Some Shortcomings of Science

In a previous post, in reference to the blog repost, I stated I would show some of the short-comings of science, so here goes.

One of the obvious failings is that people seem happy to ignore what should convince them. The first sign I saw of this type of problem was in my very early years as a scientist. Sir Richard Doll produced a report that convincingly (at least to me) linked smoking to cancer. Out came a number of papers rubbishing this, largely from people employed by the tobacco industry. Here we have a clear conflict, and while it is ethically correct to show that some hypothesis is wrong, it should be based on sound logic. Now I believe that there are usually a very few results, and maybe as few as one specific result, that makes the conclusion unassailable. In this case, chemists isolated the constituents of cigarette smoke and found over 200 suspected carcinogens, and trials with some of these on lab rats were conclusive: as an example one dab of pure 3,4-benzopyrene gave an almost 100% probability of inducing a tumour. Now that is a far greater concentration than any person will get smoking, and people are not rats, nevertheless this showed me that on any reasonable assessment, smoking is a bad idea. (It was also a bad idea for a young organic chemist: who needs an ignition source a few centimeters in front of the face when handling volatile solvents?) Yet fifty years or so later, people continue to smoke. It seems to be a Faustian attitude: the cancer will come decades later, or for some lucky ones, not at all, so ignore the warning.

A similar situation is occurring now with climate change. The critical piece of information for me is that during the 1990s and early 2000s (the period of the study) it was shown there is a net power input to the oceans of 0.64 W/m². If there is a continuing net energy input to the oceans, they must be warming. Actually, the Tasman has been clearly warming, and the evidence from other oceans supports that. So the planet is heating. Yet there are a small number of “deniers” who put their head in the sand and refuse to acknowledge this, as if by doing so, the problem goes away. Scientists seem unable to make people fact up to the fact that the problem must be dealt with now but the price is not paid until much later. As an example, in 2014 US Senate majority leader Mitch McConnell said: “I am not a scientist. I’m interested in protecting Kentucky’s economy.” He forgot to add, now.

The problem of ignoring what you do not like is general and pervasive, as I quickly learned while doing my PhD. My PhD was somewhat unusual in that I chose the topic and designed the project. No need for details here, but I knew the department, and my supervisor, had spent a lot of effort establishing constants for something called the Hammett equation. There was a great debate going on whether the cyclopropane ring could delocalise electronic charge in the same way as a double bond, only mre weakly. This equation would actually address that question. The very limited use of it by others at the start of my project was inconclusive, for reasons we need not go into here. Anyway, by the time I finished, my results showed quite conclusively that it did not, but the general consensus, based essentially on the observation that positive electric charge was strongly stabilised by it, and on molecular orbital theory (which assumes it initially, so was hardly conclusive on this question) was that it did. My supervisor made one really good suggestion as to what to do when I ran into trouble, and this was the part that showed the effect the most. But when it became clear that everyone else was agreeing the opposite and he had moved to a new position, he refused to publish that part.

This was an example of what I believe is the biggest failing. The observation everyone clung to was unexpected and needed a new explanation, and what they came up with most certainly gave the right answer for that specific case. However, many times there is more than one possible explanation, and I came up with an alternative based on classical electric field theory, that also predicted positive charge would be stabilized, and by how much, but it also predicted negative charge would be destabilized. The delocalization concept required bothto be stabilised. So there was a means of distinguishing them, and there was a very small amount of clear evidence that negative charge was destabilised. Why a small amount of evidence. Well, most attempts at making such compounds failed outright, which is in accord with the compounds being unstable but it is not definitive.

So what happened? A review came out that “convincingly showed” the answer was yes. The convincing part was that it cited a deluge of “me too” work on the stabilization of positive charge. It ignored my work, and as I later found out when I wrote a review, it ignored over 60 different types of evidence that showed results that contradicted the “yes” answer. My review was not published because it appears chemistry journals do not publish logic analyses. I could not be bothered rewriting, although the draft document is on the web if anyone is interested.

The point this shows is that once a paradigm is embedded, even if on shaky grounds, it is very hard to dislodge, in accord with what Thomas Kuhn noted in “The structure of scientific revolutions”. One of the points Kuhn noted was if the paradigm had evidence, scientists would rush to write papers confirming the paradigm by doing minor variations on what worked. That happened above: they were not interested in testing the hypothesis; they were interested in getting easy papers published to advance their careers. Kuhn also noted that observations that contradict the paradigm are ignored as long as they can be. Maybe over 60 different types of observations that contradict, or falsify, the paradigm is a record? I don’t know, but I suspect the chemical community will not be interested in finding out.

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Trappist-1, and Problems for a Theoretician

In my previous post, I outlined the recently discovered planets around Trappist-1. One interesting question is, how did such planets form? My guess is, the standard theory will have a lot of trouble explaining this, because what we have is a very large number of earth-sized rocky planets around a rather insubstantial star. How did that happen? However, the alternative theory outlined in my ebook, Planetary Formation and Biogenesis, also has a problem. I gave an equation that very approximately predicts what you will get based on the size of the star, and this equation was based on the premise that chemical or physical chemical interactions that lead to accretion of planets while the star is accreting follow the temperatures in various parts of the accretion disk. In turn, the accretion disk around Trappist-1 should not have got hot enough where any of the rocky planets are, and more importantly, it should not have happened over such a wide radial distance. Worse still, the theory predicts different types of planets in different places, and while we cannot eliminate this possibility for trappist-1, it seems highly likely that all the planets located so far are rocky planets. So what went wrong?

This illustrates an interesting aspect of scientific theory. The theory was developed in part to account for our solar system, and solar systems around similar stars. The temperature in the initial accretion disk where the planets form around G type stars is dependent on two major factors. The first is the loss of potential energy as the gas falls towards the star. The temperature at a specific distance due to this is due to the gravitational potential at that point, which in turn is dependent on the mass of the star, and the rate of gas flowing through that point, which in turn, from observation, is very approximately dependent on the square of the mass of the star. So overall, that part is very approximately proportional to the cube of the stellar mass. The second dependency is on the amount of heat radiated to space, which in turn depends on the amount of dust, the disk thickness, and the turbulence in the disk. Overall, that is approximately the same for similar stars, but it is difficult to know how the Trappist-1 disk would cool. So, while the relationship is too unreliable for predicting where a planet will be, it should be somewhat better for predicting where the others will be, and what sort of planets they will be, if you can clearly identify what one of them is. Trappist-1 has far too many rocky planets. So again, what went wrong?

The answer is that in any scientific theory, very frequently we have to make approximations. In this case, because of the dust, and because of the distance, I assumed that for G type stars the heat from the star was irrelevant. For example, in the theory Earth formed from material that had been processed to at least 1550 degrees Centigrade. That is consistent with the heat relationship where Jupiter forms where water ice is beginning to think about subliming, which is also part of the standard theory. Since the dust should block much of the star’s light, the star might be adding at most a few tens of degrees to Earth’s temperature while the dust was still there at its initial concentration, and given the uncertainties elsewhere, I ignored that.

For Trappist -1 it is clear that such an omission is not valid. The planets would have accreted from material that was essentially near the outer envelope of the actual star during accretion, the star would appear large, the distance involving dust would be small, the flow through would be much more modest, and so the accreting star would now be a major source of heat.

Does this make sense? First, there are no rocky bodies of any size closer to our sun than Mercury. The reason for that, in this theory, is that by this point the dust started to get so hot it vaporized and joined the gas that flowed into the star. It never got that hot at Trappist-1. And that in turn is why Trappist-1 has so many rocky planets. The general coolness due to the small amount of mass falling inwards (relatively speaking) meant that the necessary heat for rocky planets only occurred very close to the star, but because of the relative size of the stellar envelope that temperature was further out than mass flow would predict, and furthermore the fact that the star could not be even vaguely considered as a point source meant that the zone for the rocky planets was sufficiently extended that a larger number of rocky planets was possible.

There are planets close to other stars, and they are usually giants. These almost certainly did not form there, and the usual explanation for them is that when very large planets get too close together, their orbits become unstable, and in a form of gravitational billiards, they start throwing each other around, some even being thrown from the solar system, and some end up very close to the star.

So, what does that mean for the planets of Trappist-1? From the densities quoted in the Nature paper, if they are right, and the authors give a wide range of uncertainty, the fact that the sixth one out has a density approaching that of Earth means they have surprisingly large iron cores, which may mean there is a possibility most of them accreted more or less the same way Mercury or Venus did, i.e. they accreted at relatively high temperatures, in which case they will have very little water on them. Furthermore, it has also been determined that these planets will be experiencing a rather uncomfortable amount of Xrays and extreme ultraviolet radiation. Do not book a ticket to go to them.

Science, the nature of theory, and global warming.

My summery slumbers have passed, but while having them, I had web discussions, including one on the nature of time. (More on that in a later post.) I also got entangled in a discussion on global warming, and got one comment that really annoyed me: I was accused of being logical. It was suggested that how you feel is more important. Well, how you feel cannot influence nature. Unfortunately, it seems to influence politicians, who end up deciding. So what I thought I would do is post on the nature of theory. I have written an ebook on what theory is and how to form theories, and while the name I gave it was not one that would attract a lot of readers (Aristotelian methodology in the physical sciences) it was no worse than “How to form a theory”. Before some readers turn off, I started that ebook with this thought: everyone has theories. For most, they are not that important, e.g. a theory on who trashed the letterbox. Nevertheless, the principles of how to go about it should be the same.

In the above ebook, I gave global warming as an example of where science has failed, not because we do not understand it, but rather the public has not really been presented with the issue properly. One comment about global warming is that scientists have not resolved the issue. That depends on what you mean by “resolved”. Thus one person said scientists are still working on relativity. Yes, they are, but that does not mean that what we have is wrong. The scientific process is to continually check with nature. So, what I want to do in some of my posts this year is try to give an impression of what science is.

The first thing it is not is mathematics. Mathematics are required, and part of the problem is that only too often scientists do not state clearly what they are saying, preferring to leave a raft of maths for the few who are closely in the field. This is definitely not helpful. Nor are TV shows that imply that theories are only made by stunning mathematics. That is simply not true.

The essence of science is a sequence of simple statements, which are the premises. For me, the correct methodology was invented by Aristotle, and the tragedy is, Aristotle made some howling mistakes by overlooking his own methodology. Aristotle’s methodology is to examine nature and from it, draw the premises, then apply logic to the statements to draw some conclusions, check with observation, and if the hypothesis still stands up, try to determine whether there are any other hypotheses that could have given equivalent predictions. Proof of a concept is only possible if one can say, “if and only if X, then Y”, in which case observing Y is the proof. Part of the problem lies in the “only”; part lies in seeing the wood for the trees. One of the first steps in analyzing a problem is to try to reduce it to its essentials by avoiding complicating features. This does not mean that complicating features should be ignored; rather it means we try to find a means of avoiding them until we can sort out the basics. If we do not get the basics right, there is no point in worrying about complicating factors.

To consider global warming, the first thing to do is put aside the kilotonnes of published data. Instead, in order to focus on the critical points, try modeling something simpler. Consider a room in your house in winter, and consider you have an electric bar heater. Suppose you set it to 1 Kw and turn it on. That will deliver 1 kilojoule of heat per second. Now, suppose doors are open or not open. Obviously, if they are open, the heat can move elsewhere through the house, so the temperature will be slower to rise. Nevertheless you know it will, because you know there is 1 kilojoule per second of heat being liberated.

The condition for long term constant temperature (equilibrium) is
(P in) – (P o) = 0
where (P in) is the power in and (P o) is the power out, both at equilibrium. This works for a room, or a planet. Why power? Because we are looking to see whether the temperature will remain constant or change, and to do that we need to see whether the system is changing, i.e. gaining or losing heat. To detect change, we usually consider differentials, and power is the differential of energy with respect to time. Because we are looking at differentials, we can say, if and only if the power flow into a system equals the power flow out is it at an energy equilibrium. We can use this to prove equilibrium, or otherwise, but we may have to be careful because certain other energy flows, such as radioactive decay, may be generated internally. So, what can we say about Earth? What Lyman et al. found was there is a net power input of 0.64 watts per square meter of ocean surface. That means the system cannot be at equilibrium.

We now need a statement that could account for this. Because the net warming effect is recent, the cause must be recent. The “greenhouse” hypothesis is that humanity has put additional infrared absorbers into the air, and these absorb a small fraction of the infrared radiation that would otherwise go to space, then re-emit the radiation in random directions. Accordingly, a certain fraction is returned to earth. The physics are very clear that this happens; the question is, is it sufficient to account for the 0.64 W? If so, power into the ground increases by (P b) and the power out decreases by (P b). This has the effect of adding 2 (P b) to the left hand side of our previous equation, so we must add the same to the right hand side, and the equation is now
(P in + P b) – (P o – P b) = 2 (P b)
The system is now not in equilibrium, and there is a net power input.
The next question is, is there any other cause possible for (P b)? One obvious one is that the sun could have changed output. It has done this before, for example, the “Little Ice Age” was caused by the sun’s output dropping with a huge decrease in sunspot activity. However, NASA has also been monitoring stellar output, and this cannot account for (P b). There are few other changes possible other than atmospheric composition for radiation over the ocean, so the answer is reasonably clear: the planet is warming and these gases are the only plausible cause. Note what we have done. We are concerned about a change, so we have selected a variable that measures change. We want to keep the possible “red herrings” to a minimum, so the measurements have been carried out over the ocean, where buildings, land development, deforestation, etc are irrelevant. By isolating the key variable and minimizing possible confusing data, we have a clear answer.

So, what do we do about it? Well, that requires a further set of theories, each one giving an effect to a proposed cause, and we have to choose. And that is why I believe we need the general population to have some idea as to how to evaluate theories, because soon we will have no choice. Do nothing, and we lose our coastal cities, coastal roads and coastal agricultural land up to maybe forty meters, and face a totally different climate. Putting your head in the sand and feeling differently will not cool the planet.

* Lyman, J. M. and 7 others, 2010. Nature 465:334-337.

What is involved in developing a scientific theory? (2)

In my previous post, I showed how the protagonist in Athene’s Prophecy could falsify Aristotle’s proof that the earth did not rotate, but he could not prove it did. He identified a method, but very wisely he decided that there was no point in trying it because there was too much scope for error. At this stage, all he could do was suggest that whether the earth rotated was an open question. If it did not, then the planets could not go around the sun, otherwise the day and the year would be the same length, and they did not. At this point it is necessary, while developing a theory, to assume that as long as it has no further part to play in the theory it does, if for no other reason than it is necessary. By doing so, it creates a test by which the new theory can be falsified.

The logic now is, either the earth moves or it does not. If it does move, it must move in a circle, because the sun’s size was constant. (Actually, it moves in an ellipse, but it is so close to a circle that this test would not distinguish it. If you knew the dynamics of elliptical motion, you could just about prove it did follow an ellipse. The reason is, it moves faster when closer to the sun, and the solstices and the equinoxes were known. A proper calendar shows the northern hemisphere summer side of the equinoxes is longer than the southern hemisphere’s one by about 2 – 3 days, and is the reason why February is the shortest month. We, in the southern hemisphere, get cheated by two days of summer. Sob! However, if you have not worked out Newton’s laws of motion, this is no help.) So, before we can prove the earth moves, we must first overturn Aristotle’s proofs that it did not, and that raises the question, where can a theory go wrong?

The most likely thing to go wrong in forming a scientific theory can be summarized simply: if you start with a wrong premise, you may draw a wrong conclusion. Your conclusion may agree with observation, because as Aristotle emphasized, a wrong premise can still agree with observation. One of Aristotle’s examples of false logic is as follows:

Man is a stone

A stone is an animal

Therefore, man is an animal.

The conclusion is absolutely correct, but the means of getting there is ridiculous. A major problem when developing a theory is that a wrong premise that brings considerable agreement with observation is extremely difficult to get rid of, and invariably it has pervasive effects for a long time thereafter.

One reason why, in classical times, it was felt that the Earth must be stationary was because of Aristotle’s premise that air rises. If so, the fact that we have air at all must be because the Universe is full of it. If so, then if the earth moves, it must move through air. If so, there would be a contrary wind, the speed difference of which on either side would depend on the rate of rotation. There was no such wind, therefore no such orbit. We can forgive Aristotle here, but we forgive those who followed Archimedes less well. Had Aristotle known of Archimedes Principle, this argument would probably never have been made. According to Archimedes, air rises to the top because it is the least dense, but it still falls towards the earth. Space is empty. There were clues in classical times that space was empty. One such clue was that when a star went behind the moon, it did so sharply, which indicated there was no air to refract it. It was also known there were no clouds on the moon.

This shows another characteristic that unfortunately still pervades science. Once someone establishes a concept, evidence that falsifies that concept tends to be swept under the carpet as long as by doing so, it does not affect anything else. No clouds on the moon might mean anything. So, perhaps, you will now begin to see how difficult it was to get the heliocentric theory accepted, and how difficult it is to find the truth in science when you do not know the answer. That applies just as much today as then. The intellectual ability of the ancients was as great as now, and Aristotle would have been one of the greatest intellects of all times. He just made some mistakes.

What is involved in developing a scientific theory? (2)

In my previous post, I suggested that forming the theory that the Earth was a planet that went around the sun was an interesting example of how a scientist forms a theory. When starting, the first task is to review the literature, which at the time, was largely determined by Aristotle. Since Aristotle asserted that the earth was fixed, it therefore follows that you must first overturn his assertions. One place to start is to decide why we have day and night. Let us use Aristotle’s own methodology, which is to break the issue down into discrete issues. Thus we say, either the Earth is fixed and everything rotates around it, or everything is more or less fixed, and the Earth rotates. Aristotle had reached that step, and had “proven” that the Earth did not rotate. Therefore the day/night must occur through the sun orbiting the Earth. The heliocentric theory, despite its advantages, is falsified unless we can falsify Aristotle’s proofs.

At this point, we should recognize that Aristotle was very clear on one point, and he has been badly misrepresented on this ever since. Aristotle clearly asserted that logic must be applied to experimental observations, and that observation alone was critical. So, what was his experiment? Aristotle argued that if you threw a stone vertically into the air, it always came back to the same place. Had the earth been rotating, the path length of a rotation increased with height, in which case the stone should drag back westwards. It did not, so the earth did not rotate. Note that at this point, Aristotle was effectively arguing for the conservation of angular momentum, similarly to the ice skater slowing her spin by extending her arms. Before reading any further, what do you think about Aristotle’s experiment? What is wrong, and how would you correct it, bearing in mind you have only ancient technology?

In my ebook, Athene’s Prophecy, my protagonist dismisses the experiment by arguing that vertical is defined as the point where the stone falls back to the same place. By defining the point thus, if the stone does not come back to the same place, it was not thrown vertically. He then criticizes Aristotle by arguing that the correct way to do the experiment is to simply drop the stone from a high tower. The reason is that while Aristotle would be correct in that there should be a drag to the west going up, exactly the opposite should occur on the way back down. What should happen if dropped from a tower is that the stone would strike the ground slightly to the east of the vertical position, and in Rhodes, where this was being discussed, also slightly to the south. Can you see why?

That the stone should go east follows from the fact that the angular velocity is constant, but the path length is longer the higher you are, so it is going east faster higher up. The reason it goes south is because the stone falls towards the centre of the earth, and thus very slightly decreases its latitude, but the point at the base of the tower does not. In my ebook, however, my protagonist wisely refused to carry out the experiment, because it is not that easy to carry out, even with modern equipment, and in those days the errors in measurement would most likely exceed the effect. Notwithstanding that, the logic is correct in that any effect like that going up will be exactly countered coming down, and consequently Aristotle’s “proof” is not valid. Thus one can falsify an experiment through logic alone. Of course, disproving Aristotle does not prove the earth is rotating, but it leaves it open as a possibility. Carrying out the dropped stone experiment would, provided you could guarantee that what you saw was real and not experimental error. That is not easy to do, even now.

What is involved in developing a scientific theory?

Everyone knows about people like Galileo, Newton, etc, but how are such theories discovered? Now obviously I have no idea exactly how they did it, but I think there are some principles involved, and I also think some readers might find these of interest. I hope so, because therein lies the third task for my protagonist in my novel Athene’s Prophecy.

The reason that is in the novel is because the overall plot requires a young Roman to get help from superior aliens to avoid a disaster in the 24^th century. The reason for the time difference is, of course, relativity. Getting to the aliens involves being abducted by other aliens, but once taken to another world, the protagonist has to be something more than a specimen that can talk. To get the aliens to respond, he has to be someone of interest to talk to. Suppose you had the chance to talk to someone from the 16^th century, or to Galileo, who would you choose? My proposition is, Galileo, so the task for my young protagonist is to prove the heliocentric theory, i.e. that the earth moves around the sun. That is similar to what was in the film Agora. The big problem was, everybody was so sure the earth was fixed and everything else went around it. Not only were they sure, but they could also use their theory to calculate everything that mattered, such as when the solstices and equinoxes would be, when Easter would be, and when various planets would be where in the sky. What else did they need?

The alternative theory was due to Aristarchus of Samos. What Aristarchus maintained was that the earth was a planet, and all planets went around the sun, the moon went around the earth, and the solar system was huge. This latter point was of interest, because Aristarchus measured the system. His first measurement was to obtain the size and distance of the Moon, and what he did was to get two people to measure the angle at the exact moment an eclipse of the moon started. These two people were separated by as much distance as he could manage, and with one distance and two angles he had a triangle that would permit the measurement of the distance to the moon. The size then followed from its solid angle. The method is completely logical, although the amount of experimental error was somewhat large, and his answer was out by a factor of approximately two. He then measured the distance to the sun by measuring the angle between the sun and moon lines when the moon was half shaded, and used his moon distance and Pythagoras’ theorem. His error here was about a factor of five, and would have been about a factor of ten had not the error in the moon distance favoured him. The error range here was too great (to see why, check how tangents get very large as they approach 90 degrees) but he was the first to realize that the solar system is really very large. He also showed that the sun is huge compared to the earth.

Aristarchus, following Aristotle, also postulated that the stars were other suns, but so far away, and they would have to be going at even greater speeds. This did not make sense, so he needed an alternative theory. In my opinion, this is invariably the first step in forming a new theory: there is some observation that simply does not make sense within the old theory. Newton’s theory was born through something that did not make sense. If you believed Copernicus, or Aristarchus, if you had heard of him, or of Galileo, then the earth and the other planets went around the sun, but there was a problem: Mars could only be explained through elliptical orbits, and nobody could explain how a body could orbit in an elliptical path with only a central force. Newton showed that elliptical orbits followed from his inverse square law of gravity. Relativity was also born the same way. What did not make sense was the observation that no matter what direction you looked, the speed of light was constant. What Einstein did was to accept that as a fact, and put that into the classical Galilean relativity, and came up with what we call relativity.

So we now get to the second step in building a new theory. That involves reading about what is known, or thought to be known, about the subject. If we think about the heliocentric theory in classical times, we now know that much of what was thought to be correct was not. So, here is a challenge. If you had to, could you prove that the earth goes around the sun, while being restricted to what was known or knowable in the first century? Answers in the next few posts, but feel free to offer your thoughts.

Theory and planets: what is right?

In general, I reserve this blog to support my science fiction writing, but since I try to put some real science in my writing, I thought just once I would venture into the slightly more scientific. As mentioned in previous posts, I have a completely different view of how planets, so the question is, why? Surely everyone else cannot be wrong? The answer to that depends on whether everyone goes back to first principles and satisfies themselves, and how many lazily accept what is put in front of them. That does not mean that it is wrong, however. Just because people are lazy merely makes them irrelevant. After all, what is wrong with the standard theory?

My answer to that is, in the standard theory, computations start with a uniform distribution of planetesimals formed in the disk of gas from which the star forms. From then on, gravity requires the planetesimals to collide, and it is assumed that from these collisions, planets form. I believe there are two things wrong with that picture. The first is, there is no known mechanism to get to planetesimals. The second is that while gravity may be the mechanism by which planets complete their growth, it is not the mechanism by which it starts. The reader may immediately protest and say that even if we have no idea how planetesimals form, something had to start small and accrete, otherwise there would be no planets. That is true, but just because something had to start small does not mean there is a uniform distribution throughout the accretion disk.

My theory is that it is chemistry that causes everything to start, and different chemistries occur at different temperatures. This leads to the different planets having different properties and somewhat different compositions.

The questions then are: am I right? does it matter? To the first, if I am wrong it should be possible to falsify it. So far, nobody has, so my theory is still alive. Whether it matters depends on whether you believe in science or fairy stories. If you believe that any story will do as long as you like it, well, that is certainly not science, at least in the sense that I signed up to in my youth.

So, if I am correct, what is the probability of finding suitable planets for life? Accretion disks last between 1 to even as much as 30 My. The longer the disk lasts, the longer planets pick up material, which means the bigger they are. For me, an important observation was the detection of a planet of about six times Jupiter’s mass that was about three times further from its star (with the name LkCa 15) than Jupiter. The star is approximately 2 My old. Now, the further from the star, the less dense the material, and this star is slightly smaller than our sun. The original computations required about 15 My or more to get Jupiter around our star, so they cannot be quite correct, although that is irrelevant to this question. No matter what the mechanism of accretion, Jupiter had to start accreting faster than this planet because the density of starting material must be seriously greater, which means that we can only get our solar system if the disk was cleared out very much sooner than 2 My. People ask, is there anything special regarding our solar system? I believe this very rapid cleanout of the disk will eliminate the great bulk of the planetary systems. Does it matter if they get bigger? Unfortunately, yes, because the bigger the planets get, the bigger the gravitational interactions between them, so the more likely they are to interact. If they do, orbits become chaotic, and planets can be eliminated from the system as other orbits become highly elliptical.

If anyone is interested in this theory, Planetary Formation and Biogenesis (http://www.amazon.com/dp/B007T0QE6I )

will be available for 99 cents  as a special promo on Amazon.com (and 99p on Amazon.co.uk) on Friday 13, and it will gradually increase in price over the next few days. Similarly priced on Friday 13 is my novel Red Gold, (http://www.amazon.com/dp/B009U0458Y  ) which is about fraud during the settlement of Mars, and as noted in my previous post, is one of the very few examples of a novel in which a genuine theory got started.