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Unpredictability in Future Microprocessors

prostoalex writes "A Business Week article says increase in chip speeds and number of transistors on a single microprocessor leads to varying degrees of unpredictability, which used to be a no-no word in the microprocessor world. However, according to scientists from Georgia Tech's Center for Research in Embedded Systems & Technology, unpredictability becomes a great asset leading to energy conservation and increased computation speeds."

244 comments

  1. Three cheers! by Electroly · · Score: 5, Funny

    Three cheers for entropy!

    1. Re:Three cheers! by fm6 · · Score: 2, Interesting

      How can you cheer for something that will eventually kill you?

    2. Re:Three cheers! by chiok · · Score: 5, Funny

      Hurrah! Hurra! Hurry!

    3. Re:Three cheers! by glib909 · · Score: 1

      Delta-C cheers for entropy!

      --
      Suudsu, that stuff is G-E-W-D.
    4. Re:Three cheers! by mboverload · · Score: 2, Funny

      1 + 1 = e2924e9320?

    5. Re:Three cheers! by RebelWithoutAClue · · Score: 1

      Life always exists on the border between order and disorder. If either didnt exist, life wouldnt exist.

      --
      "However beautiful the strategy, you should occasionally look at the results" - Winston Churchill
    6. Re:Three cheers! by Eatmorecake · · Score: 1

      Use the force, Pentium.

      --
      Don't you mean.. BIZZARO! ..Signature?
    7. Re:Three cheers! by Citizen+of+Earth · · Score: 1

      How can you cheer for something that will eventually kill you?

      What will kill most of us is specifically pre-programmed obsolescence.

    8. Re:Three cheers! by fm6 · · Score: 1

      But that's still entropy. Planned obsolesence is something the species does to protect itself against entropy, at the expense of the individual.

  2. Well... by Realistic_Dragon · · Score: 4, Funny

    I'd be a lot more trusting of their results if they had worked it out on a processor with 100% certainty.

    --
    Beep beep.
    1. Re:Well... by thpr · · Score: 2, Funny
      I'd be a lot more trusting of their results if they had worked it out on a processor with 100% certainty.

      Think of the potential heartburn for the CEOs and CFOs who might have to sign off the financial statements (ala Sarbanes-Oxley) after the calculations were done using one of these processors... :*)

    2. Re:Well... by Anonymous Coward · · Score: 0

      In these matters the only certainty is that nothing is certain.
      -- Pliny the Elder (23 AD - 79 AD)

    3. Re:Well... by ATN · · Score: 1

      Are you certain of that :p

    4. Re:Well... by geekboy642 · · Score: 0

      Hmm...I thought we already had uncertainty for processors.
      I'm thinking of original-revision Pentiums.

      --
      Just another "DOJ fascist authoritarian totalitarian bootlicker" -- Zeio
  3. Soo by NIK282000 · · Score: 5, Funny

    Will the number of windows errors increase or will they just occur at even more improbable times?

    --
    Dear aunt, let's set so double the killer delete select all
    1. Re:Soo by Anonymous Coward · · Score: 1, Funny

      I don't know about you but I have no trouble opening and closing my windows.

    2. Re:Soo by Zorilla · · Score: 2, Funny

      You must have never had to ride the bus to school as a kid then.

      (God, I hated those little buttons.)

      --

      It would be cool if it didn't suck.
    3. Re:Soo by Ralph+Wiggam · · Score: 1

      If you could calculate exactly how improbable the Windows errors are, you could anticipate them, and save your work beforehand. I'm wicked smart.

      -B

    4. Re:Soo by cgenman · · Score: 1

      Will the number of windows errors increase or will they just occur at even more improbable times?

      More improbable times? Like when it's off?

    5. Re:Soo by Lusa · · Score: 1

      More improbable times? Like when it's off?

      yeah, put windows into hibernate and when it comes back it has crashed... I have a machine that happens on already

  4. Adds new meaning to this ... by tomhudson · · Score: 0, Flamebait
    Remember that old saying "It's not a bug, it's a feature"? Now they've found a way to market their hardware mistakes. Eat your heart out, Gates.

    --

    On February 7th, Russ Nelson (Open Source Initiative president) published an article called "Blacks are lazy", quoted in journal entries here and here.

    Please consider signing the online petition asking OSI to remove Russ Nelson.

    1. Re:Adds new meaning to this ... by Anonymous Coward · · Score: 0

      >On February 7th, Russ Nelson (Open Source
      >Initiative president) published an article called >"Blacks are lazy", quoted in journal entries here >[slashdot.org] and here [slashdot.org].

      >Please consider signing the online petition >[petitiononline.com] asking OSI to remove Russ >Nelson.

      Let the GNAA take care of him...

    2. Re:Adds new meaning to this ... by Anonymous Coward · · Score: 0

      Seems the 'off topic' mods are out. Nothing better to do on a Saturday night.

    3. Re:Adds new meaning to this ... by murph · · Score: 1
      Remember that old saying "It's not a bug, it's a feature"? Now they've found a way to market their hardware mistakes. Eat your heart out, Gates.

      You're kidding, right? I'm sure that they'll be paying Gates for a patent on it.

      --murph

      --
      I don't care about your karma, I don't care about what's hip. --Weird Al
  5. YMMV by ectotherm · · Score: 0

    I'm surprised M$ hasn't patented unpredictability in operations. Oh, wait, that's software...

    --
    "Nature bats last..."
    1. Re:YMMV by Anonymous Coward · · Score: 0

      You must be new here!

  6. Another use by physicsphairy · · Score: 2, Insightful
    unpredictability becomes a great asset leading to energy conservation and increased computation speeds

    Probably and even bigger boon for encryption and key-generation.

    1. Re:Another use by thpr · · Score: 4, Insightful
      Probably and even bigger boon for encryption and key-generation.

      I vote key-generation and not encryption. Otherwise, how would you decrypt it? (given that the key generation and decryption are non-deterministic with one of these...)

    2. Re:Another use by PingPongBoy · · Score: 2, Informative

      Probably and even bigger boon for encryption and key-generation.
      I vote key-generation and not encryption. Otherwise, how would you decrypt it?


      Unpredictability really is useful for encryption because random numbers are very important for better encryption.

      The second application that comes to mind is the one-time pad. Of course you have to save the random padding data somewhere but you always had to do that. The unpredictability just makes one-time pad that much better.

      Random numbers may be used to generate keys that people can't guess. Of course you have to memorize the key.

      --
      Know your pads. One time pad: good for cryptography. Two timing pad: where to take your mistress.
    3. Re:Another use by fuzzybunny · · Score: 1

      Of course you have to memorize the key.
      ...and actually have a random number. This is one of the main problems at the core of most key generation methods--the random numbers used usually aren't, allowing some predictability. It's difficult to generate a truly random number, or at least to do so in a manner easy to use by a casual encryption routine (hooking a lava lamp up to your cell phone isn't all too practical :-)

      An issue with one-time pads comes up more through usage than through the technology--if you ever, ever, ever re-use one (well, I guess then it wouldn't be a OTP any more) your security is probably shot. Sounds like a pretty obvious consideration, but it has happened. True OTPs are a bitch and a half to handle in production, leading people to get lazy and take shortcuts.

      --
      Cole's Law: Thinly sliced cabbage
  7. Robots and Unpredictability by Anonymous Coward · · Score: 2, Insightful

    "unpredictability becomes a great asset leading to energy conservation and increased computation speeds."

    When robots have this "unpredictability" tell me not to worry!

    1. Re:Robots and Unpredictability by Anonymous Coward · · Score: 0

      I for one may or may not welcome our new indeterministic robotic overlords?

    2. Re:Robots and Unpredictability by jonadab · · Score: 1

      > When robots have this "unpredictability" tell me not to worry!

      You don't have to worry until the robots get Genuine People Personalities.

      --
      Cut that out, or I will ship you to Norilsk in a box.
    3. Re:Robots and Unpredictability by Ignominious+Cow+Herd · · Score: 1

      ...and Guns.

      (or friggin lasers on their heads.)

      --
      Lump lingered last in line for brains, and the ones she got were sorta rotten and insane.
  8. Windows ME did something right by bird603568 · · Score: 0, Flamebait

    unpredictability becomes a great asset leading to energy conservation and increased computation speeds if this is the case, then windows MS is Godly.

    1. Re:Windows ME did something right by s-orbital · · Score: 2, Funny

      Nothing saves more power than a box that has been turned off due windows commiting suicide

      --
      Patent: from Latin patere, to be open
  9. Acceptable uncertainty by swg101 · · Score: 4, Informative

    Degrees of probability and uncertainty have been in given in the communications industry for quite some time. This just seems to be pointing out that the same ideas can be applied to the actual processing of the data.

    Now that I think about it, it does seem to make some sense. I am not sure that I would want to program on such a chip right now though (I imagine that debugging could become a nightmare really quickly!).

    --
    Like pi? Try 10,000 digits.
    1. Re:Acceptable uncertainty by ScrewMaster · · Score: 1

      Well, chaotic networks generally perform better than deterministic ones, as counterintuitive as that seems.

      --
      The higher the technology, the sharper that two-edged sword.
    2. Re:Acceptable uncertainty by mboverload · · Score: 1

      Your sig's link is broken, btw swg101

    3. Re:Acceptable uncertainty by IO+ERROR · · Score: 1

      This is old news. The Pentium chip first implemented unpredictability in its floating-point core.

      --
      How am I supposed to fit a pithy, relevant quote into 120 characters?
    4. Re:Acceptable uncertainty by Anonymous Coward · · Score: 0

      It makes sense if you remember the old maxim: sometimes perfection is the greatest enemy of good enough.

    5. Re:Acceptable uncertainty by swg101 · · Score: 1

      thanks for the heads up. (They changed the page from a .htm to .html)

      --
      Like pi? Try 10,000 digits.
  10. its a trick! by Foktip · · Score: 1, Interesting

    Intel's just saying that to draw your attention away from IBM's cell! Its a trick, dont listen to them; theyre just making this stuff up!

  11. The Uncertain Airbag by rhaikh · · Score: 3, Insightful

    Well, there's a 99.99% chance that airbag shouldn't be deployed right now, I'm just gonna disregard that "1".

    1. Re:The Uncertain Airbag by SCVirus · · Score: 1

      Yes theres a 99.99% chance that this airbag shouldn't be deployed once its triggers have been set off my the crushing of the front end of your car.

    2. Re:The Uncertain Airbag by Per+Abrahamsen · · Score: 1

      Eh, that is how airbags work. There is always a 0.01% chance (or whatever) that the trigger mechanism is malfunctioning, in which case releasing the airbag would be the right thing to do.

      But sinse an airbag that did so would be useless, it goes with the 99.99% chance instead.

      Uncertainty is an integral part of life. You can minimize it, but you can not remove it.

  12. TFA by shirai · · Score: 5, Interesting

    It is an interesting idea but I think there would have to be a lot of research that goes into this and here's what I mean.

    The article is right in that certain things don't need 100% accuracy and that small variations in the answers can yield very good results. This could be important when time is more important than 100% accuracy.

    That said, how do we know if the variations are small? Only 1 bit can change a huge negative number into a huge positive number in a standard integer (Okay, I haven't looked at the bit layout of an integer lately but I think it's encoded like this. If not, you still get my point right?).

    So perhaps then this idea sort of works when we are aggregating lots of small calculated numbers but then switch to a traditional chip to add them together.

    You see what I'm getting at? Computers don't really know that the small variation at the most significant bit is actually a huge variation.

    I think there would also have to be a lot of analysis based on understanding how the variations add up and their cumulative effect. For example, a well written app under this scenario means that the errors basically average out over time as opposed to errors that blow out of proportion.

    Anyways, I can think of a few good uses for this. Probably the most notable being down the DSP path (which the article metions). Our eyes probably wouldn't see small errors in an HD display during processing or hear small errors in audio processing.

    This is parallel to the fact that there is less error checking in audio CDs and video DVDs than their computer counterparts CD-ROM and DVD-ROM (or the R/RW/etc.etc. counterparts).

    --
    Sunny

    Be my Friend

    1. Re:TFA by Anonymous Coward · · Score: 0

      Obviously that point has occurred to them. (I would hope, but can't imagine it hasn't.)

    2. Re:TFA by jacksonj04 · · Score: 1

      I think the idea is that we have enough computing power to be able to throw a couple of checks at each operation...

      what a waste.

      --
      How many people can read hex if only you and dead people can read hex?
    3. Re:TFA by buraianto · · Score: 2, Interesting

      Or, you have a random bit change in your opcode and suddenly you're doing a muliply instead of an add. Or your opcode is an invalid one and your processor halts. Yeah, I don't think this makes sense given our current way of doing microprocessors. We'd have to do it some other way.

    4. Re:TFA by krunk4ever · · Score: 2, Insightful

      also, given these are microprocessors, when they have instruction jumps, wouldn't it be a concern if the address they're jumping to is slightly off?

    5. Re:TFA by fm6 · · Score: 2, Interesting
      That said, how do we know if the variations are small? Only 1 bit can change a huge negative number into a huge positive number in a standard integer (Okay, I haven't looked at the bit layout of an integer lately but I think it's encoded like this. If not, you still get my point right?).
      Sure, if you continue to use an encoding that doesn't tolerate errors. The math is beyond me, but I know there are ways to encode numbers so that a single-bit error nudges a value slightly, instead of changing it in wildly unpredictable ways.

      Also, a lot of computing deals mainly with string values, like the Google example in the story. Even without a random element in the calculations, it's hard to predict exactly what page will come out on top of a Google ranking. If the ordering's slightly different, nobody will care.

      And that's assuming that Google's secret algorithms don't already have a random element. Something I wouldn't rule out!

    6. Re:TFA by shawb · · Score: 1

      Actually it looked like the article was saying that all of those checks are wasteful, and there are situations where we should be able to deal with a wrong answer.

      My question is, what happens when that error comes not in a number being worked with, but an operation? Operations are just thrown at the CPU as a bunch of 1s and 0s, so would be succeptible to the same flaws.

      --
      I'll never make that mistake again, reading the experts' opinions. - Feynman
    7. Re:TFA by Mark_MF-WN · · Score: 1

      I know -- let's start encoding numbers in unary! Unary is highly tolerant to bit errors! Hurray!

    8. Re:TFA by gfody · · Score: 1

      you guys are talking about binary like its some sort of encoded format. binary is just base 2 nomenclature for numbers.. an estimation can be off by one bit but you know its minor because it's the bottom bit or the bottom 4 bits (the bottom 4 bits of a number could only change the number by 15). you can't write an estimation that does one arbitrary bit at a time, that's hollywood bullshit (where the guy slaps the codebreakermajig on the vault and the spinning numbers stop one random digit at a time). if you could calculate the 13th bit of the result of some problem you'd have to calculate the 12 bits behind it.

      --

      bite my glorious golden ass.
    9. Re:TFA by aprilsound · · Score: 1, Insightful

      There is already a fair amount of computer science research into this. BPP algorithms make use of randomness to deliver a "pretty good," that is, bounded error, polytime answer to problems that would otherwise take NP time.

    10. Re:TFA by aprilsound · · Score: 0

      There is already a fair amount of computer science research into this. BPP algorithms make use of randomness to deliver a "pretty good," that is, bounded error, polytime answer to problems that would otherwise take NP time.

    11. Re:TFA by aprilsound · · Score: 0

      There is already a fair amount of computer science research into this. BPP algorithms make use of randomness to deliver a "pretty good," that is, bounded error, polytime answer to problems that would otherwise take NP time.

    12. Re:TFA by Epistax · · Score: 3, Interesting

      I think you're thinking of things to specifically. Think about the human mind. It's utterly insane in speed, yet completely analog. Digital systems cannot yet grasp anywhere near the computing power of the human brain, yet they can beat the brain in any single (non-fuzzy) pursuit (such as chess). The human brain accels at fuzzy (yes, fuzzy) calculations such as identifying faces. It's quite possible we'll never be able to make a computer faster at identifying faces than the human brain without directly stealing our algorithm because it's the single thing we're best at.

      So, we can identify faces really, really well. So well that :) looks like a face despite the fact that it seriously shouldn't. Well, guess what? What if we change identifying faces into identifying something else? Perhaps a computer can identify things in data using fuzzy logic very easily--- what could we do with that? Now we'll always need the truly quasi-100% accurate side unless we're relying on a self-evaluating true AI, so I'm not arguing with that.

      Looking back, this isn't really a response to what you wrote, but moreover it's a thing that I type after I drank alcohol, but I think it stands on its own merit. Anyway a lot of research is needed and I'm, sure we can agree on that. It'a certainly interesting.

    13. Re:TFA by myukew · · Score: 1

      how comes that so many people besieve that a fuzzy processor would be sa much better at AI problems?
      if we can't do it with a normal chip why should our algorithms work so much better on a chip that doesn't even give us reliable results?

    14. Re:TFA by Dr.+Cody · · Score: 1

      Sure, if you continue to use an encoding that doesn't tolerate errors. The math is beyond me, but I know there are ways to encode numbers so that a single-bit error nudges a value slightly, instead of changing it in wildly unpredictable ways.

      Yeah, it's called base-1.

    15. Re:TFA by Anonymous Coward · · Score: 0

      "Nobody writes jokes in base-1"

    16. Re:TFA by danila · · Score: 1

      We would simply need to gradually redesign our software that a larger fraction of its processing can be done on parallel unreliable processors. You can have part of the processor working as a traditional CPU (with more error checking), while other areas would be designed to carry out simple parallel tasks. The traditional CPU part would control the execution of the main logic, but it would constantly outsource some jobs to those unreliable part of the processors where they do not speak good English but can do the job cheaper. :)

      --
      Future Wiki -- If you don't think about the future, you cannot have one.
    17. Re:TFA by Detritus · · Score: 1

      You need to use an error-correcting code that has a Hamming distance between code words that is great enough to allow for the correction of N bit errors. You need a Hamming distance of 2N+1 for N bits of error correction.

      --
      Mea navis aericumbens anguillis abundat
    18. Re:TFA by ultranova · · Score: 1

      if we can't do it with a normal chip why should our algorithms work so much better on a chip that doesn't even give us reliable results?

      Because, if your algorithm doesn't work, a normal processor will always return the predictably incorrect answer, but a fuzzy processor might, just might, get the answer changed in transit so that it mutates into the correct answer.

      So basically, unreliable programs might work better in a fuzzy processor - "made for Microsoft Windows" ;).

      --

      Forget magic. Any technology distinguishable from divine power is insufficiently advanced.

    19. Re:TFA by fm6 · · Score: 1

      Yes, I learned about Hamming codes in school. I'm proud to say that I was flunked out the encoding class by David Huffman himself!

    20. Re:TFA by myukew · · Score: 1

      ah, yes! now I understand

  13. Pbit-chip prospects by craXORjack · · Score: 5, Funny
    Whether any Wall Street firms are getting regular briefs on Palem's research, as Intel and IBM (IBM ) are, he won't say. Wall Street doesn't like people blabbering about technology that promises a competitive advantage.

    Actually this sounds more useful to Diebold and the Republican National Committee.

    --
    Liberals call everyone Nazis yet they are the closest thing to it.
    1. Re:Pbit-chip prospects by darkov · · Score: 1

      For certain (oil) companies, the Republican National Committee is the competitive advantage.

  14. I have allready heard this .... by GNUALMAFUERTE · · Score: 0, Flamebait

    "Let's learn to live with it and see what we can do with unpredictability"

    dejavu!, I said this years ago when my ex-boss decided to buy a w2k server!!

    --
    WTF am I doing replying to an AC at 5 A.M on a Friday night?
  15. Didn't work the last time by Anonymous Coward · · Score: 3, Informative

    Signed,

    FDIV

    1. Re:Didn't work the last time by Dolphinzilla · · Score: 1

      Thats pretty funny - don't know why you got modded "Offtopic" I guess the mod was unfamiliar with the famous Pentium FDIV bug....

    2. Re:Didn't work the last time by Anonymous Coward · · Score: 0

      FDiv, how have you been?! I haven't seen you since university! You're looking good - did you lose weight?

  16. Improbability drive? by mOoZik · · Score: 4, Funny

    You're sitting at your desk and out of nowhere, bam! You are transported to the edge of the galaxy. Weird.

    1. Re:Improbability drive? by arekq · · Score: 1

      Don't worry. A future you will come back to destroy the borg and get you home. :)

    2. Re:Improbability drive? by Winkhorst · · Score: 1

      Um, you already ARE at the edge of the galaxy. Perhaps you meant the OTHER edge of the galaxy?

      --
      "Is this Winkhorst a nova criminal?" "No just a technical sergeant wanted for interrogation."
    3. Re:Improbability drive? by Anonymous Coward · · Score: 0

      Maybe you know this, but I can't give up a chance to plug an incredible book:

      The parent post is actually referring to something not from Trek, but rather from Douglas Adams - "The Hitchhiker's Guide to the Galaxy". It's a nice trilogy of five books... yes, five. And it's a trilogy. Check it out, you won't be disappointed!

      Cheers,
      - AC

    4. Re:Improbability drive? by msaulters · · Score: 1
      However, if a chip can get by without all the double checks to assure absolute certainty, then energy consumption could be slashed -- and speed would get a simultaneous boost. That's the notion behind Palem's concept of probabilistic bits, or Pbits. As he puts it: "Uncertainty, contrary to being an impediment, becomes a resource."
      Dude... this is only a FINITE improbability generator. I'll leave it to you to figure out the exact finite improbability of using a few of these to generate an *infinite* improbability field. Glad to brew you a cup of tea, though.
      --
      These people looked deep into my soul and assigned me a number based on the order in which I joined.
    5. Re:Improbability drive? by strider44 · · Score: 1

      well no we're not at the edge of the galaxy, we're about two-thirds of the way there if I remember correctly. The edge of the galaxy is a long long way away.

    6. Re:Improbability drive? by Anonymous Coward · · Score: 0

      And then the universe, well, to comprehend that we'd need to understand the size of infinite: Bigger than the biggest thing ever and then some. Much bigger than that in fact, really amazingly immense, a totally stunning size, real "wow that's big," time. Infinity is just so big that, by comparison, bigness itself looks really titchy. Gigantic multiplied by colossal multiplied by staggeringly huge is the sort of concept we're trying to get across here. (With apologies to Douglas Adams)

    7. Re:Improbability drive? by fishyfool · · Score: 1

      wish i had mod points. your sig says it all.=)

      --
      Enjoy Every Sandwich
    8. Re:Improbability drive? by strider44 · · Score: 3, Funny

      Lol I was thinking of the galaxy song!

      <--Excerpt-->
      "
      Our Galaxy itself contains a hundred billion stars;
      it's a hundred thousand lightyears side to side.
      It bulges in the middle, sixteen thousand lightyears thick,
      but out by us it's just three thousand lightyears wide.

      We're thirty thousand lightyears from galactic central point,
      We go around ever two hundred million years,
      And our galaxy is only one of millions of billions
      in this amazing and expanding universe!
      "

      Creds to Eric Idle and Co.

    9. Re:Improbability drive? by TeknoHog · · Score: 1

      Me too.. I was just practising the Galaxy song with my guitar.. I think your RNG had just predicted my future ;)

      --
      Escher was the first MC and Giger invented the HR department.
  17. Re:YUO FAIL IT? by chrome · · Score: 2, Funny

    genius. Pure genius.

  18. looks like Intel's marketing department by Anonymous Coward · · Score: 1, Funny

    ... outdid themselves in their preparation for the next Pentium FPU fire drill

  19. We have this now by drsmack1 · · Score: 4, Insightful

    Before I found memtest my computers were VERY unpredicable.

    1. Re:We have this now by Anonymous Coward · · Score: 0
      unpredicable.


      And your spelling still is. :)

  20. random numbers, yay by layingMantis · · Score: 4, Funny

    so a "random" number could be ...actually random right, as opposed to the now deterministically computed pseudo random numbers....how could this NOT be useful!? The AI ramifications alone are fascinating to imagine...

    1. Re:random numbers, yay by Anonymous Coward · · Score: 0

      actually random right, as opposed to the now deterministically computed pseudo random numbers

      But the universe is deterministic. Nothing can escape causality.

    2. Re:random numbers, yay by Jeff+DeMaagd · · Score: 1

      I thought there was hardware to give truly random numbers, it just reads the noise in silicon.

      A random error in a digital number doesn't seem to bode well. Might as well stick to analog for those needs, because one of the benefits of digital processing is that transmission and storage errors can be correctable provided proper correction algorithm, and computations can be re-run.

    3. Re:random numbers, yay by Anonymous Coward · · Score: 0

      "Nothing can escape causality."

      Nothing, except maybe one man. One hero in a time of prisoners. One rebel out to smash the clockwork of the universe. 'Who is this man?' asks the Newtonian Emperor. It's

      THE QUANTUM AVENGER!

    4. Re:random numbers, yay by Winkhorst · · Score: 1

      "Nothing can escape causality."

      So all you have to do is convince the universe you are nothing. Sounds like cosmonauts of the future will have to take some classes in Zen Mind States.

      Personally, I have been escaping causality for years. But then, I don't really exist...

      --
      "Is this Winkhorst a nova criminal?" "No just a technical sergeant wanted for interrogation."
    5. Re:random numbers, yay by VoidWraith · · Score: 0

      So Descartes was wrong, then?

    6. Re:random numbers, yay by mike5904 · · Score: 1

      But how can you be so certain of this? If we make that assumption, that absolutely *everything* is a direct effect by one or more causes, then theoretically it is possible to predict this event knowing these causes. In an entirely deterministic universe, the complete knowledge of the present state allows for complete prediction of future states for an infinite amount of time. Of course we aren't saved from this, either, so everything we say, do, and even think, is also completely determinable. I'd say there are plenty of people who would disagree with you on that statement.

    7. Re:random numbers, yay by billsoxs · · Score: 1
      You have never heard of Quantum Mechanics?

      Yes this is on topic! (This is why the gate does not open the source drain channel uniformally. God it is going to be fun teaching devices then!)

      --
      This message was brought to you by "Lack of Sleep."
    8. Re:random numbers, yay by Kupek · · Score: 1

      What AI ramifications?

      We've been able to obtain truly random numbers for a long, long time. All you need to do is get information from some physical device - the Linux kernel has a random function that gets some random information from the keyboard. Sound cards work too.

      But in most applications, a simple pseudo-random number generator is going to be indistinguishable from truly random numbers.

    9. Re:random numbers, yay by Winkhorst · · Score: 1

      Descartes was neither "right" nor "wrong." He was simply positing a point at which to begin his philosophical discourse. I, for one, consider the whole field to be the rantings of a bunch of demented coon dogs, but that's just my opinion. What is (almost) universally recognized is that it has nothing to do with science. I.e., it cannot be used to prove or disprove anything resembling a scientific statement.

      --
      "Is this Winkhorst a nova criminal?" "No just a technical sergeant wanted for interrogation."
    10. Re:random numbers, yay by RGTAsheron · · Score: 1

      Also useful for games. I forget which one but there was a space sim which stored only the initial seed and would generate the same universe of multiple galaxies every time from that single seed instead of storing the positions for every last planet.

    11. Re:random numbers, yay by Anonymous Coward · · Score: 0

      Well, untill some man comes out of the total perspective vortex a little hungry and eats the piece of fairy cake.

    12. Re:random numbers, yay by Descartes · · Score: 1

      I have to disagree. I was right.

    13. Re:random numbers, yay by BillyBlaze · · Score: 1
      Well, I doubt we'll ever have complete knowledge of the present state for even a vanishingly small area. (Complete knowledge of the Earth, for example, would only allow you to make predictions for a second or two, due to the speed of light.) And of course we'd also need near-infinite (or infinite, if you want to do the whole universe) computing resources and an exactly correct understanding of physics.

      As to free will - how does anybody know they have free will? Tempting as it is, a belief in free will isn't enough to make a scientific statement about the determinism of the universe. However, it's quite possible science will never know, because to prove the universe is indeterminate, you'd need to go outside the universe and use your perfect program and infinite computer to predict the universe (if your prediction was wrong, then the universe is indeterminate). And even with this method, you could never prove the universe is completely determinable. (Actually, that's a bit like proving within a system that that system is self-consistent.)

      That said, our current understanding of physics agrees with you that at least some small-scall things are indeterminate. I guess my point is, while that's probably true, people thinking they have free will isn't very good supporting evidence. Probably better would be to ask grandparent if he could point out where the physicists are wrong and how they can predict the things they say are unpredictable.

    14. Re:random numbers, yay by Anonymous Coward · · Score: 0

      Nothing is random. Simply becuase it says "unpredictable" doesnt mean it is. It just emans its really really hard, so hard, infact, to predict that they rather not spend the R&D to do it.

    15. Re:random numbers, yay by Gil-galad55 · · Score: 1

      It would be impossible to compute the universe even if it were deterministic because you can never have a complete knowledge of the initial conditions. Even if you were to carry out the measurement for a spacetime hypersurface and measure, say, the energy eigenstate superposition of every system in the universe, there would still be unmeasurable phases that would affect the time evolution in a way you couldn't predict. That is to say, you could compute every possible solution (allowing for every possible phase difference), but you wouldn't know which one was right until you checked it, i.e., measured the universe again, so your computations were basically worthless!

      --

      To follow knowledge like a sinking star, / Beyond the utmost bound of human thought. ("Ulysses", Tennyson)

  21. I heard about this years ago.... by Anonymous Coward · · Score: 0

    "unpredictability becomes a great asset leading to energy conservation and increased computation speeds"

    It's called "scrap," "recycling," and "selling the slower chips to someone else."

  22. Please relax. by Tibe · · Score: 2, Funny

    "... three to one... two... one... probability factor of one to one... we have normality, Anything you still can't cope with is therefore your own problem. Please relax."

  23. Little problem by Anonymous Coward · · Score: 3, Insightful

    While certainly many problems can be solved using less than perfect measures, building an entire chip based on this would not work out so well. For example, while a DSP app might deal fine with small variations in results, a device driver or chunk of crypto code is probably not going to be very happy with close-but-not-quite-right results.

    Why do I have a feeling these guys have done simulations with single applications, ignoring the surrounding OS environment?

  24. Intel by TWX · · Score: 2, Funny

    I'd say that with Intel's various errors over the last fifteen years, like the fourth and ninth digit floating point division errors in the Pentium 60, and the heat throttleback due to normal operating conditions on their newer processors, Intel had done a wonderful job of embracing this new unpredictability technology.

    --
    Do not look into laser with remaining eye.
  25. Analog Processor by 10101001+10101001 · · Score: 5, Interesting

    It sounds like this is just another implementation of an analog processor, which is far from a new idea. Really simple analog processors are just a bit of plastic foam used as a manifold. There's even the idea of having 0, 1, and 1/2 (where 1/2 is seen as uncertain) in something called a Lukasiewicz Logic Array. Anyways, I wish the guy good luck with it, though it might be a good idea if he did some more reading on ideas already presented on the subject.

    Obvious google search link:
    Google Search for "lukasiewicz analog"

    --
    Eurohacker European paranoia, gun rights, and h
    1. Re:Analog Processor by ScrewMaster · · Score: 1

      And let's not forget Crzmblski's Limit.

      --
      The higher the technology, the sharper that two-edged sword.
  26. Randomness is nothing new by servognome · · Score: 1

    There is already acceptable levels of randomness in the form of soft errors. Designs already take into account the fact that you just have to live with a certain rate of error because of cosmic rays or alpha particles. It looks like they are just extending such techniques to transistor tolerances.

    --
    D6 63 0D 70 89 81 BB 8E 7B 7C 5F 5D 54 EA AB 73
  27. Check Apple's Calculator by Sophrosyne · · Score: 0

    Where 2+2 always = 4.67345234

    1. Re:Check Apple's Calculator by Anonymous Coward · · Score: 0

      It's 4. I checked. Even with 16 digit precision turn on.

  28. Indeterminate Voltage and Bad Fabrication by Inmatarian · · Score: 4, Informative

    Intel has hit a brick wall in terms of their processors. They invested heavily in their processor fabrication centers and are now coming to terms that they won't be able to produce reliably anymore. That said, lets discuss the nature of 1s and 0s. Typically, a 0 is broadcast across a chip as a lack of voltage, and a 1 brodcast as a +5 volts. Each transistor has to be capable of being just right of a resistor to not degrade the +5 volts. Heres where "unpredictability" comes into play: you have a handful of volts to play with. The article's talking about having unpredictable algorythms is the press agent not knowing what he's talking about, but certainly allowing a voltage threshold within the confines of the transistors is an okay thing. The only problem is when its across a lot of serial lines, because that compounds into significant loss. This is just my opinion, but I think this guy is talking about chip designs where the data isn't broadcast in 1s and 0s anymore, but in whatever multiples of electronvolts that would correspond to a number. I'm not comfortable with this, and I would like someone to tell me I'm just paranoid.

    1. Re:Indeterminate Voltage and Bad Fabrication by ABeowulfCluster · · Score: 1

      5 v is for TTL logic. Your CPU uses lower levels internally, and has for years.

    2. Re:Indeterminate Voltage and Bad Fabrication by ScrewMaster · · Score: 1

      Okay. You're paranoid. But we are still out to get you.

      --
      The higher the technology, the sharper that two-edged sword.
    3. Re:Indeterminate Voltage and Bad Fabrication by zcat_NZ · · Score: 2, Insightful

      "informative" ?!!

      Do you have even the faintest idea how logic actually works? Or did I just mis-read what you wrote?

      None of the gates have to reliably reproduce that actual voltage (+5, +3.3, +2.8, +/-12v, or whatever) that represents a "1" or "0", they just have to reliable recognise that it's "smallish" (less than halfway, logic 0), or "biggish" (more than halfway, logic 1) and in turn produce a voltage themselves that's reasonably close to whatever represents a "0" or "1". Binary is used for exactly this reason; it's very difficult to propigate an analog voltage through any number of circuits without losing accuracy. Digital circuits don't even try. And as I understand TFA, now they don't even have to get it right all the time either..

      --
      455fe10422ca29c4933f95052b792ab2
    4. Re:Indeterminate Voltage and Bad Fabrication by Waffle+Iron · · Score: 2, Funny
      Typically, a 0 is broadcast across a chip as a lack of voltage, and a 1 brodcast as a +5 volts.

      1974 called. It wants its CMOS logic signal voltages back.

    5. Re:Indeterminate Voltage and Bad Fabrication by bbrack · · Score: 1

      Some clarification for you. Oh, your next to the last sentence (whole eV thing) is pretty much completely wrong... The IR drop you refer to across serial lines (global interconnects) is generally taken care of through the reuse of repeaters in long wires - they increase speed, and improve operating margins. The problem with unpredictable logic in new/extremely small transistors: 1. new transistors run at much lower voltages than older chips - 90nm trahsistors run at ~1V, 65nm will run in the 800-900mV range (these are the nominal voltages these parts use in systems, not actual vmins) 2. every reduction in operating voltage reduces the separation between vil/vih and vol/voh in the various circuit subblocks 3. increases in operating speed will lead to more noise on power busses So, 30 years ago, when parts ran on 5V, in the low MHz range, vol/voh would generally be in the 0.5/4.5V range, with vil/vih in the 2/3V range, you had >1V noise margin, with very little noise on the power busses. For modern processors, the noise margin is generally in the 100mV range, and if you look at what the voltage looks like on a power bus, dips or spikes that are on the order of magnitude of the noise margin are not unusual at all. There are tricks, such as not using stacked logic, etc that can help improve your operating margins, but most of these come with a performance hit. All Intel's excess capacity in their fabs probably doesn't have much to do with this guys research, also... And to make you feel better, you're not just paranoid, you have a terrible understanding of device physics/operation/modern electronics

    6. Re:Indeterminate Voltage and Bad Fabrication by canuck57 · · Score: 1

      I'm not comfortable with this, and I would like someone to tell me I'm just paranoid.

      You are not paranoid and your comfort level is well tuned. Unreliable behavior cannot be tolerated unless it is entropy.

      I figure microprocessor development as we have seen it is nearing its end without new ideas. For example, gigahertz isn't by it self an indication of computational capability. It takes hundreds of CPU cycles on a P4 to do common operations that on an 8080 would take one CPU cycle. If you can reduce the CPU cycle per operation count and reduce transistor count you could end up with a much faster lower power counterpart. But right now the marketing is on megahertz sells and a lot of the transistor count goes into making it stable at ever-faster speeds.

      Clearly, not enough has gone into optimizing the transistors used today.

      Then with the new dye space, add multiple cores for parallel processing, 2, 4, 8 and maybe 16 cores per dye. Perhaps a 3 processor core with the 4 section of dye having a specialized audio/video processor.

      We think computers are 0 and 1 based, but there is no reason it could not be ternary or beyond. Memory states could be 1, 0 or maybe. From a software perspective this could make AI programming practical.

      But for some, put a 10GHz oscillator into an in-line divider that feeds to a 1GHz processor and it will sell premium to some.

  29. example by lithium57 · · Score: 0, Redundant

    Google is a great example of what you can achieve with probabilistic techniques. They have to deal with tons of information but still provide you with a quick answer.

  30. This is how researchers make their money. by cosmicpossum · · Score: 0, Troll

    University researchers make money by getting grants from industry and government. They get these grants by getting publicity in the business press. This is just a plea for money.

    Nothing to see here, move along...

    --
    (This sig intentionally left blank)
  31. Acceptable uncertainty-Digital Brains. by Anonymous Coward · · Score: 0

    "Now that I think about it, it does seem to make some sense. I am not sure that I would want to program on such a chip right now though (I imagine that debugging could become a nightmare really quickly!)."

    Your brain seems to handle the job just fine.

  32. Probabilistic algorithms by timeOday · · Score: 2, Interesting
    In college, my professor challenged the entire class to find an algorithm that takes an array, and returns a single value larger than the median of values in the array, in sub-linear time.

    Naturally, he had us stumped, because the task is impossible. Without checking at least half the numbers, you can't be sure of the answer.

    But, he pointed out, here's what you can do: pick 1000 numbers from the array at random and return the largest - a constant time operation! This "algorithm" just might return a wrong answer. But the chances of that happening are far less than the odds that you're in a nuthouse hallucinating this message right now. The odds are far less than the liklihood that a computer would botch a deterministic algorithm during executation anyways. The odds of making a mistake with the algorithm are 0, for all intents and purposes. So is that OK?

    1. Re:Probabilistic algorithms by Anonymous Coward · · Score: 0

      a single value larger than the median? return the maximum of the represented data type.

      Unless I've not understood the problem, that's a guaranteed answer within the limits of the computer's ability to determine.

    2. Re:Probabilistic algorithms by Anonymous Coward · · Score: 0

      That's really easy. Take the upper size limit for double-precision (or whatever type can go to the highest number for whichever was the official course language) and return that. Or better yet, something higher - maybe even a "divide by zero". :)

    3. Re:Probabilistic algorithms by Yartrebo · · Score: 1

      You have to be careful. Given an array of 999,999 copies of the number 63, and a single 64, that probabilistic method has a 99.9% chance of failing.

      Depending on the scenario, that degenerate case can be quite common.

    4. Re:Probabilistic algorithms by theguywhosaid · · Score: 2, Informative

      heh, 63 is the median in your given array. since the returned value does not need to be in the array, just add 1 and return that. or multiply by some large constant. or just return the sum of all the numbers you encountered. theres lots of options here.

    5. Re:Probabilistic algorithms by cgenman · · Score: 1

      Why not just take an unsigned 0, subtract one, and return that?

    6. Re:Probabilistic algorithms by Anonymous Coward · · Score: 0

      easy

      Look at the type of the array (assuming your arrays are typed), then spit out a string which is 1 + the largest possible value of that type

    7. Re:Probabilistic algorithms by Anonymous Coward · · Score: 0

      Why not just take an unsigned 0, subtract one, and return that?

      But what if everything in the array is unsigned 0 minus 1? This fails because it needs to be bigger.

    8. Re:Probabilistic algorithms by Yartrebo · · Score: 1

      Then take this array:

      999,999 copies of -1
      1 copy of 1,000,000,000

      Method 1 (add 1) return 0.
      Method 2 (multiply by -1,000) return -1,000.
      Method 3 (sum all numbers encountered) return -1,000 in most cases.

      Since the answer doesn't have to be in the array, you can get a valid answer (if there exists one) by returning 0x7FFF....FFFFF.

    9. Re:Probabilistic algorithms by cgenman · · Score: 1

      An unsigned 0 minus one should be the largest value a variable can hold, dependent upon the return value the calling function is expecting. If your return value needs to be larger than the max value, you can't possibly return a correct answer no matter how you reach that answer

      The point was, that any maximum-sized variable would satisfy the conditions put forth here. The test would be more meaningful if you needed to come within X of the value, or had some other constraint. Why not within 5% of the median? There is never a situation in life where you just need to be larger, and there is no other constraint pulling you back towards rational values.

    10. Re:Probabilistic algorithms by HeghmoH · · Score: 1

      0 is a correct answer to this problem for your array, though, so I don't see what you're getting at.

      Remember, it's median (middle number in the ordering) not median (average).

      --
      Mod down posts with a "Free Mac Mini/iPod" sig, they're spam!
  33. more info by mako1138 · · Score: 5, Informative

    This article left me rather insatisfied, so I looked for a better one. I found it here, a collection of papers on the subject, with real-world results, it seems. The first article is a nice overview, and there's some pics of odd-looking silicon. They have funding from DARPA, interestingly enough.

    1. Re:more info by mako1138 · · Score: 1

      Oh, heh, it's by the same people and research group featured in the article.

    2. Re:more info by Anonymous Coward · · Score: 0

      Oh, Boltzman machines and Bayesian learning.

      Yay, neural nets!

  34. and of course, nobody actually READS the article. by ABeowulfCluster · · Score: 1

    The article mentions how they just work with the fact that transistors don't match. Well, engineers have been working with mismatched transistors ever since the transistor was invented.

  35. I, for one... by melikamp · · Score: 2, Interesting

    That is one step closer to a human-like AI -- reminds me of a neural net. The technology from TFA may be just what they (computers) need to become like us: i.e. an ability to make quick decisions about complex problems, and succeeding more often than failing.

    I, for one, welcome our unpredictable silicon overlords.

    1. Re:I, for one... by myukew · · Score: 1

      sure. we can't do it right so let's just do it without predictable results and claim it always works when the press isn't watching...

  36. In the future by ICECommander · · Score: 0

    Password: ********
    I'm sorry it appears the password you have entered is incorrect. This could be due to the fact that the processor is unsure of the binary encoding of your password, have a nice day.

    --
    All your Sybase are belong to us.
    1. Re:In the future by tomhudson · · Score: 0, Offtopic
      No, in the future, it doesn't matter whatever you put in, it will say "close enough". Or "sorry". or "It depends". Or "Since I'm only 80% sure you should be logged in, I'm ignoring 20% of your keystrokes and mouse clicks - have a nice day."
      On February 7th, Russ Nelson (Open Source Initiative president) published an article called "Blacks are lazy", quoted in journal entries here and here.

      Please consider signing the online petition asking OSI to remove Russ Nelson.

  37. But is it really useful? by billsoxs · · Score: 1

    I can remember sitting in a meeting (just listening) on a future Sematech roadmap... I remember the discussion about the dopant levels in gates at the end of the roadmap and I did a quick calculation of the number of B atoms required.... It was 3. 2 would not work nor would 4. (This is indivudual atoms of B not density etc) I was amazed. (I think that the node was the second one past 45 nm - which should be about 20 nm - I don't remember.) Now we seem to have someone saying that we can live with the 30%+ error...... Sounds more like trusting a drunk to give you directions home.

    --
    This message was brought to you by "Lack of Sleep."
  38. Parent is correct; GP is ... lost. by Anonymous Coward · · Score: 0

    Yeah, i read that too as was like, "damn, someone isn't an EE". Hell, i'm not, but took enough classes on fab and silicon to know that was bunk.

  39. bad story by msblack · · Score: 3, Insightful
    It's rather a poorly-written article with a lot of 1950's science fiction predictions about the future. The field of fuzzy algorithms has existed for ages. Fuzzy algorithms don't rely on random results. Rather, they use the "p-bits" to perform their calculations. P-bits are not the same as random bits. On the contrary, p-bits are "don't care" or "flexible" values that take into account multiple possibilities at the same time.

    Random results are terrible because they are random. The scientific method depends upon experiments that can be repeated by other researchers. You can't base a theory on results that don't correlate with the inputs. You can repeat the experiment to obtain a probablistic model but not certainty.

    A computer chip that yields unpredictable results is not going to magically recognize the image of a chair, much less a face because a chip that can't execute a program is more akin to the movie Short Circuit where the appliances go whacky. To me the author confuses the concept of fuzzy algorithms with random trials.

    --
    signature pending slashdot approval
    1. Re:bad story by EndlessNameless · · Score: 1

      :::The scientific method depends upon experiments that can be repeated by other researchers. You can't base a theory on results that don't correlate with the inputs.:::

      At the heart of scientific investigation is the notion that random variances cancel each other out when there are sufficient samples. While this approach would require a new computing paradigm in order to be usable, there is already one algorithm that uses randomness to yield deterministic results--the Monte Carlo method.

      This approach is obviously nascient and untenable on any hardware in production (and probably untenable on even hardware that is presently being designed), but that does not mean that it is incapable of producing useful results. Although with the jump that other "new" models such as chaos computing and quantum computing have on it, I suspect one or the other of those would come to fruition long before this (and I also wonder how similar the underlying theory would be as compared to either of these... it does seem like the subject of uncertainty hedges in on both areas). Hell, those computing models even have portions of their fundamental computation mechanisms working.

      I honestly don't know how seriously to take this whole idea. It's either an earth-shaker or a still-born, and there's not an easy way to tell which without putting forth a monumental development effort. To me, the real question is: is this worth investigating right now? With the progress made in other computing models, I'm not sure it's worth diverting the R&D resources.

      --

      ---
      According to the latest ruleset, this post should be modded as Vorpal Flamebait +5.
    2. Re:bad story by aprilsound · · Score: 0

      The point is that in less time, an "unpredictable" chip can get an answer that is very likely to be right. You could devise an algorithm that is always right, but it would take much longer. For a variety of applications (especialy real time systems), any mistake made by an uncertain chip or a randomized algorithm will be absorbed by the majority of correct results.
      Rejecting results with a degree of uncertainty is like refusing to fly because planes occasionaly crash. As TFA says, "Live with it," the benefits outway the risks, which are easily mitigated by selective application.

    3. Re:bad story by plierhead · · Score: 1
      Random results are terrible because they are random. The scientific method [rochester.edu] depends upon experiments that can be repeated by other researchers. You can't base a theory on results that don't correlate with the inputs. You can repeat the experiment to obtain a probablistic model but not certainty.

      Most of the posts are from the traditional algorithmic view of the world. e.g., How well can we survive if our multiply instruction gives us back the wrong answer?

      Where this stuff is really useful is in more ambitious, random-by-nature endeavours that we don't even really achieve in yet. Like trying to seed, and drive, a cellular automaton network which could genuinely take on/develop intelligence.

      For such chaotic projects, gates that may or may not work and may have random race conditions might be extremely useful.

      Of course the outcome would be something irreproducible. The thing to do would be to trap it's state so we could harness it and avoid it skeynetting us.

      Personally I am with the guy from Sun and would have great trepidation at someone building an immense machine from this kind of out-of-control logic. It might just wake up and kick our arses. Our own primordial soup was not so deterministic, after all.

      --

      [x] auto-moderate all posts by this user as insightful

    4. Re:bad story by Anonymous Coward · · Score: 0

      You can't base a theory on results that don't correlate with the inputs

      Sure you can: If the results of any test are random, I theorize that Slashdotters will post that it is possibly a breakthrough in AI.

    5. Re:bad story by Eric604 · · Score: 1

      The article basically says:
      1. smaller transistors lead to unpredictability.
      2. live with it, it wil be amazing

      It's doesn't say how. If they planning to run an instruction set based cpu with this "idea", error correction or error cancelation might be the underlying technique.

      On the other hand there are fuzzy algorithms and other non-deterministic techniques that aren't running sequences of instruction.

      Or it could be something totaly different.

      In any case, the article tells me nothing.

  40. In other news... by Zangief · · Score: 1

    Famous ex-wrestler, turned programmer, Zangief, claims that the unpredictability in his programs is not caused by bugs, but by a "energy conservation" feature!

  41. I wonder how the authour would feel by earthforce_1 · · Score: 1

    if he was flying on an aircraft controlled by systems that gave somewhat unpredictable results.

    --
    My rights don't need management.
    1. Re:I wonder how the authour would feel by kiore · · Score: 1
      He already does.

      GPS - tells you where you are, plus or minus some distance a certain percentage of the time. Luckily that isn't used on commercial passenger jets.

      Intertial navigation? IIRC, this depends on analog to digital devices. Guess what? All the analog to digital devices I've heard of have a small, but measurable inaccuracy. (I'll accept that the A-D devices I've never heard of are perfect).

      Then, all the A-D outputs are fed to a human pilot. To err is human!

  42. Re:GOD HATES FAGS by Anonymous Coward · · Score: 0

    They have drugs that can help you with your issues. Please see a kind doctor and allow him to put that nice white suit with the long sleeves on you. It will make you feel better

  43. Re: Russ Nelson by Anonymous Coward · · Score: 0

    A person's personal opinions should be totally irrelevant as far as his/her job is concerned; it's job performance that counts. Now, if the person lets his/her own personal beliefs interfere with his/her job (e.g., in this case, not hiring blacks, etc.), then that is a different matter.

    BTW, many blacks are lazy. So are many whites, and many yellows, and many [insert color here]s. If one tries to generalize laziness to all blacks, however, all you have to do is point to people like Colon Powell and Whoopi Goldberg, organizations such as the SCLC and Black Panthers, and African tribes such as the Zulus.

    P.S. I just read his entire article. It starts out sounding racist, but the article as a whole is not. At the worst, he was being economicist.

  44. Breaking News by Anonymous Coward · · Score: 0

    This just in -- The future is not predictable.
    News at Eleven.

  45. One can do even faster... by Compuser · · Score: 1

    Assuming e.g. an array of ints the answer to this problem is:

    return INT_MAX;

    1. Re:One can do even faster... by timeOday · · Score: 1

      To do any theory you have to specify your computational model, and I seem to have fallen short there. I was assuming unlimited memory and range, as is usual.

    2. Re:One can do even faster... by tehdaemon · · Score: 1
      Dangit, you dodged the point.


      return infinity;


      Any machine capable of handling unlimited range can handle this return value. By definition. It may be algorithmically inpossible to determine the median of an array without examining each element, but finding a number larger than the median is dirt simple. The only way this simple algorithm could fail is if half or more of the values are infinity. (oh, and any algorithm would fail, 'cause there isn't a larger number!)

      --
      Laws are horrible moral guides, moral guides make even worse laws.
    3. Re:One can do even faster... by Anonymous Coward · · Score: 0

      return INT_MAX;

      Nope
      That fails if every value in the array is INT_MAX.
      Needs to be bigger than.

    4. Re:One can do even faster... by Anonymous Coward · · Score: 0

      Infinity is a concept, not a number.

    5. Re:One can do even faster... by timeOday · · Score: 1

      infinity isn't a number.

    6. Re:One can do even faster... by HeghmoH · · Score: 1

      Any machine capable of handling unlimited range can handle this return value. By definition.

      That is not correct. Take a machine capable of representing any natural number. It will not be able to represent infinity, but it will have unlimited range.

      --
      Mod down posts with a "Free Mac Mini/iPod" sig, they're spam!
    7. Re:One can do even faster... by tehdaemon · · Score: 1
      First off, wrong. It could represent countably infinite, but not necessarily uncountably infinite. The set of natural numbers is countably infinite. (there is a finite number of natural numbers between any two members of the set) Any machine capable of handling an unlimited range of natural numbers can represent countably infinite - because it is a natural number. (The set of real numbers is uncountably infinite, there is an infinite number of real numbers between any two (different) real numbers) You have to specify which infinity you want, but since we were limited to natural numbers by the machine, only countably infinite is possible. But it is good enough.

      Secondly, any machine capable of storing an array of numbers can return the largest possible number stored in whatever type of variable the array is composed of. Which means that :

      return <array_variable_type>_MAX;

      as was proposed in the first place, is ALWAYS possible, and will always return a value equal to or greater than the median value.

      The professor who proposed this was clearly a scientist, not an engineer.

      --
      Laws are horrible moral guides, moral guides make even worse laws.
    8. Re:One can do even faster... by tehdaemon · · Score: 1
      So - who cares?

      return <array_member_variable_type>_MAX;

      Stop nitpicking.

      --
      Laws are horrible moral guides, moral guides make even worse laws.
    9. Re:One can do even faster... by HeghmoH · · Score: 1

      Wow, you're just not making any sense.

      First off, wrong. It could represent countably infinite, but not necessarily uncountably infinite.

      This is wrong.

      The set of natural numbers is countably infinite. (there is a finite number of natural numbers between any two members of the set)

      This is correct, but you're still confused. The fact that N is countably infinite has nothing to do with the fact that there is a finite number of naturals between any two members. For proof, look at the set of rationals. There is an infinite number of rationals between any two rationals, but |Q| is countable.

      Any machine capable of handling an unlimited range of natural numbers can represent countably infinite - because it is a natural number.

      This is wrong. Infinity, whether countable or not, is not a natural number.

      You can get any natural number by starting from 0 and then adding 1 a finite number of times. Obviously you cannot get infinity with this procedure.

      You're confusing the size of the natural numbers (aleph naught) with the membership of the natural numbers. Just because the size of the natural numbers is infinite doesn't mean that anything which can represent the naturals can represent infinity; quite the contrary.

      If I allow you to write a string of arbitrary, finite length consisting only of the digits 0-9, you can write any natural number. How are you going to write infinity?

      (The set of real numbers is uncountably infinite, there is an infinite number of real numbers between any two (different) real numbers) You have to specify which infinity you want, but since we were limited to natural numbers by the machine, only countably infinite is possible. But it is good enough.

      As detailed above, no type of infinity is possible.

      Secondly, any machine capable of storing an array of numbers can return the largest possible number stored in whatever type of variable the array is composed of.

      What do you return when your type has no largest possible number, like a type which can hold any natural number?

      Which means that :

      return <array_variable_type>_MAX;

      as was proposed in the first place, is ALWAYS possible, and will always return a value equal to or greater than the median value.


      Wrong. What is <array_variable_type>_MAX for the naturals? (It's not infinity, we can't store that.) What is <array_variable_type>_MAX for the reals? What is <array_variable_type>_MAX for the rationals? Just to make sure my point gets through, what is <array_variable_type>_MAX for the reals restricted to be in the range (0, 1)?

      The professor who proposed this was clearly a scientist, not an engineer.

      You are clearly a wannabe math guy who didn't actually pay attention to his courses.

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    10. Re:One can do even faster... by tehdaemon · · Score: 1
      " Wow, you're just not making any sense." From the viewpoint of a theoretical mathematician, probably. Which leads naturally to,

      "You are clearly a wannabe math guy who didn't actually pay attention to his courses."

      No. I am an engineer who had a math major for a roommate. I don't care much for theory if it does not apply to the problem at hand. Most of what you have said, while it may be correct from a mathematician's point of view, is simply irrelevant.

      The problem at hand is to find some way to find a number larger than the median in an array of numbers in less time than it takes to look at all of the numbers. The answer is simple, the largest possible number. If this is being done in a computer, then that computer can represent any number in the array. And the computer can represent the largest value of that type. If this is being done on paper, then I can represent infinity very easily (just not in a /. post, I tried) Infinity is large enough to satisfy the problem in all cases.

      I know that what I said about countably infinite is not the proper definition. I used google, The proper definition of a countably infinite set is can it be mapped one to one with the set of natural numbers. Kind of a useless definition when I was trying to prove that a) the natural number set is countably infinite and b)that the number of natural numbers is also a natural number.

      While I may be wrong in calling the number of natural numbers 'countably intinite', the name is irrelevant. Since I do not know it's proper name, I'll call it squissh :^) What is it? well, I'll start counting them. Starting with 1.

      • 1 .. #1
      • 2 .. #2
      • 3 .. #3
      Hmmm. see a pattern? I do. The number of natural numbers is the same as the largest natural number, squissh. Which means that squissh is also a natural number, and it is larger than all other natural numbers. So if I have an array of arbitrarily large natural numbers, and can represent those numbers, then squissh is equal to or greater than their median. And since I can represent any natural number, I can also represent squissh. Done.

      "What is <array_variable_type>_MAX for the naturals?" Squissh. If the computer has a variable type that can represent the naturals, then it can represent this number, whatever it is. If this variable type cannot represent this number, then it cannot represent all naturals, only a subset of them. And this means that there is a finite largest number that can be in the array, and that number can be represented. Always.

      "What do you return when your type has no largest possible number, like a type which can hold any natural number?" Answered. Squissh. I'll just use the same variable type that the array used to return it. It has to fit, by definition. How to do so, from a computer engineering point of view, I have no clue. But since any computer capable of handling the type has already solved the problem, I do not have to worry about it.

      "Infinity, whether countable or not, is not a natural number."

      Only if it is not 'the number of natural numbers'

      "You can get any natural number by starting from 0 and then adding 1 a finite number of times."
      " If I allow you to write a string of arbitrary, finite length consisting only of the digits 0-9, you can write any natural number."

      This implies that all natural numbers are finite numbers. But the set of natural numbers is infinite, there is an infinite number of them. But I just showed that the number of nautral numbers is also a natural number. Which means that there is at least one infinite natural number.

      "You're confusing the size of the natural numbers (aleph naught) with the membership of the natural numbers. Just because the size of the natural numbers is infinite doesn't mean that anything which can represent the naturals can represent infinity; quite the contrary." I just proved that they must be one and the same. That this is the case should be obvious. This is not the case for all sets of numbers, or even all countable sets, but it is for the naturals.

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    11. Re:One can do even faster... by HeghmoH · · Score: 1

      "You are clearly a wannabe math guy who didn't actually pay attention to his courses."

      No. I am an engineer who had a math major for a roommate. I don't care much for theory if it does not apply to the problem at hand. Most of what you have said, while it may be correct from a mathematician's point of view, is simply irrelevant.

      Ok, so I was wrong. You simply can talk the talk, but you can't walk the walk. In other words, you have some of the vocabulary, but none of the knowledge.

      The problem at hand is to find some way to find a number larger than the median in an array of numbers in less time than it takes to look at all of the numbers. The answer is simple, the largest possible number.

      Such a thing does not exist in the naturals, integers, rationals, or reals. Here's a simple proof for the naturals:

      First, we observe that for every natural number x, the following property is always true: x < x+1 .

      Let x be the largest natural number. This means that for all natural numbers y where y != x, y < x. Now, let z = x + 1. By the above property, x < z. Contradiction. Thus x is not the largest natural number, and such a number does not exist.

      This is an extremely basic proof, and anybody who is even vaguely mathematician-like will verify its truth for you.

      Infinity is large enough to satisfy the problem in all cases.

      This is true. However, infinity is not a natural number.

      While I may be wrong in calling the number of natural numbers 'countably intinite', the name is irrelevant. Since I do not know it's proper name, I'll call it squissh :^) What is it? well, I'll start counting them. Starting with 1.

      1 .. #1

      2 .. #2

      3 .. #3

      Hmmm. see a pattern? I do.


      I see a pattern you do not:

      x .. #x
      x+1 .. #x+1

      This pattern is true for every x. There is always a larger number, and the list never ends.

      The number of natural numbers is the same as the largest natural number, squissh. Which means that squissh is also a natural number, and it is larger than all other natural numbers.

      False. The number of natural numbers is called aleph null. It is not a natural number.

      So if I have an array of arbitrarily large natural numbers, and can represent those numbers, then squissh is equal to or greater than their median.

      Squissh is strictly greater than their median, and every member of the array, because squissh is greater than every natural number.

      And since I can represent any natural number, I can also represent squissh. Done.

      False, as demonstrated above.

      "What is _MAX for the naturals?" Squissh. If the computer has a variable type that can represent the naturals, then it can represent this number, whatever it is. If this variable type cannot represent this number, then it cannot represent all naturals, only a subset of them. And this means that there is a finite largest number that can be in the array, and that number can be represented. Always.

      Demonstrably false.

      "You can get any natural number by starting from 0 and then adding 1 a finite number of times."
      " If I allow you to write a string of arbitrary, finite length consisting only of the digits 0-9, you can write any natural number."

      This implies that all natural numbers are finite numbers. But the set of natural numbers is infinite, there is an infinite number of them. But I just showed that the number of nautral numbers is also a natural number. Which means that there is at least one infinite natural number.


      This simply does not make sense. Just because the quantity is infinite doesn't mean the size is infinite.

      For a simple demonstration, take the number of rational numbers betwee

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    12. Re:One can do even faster... by tehdaemon · · Score: 1
      *Sigh* I guess that I'll have to stop using squissh and start using aleph null. Pity, I liked squissh better. Oh well.

      Your simple proof for the naturals is flawed, because it starts with the assumptin that aleph null is not a natural number. It should come as no surprise that you conclude that it is not a natural number. Simple proof of this: infinity + 1 = infinity. Aleph null = infinity. (one of them anyway) So, if we start with the assumption that aleph null is a natural number:

      "First, we observe that for every natural number x, the following property is always true: x < x+1" Except for aleph null, because aleph null + 1 = aleph null. It follows then that z = x + 1 = x. There is no contradiction. Therefore x is larger than all other nautral numbers. I know that this does not constitute proof that aleph null is a natural number, but it does mean that this proof cannot determine whether it is or not.

      If we assume that aleph null is a natural number, the largest rational on the interval (0,1) exclusive is 1 - 1/(aleph null) The only way to get a smaller number than 1/(aleph null) is to use a 'larger' form of infinity, like the number of reals. (whatever it's name is, I imagine you'll tell me). But then the result in not a rational. Or if you prefer, a=(aleph null - 1), b=aleph null. Redo your proof, there is no contradiction.

      "The number of natural numbers is called aleph null. It is not a natural number."

      A better proof would be welcome.

      "In other words, you have some of the vocabulary, but none of the knowledge."Yup. Would I be calling aleph null squissh if that wasn't the case? knowledge != inteligence, just facts.

      --
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    13. Re:One can do even faster... by HeghmoH · · Score: 1
      Your simple proof for the naturals is flawed, because it starts with the assumptin that aleph null is not a natural number.

      Yours is flawed because it starts with the assumption that it is.

      It should come as no surprise that you conclude that it is not a natural number. Simple proof of this: infinity + 1 = infinity. Aleph null = infinity. (one of them anyway) So, if we start with the assumption that aleph null is a natural number:

      "First, we observe that for every natural number x, the following property is always true: x

      Maybe you won't believe me, but hopefully you'll believe Wolfram Research:
      [The positive integers] are the solution to the simple linear recurrance equation a_n = a_n-1 + 1 with a_1 = 1.
      There you have it. The property above isn't even an observation, it's part of the definition of "positive integer", which is the same as "natural number".

      Princeton has a very similar definition in WordNet.

      Ditto for some site I've never heard of.

      If we assume that aleph null is a natural number, the largest rational on the interval (0,1) exclusive is 1 - 1/(aleph null)

      This doesn't work even if we allow you to use aleph null in the denominator and do arithmetic on it, because 1/(aleph null) = 0, and so 1 - 1/(aleph null) = 1, and it is not inside the desired interval.

      Any rational number in (0,1) must be less than 1 by a finite amount.

      "The number of natural numbers is called aleph null. It is not a natural number."

      A better proof would be welcome.


      Hopefully proof by definition is acceptable to you.

      "In other words, you have some of the vocabulary, but none of the knowledge."

      Yup. Would I be calling aleph null squissh if that wasn't the case? knowledge != inteligence, just facts.


      In this case, you're missing some really fundamental things, like "it's possible to have an infinite set which has no largest member", and we're spending ages just trying to convince you that it's possible and true for the naturals, when this has been established mathematical fact for hundreds of years.
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    14. Re:One can do even faster... by HeghmoH · · Score: 1

      I wasn't paying attention and copied a raw , which slashdot decided was part of an HTML tag and so destroyed a bit of the message.

      It only killed some quoted material which wasn't extremely necessary anyway, and caused some of my text to be italicized. I hope it's still understandable.

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    15. Re:One can do even faster... by tehdaemon · · Score: 1
      "Yours is flawed because it starts with the assumption that it is."

      Yes, I thought I made this clear in my post. Whatever. Both proofs are nothing more than mathematical tautologies. All that they do tell us is that, as far as this proof is conscerned, aleph null can be either a natural number or not, both are consistent.

      If we change the definitions of vegtable, fruit, and mineral so that the tomato is now a vegtable, or a mineral, does this change the nature of the tomato? Using this definition of 'natural number' only changes the names that I have to use to describe the result. Can I use the term 'the squisshes' again? What, if any practical differences would there be to defining natural numbers as a_n = a_n-1 + 1 with a_1 = 1 AND b_n+1 = b_n - 1 with b_1 = (aleph null) ? (In general, would this break anything?)

      "1/(aleph null) = 0" Not always true. Choose a random real number on the interval (0,1) inclusive or exclusive, it doesn't matter. What is the probability of choosing any particular number in this interval? 1/infinity. If this equals exactly zero, then the sum of all the probabilities is also zero, which means that it is impossible to choose any number. But you can, so 1/infinity cannot equal exactly zero.

      Think of this in the real world, Take a bar of any particualr length. Cut it in two pieces. what is the chance that one of the pieces is a particular length? 1/infinity. What is the chance that it is a length smaller than the original and greater than zero? 1. The infinite number of possible places that you can cut offset the 1/infinite chance of any particular length.

      1/(aleph null) then, must be a finite, nonzero value. And if aleph null is a natural number, then 1/(aleph null) is the smallest possible rational number. So why is 1/infinity usually equal to zero? Because, unless you have an infinite number of them, or you are dealing with other infinitesimals, their sum is not big enough to change any other finite value.

      N = some finite integer

      R = some finite real number

      P = some infinite number

      R + N*(1/infinity) = R

      R + P*(1/infinity) = something that depends on the relative values of P and infinity. Anything is possible. What the value of R is may or may not matter.

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    16. Re:One can do even faster... by HeghmoH · · Score: 1

      "Yours is flawed because it starts with the assumption that it is."

      Yes, I thought I made this clear in my post. Whatever. Both proofs are nothing more than mathematical tautologies. All that they do tell us is that, as far as this proof is conscerned, aleph null can be either a natural number or not, both are consistent.


      I thought you were claiming that this is how things are, when in fact this is not how things are.

      Aleph null is not a natural number, this is in the definition.

      If we change the definitions of vegtable, fruit, and mineral so that the tomato is now a vegtable, or a mineral, does this change the nature of the tomato?

      That's not what you're doing. You're changing the definition of "tomato" to include all fruit currently accepted as "tomato", plus one particular type of pumpkin.

      Using this definition of 'natural number' only changes the names that I have to use to describe the result. Can I use the term 'the squisshes' again? What, if any practical differences would there be to defining natural numbers as a_n = a_n-1 + 1 with a_1 = 1 AND b_n+1 = b_n - 1 with b_1 = (aleph null) ? (In general, would this break anything?)

      Yes, it would break things. There are a lot of properties that are true for the natural numbers as they are known and defined by mathematicians everywhere that would not be true for the natural numbers plus aleph null. Minor things like associativity, negation, etc. would be completely destroyed.

      (a + b) + c = a + (b + c) -- let a = infinity, b > 0
      (inf + b) + c = inf + (b + c) -- by your def. of infinity, inf + b = inf
      inf + c = inf + (b + c) -- subtract a from both sides
      c = b + c -- false

      These operations are all perfectly legitimate on the naturals, but adding "infinity" to the mix lets me come up with totally bogus statements. Here's another one:

      1 = 1 -- add a to both sides
      a + 1 = a + 1 -- let a = infinity
      inf + 1 = inf + 1 -- inf + 1 = inf
      inf = inf + 1 -- put a back
      a = a + 1 -- subtract a
      0 = 1

      Do you really want to use a mathematical theory which allows me to prove that 0 = 1?

      "1/(aleph null) = 0" Not always true. Choose a random real number on the interval (0,1) inclusive or exclusive, it doesn't matter. What is the probability of choosing any particular number in this interval? 1/infinity. If this equals exactly zero, then the sum of all the probabilities is also zero, which means that it is impossible to choose any number. But you can, so 1/infinity cannot equal exactly zero.

      I thought you said you were an engineer. Didn't they make you take calculus? Do you remember any of it? This argument hasn't made any sense in mathematics since the 1600s.

      R + N*(1/infinity) = R

      Hmm, I thought 1/infinity wasn't zero, but now you say it is. This kind of inconsistency is what happens when you toss around these terms without thinking them through the way you're doing, and it's what mathematicians strive to avoid.

      R + N*(1/infinity) = R -- subtract R
      N*(1/infinity) = 0 -- divide by N
      1/infinity = 0

      If you can't come up with a consistent answer, then your theory is flawed.

      Back to the original question: do you accept that we can have a type which does not have a largest possible value?

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    17. Re:One can do even faster... by tehdaemon · · Score: 1
      "Yes, it would break things.

      This is going to sound funny, but... Goody! That means that I can define a new set, the squissh set! ;) It is the set of natural numbers plus aleph null. There is such a set already. And it has the properties that I have been describing. Although, it would be far more practical to simply include the statement 'except where <values> are equal to aleph null' in each of those cases you gave.

      "Hmm, I thought 1/infinity wasn't zero, but now you say it is." "If you can't come up with a consistent answer, then your theory is flawed." Yes, I see my error here. I have been inconsistent somewhere, and I will now correct it. I have been using the term 'equals' (=) where I should have been using the term 'limit'.

      The limit of this: R + N*(1/I) , as I -> infinity, is R, where R=a real number, N=a finite integer.

      If you patch my previous statements with this, they are now consistent.

      That's not what you're doing. You're changing the definition of "tomato" to include all fruit currently accepted as "tomato", plus one particular type of pumpkin."

      Unless, when they came up with the definition of 'tomato' there was this one very difficult tomato that the gardners did not know how to deal with, and so they exlcuded it from the definition, to make it easier to say 'This is how to grow all tomatoes.'?

      There are lots of examples in math and science where ignoring some small problem makes many things much easier, but including them vastly complicates things, even to the point of making them intractable with the current tools/understanding. But if you try to put those small problems back in and deal with them, while it complicates things greatly, you can gain new insight that could not be reached any other way. And sometimes you have to leave those problems out until you have developed the proper tools to deal with them, in this case, tools to deal with infinity, and infinitesimals. Like the limit. (which stupid me, I forgot to use! It has been years since I touched math...)

      "Back to the original question: do you accept that we can have a type which does not have a largest possible value?"

      Sure, I just don't see how the set of natural numbers is one of these. Since we have 'numbers' like infinity that we can use, at any rate. Take away that concept, and then yea, there is no largest natural number.

      In some way, the equations infinity + 1 = infinity, and 1/infinity = 0 are wrong. It is just that we can usually ignore the rounding error. Indeed, for the latter, you can't get a smaller rounding error! But this reality is inherant in the concept of the integral. We are 'summing' an infinite number of 1/infinity width, finite height volumes, and coming up with finite, non-zero results. If 1/infinity was truely zero, then the answer to all integral problems would be zero. You said "This argument hasn't made any sense in mathematics since the 1600s" Why? Because mathematicians stopped thinking this way and started thinking about limits instead?

      --
      Laws are horrible moral guides, moral guides make even worse laws.
    18. Re:One can do even faster... by HeghmoH · · Score: 1

      "Yes, it would break things."

      This is going to sound funny, but... Goody! That means that I can define a new set, the squissh set! ;) It is the set of natural numbers plus aleph null. There is such a set already. And it has the properties that I have been describing. Although, it would be far more practical to simply include the statement 'except where are equal to aleph null' in each of those cases you gave.


      Yes, it would. In fact, you can do a lot of useful things in graph theory by defining a semiring with the "usual" operations over the the reals union plus and minus infinity. However, you have to be very careful about what operations you allow and how they work.

      "Hmm, I thought 1/infinity wasn't zero, but now you say it is." "If you can't come up with a consistent answer, then your theory is flawed." Yes, I see my error here. I have been inconsistent somewhere, and I will now correct it. I have been using the term 'equals' (=) where I should have been using the term 'limit'.

      Goodness, I hope you're not this imprecise in your engineering designs.

      The limit of this: R + N*(1/I) , as I -> infinity, is R, where R=a real number, N=a finite integer.

      If you patch my previous statements with this, they are now consistent.


      Except they aren't. You said that the largest rational in (0,1) was 1 - 1/infinity, but by your definition this is equal to 1 and is outside the range.

      There are lots of examples in math and science where ignoring some small problem makes many things much easier, but including them vastly complicates things, even to the point of making them intractable with the current tools/understanding. But if you try to put those small problems back in and deal with them, while it complicates things greatly, you can gain new insight that could not be reached any other way. And sometimes you have to leave those problems out until you have developed the proper tools to deal with them, in this case, tools to deal with infinity, and infinitesimals. Like the limit. (which stupid me, I forgot to use! It has been years since I touched math...)

      As I stated above, adding infinity to one of these sets can produce useful results. However, by definition as generally accepted by the mathematical world, infinity is not part of these sets.

      "Back to the original question: do you accept that we can have a type which does not have a largest possible value?"

      Sure, I just don't see how the set of natural numbers is one of these. Since we have 'numbers' like infinity that we can use, at any rate. Take away that concept, and then yea, there is no largest natural number.


      For the love of God... didn't we just spend a day or two showing that "natural numbers" does not include infinity? If you want a set that is "natural numbers plus infinity", by all means go ahead, but call it something else!

      In some way, the equations infinity + 1 = infinity, and 1/infinity = 0 are wrong. It is just that we can usually ignore the rounding error.

      This is not computation, this is math, there is no rounding error. If you allow me to add 1 to infinity, then the result must either equal infinity or not make any sense. Here's a brief outline of why:

      infinity + 1 > infinity -- This makes no sense, because infinity is defined as being something which is greater than all the other members of the set, but now we just found one that's even greater.

      infinity + 1 < infinity -- If you add 1 and get a smaller number, something is seriously wrong.

      infinity + 1 = infinity -- This is at least somewhat self-consistent.

      The proper answer is to disallow the operations that let you prove things like 1 = 0. For example, saying that infinity + 1 = infinity is fine, and even intuitive. However, we should not be allowed to say that infinity - infinity = 0. Similarly, saying that 1/infinity = 0 is ok, but infinity/infinity = 1 is not. Or you can simp

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    19. Re:One can do even faster... by tehdaemon · · Score: 1
      Yes, it would. In fact, you can do a lot of useful things in graph theory by defining a semiring with the "usual" operations over the the reals union plus and minus infinity. However, you have to be very careful about what operations you allow and how they work.

      I have wondered about this before. Things like tan(x) would be continuous functions. Thanks.

      infinity + 1 > infinity -- This makes no sense, because infinity is defined as being something which is greater than all the other members of the set, but now we just found one that's even greater.

      infinity + 1 infinity + 1 = infinity -- This is at least somewhat self-consistent.

      The proper answer is to disallow the operations that let you prove things like 1 = 0. For example, saying that infinity + 1 = infinity is fine, and even intuitive. However, we should not be allowed to say that infinity - infinity = 0. Similarly, saying that 1/infinity = 0 is ok, but infinity/infinity = 1 is not. Or you can simply disallow all operations on infinity, but then one wonders why it's polluting our otherwise nicely consistent set."

      Mostly agree. I especially like "This is at least somewhat self-consistent." I think you could also say 'most consistent' as well, just not completely consistent. I would like to point out that the reason that infinity - infinity != 0 is because infinity + 1 = infinity. I suspect that infinity is not consistent with addition. For example:

      1 + infinity - infinity = ?

      The answer depends on the order of operations - do we do the 1 + infinity first or the infinity - infinity? But, addition is not supposed to depend on the order of operations. This is similar to your (a + b) + c = a + (b + c) example from one of your earlier posts. Which BTW depends on infinity - infinity = 0 being true. So, which should it be? Or is there any completely consistent system? It seems that it would require infinity + 1 to be undefined, and instead use the limit of I + 1 , as I -> infinity to be infinity (as it is). Or in other words, in any equation that involves infinity, you must use 'limit of f(x) as I -> infinity' and not 'equals'. And as you said, "The difference between the two concepts [sum and limit] is enormous"

      The limit of 1 / I, as I -> 0 is infinity. but 1 / 0 is undefined, not infinity. Just so 1 / I as I -> infinity is 0, does not mean 1 / infinity = 0 too.

      To look at an integral as an infinite sum of infinitesimals is to define an unsolveable problem, but looking at it as a limit is a problem that can be solved. I suspect this is the reason mathematicians stopped thinking this way, not because it doesn't make sense, but because it doesn't work. Remember, Newton was not primarily a mathematician, he was a scientist who had to invent his own math tools. It had to work for it to be of any use to him.

      "didn't we just spend a day or two showing that "natural numbers" does not include infinity?" No. you waved at it with a tautology and a series that said nothing about it, and then threw in a definition (that has some value at least) What I was trying to point out is that that definition is inconsistent. I'll try again. After that, it may be best to agree to disagree. (although I have enjoyed the conversation)

      The value of each of the natural numbers is equal to the number of natural numbers less than or equal to itself. This property is why they are useful as, and called the 'counting numbers' You can count things with them. By definition the number of natural numbers is infinite. Since the value and the number of values are linked, if the number is infinite then one of the natural numbers must have the value of infinity. If you don't have one with the value of infinity, then you don't have an infinite number of them, or at some point before you reach infinity the relationship between value and number must break down. Specifically, for some N in the natural numbers, there must be more natural numbers less than or equal to N than N. If that is true, well mabe I don't want to see the proof, the proof that 1 is greater than 0 that my roommate did was bad enough :)

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  46. Huh? by Anonymous Coward · · Score: 0

    I thought that was what overclocking was for...

  47. math analysis. clever algorithm by slashnot007 · · Score: 5, Informative

    Problem: find a number larger than the median

    proposed solution: pick 1000 entires at random and retain the highest.

    analysis: at first glance it might seem that the problem seems ill formed since the size of the array is not specified. But note that this is not a parametric problem. You are asked for the median, so the actual numerical values of the array irrelevant, only the rank order. Some wiseguys here have suggested returning the largest double precision number as a gaurenteed bound. While a wise ass answer it does raise a second interesting false lead. Even if the number were represented in infinite precision and this could be aribtrarily large or small the proposed solution does not care. Again this is because all that matters is the ranking of the numbers not their values.

    COnsider the proposed solution. pick any cell at random and examine the number. if this number is returned there is a 50% chance it is equal to or greater than the median of the set. (if this is not obvious, dwell on the meaning of the word median: it means half the numbers are above/below that number.). So the chance it is below the median is 0.5. if you choose 1000 numbers the chance that all are below the median is 0.5^1000 which is roughly 1 part in a google.

    So the author is right, this algorithm fails less often than the probability that there is a cosmic ray that corrupts the calculation or their is a power blackout in the middle of it or that you have a heart attack.

  48. This would require a new paradigm by EndlessNameless · · Score: 1

    For this sort of idea to be successful at the hardware level, we would have to make a fundamental change in the way we view the general-purpose processor.

    Right now, at the level of assembly or microcode, it's a deterministic machine that takes known, valid, and limited combinations of inputs and produces outputs that are (or should be) entirely replicable from one piece of hardware to the next.

    Leveraging the an inherent uncertainty would require that the underlying algorithms account for its existence. At most, present silicon designs acknowledge that "errors" occur and attempt to either catch or correct the errors in flight. Uncertainty has no such things as errors--only variance.

    In order for this approach to be truly successful, the fundamental method of teaching flow control to undergraduate programmers will have to change from something resembling a flow chart (hey, it's how I was taught) to something resembling a Monte Carlo analysis. I couldn't even begin to imagine how we would have to reconceive or reimplement some types of data structures... for instance, looking up anything in an array by its index number certainly becomes an interesting proposition in the proposed environment. Something as useful and fundamental as sequential reads becomes impossible in such an "uncertain" environment, unless you have a specified "certain" region of the CPU that processes code similar to the ways that existing ISAs do.

    --

    ---
    According to the latest ruleset, this post should be modded as Vorpal Flamebait +5.
  49. How about taking a ./ login... by Anonymous Coward · · Score: 0

    and making a beowulf cluster out of it, oops... Damn! all your joke belong to us!

  50. fuzzy code vs fuzzy data by v1 · · Score: 1

    Something that was not raised was what the randomness applied to. If you're dealing with an error factor in the fabrication of the processor, you are going to more than likely alter the program running on the machine. Even a single instruction being altered in most programs generally leads to catastrophic failure of the program. Now on the other hand, if the data was being handled with 30% inaccuracy, I believe that 9assuming the program didn't crash as a result of absurd data) what we got out would be worse than worthless. A small change in initial conditions in many algorithms leads to a major change in the output data. (the "butterfly effect")

    I can only see this 'error margin' having very limited applications, where a small gain in speed is worth severely impacting the probability of correctness. Most of what we do with computers is done because we need deterministic results - every time we add 2 and 2 we NEED to get 4. In those cases, 3.999997 is no better than 115, it's still not 4.

    --
    I work for the Department of Redundancy Department.
    1. Re:fuzzy code vs fuzzy data by hugg · · Score: 1

      There are some mathematical algorithms that could still operate on a slightly-nondeterministic machine. The Miller-Rabin test is an algorithm to determine whether or not a given number is prime, by trying to find "witness" numbers to its compositness. (http://en.wikipedia.org/wiki/Miller-Rabin_test) The more numbers you search w/o finding a witness, the more likely you are to have a prime number. By choosing a high enough number of iterations, you can prove that the probability that the number is prime is higher than the probability that the machine had a hardware fault -- that is, true for all practical purposes.

      It seems that if there was a CPU that returned wrong answers occasionally, you'd simply have to run more iterations of this algorithm to make it have the same confidence level. I can think of other areas like optimization and search where nondeterminism would not be totally unwelcome, and might be even beneficial.

    2. Re:fuzzy code vs fuzzy data by Anonymous Coward · · Score: 0

      fuzzy code + fuzzy data = fuzzy math

  51. Hybrid machines. by headkase · · Score: 2, Interesting

    It seems to me that these chips would not replace the standard digital cpu's we have today, however they would instead complement their abilities. Adding a stochastic simulator chip would create a hybrid digital/probabilistic computer. Depending on the type of information that was being processed different chips would be employed. Your intel/amd chip would still do the digital/lossless functions while the stochastic chip would process data that is more resistant to loss of information or lossy.

    --
    Shh.
  52. GPU-like rather than FPU-like by buckhead_buddy · · Score: 3, Insightful
    While FPU calculations still require the precision, reproducability, and speed limitiations currently applied to all CPU chip work, this article seems to be aiming at loosening up the precision of calculations we don't really need right now.
    • the initial JPEG lossy compression
    • the texture mapping of blood splatters in first person shooters
    • mp3 playback for people who don't care about things like fidelity and consistency
    • voice compression in internet telephony
    • barcode analysis when using a symbology developed in the days of 72 dpi printers but where everyone today uses 1200dpi readers and printers.
    • people deliberately trying to add entropy for security or artistic reasons.

    I seriously doubt any accountant, music snob, or cs major would allow the main cpu to become inconsistent, but if Apple or some other trendsetting company offered a new computer with a "Right Brain" chip just for these entropic applications I'd expect it to start a whole new fashion in desktop computers.
    1. Re:GPU-like rather than FPU-like by Gil-galad55 · · Score: 1

      What a fascinating idea! Since there are so many processes nowadays that are not precision-critical, a co-processor that could take advantage of a bit of indeterminism for a significant speedup would be more than worthwhile. This would even work in nicely with the Cell processor... units would be classified by precision. I think some work would have to be done on error-correcting coding, though. Anyway, I'd mod you up, but I already posted :)

      --

      To follow knowledge like a sinking star, / Beyond the utmost bound of human thought. ("Ulysses", Tennyson)

    2. Re:GPU-like rather than FPU-like by Lord+Crc · · Score: 1

      the initial JPEG lossy compression

      Just because JPEG is lossy does not mean it can be encoded using "lossy" circuits. The reason it is lossy is the same as if you were to store a 24 bit image using 16 bits. However, the way it does this and stores the image is NOT fault tolerant.
      Disregarding the huffman compression (which must be coded/decoded using exact circuits), a slightly wrong value in one of the coefficients can result in an entire 8x8 block of wrong color.

  53. Warning: your password doesn't match... by jamesh · · Score: 1

    ... but it's close enough. Welcome to your computer.

    1. Re:Warning: your password doesn't match... by rbarreira · · Score: 1

      Actually it should be something like:

      "Warning:-) your passwor*/d doesn't m@@atch... but its closEnouWelcomour computer."

      --

      The AACS key is NOT 0xF606EEFD628B1CA427BEA93A9CA9773F
  54. hardware unpredictability isnt software NPRDCTBLT by distantbody · · Score: 1

    what i means is, hardware unpredictability is different to software unpredictability. i would feel much safer with software unpredictability (altho not ideal) as it is easier and more cost effective to fix. i would like to come up with a good analogy here like "theres a one in a billion chance that an asteroid would destroy earth, but when your on the smelly end of the luck stick...". it isnt exactly easy to make secure,reliable,consistant etc.software on /predictable/ hardware as it is, let alone on /upredictable/ hardware, however non-critical or buffered the app may be. in conclusion, i would welcome a 'tru-random' co-processor which is physically seperate from the 'predictable' chip and is only used where random-ness is /required/.

  55. But... by vistic · · Score: 1

    Johnny 5 could recognize a chair or a face... he could even see shapes in the clouds! Your whole argument fell apart at the end, hah!

  56. Re: Russ Nelson by IgnoramusMaximus · · Score: 1
    From a cursory reading of the Russ Nelson's "angry-economist" site I concluded that he is simply batshit insane .. and now also a racist, which I guess goes hand-in-hand with being insane...

    I recomend for people to read his site (but only after getting intoxicated, that way the danger of mental damage will be lessened and things might actually make sense ... in a dancing-pink-elephants sort of way)

    The fact of him being the president of OSI (never you mind a high-ranking member) casts an extremely negative light on that organization.

  57. Perhaps transistor obsolete in the future by pr0nsurf3r · · Score: 0

    Keep in mind that the transistor is an analog device that we have nearly pressed to its limits for digital devices. Check this out: http://www.hp.com/hpinfo/newsroom/feature_stories/ 2005/05crossbar.html

  58. Modems and radios have worked that way for years by Animats · · Score: 1
    There's a well-developed theory of how to maximize data transmission through a noisy channel. You can use more power or more redundancy. There's a tradeoff and an optimum, and most modern transmission systems work near it. Modems (including DSL), digital radio systems (including cell phones), and recording media (including DVD and CD) all operate below the threshold where all the bits get through correctly. Redundancy and error correction is used to compensate.

    The optimal error rate before correction is typically low. A few percent, tops, even for forgiving applications like cell phones.

  59. ohsnapthepopeishere by Anonymous Coward · · Score: 0

    Yay Gatech! Finally...

  60. These guys... by aztektum · · Score: 1
    --
    :: aztek ::
    No sig for you!!
  61. instability not activated in windows SP2 by SCVirus · · Score: 1

    Intels new 'instability' is not yet usable by windows. Microsoft has announced that Service Pack 3 will add support for this enchancement. http://www.breakmygentoo.net/ already has hacked support for this new feature! In other news IBM has announced that they will be unveiling a new microprocessor that will be 900x more unstable then anything Intel has to offer.

  62. Re:math analysis. clever algorithm by grammar+fascist · · Score: 1

    ...if the values in the array are distributed randomly (or a reasonable approximation thereof). If they're not, you might just be screwed.

    --
    I got my Linux laptop at System76.
  63. The Uncertain Airbag-Married. by Anonymous Coward · · Score: 0

    Well it's nice to know that my night out on the town, will not set off the "airbag".

  64. Not quite right by Anonymous Coward · · Score: 1, Interesting

    Actually the problem isn't speed or the number of transistors, the real problem is feature size. Current technology (the state of the art) is 90 nm. With larger features (transistor dimensions), you might have 100 million electrons turning 'on'. There is the 1 in a million chance that one of them might randomly jump 'off', but the average wins. Most stay put. As features get smaller, Heisenbergs uncertainty principle reaches out and bites certainty in the ass. So 'nearly impossible' becomes 'statistically probable' as feature size gets smaller. One in a billion becomes one in a thousand or one in a hundred (or one in ten). If it's the banks computer, my account, and a billion dollars in my favor, then: God Bless you Mr. Heisenberg!

  65. Re: Border conference? by Anonymous Coward · · Score: 0

    I've heard rumor that the folks at Georgia Tech are getting together with the paranormal psychics at Princeton that threatens to border on insanity.

    Can anyone tell me directions on how to get there? I personally prefer to drive on the disordered side of the border as I don't like feeling constrained.

  66. DVD-ROM is better by SanityInAnarchy · · Score: 1

    This is not a troll, but an objective observation. Take any given rented, badly-scratched DVD, pop it in an off-the-shelf DVD player, get tons of artifacts, stuttering, etc. Pop it in a PS2 (which is DVD-ROM in theory), and watch the video almost stop playing. Pop it in a Lite-On DVD-ROM drive, watch it play all the way through, at most stalling for a second or two at the bad parts.

    It's true that, scaling up, it may be better to have a six billion by four billion pixel display that has 90% accuracy than a 640x480 display with 100% accuracy, but I'd have to see it work, and keep that inaccuracy the HELL away from my CPU!

    --
    Don't thank God, thank a doctor!
  67. Error correction by jmv · · Score: 3, Insightful

    I'm surprised nobody has really mentioned error correction. In the same way that correction codes can work around RAM unreliability, you could have checksums built into each instruction to detect and correct errors. You would basically trade speed for reliability, something that has existed in communications for decades (refering to Shannon's work). I don't see why it wouldn't be the same for CPUs. I also remember clearly Richard Feynman proposing the idea (sorry, don't remember which book), so the idea isn't exactly new.

    1. Re:Error correction by evilviper · · Score: 1
      In the same way that correction codes can work around RAM unreliability, you could have checksums built into each instruction to detect and correct errors.

      Question is, how do you intend to do that?

      With RAM, it's trivial... The data you put in SHOULD be exactly the same as the data you get out. However, with a CPU, you put in a few numbers, are you get entirely different numbers back. How could you possibly checksum that?

      I do have a workable alternative in-mind... You just need multiple chips, performing the same operations. I would suggest 3, but it could work with just 2...

      All you do is send an operation to multiple CPUs at once... They will all return an answer, and you merely have to compare those answers. If all three answers are different, you discard the result, and re-send the operation to the CPUs. If perhaps 2 agree and 1 disagrees, depending on just how unreliable these CPUs are, you may want to use the result agreed to by the majority, or you may want to retry until you get a unanimous result. With only 2 CPUs, it's very simple. If they agree, use it, if they don't, retry. Though your odds of getting wrong answers increases as the number of CPUs decreases.
      --
      Slashdot gets worse every day... Pipedot: News for nerds, without the corporate slant
    2. Re:Error correction by Detritus · · Score: 1

      IBM did this in some of their large computers. They could detect errors in instruction execution and retry the instructions. It involved adding check-bits to operands and testing the results for certain properties This was one of those computers that could detect flakey hardware and automatically call IBM field service to schedule a service call to replace the bad boards.

      --
      Mea navis aericumbens anguillis abundat
    3. Re:Error correction by Anonymous Coward · · Score: 0

      That was soooo 1940's, dude.

      There's only 47 BAZILLION ways of doing what you think is impractical.

    4. Re:Error correction by buckhead_buddy · · Score: 1
      Why not leave part of this up to the user to decide the tradeoff in some situations? Just as we have the concept now of volume and brightness being properties that a user can adjust depending on the application and whims.

      Imagine a media player or DVD app. As one tries to playback a several videos on a machine with a slow "left brain", the display drops frames, skips, and jerks as it presents each frame extremely accurately. The user cranks up a gui widget that looks like a volume knob on the window, and this actively funnels off co-processing tasks to the "right brain" processing chips in the system. The playback becomes more fluid at the expense of color accuracy and perhaps even adding a bit of static.

      The programmer provides default values, but the user is able to actively adjust and find the level they're comfortable with. If they're unable to find a good tradeoff, they can upgrade their right brain chip (probably a cheap thing to do) if speed is what they perceive to be the problem. If they find that they just can't accept the inaccuracies introduced, then upgrading the left brain and completely lobotomizing the right brain altogether for this application is their option.

      Some programmers might perceive no need for inaccuracy and set the defaults of their program to allow no math inaccuracy in their Excel spreadsheet or Quicken checkbook calculations. But a frustrated grad student trying to see some vague trends in civil war death statistics over absurdly massive (but extremely accurate) data collections might be willing to crank up the lossiness of their calculations to at least get a vague idea of the patterns in their graphs. They'd need to remember to crank up the accuracy again for the final stats, but at least they could find where the "interesting" parts of these mountainous collections are in hours rather than waiting for five days for the stats to run, (then re-run after having made a trivial mistake).

      As an example, it seems that Apple is refactoring some of their Aqua anti-aliasing GUI code to use GPU speed if available in precisely this kind of lossy way. I wish they'd go a few steps further and do something like this to the CPU instruction set and providing a control widget for users (like me) who would really like to control the speed-hit vs. beauty-level in my GUI.

      We've had spreadsheets since the days of the Apple 2's 8-bit processors. Despite accountants insistence on complete accuracy, they found tools and techniques that worked well when they needed the speed rather than the accuracy. CPU's with a rated level of inaccuracy would be a useful thing to have even if mathematicians and accountants don't want to admit that today.

    5. Re:Error correction by Anonymous Coward · · Score: 0

      Quis custodiet ipsos custodies ?

    6. Re:Error correction by evilviper · · Score: 1

      That's not a bad idea, but likely extremely difficult to program.

      You have to divide your programs up into seperate components, that can be run on entirely seperate CPUs (and RAM?) depending on whether they require accuracy or not. I believe, of the CPU-intense tasks that most people perform (encryption, encoding, gaming), the only part that really stands to operate reasonably well is video output, and that is (mostly) handled by videocards, not CPUs, in the first place. Certainly, ASICs that aren't 100% accurate would be perfectly fine in computers, but other than that, I fail to see many uses that would make the extra complexity worthwhile.

      --
      Slashdot gets worse every day... Pipedot: News for nerds, without the corporate slant
    7. Re:Error correction by evilviper · · Score: 1
      This was one of those computers that could detect flakey hardware and automatically call IBM field service to schedule a service call to replace the bad boards.

      Do you know what models of IBM systems these were? I would like to find some specifics.
      --
      Slashdot gets worse every day... Pipedot: News for nerds, without the corporate slant
    8. Re:Error correction by Detritus · · Score: 1

      You might start with the IBM ES/9000 series, which was the last of the ECL mainframes. See Fault-tolerance design of the IBM Enterprise System/9000 Type 9021 processors. Later systems were based on CMOS microprocessor technology. See here for an issue of the IBM Journal of R & D devoted to the IBM S/390 Server G5/G6 systems. Automated failure analysis has been an important feature of IBM's large systems for many years. IBM has a great amount of information on their web sites.

      --
      Mea navis aericumbens anguillis abundat
    9. Re:Error correction by evilviper · · Score: 1
      From the first link:

      the only way to achieve 100%
      concurrent error-detection coverage is to use complete replication along with appropriately placed comparison circuits.

      Aye, there's the rub...

      They describe methods for checking some instructions, but admit they cannot verify all are correct. Their goal is detection of a failing piece of hardware, not 100% accuracy from known-unreliable hardware. Their methods are entirely appropriate for their purposes, but not for this senario.

      Were you (and the OP) assuming the use of unreliable processors only for a few specific operations? Operations that could reasonably be checked? Perhaps would explain the disagreement.

      Those documents were an interesting read in any case. They probably could have been a quarter as long without all the IBM marketing fluff, however.
      --
      Slashdot gets worse every day... Pipedot: News for nerds, without the corporate slant
  68. Re:math analysis. clever algorithm by kasperd · · Score: 1

    if the values in the array are distributed randomly

    That doesn't matter. The analysis never said anything about the distribution of the numbers in the array. You may assume a worst case distribution of the numbers in the array, and the algorithm still works. Probability is meassured over random choices made by the algorithm, not over inputs. So given an input, you can compute the probability that the algorithm fails, which is always going to be a small number. Then you take the input giving the highest error probability (and now we are no longer assuming random choices, but deterministically chosing the worst case input). Since all the probabilities are small, even the largest of them will be small. This way of analysing error probabilities shouldn't come as a surprise, because that is how it is always done when considering probalistic algorithms.

    --

    Do you care about the security of your wireless mouse?
  69. future predictability by Anonymous Coward · · Score: 1, Funny

    Just build in a random-number generator!

    1. Re:future predictability by bhima · · Score: 1

      Only old Korean people use those

      --
      Nothing in the world is more dangerous than sincere ignorance and conscientious stupidity.
  70. My, my, my; where do I start? by grep+-v+'.*'+* · · Score: 1

    I guess I'm become an old fogie and hadn't noticed it. "...leads to varying degrees of unpredictability, which used to be a no-no word in the microprocessor world."

    Sounds like they're breaking the "Principle of Least Astonishment" - the result of performing an operation should be obvious, consistant, and predicatable. (Or for GUIs, the most usable system is the one that least often leaves users astonished.) They're equivalent.

    "unpredictability becomes a great asset leading to energy conservation and increased computation speeds."

    Why yes, if you don't have to be right, you can greatly increase the computation speed and save power at the same time -

    10 PRINT "PI=3"
    20 END

    Who needs sites like:
    www.ualr.edu/~lasmoller/pi.html
    www.cecm.sfu.ca/pi/pi.html
    www.bath.ac.uk/~mfws20/having_fun_with_pi.html
    with my better program above?

    Want it more unpredictable? Use: 10 PRINT "PI=";RND()
    Want it even faster? How about: 10 END
    That program is so fast and unpredictable it didn't bother to print out the answer.

    And hey, energy conservation? That's easy, just examine the power-on bit a few times until it changes state. You'll then have all of the power you want, since your server just unpredicatably powered itself off.

    (I'm ignoring the obvious Pentium math coprocessor jokes, that's much too easy.)

    " excessive heat is now a major obstacle for speed-demon chips.... A lot of this heat stems from today's deterministic approach to chip design, Palem notes. The chip gobbles large amounts of energy to be absolutely certain that each data bit is either a 0 or 1 at every step of a calculation."

    Hey, I can't wait for my bank to get hold of one of these --
    1) deposit a dollar,
    2) withdraw a dollar,
    3) check my account for a unpredictable event - like my account balance got stored with the leading bits flipped (NO not the sign bit!)
    4) If balance is 0.00, GOTO 1 (http://www.acm.org/classics/oct95/)
    5) PROFIT!!!

    --
    If the universe is someone's simulation -- does that mean the stars are just stuck pixels?
  71. Unpredictability by MemoryDragon · · Score: 1

    Is nothing more than statistical likelyness... same things were done in various fuzzy algorithms in the past. So what you do is to feed input in and get a likelyness of something. The problem is likelyness only works in an endless domain, you feed something in and you get a likelyness which is true to 100% over endless seeds during an endless period of time. A snapshot back in time always will give a significant number of false positives or negatives. The main problem is, that if you apply those methods to concrete problems which are correlated to randomness and try to earn money from it you usally end up loosing a lot of money. People tried that in the past with gambling and trying to apply statistical methods into it and failed and from what I can see here, you end up with a fuzzy chip and likelyhood in hardware and you will get the same results in stock brockerage as you already are getting by applying current methods onto the same problems of psychology, basically garbage. But the chips are interesting however, for all fields where you really need some kind of fuzzyfication problem (which is alsmost everywhere where you know how to apply that stuff in a serious manner of trying to predict something on a statistical base), but it definitely is not the golden goose which suddenly gives you the total control over stocks. The whole stock brokerage thing reminds me on the middle ages where scientists tried to gather funds by promising to turn lead into gold while working on their own things.

  72. Meteors will destroy advanced fabrication plants! by Anonymous Coward · · Score: 0

    ...and the 386 will regain it's majesty as KING OF CPUS!

  73. Is it just an accident? by Corpus_Callosum · · Score: 1

    Is it just an accident (pun intended) that Slashdot ran this story at the same time as the current one on including random processes on-die?

    Kinda spooky (or is it the global collective consciousness expressing it's desire to us, the technical geeky guys, to do it's will)...

    --
    The reason that it can be true that 1+1 > 2 is that very peculiar nonzero value of the + operator
  74. Re:math analysis. clever algorithm by myukew · · Score: 1
  75. I haven't RTFA but... by curious.corn · · Score: 1

    ... thinking about the headline it musn't be bad at all. He's not advocating flipping opcodes in a cpu and going with the joyride guys. Currently chips work on full swing voltages, beefy noise margins and quite conservative settle timings. In signaling theory there's a lot more than that and the telecomm people developed elaborate modulation schemes that permit data encoding and very good error rejection. I'm talking out of my ass but there are codes that reliably pack a lot of data; why shouldn't computing equipment take advantage of that instead of GHz morse code? RAM and peripherial interconnect could use coherent modulation today rather than go optical (which is still On Off Keying after all) and pay for the mixed subtrate process costs. OOK has been a simple and reliable model for logical circuitry, but today we have enough processing & modeling horsepower to develop stuff that makes better use of the bandwidth.

    --
    Mi domando chi à il mandante di tutte le cazzate che faccio - Altan
  76. Great... by Oswald · · Score: 1
    Chips will get faster and faster, but with more and more uncertainty until we have computers that can understand everything in a split second, but with a 50/50 chance of being wrong.

    We're inventing Dad.

  77. The Bank and The Pizza Parlor by Ancient_Hacker · · Score: 1
    My father used to say sometimes:

    "We have an agreement with the bank, they don't make pizzas and we don't cash checks"

    Going to Business Week for accurate technical articles is like going to Phrack to get the latest prime rate prediction. Like having Paris Hilton teach string theory (not the -bikini kind). Like asking Janet Jackson to teach classes in modesty. Like having Dick Cheney lead the Andes 10-mile run.

    1. Re:The Bank and The Pizza Parlor by HeghmoH · · Score: 1
      --
      Mod down posts with a "Free Mac Mini/iPod" sig, they're spam!
  78. Could this be.... by TFGeditor · · Score: 1

    ...the first baby-step of emerging silicone-based sentience?

    --
    Ignorance is curable, stupid is forever.
    1. Re:Could this be.... by museumpeace · · Score: 1

      Uhm, I think "silicone-based sentience?" would refer to something like Anna Nicole Smith.

      --
      SLASHDOT: news for people who can't concentrate on work or have no life at all and got tired of yelling back at the TV.
  79. wrong again by Anonymous Coward · · Score: 0

    the median is -1.

  80. Re:math analysis. clever algorithm by Anonymous Coward · · Score: 0
    ...if the values in the array are distributed randomly (or a reasonable approximation thereof). If they're not, you might just be screwed.

    No no absolutely not. remember its the median were takling about. the whole whole analaysis is non-parametric meaning the array value are irrelevant to the analysis.

    to see this, sort the array, now replace every number in the array with its ordinal position in the sort. does this change the problem? no. same analysis.

  81. Re:YUO FAIL IT? by Anonymous Coward · · Score: 0

    I'm familiar with the project here at Tech.
    It doesn't work because the premise behind the chaos in the information is fundamentally flawed. The subthreshold characteristics aren't particularly reliable. It's genius, if you don't know the technology behind it.

  82. Re: Russ Nelson by joe_plastic · · Score: 1

    http://slashdot.org/~squiggleslash/journal/97860 says it got resolved. He created lots of criticism because of his statements on his blog, that's for sure.

  83. Sorry, bad example by buckhead_buddy · · Score: 1
    Lord_Crc pointed out:
    Just because JPEG is lossy does not mean it can be encoded using "lossy" circuits. The reason it is lossy is the same as if you were to store a 24 bit image using 16 bits. However, the way it does this and stores the image is NOT fault tolerant. Disregarding the huffman compression (which must be coded/decoded using exact circuits), a slightly wrong value in one of the coefficients can result in an entire 8x8 block of wrong color.
    You are clearly more experienced in this area than I am; this was probably a bad example. Forget I mentioned initial jpeg compression. (Though perhaps in rapid display of jpegs such as an iPhoto slideshow or screensaver the lossiness would be more acceptable.
    1. Re:Sorry, bad example by Lord+Crc · · Score: 1

      You are clearly more experienced in this area than I am; this was probably a bad example. Forget I mentioned initial jpeg compression. (Though perhaps in rapid display of jpegs such as an iPhoto slideshow or screensaver the lossiness would be more acceptable.

      Didn't mean to sound terse, just trying to point out that "all losses are not equal", or something like that. However, like you suggest, I can see that for very specific domains it can be usefull. (For rapid display of jpeg though there's a smarter way: Don't decode all the information. Only decode 2x2 of the coefficients or even less).

  84. Neural nets by cpghost · · Score: 1

    reminds me of a neural net

    That's indeed a good point. Considering that neural nets consist of zillion of cells that all compute the same function, a few of those cells returning bogus results (because they are unpredictable) wouldn't really pose much of a problem w.r.t. the final results.

    Of course, every program out there would have to be rewritten as a neural net. Regular von-Neumann programs would not stand a chance in systems without error-correcting codes.

    --
    cpghost at Cordula's Web.
  85. Re:YUO FAIL IT? by chrome · · Score: 1

    I was talking about the OP. :)

  86. unpredictability = insecurity by Anonymous Coward · · Score: 0
    or if harnessed correctly means more security... hmmm, maybe this pattern is a repeat?

    I think it is one of those ol' "used properly you can gain great benefit, but used improperly you stand to fall back further than before" issues myself. Take OSS and its chaotic nature. Sure there are some efforts to try and establish some real engineering, but those are usually avoided by Johnny Hacker. I don't imagine this is any different.

    If such unpredictability is basically narrowed down, then you can use it in a predictable way. Oh and to those that are throwing around the term "Entropy" please just make sure you are using it correctly... most don't. We don't need yet another term being bastardized by a society who thinks they are too smart to check their facts.

  87. Animaniacs song by JimTheta · · Score: 1

    I was thinking of a different song...

    "It's a great big universe
    and we're all really puny
    we're just tiny little specks
    about the size of Mickey Rooney..."

    Classic, second only to their countries-of-the-world song.

  88. This should be modded Funny, not Flamebait by haruchai · · Score: 1

    although it's doesn't really apply to Windows 2000 and later.

    --
    Pain is merely failure leaving the body