convey any scientific method, or is it usually just "magic" and the equivalent of the modern day sorcery tales? For those interested in my thoughts on that, rather than the dreaded "multiple publication", why not a reference!  http://greyhartpress.com/2011/12/12/guest-post-ian-miller-gives-a-scientists-view-of-science-fiction/ 
 
Meanwhile, may I wish you all a very Merry Christmas and a prosperous New Year, that reactions go as planned and discoveries flow in 2012. And, of course, Io Saturnalia!
Posted by Ian Miller on Dec 20, 2011 9:58 PM GMT
Suppose you believe that sooner or later, providing transport fuels will become a problem? What do you do, and more to the point, how do you go about it? The issues are surprisingly complicated, and as an example, consider the case of when the government wishes to promote ethanol from corn, as in the US.
 
This appears to eb a simple problem as the technology is well established, but that still leaves open the question, how do you do it? To encourage production, and avoid the moral hazard of selecting specific companies, or worse still, to defend against allegations that you selected your friends, the simplest procedure is to offer the money as a subsidy.
 
The reason for going after corn in the US is simple: when this was first considered, there was a surplus of corn and spare corn was cheap. However, corn is also a food, and the price elasticity of food is not a simple function. If you have too much food, depressing the price has little effect on increasing consumption, because you (or animals) can only eat so much. On the other hand, if you have too little, you (or animals) still have to eat, and accordingly there is competition for what is available and the price goes up significantly. Worse, there is not unlimited land on which to plant more. Accordingly, the end-result tends to be a function with a sharp bend and it is never clear where that is. Accordingly, the first corn plant makes ethanol with little downstream effect, and if the subsidy is enough, the plant makes money. Unfortunately, that encourages "me-too" investment and at some point the corn price rises.
 
While simple theory suggests that the price will rise to the point where further investment in ethanol is discouraged, simple theory overlooks the effect of response time. It takes perhaps years to construct such a plant, and if the initial indicators are good, usually there is an overinvestment in such plant. Accordingly, prices rise above where the subsidy makes a profit, which means there has to be a shakeout. What tends to be shaken out are the least efficient plants, or those with the least persistent backers, and paradoxically it is often the early plants that get shaken out.
 
From the public point of view, there is moral hazard in selecting specific companies and helping them; from the economic point of view there is hazard in subsidies; from the system point of view there is long-term hazard from doing nothing, because at some stage the transport costs will get put of hand and while eventually this problem may (or may not) be solved, eventually may follow the greatest depression of all time. So, the question is, what should be done, and how should it be done? In my opinion, there has been a serious shortage of thought on this issue. Don't we care if we all have to walk? Or is it just that the politicians do not care, because they believe that whatever else happens, they will never have to walk?
Posted by Ian Miller on Dec 11, 2011 11:39 PM GMT
The next problem relating to science funding that I wish to discuss is where will the money come from? Pure science is generally funded from the public purse. However, this may be an unreliable source in the not too distant future because most governments have funded a lot of their activities through debt. While the question of what level of debt is tolerable is something of an economic minefield, one point is clear: a number of governments are going to have to make considerable budget savings, and pure science is as likely as not to suffer.
 
Suppose such funding is cut by x per cent, how should scientists respond? My suggestion will not please everybody, but I feel that operational expenditure should be the first to go. Over the past thirty years, an enormous amount of data has been generated, and I feel much more can be mined from it. One example has come from planetary science: a limited number of papers are now being produced that revisits data obtained much earlier. Obviously this cannot go on for ever, but it might be better for the scientists to make an agreement with governments to sacrifice some current expenditure for the common good, on the understanding that the sacrifice is temporary, than the governments make the cuts anyway, and in the general fight for reduced funding, many good scientists are forced to become taxi drivers. To support my view, you might wish to read R. A. Kerr (Science 334: 1052-1053). While discussing the actions needed to combat climate change, the following points were made. First, David Behar was quoted as saying, "“We need actionable science.” He defined that as “data, analysis, and forecasts that are sufficiently predictive, accepted and understandable to support decision-making.” As Bruce Hewitson was quoted as saying that a result is actionable if you would spend your own money on it. Both men stated that they were drowning in data, but assessment was terrible, and there were very few actionable results.
 
What about applied science? Funding of science requires an actionable decision, so on what basis should decisions be made? It is usually considered that industry should fund its own research, on the grounds that there is no reason for the taxpayer to fund private benefit, and that call will grow more strident in difficult times. The call may well be reinforced through the issues relating to moral hazard, for example, why should the taxes of a company be used to support a competitor? It is one thing to have to compete; it is entirely another to have to assist your competitor. (However, I am far from convinced that some in the public sector appreciate this point.)
 
Nevertheless there are some issues that are so important to the community at large that they cannot be left to chance, and the production of fuel in the inevitable event of oil production being inadequate for demand appears to be one of these. So, who funds it? The most desirable source, in my opinion, is the private sector because they will be more focused on achievable goals, but what happens if they do not? If the governments provide funds, who benefits directly (i.e. gets to use the technology) and why? If governments provide funding, to whom do the funds go, and why? Funding on applied research should be a business decision, but who controls the expenditure, to ensure that there is a minimum of wastage? On the other hand, if nobody is funding the most critical research, is society prepared to suffer the consequences?
 
Posted by Ian Miller on Nov 28, 2011 11:04 PM GMT
A question for the reader to contemplate before: what is the primary objective of an investment in a technology development? My answer is below.
 
It is now my intention to run a small series of blogs on investment in scientific development, using biofuels as an example. The reader might like to participate by deciding which, if any, technology they would invest in if they had the money, and more importantly, why choose that? An important additional consideration is this: if nobody invests, and if there is no development such as fusion power and fuel cells, people had better get used to walking.
 
Returning to the question, the answer is clear: to make money. That should be the only primary objective. Now I guess a number of readers will object to that, so I shall explain.
 
Businesses, in a competitive environment, are in a Darwinian environment. It should also be made clear that a common explanation of Darwinian evolution, namely Survival of the fittest, is just plain wrong. It should be: Survival of the adequate to occupy continually a niche. Perhaps as an example, I might point to the red algal genus Bangia, an alga that sits at the top of the intertidal splash zone. In terms of how cells may be arranged in multicellular forms, this is a one-dimensional, i.e  the cells are in a single line. There are a number of other algae that can occupy a similar zone, such as the two-dimensional Porphyra, so it is not even the fittest in this rather limited niche, but it must be adequate because a fossil that appears indistinguishable from modern Bangia has been found that appears to be 1.3 Gy old.
 
To be adequate, life forms must feed and reproduce. Businesses simply feed; if their income does not exceed their outgoings, they do not last long. There is no point in devising the most desirable widget or health product if your business is wound up. Amongst other outcomes, no product is then made, so there is no benefit from it.  Of course a desirable product is more likely to sell, hence with any reasonable management the company thrives. A good product may be necessary, but nevertheless the profit is critical.
 
For a biofuels company to succeed, income is dependent on the fuels being sold at the required price, and the market determines price.  As oil demand exceeds supply, prices will rise, but the question is, by how much? One question that must be faced is the price/demand elasticity, i.e. how much is demand affected by increased price. At first sight, judging by certain governments' taxation policies, not much, but unfortunately there is no time symmetry in economics: what works today may not work tomorrow. As the price of fuel rises, as opposed to the price of discretionary petrol, the price of everything else with a fuel content rises. Wages could keep up, if you desire hyperinflation, but if money is to have any meaning, you have to assume wages, if anything, will decline unless there are serious productivity improvements. In this context, I have seen figures that the pound sterling has inflated by a factor of over 650 in the last ninety years, so maybe more significant inflation is on the horizon. "Quantitative easing" is certainly little different from "printing money".
 
Notwithstanding that, the rich will probably buy fuel at any price. What the social consequences of that are is anyone's guess, but the implication is that if we want a future that bears any resemblance to what we have now, a significant volume of new transport fuel is required, which means that someone has to invest in a technology for which there is a significant resource, and the technology has to be reasonably cheap to implement. That, however, does not exclude niche supplies. The fact is, the market can never be saturated in the foreseeable future with biofuel.
 
So, where would you, the reader, place your money?
Posted by Ian Miller on Nov 22, 2011 8:07 PM GMT
A question for the reader to contemplate before I offer my answer: what is the primary objective of an investment in a technology development?
 
It is now my intention to run a small series of blogs on investment in scientific development, and the example will be biofuels. The reader might like to participate by deciding which, if any, technology they would invest in if they had the money. An important consideration is this: if nobody invests, and if there is no development such as fusion power and fuel cells, people had better get used to walking.
 
Returning to the question, the answer is clear: to make money. That should be the only primary objective. Now I guess a number of readers will object to that, so I shall explain.
 
Businesses, in a competitive environment, are in a Darwinian environment. It should also be made clear that a common explanation of Darwinian evolution, namely Survival of the fittest, is just plain wrong. It should be: Survival of the adequate to occupy continually a niche. Perhaps as an example, I might point to the red algal genus Bangia. In terms of how cells may be arranged in multicellular forms, this is a one-dimensional, i.e  the cells are in a single line and the plant sits at the top of the intertidal splash zone. There are a number of other algae that can occupy a similar zone, such as the two-dimensional Porphyra, so it is not even the fittest in this rather limited niche, but it must be adequate because a fossil that appears indistinguishable from modern Bangia has been found that appears to be 1.3 Gy old.
 
To be adequate, life forms must feed and reproduce. Businesses simply feed; if their income does not exceed their outgoings, they do not last long.
 
For a biofuels company to succeed, income is dependent on the fuels being sold at the required price, and the market determines price.  As oil demand exceeds supply, prices will rise, but the question is, by how much? One question that must be faced is the price/demand elasticity, i.e. how much is demand affected by increased price. At first sight, judging by certain governments' taxation policies, not much, but unfortunately there is no time symmetry in economics: what works today may not work tomorrow. As the price of fuel rises, as opposed to the price of discretionary petrol, the price of everything else with a fuel content rises. Wages could keep up, if you desire hyperinflation, but if money is to have any meaning, you have to assume wages, if anything, will decline unless there are serious productivity improvements. In this context, I have seen figures that the pound sterling has inflated by a factor of over 620 in the last ninety years, so maybe more significant inflation is on the horizon. "Quantitative easing" is certainly little different from "printing money".
 
Notwithstanding that, the rich will probably buy fuel at any price. What the social consequences of that are is anyone's guess, but the implication is that if we want a future that bears any resemblance to what we have now, a significant volume is required, which means that someone has to invest in a technology for which there is a significant resource, and the technology has to be reasonably cheap to implement. That, however, does not exclude niche supplies. The fact is, the market can never be saturated in the foreseeable future with biofuel.
 
So, before I give you my guesses, where would you, the reader, place your money?
Posted by Ian Miller on Nov 13, 2011 8:18 PM GMT
This may seem an odd topic to discuss under alternative theories, but that depends on what you think a theory is. I argue that whoever sets up a system has a theory that it will work. They do not know, which makes it a theory, and as a theory it should be testable. That such politically based theories seldom seem to be subjected to evidence-based tests is a clear failure, but we could also argue that when scientists, whose business it is to test theories, remain silent then they fail.
 
I am far from convinced that current systems work properly, although that comment comes with a very big caveat, namely my experience is in New Zealand (I was on a funding panel for approximately 10 years, and I also applied for funding from time to time, so I know "both sides") and what happens here may not be even approximately typical of what happens elsewhere. In this context, comments or a discussion would be welcome.
 
The most obvious problem that I found on a funding panel was that there was one set of applications that were obviously excellent and they were funded, one set that should be put out of its misery and was, but unfortunately there was a substantial set in the middle that appeared to be highly to reasonably desirable, but had to be divided somewhere simply because there were not enough funds. Where to draw the line on these was very difficult, particularly since most if not all of them lay outside the specific experience of the panelists.
 
External referees were of surprisingly little help. Only too often, a referee would be an acquaintance of the applicant (this is almost inevitable in narrow fields, even when they were selected internationally), or alternatively, the referee became obsessively critical. Rather surprisingly, very few referees did a really competent job, and in its own way, that made the problem more difficult because how do you compare a rating of 5 (out of 10) from a clearly competent report, with an 8 from a fairly light airbrush? Some applicants hurt themselves (and I fell into this category more than once) by not giving too much away because they did not feel that all referees had adequate integrity. I had seen such an example when, somewhat unsportingly, I tracked referees' subsequent activity in respect to applications. Of course there is a corollary: it is unfair to dump something on a referee's desk and block the contents from his future when he may very well have had similar ideas. In short, I do not feel such use of referees is valid other than possibly for purely academic applications.
 
The next problem arose from the politics. Those who provide the funds face a barrage of issues, and they end up by breaking the first rule of strategy: they impose too many objectives by trying to make the money do too many things.  In my opinion, a grant of funds should be directed primarily at one objective. Of course there can be a number of other benefits, but what tends to happen when politicians impose too many objectives is that a nightmare of bureaucracy results and very complicated applications turn up with all sorts of statements that in many cases are little better than arm-waving.
 
So, what should be done? In my opinion, funding should be based on past performance ratings, with emphasis on the recent past. The advantage would be that much less time and money would be wasted on bureaucracy and the researchers could spend more time doing research. The young scientist should start in an established group, and at some stage be "given a chance". Then, perhaps, another. The more successful can then get on with it, with little more to worry about than their maintaining a success rate. Public funds might be preferentially given in certain areas, say, but only to those with sufficient expertise. The downside of this proposal, of course, is how to assess past performance? Nevertheless, such difficulties will always be with us, and I rather suspect that "where to draw the line" is usually based on past performance anyway, except that the assessment is more based on "public reputation" because considered assessment had not been done.
 
What do you think? I would be interested in responses. As a personal disclaimer, I have no current personal interest in seeking such funding.
Posted by Ian Miller on Oct 29, 2011 12:30 AM BST
This is a little off the topic of chemistry, but it is a very rare example of what Kuhn described as a crisis in theory. The crisis is that outside the claimed limit of experimental error, muon neutrinos exceeded light speed (c). The most obvious way this could happen is experimental error, however nobody seems to be able to locate any error. This is potentially the only example I can think of during the last 40 years, and it will be interesting to see whether the process Kuhn described will eventuate. According to Kuhn, there will be various stages: denial, grudging acceptance, a flurry of explanations, then something will settle into the new paradigm, in some cases not necessarily based on logic but often based on the reputation of the proposer.
 
From a personal point of view, there is a further lesson. Part 2 of my ebook contained outlines of what I think it would be helpful for chemists to know about theory in physics, and vice versa, and there follows 72 examples of problems. Not everything I thought of made it. One question I contemplated was along the lines, if Einsteinian mechanics were to break down, where would it, and why would it? (The concept of relativity was actually laid down by Galileo.) In the end I discarded the question as being too unlikely. So, what are some of the possibilities?
 
(1) Einstein's assumption of no preferred frame of reference, i.e. every observation point is equivalent, is wrong. I am uncomfortable with this because I cannot see why it is only seen with only this experiment now?
 
(2) An astronomer I know suggested the neutrinos were taking a short cut, making some motion through another dimension, say. The concept involves curved space, e.g. a 2 dimensional "flatlander" on the surface of the Earth could in principle send a neutrino through the Earth. Again, I don't see what is so special about this experiment, so why?
 
(3) My prejudice is for a yet to be discovered force. Einstein's relativity, according to Feynman, could be obtained from the mass enhancement equation, effectively by using the same equations that lead to the mass enhancement equation but going the other way. Mass is most likely to be measured from the resistance to acceleration. The electromagnetic force is mediated at light speed, so any accelerating force has to "catch" the particle, and as light speed approaches, this becomes increasingly less effective, the acceleration drops to zero and "mass" is effectively infinite. This would break down if there were an as yet undiscovered force that was mediated at a speed d instead of c, where d>c. Relativity would still work, but for this force c must be replaced with d in the various equations. The reason for this view lies in the question, how did such a neutrino even get that close to c? What accelerated it? A minor undiscovered source of experimental error does not solve the problem because the neutrino must still approach c; only a significant clanger in the experimental method does.
 
Chemists, of course, are hardly likely to make any impact on this problem, but this gives us a privileged position: we can watch while others scratch their heads. It should be interesting to watch what unfolds, because whatever else, this is a result that cannot be ignored, unless it is so wrong it should be!
Posted by Ian Miller on Oct 14, 2011 11:44 PM BST
Two recent announcements in the local news caught my eye. The first was that the E.U. intended to impose a carbon tax on airlines, the tax being proportional to the distance flown, the argument being that the further you fly, the greater the amounts of carbon dioxide is put into the upper atmosphere, and that, of course, is bad, at least according to those wishing to impose the tax. Estimates on the additional cost for a single flight to Europe from here amount to about $800, and, of course, Europe will keep all the money. It is also noticeable that there is no suggestion that the taxpayers pay to their own government and thus contribute to their own countries' efforts against climate change, so the suspicion here is that this has little to do with climate change and more an excuse to raise cash.
 
Be that as it may, the second article was a proposal to spend a lot of cash to find ways of sending lots of material from the surface into the stratosphere to initiate clouds, etc, and thus raise the albedo of the planet, that way reflecting more light back to space and thus cool the planet.
 
It seems to me this raises two interesting questions. The first one is, given airlines produce water that at minus 50 C tends to form ice, which is white and hence a good reflector of light, there is no evidence that airlines produce a net detrimental effect. For all we know, their total effect may be beneficial. Even if they did raise the stratospheric temperature by a couple of degrees, would that be bad? Carbon dioxide at that altitude should be a net radiator, and in this context the thermosphere of Earth is about 1400 degrees C, while that of Venus is about 300 degrees C. Yes, the carbon dioxide will eventually sink to lower altitudes, but even then there is no evidence there is ever net detrimental effect unless the airlines stop flying.
 
The second question is, can we put something in the fuels that will maintain a longer albedo enhancement? The problem with ice is that it does not take long to sublime, so the effect does not last. Suppose, however, we put in an alkyl aluminium compound, or an alkyl zinc. The oxides melt at about 2070 and 1970 respectively so they will not slag, the oxides are white, you get heat when they burn, and yes, a little more care is needed in fuel handling to avoid spontaneous combustion and self-ignition but the fuel systems on aircraft would have to be redesigned anyway because you would only desire this fuel to be burnt when cruising altitude was reached. However, when dissolved in hydrocarbon solution, these materials are safer, as shown by a Youtube video that failed to illustrate spontaneous combustion with diethyl zinc.
 
Of course there is the obvious objection: you have to do quite some redesigning of fuel systems and handling. My answer is, if you want to save a planet, you have to do more than raise tax!
 
I suppose the last question is, suppose this worked and there was a massive reduction in heat retention and the climate problem was solved; would the E.U. give put massive tax rebates or other payments as a reward for saving the world? (Note that every rhetorical question deserves a rhetorical answer!)
Posted by Ian Miller on Oct 2, 2011 10:21 PM BST
In my ebook, I maintain that choosing what to do is in effect choosing between alternative applied theories and in a previous blog, I commented on why I think the fermentation of lignocellulose first to glucose and thence to ethanol to make biofuels is not a good idea, the main reason being the first fermentation is too expensive. What nobody commented on was that that could change if ethanol was not the main product, and it is of interest to view the recent Mascoma IPO, where there is a wide range of other proposed income sources.
 
There is a broader question: should we pursue ethanol at all? Given sugars, the technology is mature, but what about feedstocks? There are many objections to the use of crops to make ethanol on the basis that with a growing population food is the priority. So, is ethanol a bad biofuel?
 
"Bad" depends on your "point of view". The farmer wants the best price for his crop, the hungry cannot pay, so who does what? There is a tendency to say, "somebody else should pay", which, in my view, is not helpful. There are also "red herrings" in the analyses, such as  "carbon efficiency", "blending efficiency" and "energy efficiency". Carbon efficiency is the worst of these: the argument is that glucose has six carbon atoms, and two disappear off as CO2. That is totally irrelevant: there is no shortage of carbon atoms. Blending efficiency is a red herring because Brazil has shown that provided proper management is undertaken, there are no inherent technical problems. The argument that ethanol has less energy density than hydrocarbons is true but somewhat misleading.  The issue is not energy, but useful work, for we have to power a transport fleet. Whether you use more (because of lower energy) is irrelevant if the issue is, can you run your motor?  Also, the work on ignition is delta PV, which increases if the pressure is increased. In a spark ignition motor, that requires a higher octane number, and ethanol has a significantly higher octane number than standard fuel, and with blending it is efficient at raising the overall octane. Accordingly we could get more efficiency by raising the motor compression, which raises a question that is seemingly always ignored: what properties will the future transport fuel have? If we do not address that, much of our planning is going to be wrong.
 
The real question is, how do we power transport once oil becomes scarce? Fermentation of sugars to ethanol has advantages. The first is, it is reasonably efficient on smaller scales. That means it can use wastes, which tend to be produced in smaller local amounts. There is also one other feedstock: synthesis gas. Certain anaerobes, including Clostridium, appear to be able to convert this gas stream to ethanol, and the microbes seem to be tolerant to a wide range of the mix of hydrogen and carbon monoxide. That means in principle we can get fuel from waste streams, such as the gas effluent of steel mills that otherwise have no use.
 
In my opinion, there appears to be no use other than to make ethanol by fermentation for small amounts of low quality synthesis gas, and no other technology that is convenient for low volumes of sugar waste. Either that ethanol can be used by the chemical industry, or we need to maintain in the long-term spark ignition motors. Long term planning for transport should take that issue into account, however in my opinion, planning for transport fuels appears to be operating on a "market rules" basis. That will have all the aspects of Darwinian evolution, and while the market enthusiasts might argue that evolution guarantees the fittest (actually, it does not – evolution involves survival of the adequate to reproduce) evolution also involves numerous extinctions. Do we wish to nearly extinguish individual transport? If not, some form of planning might seem desirable.
Posted by Ian Miller on Sep 20, 2011 11:54 PM BST
According to MO theory there can be no exceptions to the WH rules, nevertheless there are exceptions. On the other hand, in my opinion Pauling's valence bond theory that invokes canonical structures predicts where exceptions would occur, and why. In my example of the pentadienyl carbenium ion the concept of canonical structures puts positive charge evenly on C1, C3 and C5. If we substitute the ends with alkyl groups, which stabilize carbenium ions, then positive charge is preferentially located at C1 and C5. An empty orbital represents positive charge localized on a given atom and according to molecular orbital theory, the effect of an empty orbital should be the same as that of an occupied one.  As far as I can make out, this concept originated with Mullikan (Phys Rev 41: 49-71, 1932), but essentially as an assertion.
 
Why do the WH rules work? The usual argument is that a +signed function must overlap with another +signed function, and from that observation, the rotational characteristics of the WH rules follow. (Actually, the same rules follow if a bond forms only when plus interferes with minus, but the diagrams are more messy. This is actually the rule for forming antisymmetric wave functions, which at least in some formalisms is a requirement for the Exclusion Principle, but since the same outcome always arises, this issue is irrelevant here.) This gets to the point where we have to ask, what does the sign mean?
 
In general theory of wave interference it refers to the phase of the wave. When amplitudes have the same sign, they reinforce. The important point is there must be a phase relationship between the ends. Now, the phase of the wave is proportional to the action, and it changes because the action (the time integral of the Lagrange function) evolves in time. However, no matter how long zero is integrated with respect to time, you still get zero, and the Lagrange function of an entity with zero mass and zero charge, which is what an empty orbital has, is zero. The solution to the Schrodinger equation when E, V and m each equal zero is zero everywhere in all time. Zero can be added any number of times, but it makes no difference.
 
If so, the canonical structure with positive charge on an end carbon atom gives zero directional effect. Therefore, the strength of the preference (because there is always some of the canonical structure with the required phase relationship) is reduced whenever there is a carbenium ion involved in the transition state, and the carbenium site is substituted. The orientation of the substituent is significant too because the bigger the steric clash on the complying path, the easier it is for the canonical structure that permits non-compliance to become more significant because it forces rotation to start before significant orbital interactions.
 
Now, I believe this alternative interpretation is important for two reasons. The first is, it gives a specific reason why there should be exceptions to the Woodward Hoffmann rules, and it predicts where they will be found. Thus if nothing else, it will guide further experimental work. The alternative theory is either right or wrong, and there is one obvious way to find out. The second reason is more important: I believe that if this alternative interpretation is found to be correct, it forces chemists to revisit the concept canonical structures, which I believe gives far more fertile ground for understanding chemistry than the current MO theory, at least for the average bench chemist. Further, I suspect there are no aspects of organic chemistry (and probably not of other chemistry, except I am not familiar enough with that to be sure) that does not comply with the concept of canonical structures, if these are properly used. So, there is a further challenge: find some aspect of chemistry where canonical structures, properly used, fail.
Posted by Ian Miller on Sep 5, 2011 3:58 AM BST
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