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Bitcoin Hardware

Bitcoin Mining Tests On 16 NVIDIA and AMD GPUs 403

Vigile writes "For users that have known about the process of bitcoin mining the obvious tool for the job has been the GPU. Miners have been buying up graphics cards during sales across the web but which GPUs offer the most dollar efficient, power efficient and quickest payoff for the bitcoin currency? A series of tests over at PC Perspective goes through 16 different GPU configurations including older high-end cards through modern low-cost options and even a $1700+ collection with multiple dual-GPU cards installed. The article gives details on how the mining programs work, why GPUs are faster than CPUs inherently and why AMD seems to be so much faster than NVIDIA."
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Bitcoin Mining Tests On 16 NVIDIA and AMD GPUs

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  • How much is that in Bitcoins?
    • About 121 bitcoins at the current exchange rate.
    • 121 bitcoins at current exchange rates. It'd take you about 4 months to make that using that machine. Of course, that all depends on the market for bitcoins which is anyones guess.
      • Plus the electricity, to run that machine flat out for four months, which I imagine will be way more than pocket change.
        • Re:$1700+? (Score:4, Informative)

          by WaywardGeek ( 1480513 ) on Wednesday July 13, 2011 @10:38PM (#36758024) Journal

          I built a bitcoin mining machine two weeks ago. There's more you should know that TFA only hints at. First, check out these graphs. [] The total CPU power competing for the 50 BTC generated every 10 minutes has increased 10X every quarter for 6 quarters, and soon, it will drop to 30 BTC every 10 minutes. If you think you can make money given that bitcoin value is flat or falling, while you have to split pay outs with more miners every day, well... ha ha! That's a good one.

          That said, I'm a happy miner. I was looking for an excuse to build a gaming machine anyway, and I was able to do a decent machine for about $430, with an HD5770 doing just over 200 MH/s. Even if I earn nothing for mining, I'm still glad I built the machine. I needed another Ubuntu server anyway, and the mining only loads the CPU 1%. Next year, I plan to put Windoz on it and give the machine to my son. I can hardly wait to see what he thinks of the graphics.

  • Thank god (Score:4, Funny)

    by Anonymous Coward on Wednesday July 13, 2011 @07:05PM (#36755818)

    Did you know that it's been nearly a week since the last Bitcoin story on Slashdot? I was worried that the standards were changing and blatant slashvertisements for bitcoin were no longer getting through! Never been happier to be proved wrong.

    • Re:Thank god (Score:5, Insightful)

      by geekd ( 14774 ) on Wednesday July 13, 2011 @07:26PM (#36756010) Homepage

      Bitcoin is the PERFECT Slashdot topic:

      Open Source
      Peer to peer
      Computer Hardware

      THAT'S why it shows up so much. What's not to like?

      • +1

        I never understood why so many /.'ers speak so vehemently against Bitcoin, which has so many interesting comp sci. aspects, or even just social experiment. No-one's going to force them to go out and exchange any of their 'real' money for BTC.
        I figured in the end it was so they can be in the elite, cynical 'I told you so!' chorus if it fails.
        According to some, even the stories about MtGox being hacked were somehow "slashvertisments" for BTC
      • by Trogre ( 513942 )

        All those wasted CPU/GPU cycles that could have gone towards something actually useful, like F@H.

    • And before that, the last article was two weeks previous.

      Seriously, people are exaggerating how often we get a bitcoin story. Yes, for a short period we got them near daily, but now they're a lot more infrequent.

    • currency! First one to post a verifiable signature on a Slashdot story gets a Slashcoin. Taco and crew are then our new federal reserve--they can inflate the currency to pay our debt to China by posting more duplicate stories!

      Our problems are solved!

  • folding@home etc (Score:5, Insightful)

    by jaymz2k4 ( 790806 ) <> on Wednesday July 13, 2011 @07:08PM (#36755844) Homepage
    With all that computation power being used I can't help but think about projects like Folding@Home and think it's a bit wasted on the sort of margins you'd be getting back - even at the optimistic high end (which don't factor in power costs).
    • Re:folding@home etc (Score:5, Informative)

      by Vigile ( 99919 ) * on Wednesday July 13, 2011 @08:43PM (#36756964)

      We did a follow up based on finding out how much it costs to run these Bitcoin operations and looked at retail energy prices across the US! I think the results are a big hindrance for mining... []

      • Strange, then, that the 'bitcoin isn't worth the energy it's minted on!' article isn't the one that made Slashdot headlines...

    • by Trogre ( 513942 )

      That's what bugs me about Bitcoin. Perfectly good CPUs and GPUs that people are willing to run at full pelt are wasted. Instead of contributing something useful to society (like with F@H as you mentioned), these processors are participating in nothing more than a lottery.

  • Misleading Article (Score:5, Interesting)

    by OverlordQ ( 264228 ) on Wednesday July 13, 2011 @07:10PM (#36755862) Journal

    Given that the difficulty increases exponentially [] you're not going to be making their calculated B$/day for the whole year, so while the quickest to pay of is 70 days if the difficulty increases at the usual rate, you'd probably want to add on another month or two.

    For the ones taking nearly half a year to pay off at the current rate, you'll probably spend closer to a year before you'll even break even.

    • But the value of a Bitcoin can vary with the difficulty. Right now its about 1 B$ = 14 USD but if the difficulty doubled the value could double to 28 USD.

    • I thought the same way, back in the good ol' days (March of this year...). I figured that the increase in difficulty would kill my profits, but a while later it turned out that the dollar price of bitcoins increased right in step with the difficulty so that the dollar return each day stayed roughly constant. (On 1.6 GHash/s, it hovered around $40/day despite huge increases in difficulty.) This persisted until about a few weeks ago, when it seemed to stick around $14/BTC.

      I agree that it's less certain that

      • by Kjella ( 173770 )

        But then, the risk goes both ways -- if bitcoins catch their "big break" and make it mainstream, the value can go up (again) faster than the difficulty.

        Except that it's all a bunch of guys sitting around saying "Pretty please start using our money, we've now printed trillions of monopoly money but are ready to sell you a hundred dollar bill" - you have to be pretty stupid to realize you will get screwed. And the longer it goes on and the less coins - compared to all the "old money" - you get, the harder you'll be screwed. Unless you can find a bigger sucker and get out in time. Pyramid schemes look good too, until the bottom falls out.

  • by Anonymous Coward on Wednesday July 13, 2011 @07:13PM (#36755892)

    Other than being a decent applied cryptography experiment, BitCoin has no real use in the real world. It isn't anonymous, it isn't backed by anyone that matters. The currency is too unstable to trust for anything. Its architecture gives a lot more power to people who come on early, and whom likely are going to cash out if people catch on.

    I'd rather hear about an Amiga emulator, checkered ball spinning while formatting an 880K floppy disk running on the nVidia hardware than yet another BitCoin article, because BitCoin reminds me a lot of the old MAKE.MONEY.FAST posts of yore.

    • by mysidia ( 191772 ) *

      Other than being a decent applied cryptography experiment, BitCoin has no real use in the real world. It isn't anonymous, it isn't backed by anyone that matters. The currency is too unstable to trust for anything. Its architecture gives a lot more power to people who come on early, and whom likely are going to cash out if people catch on.

      More power to people who come early.... sounds a lot like the domain name system....

      Speaking of which, perhaps Bitcoin transactions could be used to facilitate a repla

      • Speaking of which, perhaps Bitcoin transactions could be used to facilitate a replacement for hierarchical DNS, due to the public and forever verifiable nature of Bitcoin transactions, you have a distributed database much like DNS, that is also peer-to-peer and universally verifiable, a technology like Bitcoin would always be able to "prove" who asked to register for a name first, and if a bitcoin transaction was required for it to happen, the registration action be free, abuse/squatting would be self-limiting, "expiration" after X years of registration would not be required, and it could be made impossible for a central authority to revoke a name registration based on "legal" demands, DMCA, etc....

        Namecoin []

        Looking at that, it looks like it could actually work if adopted. They've got most of the basics down as far as I can tell, and what they really need now is user-friendly interfaces (currently CLI only).

      • As they mentioned, Namecoin is still in its infancy but serves exactly that purpose. There's even one (maybe two) Bitcoin/Namecoin exchange sites out there. Right now there's a fee to register domains, to discourage initial domain squatting, and those coins are lost forever into the ether, but that fee will eventually dwindle down to zero (no clue what the timeframe is though).
    • by Sycraft-fu ( 314770 ) on Wednesday July 13, 2011 @08:02PM (#36756468)

      All this hype is not coincidence, and it is not because bitcoins became useful suddenly. It is people hyping it to try and get others in to the market. They want to cash out, but can't in any large amount without tanking the value. Need to get new suckers lined up.

      • Re: (Score:3, Informative)

        by fireteller2 ( 712795 ) *

        That's a theory. I have a theory too. People who poo poo bitcoin despite it's obvious success, haven't actually done their due diligence on what it is and how it works.

        Bitcoin works for me. I use it to get work done and buy things. I can do this now, I don't need you to be involved, and I don't need to "cash out."

      • Ah, so it's like the stock market expect people can make money with it?

    • by fireteller2 ( 712795 ) * on Wednesday July 13, 2011 @08:13PM (#36756614) Homepage

      Interestingly bitcoin is working despite all the arguments for or against it. The only valid question with regard to the viability of bitcoin as a currency today, is "Is it a currency today?" and the answer is without question YES.

      Aside from the uses, for which there are now many (I have personally paid for survives, from freelancers around the world with bitcoin), approximately 7200 new bitcoins are introduced into the supply every day, and yet the value of the bitcoins has be rising over the past months. Even lately with the price off it's highs the constant influx of new bitcoins is not causing the bitcoin to lose significant value.

      Fairness of early adopters doesn't enter into it. Early adopters helped to lay the foundation of the security which backs bitcoins, and were compensated for that service. You can participate and be compensated for that service too.

      I would love to have been an Apple stock, gold or even U.S. dollar early adopter. But just because I wasn't doesn't me I should adopt now.

      If you don't like the idea of it as a currency, or a commodity, then just think of it as a software tool that allows you to move money electronically without friction (unlike any other monetary device in the world), and therein you will find it's value.

      • by Kjella ( 173770 )

        Bitcoins is still far more speculative than the worst of the dotcom stocks, that it has a small market where other speculators will work or provide services for bitcoins - or simply to "prove" they're not worthless - doesn't make it a currency. That imaginary value will disappear in an instant when the bubble bursts. I don't claim to predict when or how it'll happen, but it will. Though I suppose if you can time it correctly, you can turn into a millionaire like many of the dotcom founders...

      • by Sycraft-fu ( 314770 ) on Wednesday July 13, 2011 @10:18PM (#36757832)

        I see no evidence of this at all. No major stores take it, so you can't use it for any kind of serious commerce. It isn't exchanged on any reputable currency exchange. I've seen nothing done to address some serious flaws brought up (like the possibility of spending a coin multiple times before it is noticed or the built in deflation). I've seen no analysis of the cryptography by leading authorities.

        All I see is speculators playing around and people who think Cryptonomicron is an instruction manual not an entertainment novel.

        You compare it to Apple stock, I compare it to stock. Sure, there was a time when it was "worth" something and if you had gotten in and out in the right time you could make money. However as it was a stupid idea with nothing really behind it, it collapsed to nothing.

        • I take it your concept of success is not very incremental. An all or nothing kind of thing. I on the other hand see a technology that has only moved forward in terms of its uptake and usability, the exchange rate is immaterial to that although it as also moved up.

          I agree I would love to hear Bruce Schneier give it a bit of a public go over, but it is open source and anyone can review the code and the white paper. Many people have so far and no one has published a flaw. You can't double spend, don't know

  • I get it (Score:4, Interesting)

    by melikamp ( 631205 ) on Wednesday July 13, 2011 @07:16PM (#36755912) Homepage Journal
    So now it induces nerds to stock op on GPU hardware? I get it! BitCoin is not currency at all, is just a new game genre: MMOM (pronounced like "mom"), Massively Multiplayer Online Money. The hottest MMOM in town. Spread the word.
  • Slashgold? (Score:5, Insightful)

    by MikeTheGreat ( 34142 ) on Wednesday July 13, 2011 @07:23PM (#36755984)

    I keep wondering why do BitCoin articles keep showing up here. Any given article doesn't really seem quite nerdy enough to be real 'News For Nerds' (and yes, I agree that most of the articles here haven't been News For Nerds for a quite some time), and it's kind of a weird topic.

    I kinda feel like "BitCoin articles is to Slashdot as gold advertisements is to the Fox News Network".

    So I'm going to coin a term that we can add to the Slashdot Taxonomy (or the 'slashonomy', as I like to call it: :) ): Slashgold!

    As in:
    Random dude: "So, was the article good?"
    You: "Naw, it was just another fluff piece promoting slashgold"

  • by allanw ( 842185 ) on Wednesday July 13, 2011 @07:24PM (#36755990)

    I've always thought Bitcoin was stupid, but let's do some more analysis on the energy costs here, which this site really should have included.

    The best GPU perf/watt was the 5870x2 (Ares OC) at 1.584 (Mhash/s)/watt. Not sure where they got their total watt figures from, but from a review site, it is 500W [], unoverclocked. This site says it's 50W more overclocked. I'll be generous and not include this since the CPU isn't being taxed as much. So 500W power consumption.

    So, typing 500 watts * 1 year * (10 cents / (kilowatt*hour) []) into Google: about $482. Taking their $1,666 one year profit figure (mining profits - cost of card), it is now really a cost of $1,184. Which isn't as bad as I thought it'd be.

    They didn't include the effect of increasing difficulty on decreased mining speed, but theoretically the currency should become more valuable as it goes on.

    • by allanw ( 842185 )
      Sorry, a few typos: 500 watts -> $438 per year in energy costs, which makes for a total profit of $1,228.
    • the currency should become more valuable as it goes on.

      That is a bad thing. Deflation has very destructive effects on an economy.

      • by allanw ( 842185 )
        No comment about that. I was just pointing out that profitability should theoretically be the same as time goes on. Of course, whether it does will have a huge effect on the long-time viability of bitcoin mining for profit. Even if it only lasts a few more years, you can still make 100% returns on investment in only a year which is pretty good.
  • The performance of GPU-based codes is highly dependent on the video cards. I highly doubt the dismal performance of NVIDIA cards. I think the authors most likely optimized the kernel code to AMD cards. This is evident when you look at the CL kernel code and you see that there are so many hardwired constants and fixed arrays (aligned to 128 ints or longs). Moreover, the authors GUIMiner don't seem to take advantage of NVIDIA's more local workthreads (compared to AMD's).

    I'd say that declaring AMD a victor is

  • by Anonymous Coward on Wednesday July 13, 2011 @07:30PM (#36756044)

    Nobody cares about bitcoin. We don't give a rat's ass about bitcoin. Please stop posting stories about bitcoin. I don't know how many other ways there are to say it, but we don't give a fsck about bitcoin.

    • by Dunbal ( 464142 ) * on Wednesday July 13, 2011 @07:42PM (#36756198)
      They have to keep the hype going, it's the only way to feed the bubble.
    • Glad you're here to speak for the rest of us, anonymous coward. As a physicist and longtime slashdotter, I've always been willing to learn about new tech. I may be young, but this is the most impressive thing I've seen FOSS do in my lifetime. Anyone who thinks bitcoin is unfair/a ponzi scheme, or whatever, then by all means release your source code - show us the "correct" way to build a new currency and I'm sure people will use it.
    • by arth1 ( 260657 )

      Nobody cares about bitcoin. We don't give a rat's ass about bitcoin. Please stop posting stories about bitcoin. I don't know how many other ways there are to say it, but we don't give a fsck about bitcoin.

      Obviously, we do, based on the number of posts here.

      I can't say why others do, but in my case it's pure schadenfreude, seeing grown men go "I want to believe!" and setting themselves up for losing their money, and inventing the weirdest explanations for why this is not a zero-sum game doomed to collapse.

      In short, it's amusing to see just how many are born every minute.

    • I care about bitcoins. It's a welcome change from the usual apple evangelism.
  • by istartedi ( 132515 ) on Wednesday July 13, 2011 @07:33PM (#36756090) Journal

    I'm going to issue my own Fiat currency, backed by Fiats (the automobile). I still haven't worked out how much the average Fiat should be worth. There's no real purpose in this, other than to confuse the hell out of people who think I'm issueing a fiat currency (illegal) rather than a Fiat currency (perfectly legal, AFAIK). BTW, I'm not even sure if Fiat is still making cars, and they have a repuation for being a real POS. Therefore, it shouldn't be too hard for me to fill a lot with rundown Fiats to back my currency.

    • Just for a baseline I paid $400 for a 69 Fiat 850 sport convertible with a VW drive train incompetently retrofitted.

      That's about -$300 value for the Fiat. The 1600 dual port and IRS trans is worth more then the car with it in it. But that's because the guy who did the install was a moron. After I rip it out and redo it (by welding the top of the Fiat to a bug pan) it will pull 1/8 mile wheelies. Maybe not with the 1600...

      If I didn't live in CA the sound of rust from my driveway would keep me awake at n

  • What's to stop a large corporation with a lot of computing power to generate bitcoins? What if I have a cluster doing the work?

    • Nothing would stop them. They'd make money, other miners would make slightly less money, and Bitcoin would go on.

    • Assuming it was substantial enough of a cluster, it would push the difficulty of generating them even higher.

      Essentially its setup so that there is a set number of them created in a given time. The more people trying to make them, the more computer power required to make one. So, if you double the amount of people trying to make coins, you also double the amount of computer time needed to make one. Thusly, the more people who join this fad, the less anyone is going to make.

  • by geekd ( 14774 ) on Wednesday July 13, 2011 @07:41PM (#36756182) Homepage

    Please don't start mining Bitcoin. You will not turn a profit. It's hard work. It's no fun. Don't do it.

    (the difficulty is high enough, we don't need another influx of miners)

  • I think that if there's any likelihood of Bitcoin becoming significant, there's also going to be an increasing likelihood of someone dividing the problem space in such a way that it's addressable with appropriately-designed FPGAs and thereby killing that likelihood of significance. Right now it's unlikely to be worth anyone's time & money (unless it's being examined in classes), but if there are significant $ there someone's going to be pursuing them.
    • by geekd ( 14774 )

      People are on it: []

      • by allanw ( 842185 )
        I wonder if they know that FPGA's are typically only half the online price listed if you talk to a distributor. I'm not sure what kind of minimum order quantity you need though.
    • by mrand ( 147739 )

      I think that if there's any likelihood of Bitcoin becoming significant, there's also going to be an increasing likelihood of someone dividing the problem space in such a way that it's addressable with appropriately-designed FPGAs and thereby killing that likelihood of significance. Right now it's unlikely to be worth anyone's time & money (unless it's being examined in classes), but if there are significant $ there someone's going to be pursuing them.

      There is no way to know without doing the FPGA design, at least at a high level. What you might make up for in one area, you might lose in another. The fact that the AMD's run at such a high clock rate with so many ALU's makes me doubt it would be worth it - but again, there is no way to know for sure without doing considerable work. Just going on number of ALU's (which is not really a proper way to compare, but is the only thing we for this discussion), only the latest HUGE and really expensive Virtex 7

  • by fireteller2 ( 712795 ) * on Wednesday July 13, 2011 @09:07PM (#36757164) Homepage

    The assertion that early adopters have an unfair amount of bitcoins is on the one hand completely irrelevant to the issues of usability, and on the other hand is completely typical of all inventions, commodities and the world in general.

    This continued repetition of this idea stems from the misconception that Bitcoin is a Ponzi, pyramid or other type of scheme designed with the intent to defraud later adopters. That is not the design intent of bitcoin. It is an online medium of exchange that compensates people who improve it's security. The fact that people improved the security early on helps the security for everyone later. They got paid pennies at the time, and people who are helping now are getting paid pennies too. It has turned out that those pennies (if they kept them) have become valuable now. This is EXACTLY like being an early adopter of Apple stock, and could just as easily not have happened.

    The reason bitcoin is being talked about so much is not because someone is trying to scam you and "cash out" their early adopter advantage. People are talking about it because regardless of the value of a bitcoin, it is a frictionless* way to exchange value over the internet. You needn't hold bitcoins to participate in bitcoins. You can change them to cash the second you receive them. Bitcoins are useable now. They are a currency now.

    I would respectfully recommend that people who want to talk about what's wrong with bitcoin do their due diligence, before commenting on something that they clearly have little understanding of.

    *frictionless means: 1) you can open a business and start excepting payments this very second anywhere in the world, with customers anywhere else in the world, (excepting money is no more difficult then paying money - try that with credit cards), 2) money you transfer to anyone in the world is instantaneous, in as little as an hour you can be 100% sure that you have received bitcoins that can never be taken away from you or reversed in any way. 3) It cost almost nothing to pay anyone any amount with bitcoins.

    All of these elements provide value whither you call it currency, commodity or just software. I use it to do work, and I find that valuable to me right now. The value of bitcoins is not a theory, predictions of it's failure are what is theoretical.

    • by geekd ( 14774 )

      ^^ what he said.

      If you don't mind, I'm going to use that response in the future.

    • by Animats ( 122034 )

      stems from the misconception that Bitcoin is a Ponzi, pyramid or other type of scheme designed with the intent to defraud later adopters. That is not the design intent of bitcoin.

      That wasn't the original intent. That's just how it turned out.

      The concept was supposed to be that Bitcoin would be a widely used currency for micropayments. In practice, the Bitcoin world is mostly speculators and "miners"; its use as a medium of exchange is trivial.

      It takes about $100,000 per day in new cash to keep up the price of Bitcoins as more are "mined". So there's considerable interest among current holders in finding new suckers before the whole thing goes bust.

      • It is a misconception that Bitcoins are good for are where ever intended to be used as micro-payments. As little as it is there are still fees involved, and although they are optional now it is a part of the design that all transactions will eventually required fees. The features of bitcoin lay elsewhere as I have discussed.

        It is also a misconception that the only use of bitcoins now is as a commodity. That is increasingly less true, and soon will be the smaller part of the bitcoin economy, because of th

    • by Nursie ( 632944 )

      Right, the fact that any one of the early adopters sitting on a few thousand coins (or 'Satoshi' and his millions) could destroy the market in seconds, that's not an issue for you? The complete lack of stability implied by that?

      An effect that can and will become worse over time as bitcoin prices rise and bitcoin generation for new entrants generates ever smaller amounts.

      And that's leaving out the general idiocy of building in such a tiny limit to the currency and ensuring massive deflation over time.

      Also th

  • So as I've been reading on bitcoin for the last hour - I think I realized something that I have not heard really in the criticism of it yet.

    So - a lot of people are thinking bitcoin will be REALLY huge in the future, so let's pretend it does get really huge - let's say it's the only currency that the entire world uses, for example. What would happen is... as soon as I do a single transaction with an individual, I would be able to use sophisticated software (just bear with me) to figure out their entire
    • No, the database just tells what address has how much, when. If you do a transaction with someone, all you can look up is how much that address currently has. Since anyone can have any number of addresses, all that does is give you a lower bound on their holdings ... which becomes useless the moment that address is emptied and the bitcoins transferred to other addresses, which may or may not be owned (i.e private key known) by the same person.

      You can do more sophisticated strategies, like tracing the path

  • by slashdotjunker ( 761391 ) on Thursday July 14, 2011 @01:08PM (#36764650)
    I feel that Bitcoin discussions always fall apart because people cannot make a distinction between the Computer Science of Bitcoin and the Economics of Bitcoin.

    The Bitcoin Algorithm is a peer-to-peer transaction protocol. The algorithm was self-published by S Nakamoto as "Bitcoin: A peer-to-peer electronic cash system" in 2008. To my knowledge, the paper has not been accepted in a peer reviewed Computer Science journal. Nevertheless, there appears to be growing acceptance that the underlying technology is sound. However, that says nothing about the validity of applications based on the peering transaction protocol.

    The Economics of Bitcoin is about how the original coins are generated, how new coins are minted, how the currency is regulated, etc. Nakamoto's paper has nothing to say about these issues. In particular, many people feel that Bitcoins have been distributed in a manner that makes them a Ponzi scheme. I am not aware of any paper published in a peer reviewed Economics journal that contradicts this.

    The lack of a peer reviewed CS publication is terrible, but not fatal. Bitcoin has enough popularity now that we can expect crypto researchers to be looking at it as an easy target for a quick pub. The lack of a pub on a flaw in the technology of Bitcoin is not bad. This technology might be useful for something.

    However, the lack of a peer reviewed Economics pub addressing the Ponzi Scheme issue is fatal. In addition, I'm pretty sure that there are other important things that need to be investigated by Economists. I can't say much more about this since I am a computer scientist.

    I hope people will understand that there is a distinction between Bitcoin technology and Bitcoin coins. It is possible to have a different opinion on each and an opinion on one does not imply anything about the other. I urge people in future Slashdot discussions to take care to make it clear in their posts whether or not they are talking about the technology or the coins. Thank you.

The unfacts, did we have them, are too imprecisely few to warrant our certitude.