I doubt it. Unless we find extra-terrestrial life in our solar system it will be impossible for us to get close enough to any place else to find life there within our lifetimes.
There are millions of apps written for Win32. Microsoft's market exists primarily because of backwards compatibility. MS is never going to do anything that would make their really big customers angry either. There are a lot of custom apps that big companies have written that work fine for them and don't need to be updated. When the Win64 api comes out there will be extremely few people using it, and it will support Win32. Thus anything that will be released in the next few years for the mass market will use Win32.
Look at games until about 5 years ago they still were mostly written for DOS. It will take years before the game companies switch to anything which isn't compatible with Windows 98 and we can be compatible with it rather easily.
The inclusion of a technology in the line of Microsoft operating systems does make it more mainstream. Apparently M$ sold about 180 million copies of Win '98 last year. We're lucky if Linux has 30 million seats total. (Hopefully we'll top 40 million by the end of this year, and maybe even 70 by the end of 2001).
Look at an analogous set of protocols: In filesharing we have NFS (UNIX, Linux, etc) and SMB (OS/2, WfW, Win '9x, NT, W2K, Samba, etc). Clearly SMB is the more "mainstream" protocol. Add to that the fact that NFS is far more widespread that Kerberos.
So, sadly, the support for M$ bastardized Kerberos extensions are likely to be necessary in the near future. Even if M$ only sells half of the W2K and WME (millenium edition ~~ consumer release of W2K) that will still be about twice as many seats supporting this protocol by mid next year as we have total Linux seats world wide.
BTW, I'm not ignoring the other forms of *nix and the *BSDs. The aggregate of all of those seems to represent about a quarter of the total Linux installations. Like it or not Linux is currently the most mainstream UNIX.
As for the broader issue, I wonder whether it is M$ or us that is more out of touch with the real mainstream (outside of the computing industry). I've been living in Silicon Valley for several years now. I've been a computing fanatic for a couple of decades. Most of my social contacts are computer geeks or science fiction fans (with considerable overlap, of course).
Obviously most of the public doesn't care about any of this. They've heard that M$ was involved in some long legal battle that had something to do with what icons show up on their computer screens at work or school, and maybe at home. (I guess that almost half of the people in the U.S American public don't have a general purpose computing system at home, and a fairly significant percentage don't work with them regularly). Probably many of them have heard that M$ was found guilty. The opiniontheir own personal political leanings and economic situations (I imagine that most republicans, particularly well-to-do replublicans think that M$ is "being picked on" and that most democrats tend to think that M$ is getting only a bit of what it, deserves).
One problem I have with all of the anti-MS hype is that it ignores the bigger hegemonies we face. M$ is not the worst company in the world. They didn't kill 16,000 people in Bhopal. They haven't been involved in the practical enslavement of millions of people around the world. They haven't engaged in strip mining, released billions of tons of pollutants and toxic waste into our ecosphere, etc. I don't like their products, and they have illegally stifled competition and innovation. But they aren't even on the top ten list of "worst corporations" in my book.
Indeed, compared to the injustices perpetrated by our own governments just in the "war on drugs" M$ is a shining bastion of morality. What is the current percentage? Over half of the incarcerated population is there on non-violent drug related charges? According to a reference at Human Rights, 60% of the 2 million inmates in the U.S. prison system are there are drug related charges --- and "over half" of those are "first time non-violent offenders"(sic I'd say victims).
I don't mean to say that M$ deserves leniency or that they aren't wrong. However, I must say that as I look over the greater socio-political landscape at our governments and the behemoth multi-national corporations that control them; I do think we have bigger problems! of most people about the justice of that ruling is probably related to
An API which relies on fork() to spawn new processes
Mountable and unmountable filesystems
Ownership and Group Associations for processes, files and some other resources (octal modes for files and directories)
SUID and SGID meta data on some files as a way to delegate privilege across security contexts
Abstraction of most devices (including established network sockets) as "files"
That's just a start. No repackaging of NT will really make it into "UNIX" because there are several mechanisms on this list that it implements in a fundamentally different way.
It would be nice if someone here actually showed some academic initiative and looked up Golbach's problem in standard references to comment on the work that as already been done in the field.
I happen to have a copy of the Encyclopedic Dictionary of Mathematics (Mathematical Society of Japan, translated, 1980 by MIT Press) here in my den.
Looking up Goldbach I find:
"Goldbach's problem is found in letters (1742) he exchanged with L. Euler. In them he stated that every positive integer can be expressed as the sum of primes. More precisely, he conjectured that any even integer not smaller than 6 can be expressed as the sum of two odd primes and that any odd integer not smaller than 9 can be expressed as the sum of three odd primes.
I.M. Vinogradov (1937) proved that every sufficiently large odd integer can be expressed as the sum of three primes."
The article then goes on to summarize the gist of this proof which involves a summation of (exp( - 2 * pi * i * ( a/q ) * N)) and a convergent series S(N)= sum(q=1, inf, A(q,N)) (which is "absolutely convergent and is equal to" [a copy of product expressions than can't be typeset here]).
It doesn't mention the magnitude of "sufficiently large" (read articles at Wolfram Research as referenced by the/. "related links" box near this article for more on that). Anyway --- Vinogradov solved Goldbach's conjecture for "sufficiently large odd integers."
Apparently "a finite or infinite sum of exponential functions such as this is called a trigonometric sum."
The article then discusses the case of even integers: "I.G. van der Corput, T. Estermann, and N. G. Cudakov proved simultaneously (1938) that almost all even integers (i.e., except a set of density 0) can be expressed as the sum of two primes." [emphasis mine].
All of this is in section 5.C of EDM.
The article goes on to comment on further work by Cudakov and Linnick, their introduction of "function-theoretic methods" and "the density theorem concerning the zeros of L-series" (which is greek to me).
They conclude with reference to the work of Zulauf (1952) which "continued along the same lines" as suggested by G.H. Hardy and J.E. Littlewood (1919).
I'm sure that some of the more academic participants here at/. might have access to a more comprehensive library than the bookshelf in my den. I'm not a mathematician, my education of the subject pretty much ended with high school Calculus, one audited class in combinatorics at Reed College and a few forays into Mathematica (tech support for my father, who is the arm chair mathematician and physicist of the family).
Personally I'd recommend starting with a thorough review of the literature to see what approaches have already failed. When you understand why those approaches failed then you can apply those tests to any methods you propose as a solution.
For example, if one could show that all even numbers less than some number N are the sum of pairs of primes less then N' and you could show that N and N' are related --- that N+x results in N'+y --- you might have a inductive proof in there somewhere.
If you win the $1M (or was that in pounds?) then feel free to donate a few grand to the FSF in my name.
I suspect that a proof of Goldbach's conjecture might entail a more fundamental formula or series that could generate the set of all primes. That would be a much more important finding since it would shatter the mathematical security of many cryptographic algorithms --- particularly the RSA PK (public key) system. (There's billions of $ at stake in that case).
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I doubt it. Unless we find extra-terrestrial life in our solar system it will be impossible for us to get close enough to any place else to find life there within our lifetimes.
There are millions of apps written for Win32. Microsoft's market exists primarily because of backwards compatibility. MS is never going to do anything that would make their really big customers angry either. There are a lot of custom apps that big companies have written that work fine for them and don't need to be updated. When the Win64 api comes out there will be extremely few people using it, and it will support Win32. Thus anything that will be released in the next few years for the mass market will use Win32.
Look at games until about 5 years ago they still were mostly written for DOS. It will take years before the game companies switch to anything which isn't compatible with Windows 98 and we can be compatible with it rather easily.
Look at an analogous set of protocols: In filesharing we have NFS (UNIX, Linux, etc) and SMB (OS/2, WfW, Win '9x, NT, W2K, Samba, etc). Clearly SMB is the more "mainstream" protocol. Add to that the fact that NFS is far more widespread that Kerberos.
So, sadly, the support for M$ bastardized Kerberos extensions are likely to be necessary in the near future. Even if M$ only sells half of the W2K and WME (millenium edition ~~ consumer release of W2K) that will still be about twice as many seats supporting this protocol by mid next year as we have total Linux seats world wide.
BTW, I'm not ignoring the other forms of *nix and the *BSDs. The aggregate of all of those seems to represent about a quarter of the total Linux installations. Like it or not Linux is currently the most mainstream UNIX.
As for the broader issue, I wonder whether it is M$ or us that is more out of touch with the real mainstream (outside of the computing industry). I've been living in Silicon Valley for several years now. I've been a computing fanatic for a couple of decades. Most of my social contacts are computer geeks or science fiction fans (with considerable overlap, of course).
Obviously most of the public doesn't care about any of this. They've heard that M$ was involved in some long legal battle that had something to do with what icons show up on their computer screens at work or school, and maybe at home. (I guess that almost half of the people in the U.S American public don't have a general purpose computing system at home, and a fairly significant percentage don't work with them regularly). Probably many of them have heard that M$ was found guilty. The opiniontheir own personal political leanings and economic situations (I imagine that most republicans, particularly well-to-do replublicans think that M$ is "being picked on" and that most democrats tend to think that M$ is getting only a bit of what it, deserves).
One problem I have with all of the anti-MS hype is that it ignores the bigger hegemonies we face. M$ is not the worst company in the world. They didn't kill 16,000 people in Bhopal. They haven't been involved in the practical enslavement of millions of people around the world. They haven't engaged in strip mining, released billions of tons of pollutants and toxic waste into our ecosphere, etc. I don't like their products, and they have illegally stifled competition and innovation. But they aren't even on the top ten list of "worst corporations" in my book.
Indeed, compared to the injustices perpetrated by our own governments just in the "war on drugs" M$ is a shining bastion of morality. What is the current percentage? Over half of the incarcerated population is there on non-violent drug related charges? According to a reference at Human Rights, 60% of the 2 million inmates in the U.S. prison system are there are drug related charges --- and "over half" of those are "first time non-violent offenders "(sic I'd say victims).
I don't mean to say that M$ deserves leniency or that they aren't wrong. However, I must say that as I look over the greater socio-political landscape at our governments and the behemoth multi-national corporations that control them; I do think we have bigger problems! of most people about the justice of that ruling is probably related to
- A clearly defined kernel/user space interface
- A set of system calls --- handled by the kernel
- An API which relies on fork() to spawn new processes
- Mountable and unmountable filesystems
- Ownership and Group Associations for processes, files and some other resources (octal modes for files and directories)
- SUID and SGID meta data on some files as a way to delegate privilege across security contexts
- Abstraction of most devices (including established network sockets) as "files"
That's just a start. No repackaging of NT will really make it into "UNIX" because there are several mechanisms on this list that it implements in a fundamentally different way.I happen to have a copy of the Encyclopedic Dictionary of Mathematics (Mathematical Society of Japan, translated, 1980 by MIT Press) here in my den.
Looking up Goldbach I find:
The article then goes on to summarize the gist of this proof which involves a summation of (exp( - 2 * pi * i * ( a/q ) * N)) and a convergent series S(N)= sum(q=1, inf, A(q,N)) (which is "absolutely convergent and is equal to" [a copy of product expressions than can't be typeset here]).It doesn't mention the magnitude of "sufficiently large" (read articles at Wolfram Research as referenced by the /. "related links" box near this article for more on that). Anyway --- Vinogradov solved Goldbach's conjecture for "sufficiently large odd integers."
Apparently "a finite or infinite sum of exponential functions such as this is called a trigonometric sum."
The article then discusses the case of even integers: "I.G. van der Corput, T. Estermann, and N. G. Cudakov proved simultaneously (1938) that almost all even integers (i.e., except a set of density 0) can be expressed as the sum of two primes." [emphasis mine].
All of this is in section 5.C of EDM.
The article goes on to comment on further work by Cudakov and Linnick, their introduction of "function-theoretic methods" and "the density theorem concerning the zeros of L-series" (which is greek to me).
They conclude with reference to the work of Zulauf (1952) which "continued along the same lines" as suggested by G.H. Hardy and J.E. Littlewood (1919).
I'm sure that some of the more academic participants here at /. might have access to a more comprehensive library than the bookshelf in my den. I'm not a mathematician, my education of the subject pretty much ended with high school Calculus, one audited class in combinatorics at Reed College and a few forays into Mathematica (tech support for my father, who is the arm chair mathematician and physicist of the family).
Personally I'd recommend starting with a thorough review of the literature to see what approaches have already failed. When you understand why those approaches failed then you can apply those tests to any methods you propose as a solution.
For example, if one could show that all even numbers less than some number N are the sum of pairs of primes less then N' and you could show that N and N' are related --- that N+x results in N'+y --- you might have a inductive proof in there somewhere.
If you win the $1M (or was that in pounds?) then feel free to donate a few grand to the FSF in my name.
I suspect that a proof of Goldbach's conjecture might entail a more fundamental formula or series that could generate the set of all primes. That would be a much more important finding since it would shatter the mathematical security of many cryptographic algorithms --- particularly the RSA PK (public key) system. (There's billions of $ at stake in that case).