Talk:Aneutronic fusion/Archive 3

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Conditions observed in DPFs

Eric, you referenced the observation of magnetic fields of 0.02-0.04 megatesla to Bostick, W.H. et al, Ann. NY Acad. Sci., 251, 2 (1975). As I already mentioned, this journal is not in our library. Do you have an electronic or scanned version you can send to me? Do you have another reference for this value in a more accessible journal, or even online? Have fields close to this value been measured and published more recently than 30 years ago? Could you tell me what measurement technique was used? --Art Carlson 12:40, 31 July 2006 (UTC)

I cited alternatives above:Colloques internationaux CNRS no. 242, p.129-138. Also J. Plasma Physics 8, 7(1972). My own paper cited in the refs is far more recent and we observed 0.4 GG.Elerner 20:14, 31 July 2006 (UTC)
And I already told you that these sources are not in our library. Since you are either unable or unwilling to send me a copy and are either unable or unwilling to tell me in detail what they say, let me ask another question: What is the highest field in a DPF ever reported in a journal that is available in the large library of a major plasma research institute?
As for your own paper, you state in the abstract: "While fields of only 0.4 gigagauss have so far been demonstrated with the DPF, scaling laws indicate that much higher fields can be reached." And on page 23: "If we use (4) to predict Bc we obtain 0.43 GG, in excellent agreement with the observed value of 0.4 GG." That is, you do not report the "demonstration" or the "observation" in this paper, but only refer to it, and you do not cite any source, directly or indirectly. This is not the first time that you have claimed a paper says something that it does not. That forces me to question whether the evidence for fields of this strength is really strong enough that we can report this claim in Wikipedia. --Art Carlson 08:13, 1 August 2006 (UTC)
J. of Plasma Physics is not in your library? All of the references are in PPPL's library. As to my paper, if you follow the link on arXiv, you will get to it. The whole first half of the paper describes the experimental results. Just read it.Elerner 14:32, 1 August 2006 (UTC)
I've got egg on my face. I did a search on "0.4" and "gauss" and "gigagauss" in your paper. I found the two sentences I mentioned, but of course missed the mention of "4x108 G". I just found "Journal of Plasma Physics" in the online catalog, so I must have somehow overlooked it on the shelfs. I'll pick up that article tomorrow. (The online catalog confirms that the other two journals are not carried, though.) --Art Carlson 16:00, 1 August 2006 (UTC)
Just read the paper. It's always a good idea to read something you are commenting on, not just search it.Elerner 22:15, 1 August 2006 (UTC)
In the J. of Plasma Physics paper there is a plethora of detail on spatial and temporal structure and a good deal on energy. I can't find a word about measured maximum magnetic fields or densities. Can you point it out to me, or were you mistaken? (Of course, I might have overlooked something in the 14 pages. Unfortunately I can't search it electronically to be sure ... ) --Art Carlson 08:07, 3 August 2006 (UTC)
I have reread your paper, Eric, particularly the experimental part. I couldn't find any major flaws. (And believe me, I would not hesitate to say so if I could.) There are two things that still puzzle me. One, which we are not likely to resolve anytime soon, is the apparent discrepancy between your observations and the virial theorem. The other is the fact that the D-T neutron pulse is 5 times shorter than the D-D neutron pulse. Do you understand how that can be? I can't think of any explanation that would not imply a density at least 5 times higher than the value you report. --Art Carlson 13:51, 3 August 2006 (UTC)
The more I think about it, the more the short DT neutron pulse bugs me. If I recall correctly, you also mention the fact that the short pulse, which would be even shorter if the response time of the detector was taken into account, indicates a small spread of velocities along the line of sight. You interpret that as a small speed perpendicular to the magnetic field, but the field must twist around in several ways, and I doubt that you can maintain a significant non-Maxwellian distribution very long. Is there any chance of getting at look at the whole scintillator trace, from before the discharge to after the DD neutron pulse? Or at least hearing your best estimate of the triton temperature perpendicular to the line of sight? --Art Carlson 19:51, 4 August 2006 (UTC)
First, the DT pulse has to be shorter that the DD because there has to be time for the tritium to accumulate. Second, the trace is really flat as it is shown in the figure from the end of the gamma ray pulse to the beginning of the DD pulse except for the peaks shown.

Since the FWHM was 8 ns at both detectors, I cold only put an upper limit on the perpendicular temperature based on a 1 ns spread between them. This would be somewhere around 14 keV. That would not imply an extreme difference between axial and radial velocities. However it is only an upper limit.Elerner 22:21, 4 August 2006 (UTC)

From previous comments, I gather that the record density reported is a few times 10^26 m^-3, which makes it about 10,000 lower than that required to simultaneously suppress bremstrahlung and synchrotron radiation. Correct? --Art Carlson 12:40, 31 July 2006 (UTC)

Again your math is a bit off. The density required for trapping at 10GG is 2.4x10^30 m^-3 and the peak density observed is about 3x10^27 m^-3, about 800 times lower, not 10,000.Elerner 20:14, 31 July 2006 (UTC)

additions to page

Direct conversion and economics

I have added new sections on direct conversion which is the main advantage of aneutronic fusion and on current research in the field. I took portions of "energy balance" and reorganized it into a new section on technical challenges. I hope to add needed references over the next day or two.Elerner 18:09, 7 August 2006 (UTC)

Well, well, well. We've been busy, haven't we? You will not be surprised to learn that I take umbridge with many of your changes. I do see some logic to the new structure, so I will try to deal with the content within that form, rather than (shudder!) resorting to massive reversions. It may be next month before I have much time for this, though. --Art Carlson 20:44, 21 August 2006 (UTC)
Can I take that back? A section on direct conversion makes sense here because it is a subject that is important to aneutronic fusion and only of marginal interest to conventional fuel cycles like DD and DHe3. The section should explain what direct conversion is and what the advantage is (efficiency, mostly), and list/describe the major proposals, whereby a reference for each of these would be very helpful. However, its place of honor at the beginning of the article is predicated on the correctness of the assertion that direct conversion is "the principle advantage of aneutronic fusion", which I do not believe is tenable. My impression of the literature is that most people think the principle advantage of aneutronic fusion is that it is aneutronic. The fact that direct conversion is possible is welcomed in order to have any chance at all of making the energy balance positive.
The other major problem with the current version is the discussion of economics. The statement that "about 80% of the capital cost of a typical electric power generating station is in the thermal conversion equipment" is not true except for fossil fuel plants, possibly only for natural gas power plants. (That is why gas plants are used for peaking and emergency power: They are so cheap that you can afford to leave them idle most of the time.) For any design of a tokamak power plant, the cost of the turbines and generators is a very small fraction of the total cost. Since the cost of fusion power depends on the captital cost of producing the fusion, the capital cost of the energy conversion, and the recirculating power fraction, it is not possible to make sweeping statements about "sharply reduced costs". Furthermore, the current version states that direct conversion is as a rule easy, compact, and cheap, but many proposals that have been made have high technological risk and are both voluminous and expensive. Direct conversion is not even necessarily efficient. (Think of solar cells.) This section needs major revisions. Would you like to have a go at it, Eric, before I come back with my sledge hammer? --Art Carlson 10:45, 22 August 2006 (UTC)
While there have been no extensive analysis of direct conversion costs, it is very reasonable to state that the potential exists for great cost reductions. To give one example, technology exists for conversion of pulsed charged particle beams into elctric power--high power microwave generators. MW generators that are now produced on a one-of-akind or few-of-a-kind volume already cost about the same as turbines of the same capacity which are mass-produced in large volume. Since it is a well-know manufacturing rule of thumb that mass production leads to cost reductions of at least a factor of ten over small-volume production, it is perfectly defensible to say that there is a potential for major cost reductions. Also this is stated as a motivation for the apporach, which it certainly is.Elerner 18:17, 31 August 2006 (UTC)
Art Carlson's introduction to the direct conversion section is a non-sequitor. Instead of talking about direct conversion, it talks about the Lawson criterion, which belongs in the section on technical challenges. I have again moderated the language of my introduction and clarifed the 80% figure, which does refer to fossil-fuel plants, which have the lowest capital costs over all, so are the reasonable comparison on thsoe costs.Elerner 18:26, 31 August 2006 (UTC)

I've changed the economic comparison paragraph. I put in a new version of my old graph, which, I think is more accurate. I think that Art's paragraph is very close to incomprehensible by the average reader. Let's try nto to get into reverts, but edit instead.Elerner 01:08, 13 September 2006 (UTC)

I agree that my version is incomprehensible. There is nothing directly false in either version. But I find your version misleading. While the rest of the world is debating whether aneutronic fusion is even theoretically possible, and has postponed the question of whether it would be cheaper or more expensive than D-T fusion, you have jumped at least two orders of magnitude in the price projections and raised the question of whether aneutronic fusion would be cheaper than electricity from natural gas plants, if the natural gas were free! You may think that is a reasonable question, but it does not accurately represent to the readers the current state of the debate. We either need to make clearer the assumptions and background involved, or - better - we need to eliminate the discussion of economics altogether. It would, of course, help if we could find some serious, verifiable discussion of the economics of direct conversion. I will not delete the material until you have had a chance to propose a better version. --Art Carlson 08:58, 13 September 2006 (UTC)

Power density and Lawson criterion

OK. I fixed up the discussion of direct conversion and economics. The next worst thing about the August edits is the elimination of the information that, "for p-11B compared to D-T, the triple product nTτ required for ignition is 500 times higher and the power density is 2500 times lower." If that's not a "technical challenge", then I don't know what is! Change coming soon. Comments before? --Art Carlson 15:07, 28 August 2006 (UTC)
Yes I will get back to this shortly. I made it clear that higher nt and T are required. The power density is simply wrong. That depends on many variables such as density and T. The power density in a pB11 plasma focus is much higher than that in a DT tokamak.Elerner 02:58, 29 August 2006 (UTC)
I deleted the power density discussion, which is just wrong. You can’t compare the two fuels “at the same pressure” without specifying the temperature. Reactivity at the same pressure and different temperatures can vary widely. If the two fuels are compared at 600keV, the power density of pB11 is 60% that of DT at the same pressure. If they are compared at 66keV the power density of pB11 is 150 times less than DT at the same pressure.
The only valid apples-to-apples comparison is comparing the optimum conditions for the two fuels, which I did. The Lawson criterion for optimal burn is a factor of 30 times more for pB11, a substantial difference.Elerner 19:04, 31 August 2006 (UTC)
What? This strikes me as wrong. This completely ignores feasibility! I think that in such a circumstance it's an error to say such things. Ideally the power density section should include a graph versus temperature at different pressures. Do you agree?
Welcome to the discussion! Eric and I get in each others' hair a lot, so if you are interested, I think it would help a lot to have a third party around. The article is rather specialized, so it helps that you are a nascent plasma physicist, but on the other hand, if you don't understand the our technical arguments, then they must be too subtle for a general encyclopedia. I'm not asking you to take sides, just to comment on which formulation is more understandable, which arguments make more sense, and where external references are needed. Thanks. --Art Carlson 14:48, 5 September 2006 (UTC)
Dear Art, I'll make an attempt, but at the moment everything looks like a spaghetti argument on the talk page. I can't detect any real problems with the article, except the neutronicity argument could use some embellishing. It's my feeling that the advantage of 'aneutronic' fusion won't really be the lack of shielding, you'll just be able to get away with less of it, and you will have a replace it at a much lower frequency (meaning there will be much less expensive waste disposal). I would like to see some estimations on the savings you'd get with regards to shielding, if so possible. I'd also probably like to see some of the arguments shift towards D-He3 (which won't be totally aneutronic, but will cut neutron emissions by a bundle).
Eric, I have presented my calculations in detail here. In particular, I do clearly specify the temperature in my calculation as being that which yields the highest power density for the reaction at hand. You have not pointed to any mistake in these calculations, nor to any other set of assumptions that would be more instructive. You seem to have something of the sort in mind, but I have not been able to fathom what it is on the basis of what you have written. Maybe you can talk in complete equations? In short, my version is the only one which is documented. In addition, no flaws in it have been pointed out. So let's use it. --Art Carlson 11:57, 5 September 2006 (UTC)

Rather than get into reversions on this, I would like to ask Art to give his calculations defending the figures of 600 and 2500 in the power density paragraph. I can't duplicate them. And, may I point out, Art has posted a few arithmetical errors on wiki.Elerner 01:12, 13 September 2006 (UTC)

Once again, my calculations can be found here. If you still have trouble following some step, then I need to clarify the calculation in that article. --Art Carlson 09:03, 13 September 2006 (UTC)
If I am understanding you correctly, you want to use fusion power density / pressure squared as a figure of merit for fusion reactors. Now, I don’t think that is a good figure of merit, because some reactors, like the DPF may have plasma pressures orders of magnitude greater than a tokamak. In the article you reference, you say that this figure of merit is a measure of economical viability, but it clearly is not—actual power density is.
I'm not sure sure we are on the same wavelength. I calculate two figures of merit. The first is the Lawson criterion in the triple-product form. This is used all the time and should not be controversial. The second is the (relative) power density at a given pressure. (These have in common that the optimum temperature is that which maximizes <σT>/T²). Since the power density depends on the density and temperature as well as the fuel cycle, you have to specify the other conditions. I compare the power densities of different fuel cycles at the same pressure. I think you are comparing the power density of D-T at the pressure attainable in a tokamak with the power density at the pressure (you think) attainable in a DPF. That is not fair. My figure of merit would apply (at least within a factor of two or so) to a D-T tokamak compared to a p-B11 tokamak, or to a D-T DPF compared to a p-B11 DPF. Remember we are not discussing alternative confinement concepts here, but alternative fuel cycles. --Art Carlson 20:49, 14 September 2006 (UTC)
I don't agree at all. You can't separate fuels and devices--some fuels are more suitable to some devices. The article already points out that extremely high magnetic fields make things more favorable to pB11. Such fields can't be reacehd in a tokamka. A neutron-rich fuel like DT would blast apart a compact device like a DPF. The material damage rate would be pretty spectacular. So I don't see your figure of merit as a valid one at all. It does not relate to anything practical. The Lawson criterion gives an idea of technical difficulty. But then it should be the minimum triple product for complete burn-up, not for ignition. Ignition depends on the energy loss rate, which is device-dependent for both fuels.Elerner 02:04, 15 September 2006 (UTC)
It seems you agree that my math is right (this time), and that the results as I state them in the article, with the assumptions made there, are correct. That's a good start. Can we at least agree that the Lawson criterion has a place here? First, it is the figure of merit "everybody" uses, so we can't leave it out. Second, it is the best you can do to order the difficulty of various fuel choices before you start to discuss the confinement device. And third, it is a minimum requirement: If the DPF is the sooper-dooper device you believe it is, then it is so far above the minimum requirement that it doesn't matter any more. But the place to start is with Lawson. The role of the confinement concept comes into play when we take a closer look at the τ in nTτ. --Art Carlson 08:43, 15 September 2006 (UTC)
OK, I've added another comparison, which includes the fact that DT is more energetic. Hope this is OK with you now.Elerner 13:37, 18 September 2006 (UTC)

---Continuing dialog but restarting indentation---

Fine, why don't we include the minimum lawson criterion for burn-up and drop your pressure-based figure?Elerner 23:19, 15 September 2006 (UTC)

I'm glad we have agreed on the importance of the Lawson criterion as a measure (not the whole story!) of the technical feasibility of producing net energy. The next natural question after whether it is possible, is whether it is worthwhile. As you yourself have already pointed out, a very valuable figure of merit, commonly used in every area of energy technology not just fusion, is the power density. Since the reaction rate is proportional to the square of the density, the density or some function of the density and temperature has to be held fixed to compare different fuels. Since most, perhaps all, confinement concepts have a pressure limit, the natural choice is to compare different fuels at the same pressure. (Taking the same density is less common but might be a defensible alternative.) It is also of interest to note that the nTτ form of the Lawson criterion, as opposed to nτ or even nτ/T, is also justified on the basis of maximizing the power density for a given pressure.) The usefulness of this figure of merit is immediately evident if we consider burning p-B11 in a tokamak: Even if we could get it to burn, and even if we found some tricks to improve the performance of the fuel and the device, the power density is so low that an economic aneutronic tokamak is out of the question. One reason to include this number is to point out that, if aneutronic magnetic fusion has any chance at all, it will be in conjunction with an "alternate concept". --Art Carlson 10:40, 16 September 2006 (UTC)
In addition, your penalty factor assumes equal ion and electron temperatures, which is not a justifiable assumption.
It is correct that I assume equal ion and electron temperatures, which I believe to be justifiable from the literature. If you can succeed in supressing the transfer of energy from ions to electrons, of course, it's a new ball game. I have added a footnote to this effect. Can we postpone this fight until we have settled the one above? --Art Carlson 20:49, 14 September 2006 (UTC)
It is not justifiable from the literature. Just the x-ray loss alone make the electron temperature lower, and the high magnetic field effect can lead to temperatures that are an order of magnitude or more lower.Elerner 02:04, 15 September 2006 (UTC)
With "justifiable from the literature" I mean that most publications dealing with fusion either make the assumption or conclude from detailed considerations that the temperatures will be nearly equal. Admittedly, most publications also deal with tokamaks, but the article should try to reflect the state of the discussion as it is, not as some editor thinks it should be. We can get into exceptions later in the text. Remember, too, that radiation loses will selectively cool the electrons, but energy transfer from fusion products will under many conditions of interest selectively heat them, so the electrons are not automatically cooler than the ions at all, much less negligibly cold. --Art Carlson 08:52, 15 September 2006 (UTC)
Finally, I don’t even get the exact same numbers as you do. I find the maximum value for pB11 is 4.8x10^-27, not 3.0, but that is a minor point compared to the fact that the real measure should be power density, not power density/pressure squared.Elerner 15:20, 14 September 2006 (UTC)
I didn't give a reference for my number in the article, and I don't remember for sure where it came from, but I suspect from R. Feldbacher and M. Heindler. "Basic Cross Section Data for Aneutronic Reactor". Nucl. Instrum. & Meth. in Physics Research A271 (1988). Pp. 55-64. What is your reference? --Art Carlson 20:49, 14 September 2006 (UTC)
My reference includes better and more recent data "Thermonuclear Cross Section and Reaction Rate Parameter Data Compilation" Larry T. Cox, 1991 Phillips Laboratory report AL-TR -90-053Elerner 02:04, 15 September 2006 (UTC)
Thanks. I'll check it out. --Art Carlson 08:53, 15 September 2006 (UTC)
It looks like I don't have easy access to the original, but the formulas and coefficients in Talk:Nuclear_fusion#Optimum_fusion_temperatures apparently come from there. Can you verify that? The rest is just a bit of math. --Art Carlson 09:11, 15 September 2006 (UTC)
All right. I did the math. The results are on Talk:Nuclear_fusion#Optimum fusion temperatures. In particular, I get 3.0x10^-27, not 4.8, for p-B11. Your turn, Eric. --Art Carlson 14:03, 15 September 2006 (UTC)

I hope I am not starting another edit war here. But you are not using valid comparisons. First of all, getting ignition depends on many factors other than fuel, as I have explained several times. Second, ignition in no way guarantees for either fuel or for any device, that the fuel will then burn up completely. If ignition causes your plasma to become unstable, you may burn very little.
However, the requirements for burning the fuel entirely are much less ambiguous. The triple product is the minimum product of pressure and confinement time needed to burn the fuel entirely. Twenty seven is not a small factor and makes clear that pB11 is much, not a little more difficult. But we avoid totally invalid comparison that make the task seem impossible.
My calculations are as follow: for DT the triple product minimum occurs at 26 keV and is 4.42x10^16 keV-sec/cm^3. For pB11, the minimum is at 238keV and is 1.177x10^18keV-sec/cm^3. In each case, the triple product for burn-up is T/<σv>. The ratio is 26.6.
If you still disagree, Art, maybe we can call in Croquant?Elerner 20:31, 17 September 2006 (UTC)
Eric, would you mind telling me finally how you come up with these numbers?! What's the idea of saying "My calculations are as follows" and then just stating your results (without even giving any units)?! My calculations and the assumptions underlying them are laid out here and here and here. I find the optimum temperatures to be 13 keV and 125 keV, and the minimum triple products to be 2.76×1021 m-3 keV s and 1.37×1024 m-3 keV s. --Art Carlson 20:59, 17 September 2006 (UTC)
Sorry, see corrected version above.Elerner 21:44, 17 September 2006 (UTC)
That's still pretty sketchy, but I think I can piece it together now.
First, your numbers. Your temperatures are higher than mine because you are looking at the temperature that maximizes <σv>/T, and I am maximizing <σv>/T². Your values for the two fuels are closer together because you leave out a factor of T/E_ch that is in these formulas, and because you leave out my factor of three penalty. Your values for both are higher because of (apart from the cm to m conversion) that factor T/E_ch, mitigated by the factor of 12 in the Lawson formula. I haven't checked your math, but I assume your numbers are correct given your assumptions.
Second, your assumptions. You seem to be taking the burn-up fraction as the figure of merit. This is an unconventional choice, and for good reason. Recycling un-burned fuel is not a big deal. Energy is the name of the game. Just think about it. Of two reactions that had similar burn-up, would you take the one that produced 100 MeV per reaction or the one that produced nothing? It is true the derivation in the Lawson criterion article, except for the ICF section, makes the tacit assumption that the fusion products are confined and keep the plasma hot. If all fusion products are lost, you can still make a reactor, but it will be driven, not ignited. The relevant figure of merit then is the gain. The optimum is still where <σv>/T² is maximum, but you need to use the total fusion energy, not just the fusion energy released as charged particles. This would make D-T another factor of 5 more favorable over p-B11.
--Art Carlson 08:39, 18 September 2006 (UTC)
The nτ for burn up is just 1/<σv>. The nτ for fusion energy/thermal energy=1 is T/<σv>E, where E is fusion energy per reaction. The ratio of T/<σv> is 26.6 and the ratio of E is 1.68. Multiply then together and you get 44.63, rounded up to 45.
And since the temperature needed for p-B11 is ten times higher, the triple product is a factor of 500 higher. The limits on both nτ and nTτ are refered to in the literature as the Lawson criterion. My experience, at least in the tokamak world, is that the triple product is considered to be a better measure of technical difficulty. (See, for example, this). The triple product also follows naturally from any analysis which includes a pressure limit. There is no such natural motivation for choosing nτ as the figure of merit. For these reasons, I argue that we should in any case include the triple product in the article and let the chips fall where they may. (Note that trying to make aneutronic fusion look bad was not one of my arguments, and it is not one of my personal aims.) I have no objection to including the limit on nτ as a second figure of merit.--Art Carlson 09:07, 19 September 2006 (UTC)
The pressure comparison just does not make sense, since you MUST make further assumptions about electron temperatures.
Do you mean comparing the power density at given pressure? Of course you have to make an assumption! If you have been listening, you will know that I have stated in the articles that I am assuming equal temperatures for electrons and ions, like most authors do because most fusion devices have this characteristic. Since, later in this article, we consider systems with cold electrons, I am willing to also report the numbers using this assumption. All these alternatives are getting cumbersome, but I think an intelligent reader can find his way.--Art Carlson 09:07, 19 September 2006 (UTC)
Can we try to compromise, or do you just want to edit war like Joshua?Elerner 02:47, 19 September 2006 (UTC)
I don't want an edit war. What I want is an accurate, understandable, helpful, and neutral article. On that I am not willing to compromise. As a I say above, I am not willing to replace my figures of merit with others, but I am willing to supplement them. Feel free to add to the article, or just wait a few days until I have time to do the numbers carefully. --Art Carlson 09:07, 19 September 2006 (UTC)
Look, your calculations are "original research" unless you can cite them somewhere in the literature. The assumptions you use are just wrong and unsupported. And your arguing that power density at a given pressure is a valid measure of economic value, independent of device, is also unsupported in the literature. If you want to say pB11 requires higher pressure, that would be OK. But otherwise, find this analysis in the literature. Other wiki articles are not citations.Elerner 22:03, 19 September 2006 (UTC)
I don't understand what you are asking for here. Do you want citations that nTτ is used as a figure of merit for fusion reactions? Do you want citations that power density is used as a figure of merit for fusion reactions? Since some assumptions have to be made to compare the power density of different fuel cycles, are you proposing holding something other than pressure constant? What assumption of mine do you consider to be "just wrong" (as opposed to useful only under some circumstances)? Since I do say that p-B11 requires higher pressure (50 times higher), why do you not consider my version to be "OK"? --Art Carlson 20:55, 20 September 2006 (UTC)
Maybe this (p.6) will help:
Power Density. At fixed plasma pressure, and accounting for the greater a/p –ash fraction expected at similar ash pumping efficiencies (i.e., similar tp*/tE) in a D-3He burn, the fusion power density in D-3He is about 100 times less than that of D-T. Hence, a factor of ~10 increase in the plasma pressure is required to achieve fusion power densities in D-3He similar to that anticipated for the D-T fuel cycle.
Sounds an awful lot like my approach. --Art Carlson 21:06, 20 September 2006 (UTC)

I wrote some comments in the Dispute_between_Art_and_Eric section of this page (I began my comment before seeing this part of your discussion, which explains my creation of a new section). Croquant 05:41, 21 September 2006 (UTC)