What we have here is (and this is all it is) a statement
that there must be an infinite number of primes.
IF there could be a finite list of all primes (not that
I know them) THEN
I can find one more prime with this formula.
Wait a second, that's a contradiction, therefore there
can't be a finite list of all primes.
Using that formula to find more primes is the logical
equivelent of saying: If I had a purple cow on my head
that spit all primes, I could use it to find more primes.
I will use purple cow spit to find more primes.
If you want a real proof it should be easy enough to
find...usually somewhere before page 50 in any first
number theory book. It really is short as such things go
and quite a jaw dropper first time it is seen. If you
care you deserve seeing it done right.
I apologize for errors in my sketch of a proof, it was wrong to call it a proof.
I need to follow an old theorem here:
Seawall should NEVER post a reply to troll in anger at 1am
especially wth math.
> Sometimes I get off the toilet and think I discovered the biggest prime...
Most people here probably know this but:
There is no biggest prime number and the proof is 2 sentences long....
here it is:
Assume there is a largest prime P(n) and thus there is a finite list of all prime numbers:
P(1), P(2), P(3),.....P(n). "*" here means multiply.
Well then (P(1)*P(2)*...*P(n))+1 must be prime: whenever you divide that number by prime(s)
you always have a 1 left over....but (P(1)*.....*P(n))+1 is obviously bigger than P(n) so
our initial assumption of a largest prime number must be wrong. QED.
One of the interesting things for mathematicians (or at least this ex-mathematician) is
that you tweak the question just a little bit: "Is there a largest "twin prime"?" and
heavy duty brains pound on the question for centuries with no answer. I have had NIGHTMARES
over that one....which is one reason I am an ex-mathematician.
Another funny thing about higher math is it has been defended as useless (Hardy: A Mathematicians
Apology) but then three guys go and invent RSA and all of a sudden my privacy depends on the
properties of prime numbers.
> DPS worked great on that old hardware - just as did X11.
True to a point but I do have some old hardware around and I used to have WAY more patience back in the day; "fast" response then isn't even slow response now.
In particular I remember sitting at a NeXT cube and going "WOW! This will be GREAT! as soon as they speed it up to something useable!"...but, like the Mac before it, those speedups were a looooooong time coming. Even at the time the NeXT was slow at its introduction (in part because getting a model with a hard drive was like pulling teeth; you run the NeXT OS off a Magneto-optic drive and it's gonna be slow).
Speedups have been nowhere near linear with better hardware but Aqua on my G4 laptop spins circles around X11 on a Sun 4/110.....and as for the relationship between NeXT-step and Aqua; an awful lot of those Aqua functions start with "NS"....and I'm pretty sure NS doesn't stand for "New Stuff"!
It's repetitive stress so stop the repetitive part!
For this user at least: I found using any one device all day led to problems.
By using different keyboards and pointers over the course of the day; the pain
mostly stays away.
I don't even use ergonomic keyboards; just decent ones with
different sizes and touch. Mice I use good ergonomic ones but with varied
shapes and sometimes a trackpad.
To get to the pain to go away in the first place I had to use the
computer a lot less for a few months but it seemed a small price
to pay.
I don't mean to take anything away from IBM. They have answers to questions most (maybe all) of the competition doesn't even know they should be asking in regards to VM.
but: No, IBM didn't invent virtual memory. I believe the first commercial machine with virtual memory was from Burroughs. A weird stack-based box (FORTH is what it is in part because its developer used a Burroughs) that pushed the envelope of the day mighty hard.
That said: I have fairly fond memories of IBM VM. Not so fond memories of the OS's I was using under VM but fond memories of VM nonetheless.
Scary accuracy. Virtual Cardpunches that were compatable down to the bugs against specific models of IBM physical cardpunches.
Host machine with Vserver kernel running Tripwire or Aide
with configuration adjustments to detect changes in client "machines"
Host machine well protected
client machines doing ftp or web services or email or.....
Although Vserver is particular to Linux: Other schemes doing reasonably strong virtualization can also do the job in Linux, Solaris (Zones), BSD (Containers), Windows, etc.
It should greatly decrease the ability of something as clever as BluePill to do damage if it was infecting a well-partitioned virtual machine rather than a regular machine.
A hideous number of applications assume you have the whole PC to yourself.
This isn't just games. Example:
A government site might (and some do) require
running a specific (Windows Only) application.
The application might (and at least one does) write various
configuration files to various places with NO idea of sharing. To use
thin clients in this situation I've only seen 3 choices:
Let users write over each others files (bad)
Let one user have total configuration control (not quite as bad sometimes)
Go in and tweak the app somehow so each user has their own configuration filespace (Often doable but forget about support)
Microsoft Office apps are not among these but an awful lot of 3rd party apps
are, companies aren't necessarily interested in worrying about the (currently small) slice of the market that uses thin clients.
....and licensing! It can be distinctly unfun to get a company to sell you a license for thin clients. I've seen companies simply say "no" as if thin clients don't exist at all....maybe there is someone in the company that can say "yes" but I couldn't find them.
I really hope thin clients catch on enough that the above gotchas go away.
It has been both a boon: My current office is near my co-workers, has a window, a view and a door. I can have meetings in here, I can look at stuff for my job that is confidential. I leave my door open most of the time. I can lock the door and be fairly sure my equipment and papers will be undisturbed and, if they are, there are a limited number of people I have to hunt down to get my external backup drive back. Just the sunlight alone makes it worthwhile. About half of a chronic decade-long depression lifted. Please note I spent a decade and a half in (literally) offices made out of bathrooms and closets to get here.
They mostly were horrible: My first office isolated me from other grad students and probably had more to do with not finishing postgraduate education than anything. If my personality had been different, maybe, but I was a heavy isolater at the time.
Most of my offices were not helpful: too grim (converted bathrooms and closets mostly), too isolation prone, too depressing.
Formal office or no, a depressing space will get to you after awhile. It may take a month, it may take 5 years, but it isn't worth doing that to yourself!
WARNING: it's a SUN video ad but it's pretty apropos to
this discussion: about a datacenter built near the
North Pole for space and A/C reasons.
Dealing with number cruncher clusters (where Niagara is almost no
help at all unless you recode everything in fixed point); I don't
find the "North to the Future" datacenter idea as silly as some.
In fact, since my workplace has underice instrumentation near the
pole maybe it would even be a win:-).
We may be in violent agreement here. Of course people have to have access to what
they need. The traditional Unix scheme isn't always enough (although it can be pushed
pretty hard, eventually it can become a total collection of hacks, which is bad).
Currently I work in an organzation of only a few hundred people, with
a limited number of job descriptions and not everything is on central servers. Here the old Unix scheme works fine.
But yes the group permission scheme tends to break down as an organization gets big and complicated, never said it didn't. What I am trying to say is: If you have a big complicated structure then it's a non-trivial thing to make it not any more complicated than it has to be.
The very non-trivial part comes with things like anticipating mergers and company restructuring.
ACL's and all the rest are lovely tools used
with restraint but it is DARN easy to get into
a security mess if you aren't very very careful.
In the traditional Unix model there isn't as much to worry about:
"Make sure you can't get to root from joe user" is most of the problem.
We can't get that right but at least it's just one
account, oops, I mean "role", to worry about.
So let's make it more complicated. Instead of 1 role
let's have 12: user admins, backup admins, repair admins,
each with enough oomph to do some real damage, some with
enough oomph to ratchet themselves up to effectively being
the near-equivelent of root.
I'm not saying the "role" approach and ACL's and the rest
are the wrong way to go. I am saying they are tools to be
used with care. There is a real cost of overhead in keeping
track of all the cross dependencies and cross exploits...and
that overhead can increase combinatorically.
Personally I think of them like softlinks: Overuse softlinks
and you have a speghetti filesystem. Overuse roles and ACLs
and you have speghetti security.
Use them right (and you can use them right in VMS, Solaris 10, SeLinux, etc.)
and they can be your friends. Your high-maintenance friends, but friends.
Not to be difficult (well maybe not) but care to add:
Why GNUnet is better?
Not saying it is or isn't, I'd just like to know
why you think so. A GNUnet canononical website has a comparison
chart with some other file-sharing apps but BitTorrent isn't on
it.
Light rail is being paid for radically differently. The cost to build the
monorail (exclusive of financing) isn't all that bad: IF you had the same financing
THEN it would look better. Of course, we live in a world where light
rail is getting breaks the monorail can only dream of....and highways get
financing rail can only dream of. That monorail junk bond plan really was the pits
though, yes.
Unless the airport you are going to is Boeing Field (which currently has
exactly 0 major
airlines) then, good luck carrying your bags from the (currently planned) light
rail terminus to SeaTac airport. Personally I wouldn't want to carry my bags
that many miles but then many people are in better shape than I.
BTW: My car tabs, just for the monorail, cost 20x more than the year
before. I STILL want to see the darn thing get built.
Finally, I want to see light rail do OK. I am just bitter about not having
both...or rather EITHER! Area light rail is extremely late, are we up to
a decade late yet?
At USENIX '05 a Sun engineer was asked about Sun's then newfound (again) support for Solaris on x86 (especially AMD 64-bit) and how do we know the enthusiasm is real?
One part of his multipart answer was pulling out his Ferrari laptop running Solaris 10 and saying 80% (? - this is from memory) of the Solaris kernel engineers have Ferrari-model 64-bit laptops, running Solaris 10 of course.
The idea being: if it's your workday laptop, you support it.
I know the connection with Linux here is somewhat tenuous but having another good Unix on these laptops, especially an opensourced Unix, bodes well for future Linux laptop support.
I was recently in Apalachicola, where an A/C and ice machine was invented (and believe me, if you're ever there in August you'll understand why) in the mid-1800's and it didn't require electricity (although that is convenient), freon or ammonia (although that improves the efficiency). You can
do this kind of thing with air, brine, a piston, an expansion box and copper tubes.
I don't know if it'd be a good choice but the tech was certainly simple enough.
Of course not everyone liked Firefly but the "1st" episode wasn't the 1st. It was the 1st aired.
In the correct order it's better than in its original aired order. Of that I have heard little disagreement.
....of course you may still think it not worth your time and that's OK. I like the no-aliens, no-latex-face-appliances premise and wildly different tech for poor and rich terraformed planets but it's not everyones cup of green tea. I liked the preview just fine.
Paraphrasing Joss Whedon: "About the same number of people as worked on the show, saw the show. But you people insisted we make this movie....so if it sucks, it's your fault."
There have been a few previews of the almost-complete film. I really enjoyed it rather a lot, as did a friend who had never seen the series and didn't know who Joss Whedon is.
Sun is doing a LOT better (hopefully not too little too late). They make reasonably priced Opteron boxes, Solaris 10 x86 is a very nice 64-bit Unix, they are opensourcing (not GPL'ing but nonetheless) the OS, they have a tool in DTRACE that Linux doesn't have, the OS is downloadeable for free, they come out of the box a lot more ready-to-run than they were.
The Opteron 64-bit version is compiled with GCC by the way.
It really looks to me like they are going to support Opteron in a big way, they can read CPU/$ as well as anyone.
I think they are trying to pull an Apple turnaround and they have a shot. Hopefully it won't be DEC, the sequel.
If you want to dismiss Sun after running Solaris 10 x86 (for free, any number of CPU's) that's fine but at least boot it first!
Slashdot Mirror
What we have here is (and this is all it is) a statement that there must be an infinite number of primes.
IF there could be a finite list of all primes (not that I know them) THEN
I can find one more prime with this formula.
Wait a second, that's a contradiction, therefore there can't be a finite list of all primes.
Using that formula to find more primes is the logical equivelent of saying: If I had a purple cow on my head that spit all primes, I could use it to find more primes. I will use purple cow spit to find more primes.
If you want a real proof it should be easy enough to find...usually somewhere before page 50 in any first number theory book. It really is short as such things go and quite a jaw dropper first time it is seen. If you care you deserve seeing it done right.
I apologize for errors in my sketch of a proof, it was wrong to call it a proof.
I need to follow an old theorem here: Seawall should NEVER post a reply to troll in anger at 1am especially wth math.
Proof left as an exercise to reader.
Most people here probably know this but:
There is no biggest prime number and the proof is 2 sentences long.... here it is:
Assume there is a largest prime P(n) and thus there is a finite list of all prime numbers: P(1), P(2), P(3),.....P(n). "*" here means multiply.
Well then (P(1)*P(2)*...*P(n))+1 must be prime: whenever you divide that number by prime(s) you always have a 1 left over....but (P(1)*.....*P(n))+1 is obviously bigger than P(n) so our initial assumption of a largest prime number must be wrong. QED.
One of the interesting things for mathematicians (or at least this ex-mathematician) is that you tweak the question just a little bit: "Is there a largest "twin prime"?" and heavy duty brains pound on the question for centuries with no answer. I have had NIGHTMARES over that one....which is one reason I am an ex-mathematician.
Another funny thing about higher math is it has been defended as useless (Hardy: A Mathematicians Apology) but then three guys go and invent RSA and all of a sudden my privacy depends on the properties of prime numbers.
> DPS worked great on that old hardware - just as did X11.
....and as for the relationship between NeXT-step and Aqua;
True to a point but I do have some old hardware around and I used to have WAY
more patience back in the day; "fast" response then isn't even slow response now.
In particular I remember sitting at a NeXT cube and going "WOW! This will be
GREAT! as soon as they speed it up to something useable!"...but, like the Mac
before it, those speedups were a looooooong time coming. Even at the time the
NeXT was slow at its introduction (in part because getting a model with a hard
drive was like pulling teeth; you run the NeXT OS off a Magneto-optic drive and
it's gonna be slow).
Speedups have been nowhere near linear with better hardware but Aqua on my
G4 laptop spins circles around X11 on a Sun 4/110.
an awful lot of those Aqua functions start with "NS"....and I'm pretty sure
NS doesn't stand for "New Stuff"!
They aren't the same school.
Also: "Pine" has supposed to stand for many different things but
the first one I heard (and I was there pretty early) was:
"Pine Is Not Elm".
The idea being it was easier to build pine than support
umpteen mail clients.
Some titles during the first internet bubble got pretty out-there.
I really was handed a business card that said "Cyberspace Engineer" on it and I have to confess to bursting out laughing.
Clever guy, important work, and the title wasn't entirely bogus but yikes.
It's repetitive stress so stop the repetitive part!
For this user at least: I found using any one device all day led to problems. By using different keyboards and pointers over the course of the day; the pain mostly stays away. I don't even use ergonomic keyboards; just decent ones with different sizes and touch. Mice I use good ergonomic ones but with varied shapes and sometimes a trackpad.
To get to the pain to go away in the first place I had to use the computer a lot less for a few months but it seemed a small price to pay.
I don't mean to take anything away from IBM. They have answers to questions
most (maybe all) of the competition doesn't even know they should be asking
in regards to VM.
but: No, IBM didn't invent virtual memory. I believe the first commercial
machine with virtual memory was from Burroughs. A weird stack-based box
(FORTH is what it is in part because its developer used a Burroughs) that
pushed the envelope of the day mighty hard.
That said: I have fairly fond memories of IBM VM. Not so fond memories
of the OS's I was using under VM but fond memories of VM nonetheless.
Scary accuracy. Virtual Cardpunches that were compatable down to the
bugs against specific models of IBM physical cardpunches.
This is regarding Linux rather than Windows but:
Host machine with Vserver kernel running Tripwire or Aide
with configuration adjustments to detect changes in client "machines"
Host machine well protected
client machines doing ftp or web services or email or.....
Although Vserver is particular to Linux: Other schemes doing
reasonably strong virtualization can also do the job in Linux,
Solaris (Zones), BSD (Containers), Windows, etc.
It should greatly decrease the ability of something as clever as
BluePill to do damage if it was infecting a well-partitioned virtual
machine rather than a regular machine.
Vserver: http://linux-vserver.org/
AIDE: http://www.securityfocus.com/infocus/1424
This isn't just games. Example: A government site might (and some do) require running a specific (Windows Only) application. The application might (and at least one does) write various configuration files to various places with NO idea of sharing. To use thin clients in this situation I've only seen 3 choices:
Let users write over each others files (bad)
Let one user have total configuration control (not quite as bad sometimes)
Go in and tweak the app somehow so each user has their own configuration filespace (Often doable but forget about support)
Microsoft Office apps are not among these but an awful lot of 3rd party apps are, companies aren't necessarily interested in worrying about the (currently small) slice of the market that uses thin clients.
I really hope thin clients catch on enough that the above gotchas go away.
I hope they don't qualify as porn but they may qualify as comedy or maybe tragedy.
They mostly were horrible: My first office isolated me from other grad students and probably had more to do with not finishing postgraduate education than anything. If my personality had been different, maybe, but I was a heavy isolater at the time.
Most of my offices were not helpful: too grim (converted bathrooms and closets mostly), too isolation prone, too depressing.
Formal office or no, a depressing space will get to you after awhile. It may take a month, it may take 5 years, but it isn't worth doing that to yourself!
Dealing with number cruncher clusters (where Niagara is almost no help at all unless you recode everything in fixed point); I don't find the "North to the Future" datacenter idea as silly as some. In fact, since my workplace has underice instrumentation near the pole maybe it would even be a win :-).
http://sun.r.delivery.net/r?1.1.3J1.2U2.11FNWo.Bx3 E_i...CoF6.1PF8.37719z
Currently I work in an organzation of only a few hundred people, with a limited number of job descriptions and not everything is on central servers. Here the old Unix scheme works fine.
But yes the group permission scheme tends to break down as an organization gets big and complicated, never said it didn't. What I am trying to say is: If you have a big complicated structure then it's a non-trivial thing to make it not any more complicated than it has to be.
The very non-trivial part comes with things like anticipating mergers and company restructuring.
In the traditional Unix model there isn't as much to worry about: "Make sure you can't get to root from joe user" is most of the problem. We can't get that right but at least it's just one account, oops, I mean "role", to worry about.
So let's make it more complicated. Instead of 1 role let's have 12: user admins, backup admins, repair admins, each with enough oomph to do some real damage, some with enough oomph to ratchet themselves up to effectively being the near-equivelent of root.
I'm not saying the "role" approach and ACL's and the rest are the wrong way to go. I am saying they are tools to be used with care. There is a real cost of overhead in keeping track of all the cross dependencies and cross exploits...and that overhead can increase combinatorically.
Personally I think of them like softlinks: Overuse softlinks and you have a speghetti filesystem. Overuse roles and ACLs and you have speghetti security.
Use them right (and you can use them right in VMS, Solaris 10, SeLinux, etc.) and they can be your friends. Your high-maintenance friends, but friends.
Why GNUnet is better?
Not saying it is or isn't, I'd just like to know why you think so. A GNUnet canononical website has a comparison chart with some other file-sharing apps but BitTorrent isn't on it.
No but my iPod does: http://ipodlinux.sourceforge.net/index.shtml ...well, at least sometimes.
Clueless widespread adoption by the powers-that-be with widespread grassroots resistance (more effective in the office than in voting I expect)?
Sounds like a good business to be in to me: Lots of customers who buy but don't pesky up your life by actually using your product!
Tabs were 8x higher, not 20.
Light rail is being paid for radically differently. The cost to build the monorail (exclusive of financing) isn't all that bad: IF you had the same financing THEN it would look better. Of course, we live in a world where light rail is getting breaks the monorail can only dream of....and highways get financing rail can only dream of. That monorail junk bond plan really was the pits though, yes.
Unless the airport you are going to is Boeing Field (which currently has exactly 0 major airlines) then, good luck carrying your bags from the (currently planned) light rail terminus to SeaTac airport. Personally I wouldn't want to carry my bags that many miles but then many people are in better shape than I.
BTW: My car tabs, just for the monorail, cost 20x more than the year before. I STILL want to see the darn thing get built.
Finally, I want to see light rail do OK. I am just bitter about not having both...or rather EITHER! Area light rail is extremely late, are we up to a decade late yet?
One part of his multipart answer was pulling out his Ferrari laptop running Solaris 10 and saying 80% (? - this is from memory) of the Solaris kernel engineers have Ferrari-model 64-bit laptops, running Solaris 10 of course.
The idea being: if it's your workday laptop, you support it.
I know the connection with Linux here is somewhat tenuous but having another good Unix on these laptops, especially an opensourced Unix, bodes well for future Linux laptop support.
I don't know if it'd be a good choice but the tech was certainly simple enough.
I seem to recall Apple has had buildings at that address when the Mac was under development e.g. 1983....or am I wrong?
In the correct order it's better than in its original aired order. Of that I have heard little disagreement.
Paraphrasing Joss Whedon: "About the same number of people as worked on the show, saw the show. But you people insisted we make this movie....so if it sucks, it's your fault."
Looking forward to seeing it again in September.
The Opteron 64-bit version is compiled with GCC by the way.
It really looks to me like they are going to support Opteron in a big way, they can read CPU/$ as well as anyone.
I think they are trying to pull an Apple turnaround and they have a shot. Hopefully it won't be DEC, the sequel.
If you want to dismiss Sun after running Solaris 10 x86 (for free, any number of CPU's) that's fine but at least boot it first!