Consider the computerised proof of the 4-Colour theorem.
It may be that there is a nice, clean analytical proof out there waiting to be discovered, but every attempt to find it so far has failed.
What was possible was to reduce the problem to one that was solvable by enumerating a finite set of possible graphs.
TFA (well, one of them) explains the process quite well.
I still spend the odd insomniac night trying to figure out a purely analytical proof, though - for no other reason than pure stubbornness and Luddite tendencies:o)
The other example I gave was first order logic. The incompleteness theorems don't talk about this either because you can't do arithmetic in first order logic. The theorems only apply to formal systems in which you can do arithmetic. Check out the wording at wikipedia [wikipedia.org].
Correct me if I'm wrong, but doesn't Godel's second theorem explicitly address Peano arithmetic, which is all first order logic?
True, you can't address countability (and by extension the halting problem) completely within first order logic, so your point that it is impossible to write a program that creates all true propositions and only true propositions of a formal system holds, but it is possible to create a first order arithmetic, although you can't use it to prove its own consistency.
That's what I remember from 20-odd years ago, anyway:o)
As it stands, they aren't going to store the raw data - just information on the endpoints.
This in itself is disturbing, since as Bruce Schneier points out, data mining of this sort is inherently flawed.
It strikes me that this is politically driven - i.e. that GCHQ has an ample supply of mathematicians who can see that this is useless, but that the idiocracy that is Neues Arbeit still believes the bullshit that their highly paid, poorly educated advisors spew out.
Trouble is, the idiots won't listen to sense, so we'll have to wait until the next election to vote in another lot of idiots who may or may not be as stupid as this lot.
I always thought it was reality TV, but then again I work in a shoe shop and spend my nights either scratching my bollocks or on the beer with the lads.
All right, I'll bite - Obama's citizenship is a minor constitutional issue compared to the excesses perpetrated by Bush for the last 8 years - warrantless wiretapping, the effective suspension of habeus corpus, etc.
If you're really that concerned about your constitution, you should be refreshing the tree of liberty with whatever you find available - Bush has around 8 pints, IIRC.
Fermentation is already a well-understood process - GM yeasts, bacteria and fungi are all used in enzyme production.
It may be that a yeast is a better target for manipulation - they are already used in the production of cellulases used to increase the energy available from animal feed, and this looks similar.
Your sort created the situation in Iraq and Afghanistan - a situation that isn't sustainable without the presence of foreign troops, ever.
I bet you like Israel too, you twat - it's the terrorist cancer eating the life out of the region, but 'islamists' are obviously far more scary in your mind than expansionist terrorist Zionists.
I'd guess that anyone finding a USB stick who didn't realise what it was would ask their friendly local BOFH to take a look - thus ensuring the flow of beer tokens from the tabloids to said BOFH.
But even the Home Office is eclipsed in doltishness by MAFF (or whatever it's called nowadays) - the people that brought you mounds of cremated cows and sheep because nobody had the balls to vaccinate against foot and mouth.
I'll be driving past the source of the last outbreak (the Pirbright labs) later this morning - uttering silent curses at the incompetents who failed basic biosecurity as I do so.
Well, that figures - if you've got 200 MCSE drones hanging about looking after your systems, it's going to take a bit of work to convince them to learn new skills that don't depend on clicking here, there and everywhere.
Still, it looks like they've got it all up and running now, and at least some of the original drones must have blossomed into real admins along the way.
If an employee is ethical, non-compete clauses aren't necessary.
I've been in a situation where I have moved jobs and been asked by my boss at the new employer for technical details of something I developed at my previous company, and refused - my position was that I would happily develop something different but equally effective for my new employer, but that the particular formulation belonged exclusively to my previous employer. I was prepared to use my expertise, but not any knowledge of the other company's implementation.
What was upsetting was that the second employer had an explicit non-compete clause in the contract I signed (without any intent of being held to it - here in the EU they can't be upheld as they restrict the employees freedom of movement), but seemed to think it OK to try to steal trade secrets from a competitor.
My thinking is that the end of the world will come when all the lost socks suddenly pop back into existence, smothering the entire population of Earth.
Slashdot Mirror
My favourite is the new New Labour motto - Kraft Durch Dummheit
I'm not going anywhere, but these idiots make me despair for what was once a decent place to live.
And that's despite 638 attempts at forced termination.
Consider the computerised proof of the 4-Colour theorem.
It may be that there is a nice, clean analytical proof out there waiting to be discovered, but every attempt to find it so far has failed.
What was possible was to reduce the problem to one that was solvable by enumerating a finite set of possible graphs.
TFA (well, one of them) explains the process quite well.
I still spend the odd insomniac night trying to figure out a purely analytical proof, though - for no other reason than pure stubbornness and Luddite tendencies :o)
Correct me if I'm wrong, but doesn't Godel's second theorem explicitly address Peano arithmetic, which is all first order logic?
True, you can't address countability (and by extension the halting problem) completely within first order logic, so your point that it is impossible to write a program that creates all true propositions and only true propositions of a formal system holds, but it is possible to create a first order arithmetic, although you can't use it to prove its own consistency.
That's what I remember from 20-odd years ago, anyway :o)
As it stands, they aren't going to store the raw data - just information on the endpoints.
This in itself is disturbing, since as Bruce Schneier points out, data mining of this sort is inherently flawed.
It strikes me that this is politically driven - i.e. that GCHQ has an ample supply of mathematicians who can see that this is useless, but that the idiocracy that is Neues Arbeit still believes the bullshit that their highly paid, poorly educated advisors spew out.
Trouble is, the idiots won't listen to sense, so we'll have to wait until the next election to vote in another lot of idiots who may or may not be as stupid as this lot.
Kurzweil?
You gotta be kidding.
OK, so the man's got vision, but so has any brain-addled acid-crazed schizo hippy you care to mention.
You need someone with real vision and practical common-sense, like Joy, or maybe Jobs (yes, I know I'll get flamed for that) or even Wozniak.
You might as well suggest Eric Drexler - another self-publicist with no notable contribution to make.
Ok - you're offtopic, but I'll bite.
What African-American wouldn't vote for Obama?
There are two good reasons -
a) to see a brother in the White House, and
b) to stick it to the Man.
It's not anti-white, it's pro-black, and I feel sorry for you sad little whingers.
You lost - get over it, and concentrate on important things like regaining control over your own Constitution after the last 8 years of perversion.
They are in the UK - ever since Thatcher and her voodoo economics decided that profits for shareholders were better than service for customers.
I always thought it was reality TV, but then again I work in a shoe shop and spend my nights either scratching my bollocks or on the beer with the lads.
All right, I'll bite - Obama's citizenship is a minor constitutional issue compared to the excesses perpetrated by Bush for the last 8 years - warrantless wiretapping, the effective suspension of habeus corpus, etc.
If you're really that concerned about your constitution, you should be refreshing the tree of liberty with whatever you find available - Bush has around 8 pints, IIRC.
Fermentation is already a well-understood process - GM yeasts, bacteria and fungi are all used in enzyme production.
It may be that a yeast is a better target for manipulation - they are already used in the production of cellulases used to increase the energy available from animal feed, and this looks similar.
Does anyone apart from dumb fuck rednecks like you care?
What an arse you are.
Your sort created the situation in Iraq and Afghanistan - a situation that isn't sustainable without the presence of foreign troops, ever.
I bet you like Israel too, you twat - it's the terrorist cancer eating the life out of the region, but 'islamists' are obviously far more scary in your mind than expansionist terrorist Zionists.
Excellent news.
Good luck prosecuting any new wars on your own - we'll just keep our boys at home.
Oh, and extraordinary rendition? Sorry, but we're not playing any more.
Fuck off, you parochial, colonial twat.
I'd guess that anyone finding a USB stick who didn't realise what it was would ask their friendly local BOFH to take a look - thus ensuring the flow of beer tokens from the tabloids to said BOFH.
LOL - great parody :o)
You missed Geoff Hoon, though - "the next thing we lose will be your liberty, for the sake of the fight against terror".
Oh, bugger - that's nearly a real quote - here's the reality.
But even the Home Office is eclipsed in doltishness by MAFF (or whatever it's called nowadays) - the people that brought you mounds of cremated cows and sheep because nobody had the balls to vaccinate against foot and mouth.
I'll be driving past the source of the last outbreak (the Pirbright labs) later this morning - uttering silent curses at the incompetents who failed basic biosecurity as I do so.
Well, that figures - if you've got 200 MCSE drones hanging about looking after your systems, it's going to take a bit of work to convince them to learn new skills that don't depend on clicking here, there and everywhere.
Still, it looks like they've got it all up and running now, and at least some of the original drones must have blossomed into real admins along the way.
Why did I have to read right to the end of the comments to find the first really insightful one?
And from an AC, at that!
If an employee is ethical, non-compete clauses aren't necessary.
I've been in a situation where I have moved jobs and been asked by my boss at the new employer for technical details of something I developed at my previous company, and refused - my position was that I would happily develop something different but equally effective for my new employer, but that the particular formulation belonged exclusively to my previous employer. I was prepared to use my expertise, but not any knowledge of the other company's implementation.
What was upsetting was that the second employer had an explicit non-compete clause in the contract I signed (without any intent of being held to it - here in the EU they can't be upheld as they restrict the employees freedom of movement), but seemed to think it OK to try to steal trade secrets from a competitor.
My thinking is that the end of the world will come when all the lost socks suddenly pop back into existence, smothering the entire population of Earth.
Sorry, Morgan, you're usually quite insightful, but water vapour is quite good at absorbing infra-red radiation - see here for some details.
You've obviously never heard of Sly and Robbie, then?
Just so long as I don't have to marry a tuneless cow and then get shot in the back...
And double bonus points for off-rhythm drumming?