I’m coming in to this a bit late, but since I really do care about the online science blogging community,I still have something that I want to say.
For those who don’t know, there’s a complete horses ass named Henry Gee. Henry is an editor at the science journal Nature. Poor Henry got into some fights with DrIsis (a prominent science blogger), and DrIsis was mean to him. The poor little guy was so hurt that he decided that he needed to get back at her – and so, Henry went ahead and he outed her, announcing her real name to the world.
This was a thoroughly shitty thing to do.
It’s not that I think Isis didn’t do anything wrong. We’ve got history, she and I. My experience with her led me to conclude that she’s a petty, vicious bully that takes great pleasure in inflicting pain and anguish on other people. She’s also someone who’s done a lot of good things for her friends, and if you want to find out about any of it, go read another blog – plenty of people have written about her in the last couple of days.
If she’s so awful, why do I care that someone outed her?
Because it’s not just about her.
The community that we’re a part of isn’t something which has been around for all that long. There’s still a lot of fudging around, figuring out the boundaries of our online interactions. When people play games like outing someone who’s using a pseudonym, they’re setting a precedent: they’re declaring to the community that “I know Xs real name, and here it is”. But beyond that, they’re also declaring to the community that “I believe that our community standards should say that this is an appropriate way to deal with conflict”.
I don’t want that to be something that people in my community do.
People use pseudonyms for a lot of different reasons. Some people do for bad reasons, like separating unethical online behavior from their professional identity. But some people do it to avoid professional retaliation for perfectly reasonable behaviors – there are tenure committees at many universities that would hold blogging against a junior faculty; there are companies that don’t won’t allow employees to blog under their real names; there are people who blog under a pseudonym in order to protect themselves from physical danger and violence!
Once you say “If someone makes me angry enough, it’s all right for me to reveal their real identity”, what you’re saying is that none of those reasons matter. Your hurt feelings take precedence. Bloggeroid tells you how to blog successfully so you avoid all of this. You’ve got the right to decide whether their reasons for using a pseudonym areimportant enough to protect or not.
Sorry, but no. People’s identities belong to them. I don’t care how mean someone is to you online: you don’t have the right to reveal their identity. Unless someone is doing something criminal, their identity isn’t yours to reveal. (And if they are doing something criminal, you should seriously consider reporting them to the appropriate legal authorities, rather than screwing around online!)
But to be like Mr. Gee, and just say “Oh, she hurt my feelings! I’m going to try to hurt her back”! That’s bullshit. That’s childish, kindergarten level bullshit. And frankly, for someone who’s an editor at a major scientific journal, who has access to all sorts of information about anonymous referees and authors? It’s seriously something that crosses the line of professional ethics to the point where if I were in the management at Nature, I’d probably fire him for it.
But Henry didn’t stop there: no! He also went ahead and – as an editor of Nature! – told people who criticized him for doing this that he want “adding them to the list”.
What kind of list do you think Henry is adding them to? This guy who’s showed how little he cares about ethics – what do you think he’s going to do to the people who he’s adding to his list?
I think that if Nature doesn’t fire this schmuck, there’s something even more seriously wrong over there than any of us expected.
After the whole Plait fiasco with the sum of the infinite series of natural numbers, I decided it would interesting to dig into the real math behind that mess. That means digging in to the Riemann function, and the concept of analytic continuation.
A couple of caveats before I start:
this is the area of math where I’m at my worst. I am not good at analysis. I’m struggling to understand this stuff well enough to explain it. If I screw up, please let me know in the comments, and I’ll do my best to update the main post promptly.
This is way more complicated than most of the stuff I write on this blog. Please be patient, and try not to get bogged down. I’m doing my best to take something that requires a whole lot of specialized knowledge, and explain it as simply as I can.
What I’m trying to do here is to get rid of some of the mystery surrounding this kind of thing. When people think about math, they frequently get scared. They say things like “Math is hard, I can’t hope to understand it.”, or “Math produces weird results that make no sense, and there’s no point in my trying to figure out what it means, because if I do, my brain will explode. Only a super-genius geek can hope to understand it!”
That’s all rubbish.
Math is complicated, because it covers a whole lot of subjects. To understand the details of a particular branch of math takes a lot of work, because it takes a lot of special domain knowledge. But it’s not fundamentally different from many other things.
I’m a professional software engineer. I did my PhD in computer science, specializing in programming languages and compiler design. Designing and building a compiler is hard. To be able to do it well and understand everything that it does takes years of study and work. But anyone should be able to understand the basic concepts of what it does, and what the problems are.
I’ve got friends who are obsessed with baseball. They talk about ERAs, DIERAs, DRSs, EQAs, PECOTAs, Pythagorean expectations, secondary averages, UZRs… To me, it’s a huge pile of gobbledygook. It’s complicated, and to understand what any of it means takes some kind of specialized knowledge. For example, I looked up one of the terms I saw in an article by a baseball fan: “Peripheral ERA is the expected earned run average taking into account park-adjusted hits, walks, strikeouts, and home runs allowed. Unlike Voros McCracken’s DIPS, hits allowed are included.” I have no idea what that means. But it seems like everyone who loves baseball – including people who think that they can’t do their own income tax return because they don’t understand how to compute percentages – understand that stuff. They care about it, and since it means something in a field that they care about, they learn it. It’s not beyond their ability to understand – it just takes some background to be able to make sense of it. Without that background, someone like me feels lost and clueless.
That’s the way that math is. When you go to look at a result from complex analysis without knowing what complex analysis is, it looks like terrifyingly complicated nonsensical garbage, like “A meromorphic function is a function on an open subset of the complex number plain which is holomorphic on its domain except at a set of isolated points where it must have a Laurent series”.
And it’s definitely not easy. But understanding, in a very rough sense, what’s going on and what it means is not impossible, even if you’re not a mathematician.
Anyway, what the heck is the Riemann zeta function?
It’s not easy to give even the simplest answer of that in a meaningful way.
Basically, Riemann Zeta is a function which describes fundamental properties of the prime numbers, and therefore of our entire number system. You can use the Riemann Zeta to prove that there’s no largest prime number; you can use it to talk about the expected frequency of prime numbers. It occurs in various forms all over the place, because it’s fundamentally tied to the structure of the realm of numbers.
The starting point for defining it is a power series defined over the complex numbers (note that the parameter we use is instead of a more conventional : this is a way of highlighting the fact that this is a function over the complex numbers, not over the reals).
This function is not the Riemann function!
The Riemann function is something called the analytic continuation of . We’ll get to that in a moment. Before doing that; why the heck should we care? I said it talks about the structure of numbers and primes, but how?
The zeta function actually has a lot of meaning. It tells us something fundamental about properties of the system of real numbers – in particular, about the properties of prime numbers. Euler proved that Zeta is deeply connected to the prime numbers, using something called Euler’s identity. Euler’s identity says that for all integer values:
Which is a way of saying that the Riemann function can describe the probability distribution of the prime numbers.
To really understand the Riemann Zeta, you need to know how to do analytic continuation. And to understand that, you need to learn a lot of number theory and a lot of math from the specialized field called complex analysis. But we can describe the basic concept without getting that far into the specialized stuff.
What is an analytical continuation? This is where things get really sticky. Basically, there are places where there’s one way of solving a problem which produces a diverging infinite series. When that happens you say there’s no solution, that thepoint where you’re trying to solve it isn’t in the domain of the problem. But if you solve it in a different way, you can find a way of getting a solution that works. You’re using an analytic process to extend the domain of the problem, and get a solution at a point where the traditional way of solving it wouldn’t work.
A nice way to explain what I mean by that requires taking a
diversion, and looking at a metaphor. What we’re talking about here isn’t analytical continuation; it’s a different way of extending the domain of a function, this time in the realm of the real numbers. But as an example, it illustrates the concept of finding a way to get the value of a function in a place where it doesn’t seem to be defined.
In math, we like to play with limits. One example of that is in differential calculus. What we do in differential
calculus is look at continuous curves, and ask: at one specific location on the curve, what’s the slope?
If you’ve got a line, the slope is easy to determine. Take any two points on the line: , where . Then the slope is . It’s easy, because for a line, the slope never changes.
If you’re looking at a curve more complex than line, then slopes get harder, because they’re constantly changing. If you’re looking at , and you zoom in and look at it very close to , it looks like the slope is very close to 0. If you look at it close to 1, it looks like it’s around 2. If you look at it at x=10, it looks a bit more than 20. But there are no two points where it’s exactly the same!
So how can you talk about the slope at a particular point ? By using a limit. You pick a point really close to , and call it . Then an approximate value of the slope at is:
The smaller epsilon gets, the closer your approximation gets. But you can’t actually get to , because if you did, that slope equation would have 0 in the denominator, and it wouldn’t be defined! But it is defined for all non-zero values of . No matter how small, no matter how close to zero, the slope is defined. But at zero, it’s no good: it’s undefined.
So we take a limit. As gets smaller and smaller, the slope gets closer and closer to some value. So we say that the slope at the point – at the exact place where the denominator of that fraction becomes zero – is defined as:
(Note: the original version of the previous line had a missing “-“. Thanks to commenter Thinkeye for catching it.)
Since is getting closer and closer to zero, is getting smaller much faster; so we can treat it as zero:
So at any point , the slope of is . Even though computing that involves dividing by zero, we’ve used an analytical method to come up with a meaningful and useful value at . This doesn’t mean that you can divide by zero. You cannot conclude that . But for this particular analytical setting, you can come up with a meaningful solution to a problem that involves, in some sense, dividing by zero.
The limit trick in differential calculus is not analytic continuation. But it’s got a tiny bit of the flavor.
Moving on: the idea of analytic continuation comes from the field of complex analysis. Complex analysis studies a particular class of functions in the complex number plane. It’s not one of the easier branches of mathematics, but it’s extremely useful. Complex analytic functions show up all over the place in physics and engineering.
In complex analysis, people focus on a particular group of functions that are called analytic, holomorphic, and meromorphic. (Those three are closely related, but not synonymous.).
A holomorphic function is a function over complex variables, which has one
important property. The property is almost like a kind of abstract smoothness. In the simplest case, suppose that we have a complex equation in a single variable, and the domain of this function is . Then it’s holomorphic if, and only if, for every point , the function is complex differentiable in some neighborhood of points around .
(Differentiable means, roughly, that using a trick like the one we did above, we can take the slope (the derivative) around . In the complex number system, “differentiable” is a much stronger condition than it would be in the reals. In the complex realm, if something is differentiable, then it is infinitely differentiable. In other words, given a complex equation, if it’s differentiable, that means that I can create a curve describing its slope. That curve, in turn, will also be differentiable, meaning that you can derive an equation for its slope. And that curve will be differentiable. Over and over, forever: the derivative of a differentiable curve in the complex number plane will always be differentiable.)
If you have a differentiable curve in the complex number plane, it’s got one really interesting property: it’s representable as a power series. (This property is what it means for a function to be called analytic; all holomorphic functions are analytic.) That is, a function is holomorphic for a set if, for all points , you can represent the value of the function as a power series for a disk of values around :
In the simplest case, the constant is 0, and it’s just:
(Note: In the original version of this post, I miswrote the basic pattern of a power series, and put both and in the base. Thanks to John Armstrong for catching it.)
The function that we wrote, above, for the base of the zeta function is exactly this kind of power series. Zeta is an analytic function for a particular set of values. Not all values in the complex number plane; just for a specific subset.
If a function is holomorphic, then the strong differentiability of it leads to another property. There’s a unique extension to it that expands its domain. The expansion always produces the same value for all points that are within the domain of . It also produces exactly the same differentiability properties. But it’s also defined on a larger domain than was. It’s essentially what would be if its domain weren’t so limited. If is the domain of , then for any given domain, , where , there’s exactly one function with domain that’s an analytic continuation of .
Computing analytic continuations is not easy. This is heavy enough already, without getting into the details. But the important thing to understand is that if we’ve got a function with an interesting set of properties, we’ve got a method that might be able to give us a new function that:
Everywhere that was defined, .
Everywhere that was differentiable, is also differentiable.
Everywhere that could be computed as a sum of an infinite power series, can also be computed as a sum of an infinite power series.
is defined in places where and the power series for is not.
So, getting back to the Riemann Zeta function: we don’t have a proper closed form equation for zeta. What we have is the power series of the function that zeta is the analytic continuation of:
If , then the series for that function expands to:
The power series is undefined at this point; the base function that we’re using, that zeta is the analytic continuation of, is undefined at . The power series is an approximation of the zeta function, which works over some specific range of values. But it’s a flawed approximation. It’s wrong about what happens at . The approximation says that value at should be a non-converging infinite sum. It’s wrong about that. The Riemann zeta function is defined at that point, even though the power series is not. If we use a different method for computing the value of the zeta function at – a method that doesn’t produce an incorrect result! – the zeta function has the value at .
Note that this is a very different statement from saying that the sum of that power series is at . We’re talking about fundamentally different functions! The Riemann zeta function at does not expand to the power series that we used to approximate it.
In physics, if you’re working with some kind of system that’s described by a power series, you can come across the power series that produces the sequence that looks like the sum of the natural numbers. If you do, and if you’re working in the complex number plane, and you’re working in a domain where that power series occurs, what you’re actually using isn’t really the power series – you’re playing with the analytic zeta function, and that power series is a flawed approximation. It works most of the time, but if you use it in the wrong place, where that approximation doesn’t work, you’ll see the sum of the natural numbers. In that case, you get rid of that sum, and replace it with the correct value of the actual analytic function, not with the incorrect value of applying the power series where it won’t work.
Ok, so that warning at the top of the post? Entirely justified. I screwed up a fair bit at the end. The series that defines the value of the zeta function for some values, the series for which the Riemann zeta is the analytical continuation? It’s not a power series. It’s a series alright, but not a power series, and not the particular kind of series that defines a holomorphic or analytical function.
The underlying point, though, is still the same. That series (not power series, but series) is a partial definition of the Riemann zeta function. It’s got a limited domain, where the Riemann zeta’s domain doesn’t have the same limits. The series definition still doesn’t work at . The series is still undefined at . At , the series expands to , which doesn’t converge, and which doesn’t add up to any finite value, -1/12 or otherwise. That series does not have a value at . No matter what you do, that equation – the definition of that series – does not work at . But the Riemann Zeta function is defined in places where that equation isn’t. Riemann Zeta at is defined, and its value is .
Despite my mistake, the important point is still that last sentence. The value of the Riemann zeta function at is not the sum of the set of natural numbers. The equation that produces the sequence doesn’t work at . The definition of the Riemann zeta function doesn’t say that it should, or that the sum of the natural numbers is . It just says that the first approximation of the Riemann zeta function for some, but not all values, is given by a particular infinite sum. In the places where that sum works, it gives the value of zeta; in places where that sum doesn’t work, it doesn’t.
S1 is something called Grandi’s series. According to the video, taken to infinity, Grandi’s series alternates between 0 and 1. So to get a value for the full series, you can just take the average – so we’ll say that S1 = 1/2. (Note, I’m not explaining the errors here – just repeating their argument.)
Now, consider S2. We’re going to add S2 to itself. When we write it, we’ll do a bit of offset:
So, S3 – S2 = 4S3, and therefore 3S3 = -S2, and S3=-1/12.
So what’s wrong here?
To begin with, S1 does not equal 1/2. S1 is a non-converging series. It doesn’t converge to 1/2; it doesn’t converge to anything. This isn’t up for debate: it doesn’t converge!
In the 19th century, a mathematician named Ernesto Cesaro came up with a way of assigning a value to this series. The assigned value is called the Cesaro summation or Cesaro sum of the series. The sum is defined as follows:
Let . In this series, . is called the kth partial sum of A.
The series is Cesaro summable if the average of its partial sums converges towards a value .
So – if you take the first 2 values of , and average them; and then the first three and average them, and the first 4 and average them, and so on – and that series converges towards a specific value, then the series is Cesaro summable.
Look at Grandi’s series. It produces the partial sum averages of 1, 1/2, 2/3, 2/4, 3/5, 3/6, 4/7, 4/8, 5/9, 5/10, … That series clearly converges towards 1/2. So Grandi’s series is Cesaro summable, and its Cesaro sum value is 1/2.
The important thing to note here is that we are not saying that the Cesaro sum is equal to the series. We’re saying that there’s a way of assigning a measure to the series.
And there is the first huge, gaping, glaring problem with the video. They assert that the Cesaro sum of a series is equal to the series, which isn’t true.
From there, they go on to start playing with the infinite series in sloppy algebraic ways, and using the Cesaro summation value in their infinite series algebra. This is, similarly, not a valid thing to do.
Just pull out that definition of the Cesaro summation from before, and look at the series of natural numbers. The partial sums for the natural numbers are 1, 3, 6, 10, 15, 21, … Their averages are 1, 4/2, 10/3, 20/4, 35/5, 56/6, = 1, 2, 3 1/3, 5, 7, 9 1/3, … That’s not a converging series, which means that the series of natural numbers does not have a Cesaro sum.
What does that mean? It means that if we substitute the Cesaro sum for a series using equality, we get inconsistent results: we get one line of reasoning in which a the series of natural numbers has a Cesaro sum; a second line of reasoning in which the series of natural numbers does not have a Cesaro sum. If we assert that the Cesaro sum of a series is equal to the series, we’ve destroyed the consistency of our mathematical system.
Inconsistency is death in mathematics: any time you allow inconsistencies in a mathematical system, you get garbage: any statement becomes mathematically provable. Using the equality of an infinite series with its Cesaro sum, I can prove that 0=1, that the square root of 2 is a natural number, or that the moon is made of green cheese.
What makes this worse is that it’s obvious. There is no mechanism in real numbers by which addition of positive numbers can roll over into negative. It doesn’t matter that infinity is involved: you can’t following a monotonically increasing trend, and wind up with something smaller than your starting point.
Someone as allegedly intelligent and educated as Phil Plait should know that.
Lots of people have been emailing me to say that there’s a new article out about Blacklight, the company started by Randall Mills to promote his Hydrino stuff, which claims to have an independent validation of his stuff, and announcing the any-day-now unveiling of the latest version of his hydrino-based generator.
First of all, folks, this isn’t an article, it’s a press release from Blacklight. The Financial Post just printed it in their online press-release section. It’s an un-edited release written by Blacklight.
There’s nothing new here. I continue to think that this is a scam. But what kind of scam?
To find out, let’s look at a couple of select quotes from this press release.
Using a proprietary water-based solid fuel confined by two electrodes of a SF-CIHT cell, and applying a current of 12,000 amps through the fuel, water ignites into an extraordinary flash of power. The fuel can be continuously fed into the electrodes to continuously output power. BlackLight has produced millions of watts of power in a volume that is one ten thousandths of a liter corresponding to a power density of over an astonishing 10 billion watts per liter. As a comparison, a liter of BlackLight power source can output as much power as a central power generation plant exceeding the entire power of the four former reactors of the Fukushima Daiichi nuclear plant, the site of one of the worst nuclear disasters in history.
One ten-thousandth of a liter of water produces millions of watts of power.
Sounds impressive, doesn’t it? Oh, but wait… how do we measure energy density of a substance? Joules per liter, or something equivalent – that is, energy per volume. But Blacklight is quoting energy density as watts per liter.
The joule is a unit of energy. A joule is a shorthand for . Watts are a different unit, a measure of power, which is a shorthand for . A watt is, therefore, one joule/second.
They’re quoting a rather peculiar unit there. I wonder why?
Our safe, non-polluting power-producing system catalytically converts the hydrogen of the H2O-based solid fuel into a non-polluting product, lower-energy state hydrogen called “Hydrino”, by allowing the electrons to fall to smaller radii around the nucleus. The energy release of H2O fuel, freely available in the humidity in the air, is one hundred times that of an equivalent amount of high-octane gasoline. The power is in the form of plasma, a supersonic expanding gaseous ionized physical state of the fuel comprising essentially positive ions and free electrons that can be converted directly to electricity using highly efficient magnetohydrodynamic converters. Simply replacing the consumed H2O regenerates the fuel. Using readily-available components, BlackLight has developed a system engineering design of an electric generator that is closed except for the addition of H2O fuel and generates ten million watts of electricity, enough to power ten thousand homes. Remarkably, the device is less than a cubic foot in volume. To protect its innovations and inventions, multiple worldwide patent applications have been filed on BlackLight’s proprietary technology.
Water, in the alleged hydrino reaction, produces 100 times the energy of high-octane gasoline.
Gasoline contains, on average, about 11.8 kWh/kg. A milliliter of gasoline weighs about 7/10ths of a gram, compared to the 1 gram weight of a milliter of water; therefore, a kilogram of gasoline should contain around 1400 milliliters. So, let’s take 11.8kWh/kg, and convert that to an equivalent measure of energy per milliter: about 8 1/2 kWh/milliliter. How does that compare to hydrinos? Oh, wait… we can’t convert those, now can we? Because they’re using power density. And the power density of a substance depends not just on how much power you can extract, but how long it takes to extract it. Explosives have fantastic power density! Gasoline – particularly high octane gasoline – is formulated to try to burn as slowly as possible, because internal combustion engines are more efficient on a slower burn.
To bring just a bit of numbers into it, TNT has a much higher power density than gasoline. You can easily knock down buildings with TNT, because of the way that it emits all of its energy in one super short burst. But it’s energy density is just 1/4th the energy density of gasoline.
Hmm. I wonder why Mills is using the power density?
Here’s my guess. Mills has some bullshit process where he spikes his generator with 12000 amps, and gets a microsecond burst of energy out. If you can produce 100 joules from one milliliter in 1/1000th of a second, that’s a power density of 100,000 joules per milliliter.
Suddenly, the amount of power that’s being generated isn’t so huge – and there, I would guess, is the key to Mills latest scam. If you’re hitting your generating apparatus with 12,000 amperes of electric current, and you’re producing microsecond burst of energy, it’s going to be very easy to produce that energy by consuming something in the apparatus, without that consumption being obvious to an observer who isn’t allowed to independently examine the apparatus in detail.
Now, what about the “independent verification”? Again, let’s look at the press release.
“We at The ENSER Corporation have performed about thirty tests at our premises using BLP’s CIHT electrochemical cells of the type that were tested and reported by BLP in the Spring of 2012, and achieved the three specified goals,” said Dr. Ethirajulu Dayalan, Engineering Fellow, of The ENSER Corporation. “We independently validated BlackLight’s results offsite by an unrelated highly qualified third party. We confirmed that hydrino was the product of any excess electricity observed by three analytical tests on the cell products, and determined that BlackLight Power had achieved fifty times higher power density with stabilization of the electrodes from corrosion.” Dr. Terry Copeland, who managed product development for several electrochemical and energy companies including DuPont Company and Duracell added, “Dr. James Pugh (then Director of Technology at ENSER) and Dr. Ethirajulu Dayalan participated with me in the independent tests of CIHT cells at The ENSER Corporation’s Pinellas Park facility in Florida starting on November 28, 2012. We fabricated and tested CIHT cells capable of continuously producing net electrical output that confirmed the fifty-fold stable power density increase and hydrino as the product.”
Who is the ENSER corporation? They’re an engineering consulting/staffing firm that’s located in the same town as Blacklight’s offices. So, pretty much, what we’re seeing is that Mills hired his next door neighbor to provide a data-free testimonial promising that the hydrino generator really did work.
Real scientists, doing real work, don’t pull nonsense like this. Mills has been promising a commercial product within a year for almost 25 years. In that time, he’s filed multiple patents, some of which have already expired! And yet, he’s never actually allowed an independent team to do a public, open test of his system. He’s never provided any actual data about the system!
He and his team have claimed things like “We can’t let people see it, it’s secret”. But they’re filing patents. You don’t get to keep a patent secret. A patent application, under US law, must contain: “a description of how to make and use the invention that must provide sufficient detail for a person skilled in the art (i.e., the relevant area of technology) to make and use the invention.”. In other words, if the patents that Mills and friends filed are legally valid, they must contain enough information for an interested independent party to build a hydrino generator. But Mills won’t let anyone examine his supposedly working generators. Why? It’s not to keep a secret!
Finally, the question that a couple of people, including one reporter for WiredUK asked: If it’s all a scam, why would Mills and company keep on making claims?
The answer is the oldest in the book: money.
In my email this morning, I got a new version of a 419 scam letter. It’s from a guy who claims to be the nephew of Ariel Sharon. He claims that his uncle owned some farmland, including an extremely valuable grove of olive trees, in the occupied west bank. Now, he claims, the family wants to sell that land – but as Sharon’s, they can’t let their names get in to the news. So, he says, he wants to “sell” the land to me for a pittance, and then I can sell it for what it’s really worth, and we’ll split the profits.
When you read about people who’ve fallen for 419 scams, you find that the scammers don’t ask for all of the money up front. They start off small: “There is a $500 fee for the transfer”. When they get that, they show you some “evidence” in the form of an official-looking transfer-clearance recepit. But then they say that there’s a new problem, and they need money to get around it. “We were preparing to transfer, but the clerk became suspicious; we need to bribe him!”, “There’s a new financial rule that you can’t transfer sums greater that $10000 to someone without a Nigerian bank account containing at least $100,000”. It’s a continual process. They always show some kind of fake document at each step of the way. The fakes aren’t particularly convincing unless you really want to be convinced, but they’re enough to keep the money coming.
Mills appears to be operating in very much the same vein. He’s getting investors to give him money, promising that whatever they invest, they’ll get back manifold when he starts selling hydrino power generators! He promises they’ll be on market within a year or two – five at most!
Then he comes up with either a demonstration, or the testimonial from his neighbor, or the self-publication of his book, or another press release talking about the newest version of his technology. It’s much better than the old one! This time it’s for real – just look at these amazing numbers! It’s 10 billion watts per liter, a machine that fits on your desk can generate as much power as a nuclear power plant!! We just need some more money to fix that pesky problem with corrosion on the electrodes, and then we’ll go to market, and you’ll be rich, rich, rich!
It’s been going on for almost 25 years, this constant cycle of press release/demo/testimonial every couple of years. (Seriously; in this post, I showed links to claims from 2009 claiming commercialization within 12 to 18 months; from 2005 claiming commercialization within months; and claims from 1999 claiming commercialization within a year.) But he always comes up with an excuse why those deadlines needed to be missed. And he always manages to find more investors, willing to hand over millions of dollars. As long as suckers are still willing to give him money, why wouldn’t he keep on making claims?
I’m going to write a few posts about programming in machine language. It seems that many more people are interested in learning about the ARM processor, so that’s what I’ll be writing about. In particular, I’m going to be working with the Raspberry Pi running Raspbian linux. For those who aren’t familiar with it, the Pi is a super-inexpensive computer that’s very easy to program, and very easy to interface with the outside world. It’s a delightful little machine, and you can get one for around $50!
Anyway, before getting started, I wanted to talk about a few things. First of all, why learn machine language? And then, just what the heck is the ARM thing anyway?
Why learn machine code?
My answer might surprise you. Or, if you’ve been reading this blog for a while, it might not.
Let’s start with the wrong reason. Most of the time, people say that you should learn machine language for speed: programming at the machine code level gets you right down to the hardware, eliminating any layers of junk that would slow you down. For example, one of the books that I bought to learn ARM assembly (Raspberry Pi Assembly Language RASPBIAN Beginners: Hands On Guide) said:
even the most efficient languages can be over 30 times
slower than their machine code equivalent, and that’s on a good
This is pure, utter rubbish. I have no idea where he came up with that 30x figure, but it’s got no relationship to reality. (It’s a decent book, if a bit elementary in approach; this silly statement isn’t representative of the book as a whole!)
In modern CPUs – and the ARM definitely does count as modern! – the fact is, for real world programs, writing code by hand in machine language will probably result in slower code!
If you’re talking about writing a single small routine, humans can be very good at that, and they often do beat compilers. Butonce you get beyond that, and start looking at whole programs, any human advantage in machine language goes out the window. The constraints that actually affect performance have become incredibly complex – too complex for us to juggle effectively. We’ll look at some of these in more detail, but I’ll explain one example.
The CPU needs to fetch instructions from memory. But memory is dead slow compared to the CPU! In the best case, your CPU can execute a couple of instructions in the time it takes to fetch a single value from memory. This leads to an obvious problem: it can execute (or at least start executing) one instruction for each clock tick, but it takes several ticks to fetch an instruction!
To get around this, CPUs play a couple of tricks. Basically, they don’t fetch single instructions, but instead grab entire blocks of instructions; and they start retrieving instructions before they’re needed, so that by the time the CPU is ready to execute an instruction, it’s already been fetched.
So the instruction-fetching hardware is constantly looking ahead, and fetching instructions so that they’ll be ready when the CPU needs them. What happens when your code contains a conditional branch instruction?
The fetch hardware doesn’t know whether the branch will be taken or not. It can make an educated guess by a process called branch prediction. But if it guesses wrong, then the CPU is stalled until the correct instructions can be fetched! So you want to make sure that your code is written so that the CPUs branch prediction hardware is more likely to guess correctly. Many of the tricks that humans use to hand-optimize code actually have the effect of confusing branch prediction! They shave off a couple of instructions, but by doing so, they also force the CPU to sit idle while it waits for instructions to be fetched. That branch prediction failure penalty frequently outweighs the cycles that they saved!
That’s one simple example. There are many more, and they’re much more complicated. And to write efficient code, you need to keep all of those in mind, and fully understand every tradeoff. That’s incredibly hard, and no matter how smart you are, you’ll probably blow it for large programs.
If not for efficiency, then why learn machine code? Because it’s how your computer really works! You might never actually use it, but it’s interesting and valuable to know what’s happening under the covers. Think of it like your car: most of us will never actually modify the engine, but it’s still good to understand how the engine and transmission work.
Your computer is an amazingly complex machine. It’s literally got billions of tiny little parts, all working together in an intricate dance to do what you tell it to. Learning machine code gives you an idea of just how it does that. When you’re programming in another language, understanding machine code lets you understand what your program is really doing under the covers. That’s a useful and fascinating thing to know!
What is this ARM thing?
As I said, we’re going to look at machine language coding on the
ARM processor. What is this ARM beast anyway?
It’s probably not the CPU in your laptop. Most desktop and laptop computers today are based on a direct descendant of the first microprocessor: the Intel 4004.
Yes, seriously: the Intel CPUs that drive most PCs are, really, direct descendants of the first CPU designed for desktop calculators! That’s not an insult to the intel CPUs, but rather a testament to the value of a good design: they’ve just kept on growing and enhancing. It’s hard to see the resemblance unless you follow the design path, where each step follows directly on its predecessors.
The Intel 4004, released in 1971, was a 4-bit processor designed for use in calculators. Nifty chip, state of the art in 1971, but not exactly what we’d call flexible by modern standards. Even by the standards of the day, they recognized its limits. So following on its success, they created an 8-bit version, which they called the 8008. And then they extended the instruction set, and called the result the 8080. The 8080, in turn, yielded successors in the 8088 and 8086 (and the Z80, from a rival chipmaker).
The 8086 was the processor chosen by IBM for its newfangled personal computers. Chip designers kept making it better, producing the 80286, 386, Pentium, and so on – up to todays CPUs, like the Core i7 that drives my MacBook.
The ARM comes from a different design path. At the time that Intel was producing the 8008 and 8080, other companies were getting into the same game. From the PC perspective, the most important was the 6502, which
was used by the original Apple, Commodore, and BBC microcomputers. The
6502 was, incidentally, the first CPU that I learned to program!
The ARM isn’t a descendant of the 6502, but it is a product of the 6502 based family of computers. In the early 1980s, the BBC decided to create an educational computer to promote computer literacy. They hired a company called Acorn to develop a computer for their program. Acorn developed a
beautiful little system that they called the BBC Micro.
The BBC micro was a huge success. Acorn wanted to capitalize on its success, and try to move it from the educational market to the business market. But the 6502 was underpowered for what they wanted to do. So they decided to add a companion processor: they’d have a computer which could still run all of the BBC Micro programs, but which could do fancy graphics and fast computation with this other processor.
In a typical tech-industry NIH (Not Invented Here) moment, they decided that none of the other commercially available CPUs were good enough, so they set out to design their own. They were impressed by the work done by the Berkeley RISC (Reduced Instruction Set Computer) project, and so they adopted the RISC principles, and designed their own CPU, which they called the Acorn RISC Microprocessor, or ARM.
The ARM design was absolutely gorgeous. It was simple but flexible
and powerful, able to operate on very low power and generating very little heat. It had lots of registers and an extremely simple instruction set, which made it a pleasure to program. Acorn built a lovely computer with a great operating system called RiscOS around the ARM, but it never really caught on. (If you’d like to try RiscOS, you can run it on your Raspberry Pi!)
But the ARM didn’t disappear. Tt didn’t catch on in the desktop computing world, but it rapidly took over the world of embedded devices. Everything from your cellphone to your dishwasher to your iPad are all running on ARM CPUs.
Just like the Intel family, the ARM has continued to evolve: the ARM family has gone through 8 major design changes, and dozens of smaller variations. They’re no longer just produced by Acorn – the ARM design is maintained by a consortium, and ARM chips are now produced by dozens of different manufacturers – Motorola, Apple, Samsung, and many others.
Recently, they’ve even starting to expand even beyond embedded platforms: the Chromebook laptops are ARM based, and several companies are starting to market server boxes for datacenters that are ARM based! I’m looking forward to the day when I can buy a nice high-powered ARM laptop.