Well, the rules under which the transfer or property rights occurs should be left to the participants of the transaction. Employee has a choice of working as a consultant on per project basis. And if employer believes they'd be best served by a different arrangement, why not leave that choice to the people involved and have the government mandate it?
Archimedes did not understand the least upper bound property. Without it, real analysis is impossible. Nor did he understand log and exponential function. Without those, harmonic analysis doesn't exist at all.
Without Newton, string theory would have been invented hundreds of years ago. Good choice of words. invented -- not discovered. Although how harmonic analysis would have been discovered or invented without calculus is something I would really like to know.
Not a bad idea, but it should be a doubling in constant dollars, i.e. after adjustment for inflation. Otherwise, inflation would significantly reduce the real effect of that doubling. That's why it would be based off of "base line" value. It wouldn't be doubling of what they paid originally, but ba*f(time).
Prohibiting "work for hire" contracts, to ensure that the exclusive rights are secured for the author. According to the Holy Constitution, all authors should be freelance, not toiling on Massa Mickey's content plantation. Well, why shouldn't property rights be transferable? And anything which allows one to charge others for its use is (at least partially) a property right. "Partially" because it may have other aspects (such as zero reproduction cost).
Setting up a body to make subjective value judgements about whether an artwork is "useful" or not, as the Constitution mandates, with an assumption that it is not (otherwise why would the Unquestionable Constitution specify "useful" at all?). That's not necessary. It is "useful" if it is used. And if it's never used, the issue of ownership will never come up.
Repeal the Mickey Mouse Protection Act and "limit" the duration of copyright in order to promote "progress", rather than eternal milking of the same work.
This is very much true. The market place establishes fair price for the value provided by the asset. But the actual value, in the case of copyrighted work, is derived from 2 aspects -- usefulness and time until copyright expiration. The first is inherent property of the work and the second is established by the government. If most of the value ends up being in the second (as it does now), then by comparison only a very small part of the value of work comes from its usefulness.
So how is the government determine that fair sweet spot where the value of copyrighted work would be relatively equally composed of the value that comes from usefulness and the value that comes from time until expiration? The link from one of your responses has a brilliant idea http://zotzbro.blogspot.com/2007/04/some-thoughts-on-copyright-offensive.html. He says have a property tax on holding a copyright. I can't believe no one has said this before. But I'd say make it more subtle.
There will always be the argument that you have starving artists who rely on copyrights to be compensated by the time they "make it" to incentivise them. Ok. So how's this. Allow for copyright to be held freely for 10 years (not sure what's really fair) from the date of creation. After that, impose a property tax on them which would grow with every year of holding a copyright. The tax should approximately double every 10 years. This way copyrighted materials that are bringing more and more revenue because the owners spend more resources to increase the value of the material would be still copyrightable in 10,20,30,40 years. But since most of the value at that point would be derived from copyright rather than usefulness, they would be paying tax which would grow 2,4,8,16 times. Start the tax at something small... say $1000 a year. After all if you can't spend $1000 a year on something that you created 10 years ago, you probably will never make any money off of it. So you might as well let the public domain benefit from it. And it's not really unfair for Madonna to pay $2000 for songs that she wrote 30 year ago. Of course, if some corp wants to keep ownership of something copyrighted 80 years ago, there is not reason not to demand they shell out 128k a year for it.
Oh, and $1000 a year is too arbitrary. It should be some "base line" number that is adjusted every year by Congress.
Umm... before more people accuse me of killing babies, spreading fud, and being a tool of all kinds, I'll just say that I was, in fact, speaking from memory of college courses. I am not a physicist or engineer -- I am a mathematician.
With that out of the way, figure 3.11 in http://web.mit.edu/16.unified/www/SPRING/propulsion/notes/node25.html shows that theoretical thermal efficiency of an internal combustion engine peaks at 70%. I was trying to be conservative when I wrote the original post, so I said 55%. Yes, there is loss during friction, but I was assuming that the same loss would occur for an electric engine. One of the posts above pointed out that an electric engine has less moving parts so less is lost due to friction. I am willing to accept that on faith at this point.
The 2-3 times number that I came up with was based on the assumption that with electricity there is 2 costs of inefficiency -- first in generation and second in the engine itself. I was also assuming that the cost of "generating" (ie, pumping) oil was nominal. But as someone pointed out in a different post, there is a large cost of delivering oil compared to the cost delivering electricity. And, of course, as everyone points out, I did mess up the efficiency of an electric engine.
Thanks for the link. This is clearly not the engine I saw back in school. As for
do you enjoy spreading FUD? No, but have you stopped beating your wife?
I see. I did not account for the deliver cost of electricity vs delivery cost of gas. The 22% efficiency figure was after you factored in the 55% efficiency of production. They must have a different electric engine design from the one I was taught if they get 95% efficiency out it.
First, efficiency of generating electricity (work done/energy produced) is 60% tops. Then there is attenuation loss while its delivered to the consumer. Then it has to be stored in batteries which lose energy over time. Assuming that you get (and this is very optimistic) 55% efficiency at this point, you now have to spend this energy in an electric engine. Electric engine has THEORETICAL top efficiency of around 45%. Assume the engine actually works at 40%. So now you have.4*.55=22% efficiency. The theoretical efficiency of gasoline engine (which I don't remember at the moment) is 2-3 times that. So for every calory of heat we burn (and release into atmoshere) with a gasoline engine we'd get 2-3 as much work. Assuming that the energy is generated with coal or diesel power plants, this also means that that we release 2-3 times as much greenhouse gases while using electric engines. So the reason for this is what? Nuclear power plants and hydro plants? How much of the electric energy is produced using those? 20% using nuclear and about 10% using hydro. About 55% is produced using coal. These cars will just end up burning more coal and release massive amount of greenhouse gases. But hey, it's cool to be green.
What I want to know is how does one define "customization" ? Macro? Shell script? showing someone how to download something? installing something? Eh... Pretty sure it would be anything not offered at a standardized price to general public as an already-developed product. Which begs the question, does Internet access modify your computer?
Funny how you said "cases". A friend of mine recently avoided most of the tariff for a computer he sent to Germany by declaring it as a computer "case". Yes, I know you meant something else. I am just wondering... what pun?
Not really: I should love him, because he showed us the limitations of logical systems in general, so that when we speak we speak the truth in its entirety and when we are silent we can mathematically prove that we should indeed be silent. I wish! He showed that when we speak we can always say things which are true and yet cannot be shown to be true. So we are never sure if inability to prove something is due to our limitations or due to the nature of a particular axiomatic system. So he showed the opposite of
when we are silent we can mathematically prove that we should indeed be silent
By the way the quote is ripped right out of the Opus Dei prayer in Latin, with slight modification:) I know. That was cute.:)
Umm... this doesn't apply here. The original accusation was of breaking the law -- not of committing atrocities. Before you shoot back an argument that atrocities are also illegal, as a friendly reminder I'll just say that "A is I" does not imply that "I is A".
Who else would you ask as a government employee whether what your boss tells you to do is legal if not the lawyers? In case of an atrocity, it's very clear what you should do.
Do you think mathematicians working for the NSA should question everyone of their technical assignments? No one works like that. And most people even in the regular jobs never understand what their specific job contributes to the overall picture of what the organization does. NSA employees are not even allowed to discuss their job with each other (unless they work on the same project). Do you really think it's this Hollywood-movie-type frat-house-like collective? Seriously, sometimes I really wonder why people bother taking a high moral ground while talking to (or about) the people who have no control or even clue about what's the big picture.
I was giving just a random site that had a collection of quotations. If you google it, you get hundreds of sites that attribute this to Napoleon. I don't know the original source though, so I'll agree to be agnostic on this. No offense, but Wikipedia is really not a source to use for resolving a controversy.
I assume you are talking about my example of algebraic geometry? Or is it Mathematica? Who is the straw man? I am not trying to bring anyone down here. Any example was hypothetical. So if you don't like the details, that's Ok. They are not meant to be accurate. Examples are only there to demonstrate a principle. I didn't even know we were having an argument at this point. I thought I was just outlying why and when omitting certain details in a proof would not cause trouble.
Yes, I read it. It doesn't specifically say that the Campbell example relies on an unknown sequence of steps. You can publish a sequence of steps which your prove to be finite and say that how one would go about performing each of these steps is well-known and can be done with any number of software packages. This is no different from publishing a proof in which each sentence states a result that previously required an entire paper to demonstrate. As a matter of fact, this is often how math is written today, so... I don't see any difference there. As long as we are talking about results that can be reproduced in a finite number of known steps, it doesn't matter that a package was used. Any package that uses undocumented ways of solving a problem would not be trusted anyway -- not in math.
For example, let's say you need to find a small set of polynomials that has zeros in common with a set of 10,000 other polynomials. This is a simple problem in Algebraic Geometry. Obviously, it's not doable by hand or through any sort of estimation of roots -- you are looking for exact solution. You can use Mathematica which will use highly optimized algorithms or you can roll your own code for finding Groebner bases, etc. Does it matter that Mathematica will be out of business in 10 years and the statement in your paper that it has a command for doing this will be useless? No. Because you can only make these statements for procedures that have well-known (to the cognoscenti, at least) intermediate steps. So it is possible to reproduce those steps in any programming language on your own. Of course, if you want to make the argument that we should be able to do math with no computers available at all, then I'd ask why not without paper as well?
Another example from the intelligence community... ho hum. Again, as I said in my previous post, these kinds of situations are the exception, not the rule. There are only a handful of them with any real clout, and since neither of us work with them neither of us is particularly qualified to comment on what sort of stuff they do behind closed doors. As I said earlier, I'm willing to believe that they come up with innovative stuff, but the reason I responded to your post was because you were sitting here talking about how lots of math is done closed and how we all had to accept it etc etc because if there was money to be made keeping it closed, then it would be kept closed. You then gave investment bankers as an example, a field you clearly know nothing about, no offense. That seems to be your only financially-motivated example, because intelligence agencies are not under much financial pressure. I am pretty sure I was careful to talk about competitive advantage in the original rather than plain financial advantage. You don't think spy agencies fall in the category of those seeking competitive advantage (over other spy agencies)?
Basically, all the basic building blocks of our models are well known in the industry, and yet we still win 4 out of 5 deals: it's how we put it together keeps us ahead of the market and ahead of our competition. I chose Renaissance as an example earlier because if any firm was likely to be a counterexample, it's them, but even in their case, I suspect they're just making innovative use of existing ideas rather than truly innovating in the way, say, Evariste Galois or even Stephen Smale were when they did the work they did. I am not sure why you bring that time. A lot of that was just math done for entertainment. Certainly Galois cared as much for politics as he did for math and he never derived any money from publishing his theory. I am sure you know that he stated most of it in a letter he wrote the night before the duel. A lot of math done then was done by hobbyists. Again, not really sure what your point is there.
Another example from the intelligence community... ho hum. Again, as I said in my previous post, these kinds of situations are the exception, not the rule. There are only a handful of them with any real clout, You said you were a topologist, right? Well, if some work was done to efficiently read captchas that work would probably stay secret. And it would most likely be in topology.
That seems to be your only financially-motivated example, because intelligence agencies are not under much financial pressure. Again, not all competition comes from finances. There is a great deal of competition in espionage.
I'm sorry, attempting to insult my pedigree won't get you far in an argument. I was using "you" as in "one". So it was not ad hominem per se. But your statement is still wrong. My statement was not insulting your pedigree -- it was insulting your (or one's) lack of pedigree as would be evidenced by inability to secure funding for graduate schooling.
Man, for a mathematician, you're not that good with logic, are you? How does this follow? Undergraduates choose schools based on pedigree, and they're the ones who pay. Ok. I'll stop this line of argument here. I am tired of this egg throwing.
Unix system administration? Well, gee, now I get it!
Really? I figured this example would not be so out of left field for someone in finance. Certainly, if anyone of the rest of slashdot is still following this, they might relate.
But ok, I don't know topology beyond the qual level, but has anyone rigorously proved all the basic results about cell complexes before Hatcher? It seems like people just state (even in books) without ever bothering to prove them.
The article in the AMS that this is all about was specifically raising the question of whether this will remain true. You can't challenge that question simply by stating its opposite.:) No, you can't. But if you describe the details of your point, you are are not doing that. And I did describe the details. I set a very specific criteria for the cases when it will continue to be true. I won't restate them here.
Ah. So we are on the actual subject of the article now. Good. I was tired of having to talk about philosophy of life as it applies to math.
Well, here how computer programs have place in math. Some proves can be accomplished by showing a finite set of objects has a certain property. This set might be huge. Certainly, it can easily be larger than anything than can be checked by hand. If one manages to describe a procedure that is proven to exhaustively produce (in a finite number of steps) every element of the set and one manages to describe a procedure that manages to test (in a finite number of steps) that a given element of the set has the property in question, then it is enough to then write a program that goes through the steps and checks the property. This is reproducible because the steps are documented and anyone can write their own program to check these property for every element of the set. As far as I am concerned, this constitutes a proof. After all, what difference does it make if someone says that "a simple computation shows that" in a paper or if someone says "a simple exhaustive check of these properties shows that"? Both require the reader to go through well-documented, albeit labor-intensive, effort to verify the claim.
It really doesn't matter if you accomplish the verification of these steps in your favorite package or "roll" your own objects in python, ruby, perl, etc.
I am not sure why you say that mathematics is exceptional in that its point is publication. The same is true of all scientific disciplines I can think of right now. Maybe I am overlooking some, but certainly this is predominately the case. Assuming, of course, that we are talking about academia. The reason for that is that in academia people get paid essentially for being famous.
I would agree with you for the most part. But the same is true for most of academic research. Most publications are very incremental work. There only very occasional breakthroughs. And occasional breakthroughs happen in private as well. I mentioned it in another post, but Student's distribution is the first that comes to mind. Every undergraduate that takes differential equations learns of the history of Dirac's delta function (discovered by an engineer who was first laughed at by the mathematicians and which later on redefined how analysis was done). By the way, theoretical statistics is very much a pure and applied endeavor. It is heavily rooted in real analysis. I guess the best example of a mathematician (Euler) would also be a good example of what I am talking about here. He proved a great deal of theoretical results but he only did it because he needed them to make many calculations to design real world objects. Some of it he also did for amusement. And a lot of his results are still secret. They are stored in archives of (if memory serves) St. Petersburg University and are not open to the general public. But it is his work process that demonstrates what working in mathematics is like. Calculations breed generalizations which breed hypothesis which allow for new results which allow for a wider range of calculations. So even if the crypto work is "mining" for theorems, I am sure they stumble across a great deal of results they never publish. And it is generally assumed that anything known from the currently published theorems is already used in cryptography. So if you think that they don't try to establish new results, you don't give them enough credit. Anyway, I am not arguing for or against open math. I am just saying that both have their place and both are a way of life. Cheers.
Slashdot Mirror
Well, the rules under which the transfer or property rights occurs should be left to the participants of the transaction. Employee has a choice of working as a consultant on per project basis. And if employer believes they'd be best served by a different arrangement, why not leave that choice to the people involved and have the government mandate it?
Archimedes did not understand the least upper bound property. Without it, real analysis is impossible. Nor did he understand log and exponential function. Without those, harmonic analysis doesn't exist at all.
Coward? You post as AC to call other people cowards? Am I the only one who sees the irony?
This is very much true. The market place establishes fair price for the value provided by the asset. But the actual value, in the case of copyrighted work, is derived from 2 aspects -- usefulness and time until copyright expiration. The first is inherent property of the work and the second is established by the government. If most of the value ends up being in the second (as it does now), then by comparison only a very small part of the value of work comes from its usefulness.
So how is the government determine that fair sweet spot where the value of copyrighted work would be relatively equally composed of the value that comes from usefulness and the value that comes from time until expiration? The link from one of your responses has a brilliant idea http://zotzbro.blogspot.com/2007/04/some-thoughts-on-copyright-offensive.html. He says have a property tax on holding a copyright. I can't believe no one has said this before. But I'd say make it more subtle.
There will always be the argument that you have starving artists who rely on copyrights to be compensated by the time they "make it" to incentivise them. Ok. So how's this. Allow for copyright to be held freely for 10 years (not sure what's really fair) from the date of creation. After that, impose a property tax on them which would grow with every year of holding a copyright. The tax should approximately double every 10 years. This way copyrighted materials that are bringing more and more revenue because the owners spend more resources to increase the value of the material would be still copyrightable in 10,20,30,40 years. But since most of the value at that point would be derived from copyright rather than usefulness, they would be paying tax which would grow 2,4,8,16 times. Start the tax at something small... say $1000 a year. After all if you can't spend $1000 a year on something that you created 10 years ago, you probably will never make any money off of it. So you might as well let the public domain benefit from it. And it's not really unfair for Madonna to pay $2000 for songs that she wrote 30 year ago. Of course, if some corp wants to keep ownership of something copyrighted 80 years ago, there is not reason not to demand they shell out 128k a year for it.
Oh, and $1000 a year is too arbitrary. It should be some "base line" number that is adjusted every year by Congress.
Umm... before more people accuse me of killing babies, spreading fud, and being a tool of all kinds, I'll just say that I was, in fact, speaking from memory of college courses. I am not a physicist or engineer -- I am a mathematician.
With that out of the way, figure 3.11 in http://web.mit.edu/16.unified/www/SPRING/propulsion/notes/node25.html shows that theoretical thermal efficiency of an internal combustion engine peaks at 70%. I was trying to be conservative when I wrote the original post, so I said 55%. Yes, there is loss during friction, but I was assuming that the same loss would occur for an electric engine. One of the posts above pointed out that an electric engine has less moving parts so less is lost due to friction. I am willing to accept that on faith at this point.
The 2-3 times number that I came up with was based on the assumption that with electricity there is 2 costs of inefficiency -- first in generation and second in the engine itself. I was also assuming that the cost of "generating" (ie, pumping) oil was nominal. But as someone pointed out in a different post, there is a large cost of delivering oil compared to the cost delivering electricity. And, of course, as everyone points out, I did mess up the efficiency of an electric engine.
So mia culpa on the facts.
I see. I did not account for the deliver cost of electricity vs delivery cost of gas. The 22% efficiency figure was after you factored in the 55% efficiency of production. They must have a different electric engine design from the one I was taught if they get 95% efficiency out it.
Electric engine is less efficient (~40%) than internal combustin engine (~55%).
First, efficiency of generating electricity (work done/energy produced) is 60% tops. Then there is attenuation loss while its delivered to the consumer. Then it has to be stored in batteries which lose energy over time. Assuming that you get (and this is very optimistic) 55% efficiency at this point, you now have to spend this energy in an electric engine. Electric engine has THEORETICAL top efficiency of around 45%. Assume the engine actually works at 40%. So now you have .4*.55=22% efficiency. The theoretical efficiency of gasoline engine (which I don't remember at the moment) is 2-3 times that. So for every calory of heat we burn (and release into atmoshere) with a gasoline engine we'd get 2-3 as much work. Assuming that the energy is generated with coal or diesel power plants, this also means that that we release 2-3 times as much greenhouse gases while using electric engines. So the reason for this is what? Nuclear power plants and hydro plants? How much of the electric energy is produced using those? 20% using nuclear and about 10% using hydro. About 55% is produced using coal. These cars will just end up burning more coal and release massive amount of greenhouse gases. But hey, it's cool to be green.
Like I said in a previous post, it's a lot easier to run on the platform of taking care of the poor if you create more poor.
Hey, it's a lot easier to run on the platform of helping the poor if you have more poor.
Funny how you said "cases". A friend of mine recently avoided most of the tariff for a computer he sent to Germany by declaring it as a computer "case". Yes, I know you meant something else. I am just wondering... what pun?
By the way the quote is ripped right out of the Opus Dei prayer in Latin, with slight modificationUmm... this doesn't apply here. The original accusation was of breaking the law -- not of committing atrocities. Before you shoot back an argument that atrocities are also illegal, as a friendly reminder I'll just say that "A is I" does not imply that "I is A".
Who else would you ask as a government employee whether what your boss tells you to do is legal if not the lawyers? In case of an atrocity, it's very clear what you should do.
Do you think mathematicians working for the NSA should question everyone of their technical assignments? No one works like that. And most people even in the regular jobs never understand what their specific job contributes to the overall picture of what the organization does. NSA employees are not even allowed to discuss their job with each other (unless they work on the same project). Do you really think it's this Hollywood-movie-type frat-house-like collective? Seriously, sometimes I really wonder why people bother taking a high moral ground while talking to (or about) the people who have no control or even clue about what's the big picture.
I was giving just a random site that had a collection of quotations. If you google it, you get hundreds of sites that attribute this to Napoleon. I don't know the original source though, so I'll agree to be agnostic on this. No offense, but Wikipedia is really not a source to use for resolving a controversy.
I assume you are talking about my example of algebraic geometry? Or is it Mathematica? Who is the straw man? I am not trying to bring anyone down here. Any example was hypothetical. So if you don't like the details, that's Ok. They are not meant to be accurate. Examples are only there to demonstrate a principle. I didn't even know we were having an argument at this point. I thought I was just outlying why and when omitting certain details in a proof would not cause trouble.
Yes, I read it. It doesn't specifically say that the Campbell example relies on an unknown sequence of steps. You can publish a sequence of steps which your prove to be finite and say that how one would go about performing each of these steps is well-known and can be done with any number of software packages. This is no different from publishing a proof in which each sentence states a result that previously required an entire paper to demonstrate. As a matter of fact, this is often how math is written today, so... I don't see any difference there. As long as we are talking about results that can be reproduced in a finite number of known steps, it doesn't matter that a package was used. Any package that uses undocumented ways of solving a problem would not be trusted anyway -- not in math.
For example, let's say you need to find a small set of polynomials that has zeros in common with a set of 10,000 other polynomials. This is a simple problem in Algebraic Geometry. Obviously, it's not doable by hand or through any sort of estimation of roots -- you are looking for exact solution. You can use Mathematica which will use highly optimized algorithms or you can roll your own code for finding Groebner bases, etc. Does it matter that Mathematica will be out of business in 10 years and the statement in your paper that it has a command for doing this will be useless? No. Because you can only make these statements for procedures that have well-known (to the cognoscenti, at least) intermediate steps. So it is possible to reproduce those steps in any programming language on your own. Of course, if you want to make the argument that we should be able to do math with no computers available at all, then I'd ask why not without paper as well?
Really? I figured this example would not be so out of left field for someone in finance. Certainly, if anyone of the rest of slashdot is still following this, they might relate.
But ok, I don't know topology beyond the qual level, but has anyone rigorously proved all the basic results about cell complexes before Hatcher? It seems like people just state (even in books) without ever bothering to prove them.
Ah. So we are on the actual subject of the article now. Good. I was tired of having to talk about philosophy of life as it applies to math.
Well, here how computer programs have place in math. Some proves can be accomplished by showing a finite set of objects has a certain property. This set might be huge. Certainly, it can easily be larger than anything than can be checked by hand. If one manages to describe a procedure that is proven to exhaustively produce (in a finite number of steps) every element of the set and one manages to describe a procedure that manages to test (in a finite number of steps) that a given element of the set has the property in question, then it is enough to then write a program that goes through the steps and checks the property. This is reproducible because the steps are documented and anyone can write their own program to check these property for every element of the set. As far as I am concerned, this constitutes a proof. After all, what difference does it make if someone says that "a simple computation shows that" in a paper or if someone says "a simple exhaustive check of these properties shows that"? Both require the reader to go through well-documented, albeit labor-intensive, effort to verify the claim.
It really doesn't matter if you accomplish the verification of these steps in your favorite package or "roll" your own objects in python, ruby, perl, etc.
I am not sure why you say that mathematics is exceptional in that its point is publication. The same is true of all scientific disciplines I can think of right now. Maybe I am overlooking some, but certainly this is predominately the case. Assuming, of course, that we are talking about academia. The reason for that is that in academia people get paid essentially for being famous.
I would agree with you for the most part. But the same is true for most of academic research. Most publications are very incremental work. There only very occasional breakthroughs. And occasional breakthroughs happen in private as well. I mentioned it in another post, but Student's distribution is the first that comes to mind. Every undergraduate that takes differential equations learns of the history of Dirac's delta function (discovered by an engineer who was first laughed at by the mathematicians and which later on redefined how analysis was done). By the way, theoretical statistics is very much a pure and applied endeavor. It is heavily rooted in real analysis. I guess the best example of a mathematician (Euler) would also be a good example of what I am talking about here. He proved a great deal of theoretical results but he only did it because he needed them to make many calculations to design real world objects. Some of it he also did for amusement. And a lot of his results are still secret. They are stored in archives of (if memory serves) St. Petersburg University and are not open to the general public. But it is his work process that demonstrates what working in mathematics is like. Calculations breed generalizations which breed hypothesis which allow for new results which allow for a wider range of calculations. So even if the crypto work is "mining" for theorems, I am sure they stumble across a great deal of results they never publish. And it is generally assumed that anything known from the currently published theorems is already used in cryptography. So if you think that they don't try to establish new results, you don't give them enough credit. Anyway, I am not arguing for or against open math. I am just saying that both have their place and both are a way of life. Cheers.