On the Datatype of Matrix Indices

Computer science purists often try to convince me that size_t is the appropriate type for matrix and vector indices in C or C++. This is always asserted without further justification as if it were commonly accepted. When I say “a matrix index isn't the size of anything, so the burden of establishing that size_t is the ‘one true type’ for these indices lies with you”, I'm generally either insulted or berated, but a strong rational justification has yet to be presented.

My position is that any unsigned integral type is unsuitable for use as a general matrix or array index in computational science.  My argument is essentially a utilitarian one: that pragmatism should win over naïve pedantry.

The most succinct expression of my reasoning is that, from an algorithmic perspective, it is, in general, highly desirable that indices approximate a group under addition (as closely as we can with finite size), and that using any unsigned integer type unnecessarily deprives index variables of the ability to store the additive inverse.



The argument that, formally, matrix indices are natural numbers, {1, 2, 3, ...}, holds very little weight in this argument, since C and C++ already base arrays at zero. I maintain that the ultimate reason for this is the utility of having the additive identity, 0 (zero).

Matrix-oriented languages, like Fortran and Matlab, despite basing indices at 1, do not restrict the datatype of variables used as indices strictly to the set of natural numbers. That is to say that, in these languages that are specifically and explicitly matrix- and vector-oriented, provided that an index variable is a valid index when it is used as an index, the values that it takes at other points in a program are unconstrained. I would take some convincing that the exact opposite should be the case in C or C++, yet this is precisely the position that purists ridicule me for opposing. If you were to suggest to a Fortran or Matlab programmer that assigning zero or a negative number to an index variable at any point in a program should cause an error, I would expect them to be so puzzled by the sheer stupidity of it that they would have extreme difficulty articulating why this is a bad idea.

If unsigned indices were genuinely as good an idea as the pedants would have you believe, one might expect that in 57 years of Fortran and 30 years of Matlab, it would have been tried out and been such a great success that it would have caught on, but that is clearly not the case. Fortran, in fact, allows you to define the index range of arrays to accommodate negative indices. If this were something C-specific, one might expect that the C standard would incorporate this idea, yet it does not (§6.5.2.1 “Array subscripting” uses int) and x[-5] is perfectly valid.

The reality of doing computational linear algebra is that, although indices are non-negative integers, the arithmetic manipulation of indices in the course of executing an algorithm often, if not usually, involves not just subtraction, but negative numbers even if the eventual index computed is always non-negative. Consider, for example, the diagonal matrices formed from the stencils of finite difference methods. It would add nightmarish complexity to restrict the relative indices of the stencil to non-negative integers. What would a lower boundary check, now a trivial if(i<0) {... }, become if i were not allowed to be negative?

It might be argued that, in these cases, one “ought” to do these index computations with a signed type so as not to “pollute” the index type with negative numbers, but what exactly is the benefit of doing this? I mean, other than the smug self-satisfaction of being an über-pedant?

In practice, if you attempt to use an unsigned integer type for indices, but a signed type for index calculations, you have to add a lot of casts to silence warnings, and this quickly becomes so onerous that one either ends up either with ill-considered casts that may accidentally mask true errors, or such diligent consideration of whether a cast is truly correct that “cast contemplation” becomes a major, if not the dominant, contributor to development effort.

Again, the pedant might argue that you should have to consider these cases; that it is not a bad thing to have your development time doubled if that means it's correct. But is it “correct”? What does this “correctness” buy me? What are the actual benefits?

Well, the only one I've ever heard is this: “because size_t is the canonical type used to represent sizes in C, such as in calls to malloc(), size_t is the correct type for indexes because it guarantees that they can index any array returned by malloc() irrespective of the platform”. Really? That's it?

Leaving aside the fact that this is really an argument for choosing one of size_t and ssize_t, and I hope I've convinced you that ssize_t would be the better option, this “guarantee” is worthless, because flexibility in the representational range of a datatype used as a matrix index is, at best, useless.

The range of values that you need to use as a vector or matrix index isn't defined by what size objects you can malloc(), it's defined by the problem that you're trying to solve. So, there are actually only two scenarios that merit consideration:

• size_t is big enough to represent all problem indices; and
• size_t is too small to represent all problem indices.

In the former case, which is usual, choosing size_t over, say, int32_t doesn't matter, and in the latter case, you have an issue so major that, not only does it not help, but it probably exacerbates.

Suppose that the problem of interest is such that indices need to go up to 1,000,000. You develop a solution under a 32-bit memory model where size_t is 4 bytes. Going to a 64-bit memory model where size_t is 8 bytes is essentially trivial and presents no problem (no matter the choice of datatype for indices) other than doubling the memory requirement for indices, which is not a good thing. However, going to a platform where size_t is 2 bytes is going to be very difficult: you're going to have to do quite a bit of memory management and index segmentation and manipulation to be able to solve your problem under this constraint, and direct indexing is more-or-less off the table. If you have chosen size_t for your indices, you now also have to contend with having 2 bytes automatically hacked off all of them, even in places in your code where no array is indexed; in all likelihood, this is going to make solving the issue more difficult instead of less.

So the correct answer to the question “what datatype should I use for matrix indices” is a signed integer type that is sufficiently large to represent all anticipated indices. Moreover, the correct answer to the question “what datatype should I choose for problem X” is “whatever is required by problem X” and not something provided by the compiler or platform for some other purpose.

The “Secret to Happiness” Isn't on LinkedIn

LinkedIn's machine learning algorithms have decided that I need to be emailed daily with vacuous deepities from every self-proclaimed “life coach” on their multi-million user site, when, in fact, I hold them in contempt and put them into two categories: charlatans and clowns.

The charlatans prey on the insecurities that about half of us share: we don't like our jobs, we wonder if we were “meant to do” something else, our marriages or relationships could be better, we procrastinate, we feel guilty, or trapped, or unhappy or all of the above. The “cure” to all your ills is their patent medicine, their “Secret of Happiness” and as surely as snake-oil comes in a bottle, it's always the same hackneyed aphorism: “work towards being able to “pursue your passion” as a job even if it means taking a small pay-cut”, swiftly followed by a liberal dose of loosely connected banalities.

Almost worse than the charlatans are the semi-literate deluded clowns, who — having, to all appearances, dropped out of school and never been within a bull's bellow of an introductory philosophy or psychology book — nevertheless believe they're in a position to hawk hokey cornball platitudes to the rest of us (in fairness, I don't know if this particular “coach” is a charlatan or a clown, but, either way, I wouldn't give you the gum off the back of a stamp for five hundred of her moth-eaten potboilers).

The reality is that happiness is amenable to scientific inquiry and can be studied empirically. There are legitimate “happiness researchers” in psychology, psychiatry, and neuroscience. Here's the upshot of what we know: happiness is approximately

• 50% genetic,
• 40% attitude, and
• 10% all the shit people think it's about.

If you're wondering what the hell I'm talking about, then you may have lucked out in the genetic component and just be naturally predisposed toward happiness, as opposed to your less fortunate counterpart on the other side with dysthymia.

But the really important points here are twofold:

• your “career”, relationships, finances, etc. basically don't matter a shit; and
• you can learn to change your “attitude”.

So you're really happy with the promotion you got today? Won the lottery today? Feeling on top of the world? In 6 months, you'll be at about the same level of happiness that you were up to yesterday. Just lost your legs in a car accident? Feeling suicidal? In 6 months you'll be at about the same level of happiness that you were up to yesterday. We adjust.

Empirical evidence suggests that spending 15–30 minutes every day cultivating mindful awareness or practising CBT techniques will do more for your long-term happiness than any new job, spouse, or money, and certainly more than any vapid drivel peddled on LinkedIn.

Seanad Reform

In the wake of the failure of the constitutional referendum to abolish the upper house, or Seanad, in Ireland, many people are clamouring for Seanad reform to make it “more democratic” and “less élitist” — in other words, they seem to want the Seanad elected by the exact same procedure that has given us an incompetent shower of party-political asshats in the Dáil for as long as anyone can remember.

What would be the point of two parallel houses directly elected by general franchise? We need only look to Washington to see how well that works. And what's wrong with élitism anyway? It's not like we need more publicans in Leinster House and fewer professors, nor does the Seanad have any real power to subvert the intentions of the democratically and directly elected Dáil in any case.

There's little disagreement that reform of both houses of the Oireachtas is highly desirable, so how about this...

The general idea here is that ministerial portfolios should be fixed prior to a general election, and three seanadóirí, suitably qualified in subject-matter related to that portfolio, would be directly elected by general franchise to a corresponding 3-member “bench”. This would mean that every minister would be “shadowed” by 3, at least somewhat knowledgeable, senators. Their job would be to directly scrutinise the his/her legislative and executive actions. Any scope or mechanism for the government to make the seanadóirí rubber-stamping cronies, or redefine their roles or the roles of ministers, is eliminated. This is the germ of an idea; we can argue the details, but what follows in an outline of how I think this could work.

First, the status quo in Ireland in relation to ministerial portfolios would be abolished with extreme prejudice. The brain-dead state of affairs where the Minister for Agriculture and Fisheries today can be replaced with a Minister for Ice Cream tommorrow — is both staggeringly wasteful and subject to populism. I originally got my ham radio license in 1988 from the “Department of Tourism, Transport, and Communications”, I now get it from the “Department of Communications, Energy & Natural Resources”, with I don't know how many “different” bizarrely-named departments, redesigned logos and letterheads, and civil service reorganizations in between.

For my idea to work, we need some kind of consistent and static — or at least not easily changed — set of ministerial portfolios, fixing ministers' roles and corresponding government departments prior to a general election. I can think of no argument against this other than that it's different from the an existing “system” that has little or nothing to recommend it.

To support this up-front fixing of ministerio-departmental portfolios, amended constitutional provisions are required: either the portfolios must be explicitly enumerated, or any change must be encumbered by requiring a supermajority in both houses, or, even better, some combination. A workable solution might be to fix the size of the cabinet at 15, and stipulate that “there shall be ministries for finance, health, education, and basket-weaving, the names and areas of responsibility of the remaining 9 ministries to be decided by two-thirds majority of both Houses, no changes to take effect until after the following general election”. That immediately does away with the stupid and wasteful gerrymandering of portfolios every year or two.

Having decided the 13 portfolios before the election, the Seanad could be constituted, with its current 60 members, as follows:

• 11 to be appointed by the Taoiseach, as is currently the case;
• 10 to be elected by extending the university franchise to all university graduates, an increase of four; and
• 39 to be elected by general franchise to 13 three-member “benches” (three seats is a bench, right?), each bench directly corresponding to a ministerial portfolio.

The following “qualification rule” shall apply:

• Candidates for each bench must be formally qualified for that bench; and
• No candidate shall be a current member of, funded by or on behalf of, nor run under the imprimatur or official endorsement of, any political party.

In addition, three “5 year rules” shall apply:

• No person, having been a candidate in a non-Seanad political election in the preceding 5 years, may be a senator or a candidate for election or appointment to the Seanad — the “no has-beens” rule; and
• No person, having been a senator in the last 5 years, may be a candidate in a non-Seanad political election — the “no wannabes” rule.
• No person, having lost in a Seanad election, may be appointed to the Seanad by the Taoiseach for 5 years — the “no second bite at the cherry” rule.

Now, admittedly, the “formally qualified” rule is a bit tough to nail down — it's easy enough to expect candidates in the “Finance” bench to be accountants or economists, but it's harder to define for, say, “Education”; how would qualification for that be assessed? Is being a schoolteacher enough or would you have to have an Ed.D.? It's a problem, for sure, but not an insurmountable one.

Also, in this context, a “non-Seanad political election” means a general, local, or European election anywhere in Europe. Together, these two rules remove the “wannabes” — cronies appointed to raise their political profile in preparation for running in a general election for the Dáil — and “has-beens” — cronies who just lost their seat in the Dáil (or other political assembly). The extension to Europe as a whole prevents cross-border wannabes and has-beens from the UK Parliament or Northern Ireland Assembly. Although we lack the jurisdiction to prevent a former senator running for the Northern Ireland Assembly, we can disenfranchise and disbar him/her from ever voting or being a candidate in any future election in Ireland if he/she does, or subject him/her to fines or imprisonment.

How about that for accountability? Every minister has 3 senators on his/her ass, permanently. With no way to stack the deck with has-beens and wannabes, even with no increase in power, the new Seanad would raise the standard of political discourse, while being more democratic.

The chief objection I anticipate is that voting for 13 people is too complicated for the average dimwit or that counting the votes would be too time-consuming. Fine, then: let everyone vote for just one bench, or a few benches, of their choice. That way, everyone decides what's important to them, and few people are voting purely for the sake of it on benches they have no knowledge of or don't care about. This would be at least different from the party political voting pattern that characterizes Dáil elections. That doesn't seem like a bad thing to me at all, and having a different second house is the entire point of the bicameral system.

Footnote on the Irish Parliamentary System

In Ireland, the Oireachtas, consists of Uachtarán na hÉireann (President of Ireland), who is directly elected to this largely ceremonial and powerless position; the 60-seat Seanad (Senate), an indirectly elected “upper house” with no real power; and the 166-seat Dáil, (House of Representatives or National Assembly), which effectively holds all legislative and executive power. This power is wielded by a 15-member cabinet (comh-aireacht, a seldom-used word since it is almost never necessary to distinguish between the cabinet and the Government, or Rialtas), elected by the Dáil from amongst their membership, with a seldom-exercised constitutional provision to have up to two seanadóirí (senators).

Constitutionally and practically, the Seanad is almost entirely powerless, apart from a smattering of limited and never-used constitutional functions, such as the impeachment of a judge or the president. The Seanad can amend legislation, but the amendments are more like suggestions: they go back to the Dáil, and if the government of the day doesn't like the amendments, the bill can pass into law without Seanad support after 180 days or less, in the case of financial bills. At worst, the Seanad can delay non-financial legislation by about 9 months.

In practice, once a general election — in which members are elected to the Dáil by general franchise — is over, one of the two large parties (Fine Gael and Fianna Fáil), in conjunction with one of the smaller parties or a group of independents, will have a majority in the Dáil, which will “elect” the leaders of those parties to the cabinet, which is the new government. The leader of the largest party will be the new Taoiseach (Prime Minister), the leader of the second largest party (of the coalition making up the cabinet, not the Dáil overall) will be the Tánaiste (Deputy Prime Minister), and the cabinet positions — Ministers for Finance, Health, etc. — will be assigned to senior figures in the governing parties according to their relative strengths and the importance of the position. It is usual for the largest party to keep the Ministry for Finance for one of their own, for example.

The Taoiseach, once elected, then appoints 11 people to the Seanad. The original idea was that these would be trusted advisers and experts, but, in practice, they have always been political cronies: has-beens, who just lost their seat in the Dáil, and wannabes, who are hoping for a seat in the Dáil in the future and have been appointed to the Seanad to raise their public profile in preparation for the next general election.

The remaining 49 seanadóirí (senators) consist of 6 elected by graduates of certain Irish universities, and 43 elected from 5 so-called “vocational panels”, which consist of union, local government, and other representatives.

Installer Tips for Open Source Developers

So, I've recently had to install a lot of software from source. I used to do this a lot — back in the days when I was a Linux hobbyist and had nothing better to do — but in recent years, I have tended to just live with whatever versions of software libraries come with whatever Linux distro I happen to be using on a particular machine, usually the latest Ubuntu LTS (although I've used Slackware, Red Hat, SuSE, Mandriva, Yellow Dog, and CentOS in addition to Irix, Solaris, and FreeBSD).

One thing that hasn't changed one iota in (almost) twenty years is the utter cluelessness of niche developers when it comes to packaging their software, and it's driving me nuts. Just because your software isn't totally mainstream doesn't mean you can subject your (potential) users to an installation nightmare of manually editing Makefiles and making decisions about minutiae of configuration and installation.

The rules are very, very, simple indeed. Everyone who's ever installed anything from source knows the rules, so why the hell don't niche developers?

Here it is. The standard way of installing from source is

After I download a (well-behaved tarball), I expect to be able to do this:

    $ tar xzf foo-1.2.3.tar.gz
    $ cd foo-1.2.3
    $ ./configure
    $ make
    $ make test|check
    $ sudo make install

There are a small number of variations, of course, you can use 7zip or bzip2 instead of gzip, and so on. At a push, you can inflict CMake or SCons on me, but, frankly, I don't care how much of a pain in the hole the Autotools are (and, as a developer, I hate them), ideally you should use them because that's what your users expect, and they don't really care if it takes you a day of frustration to figure out. If that's significant in the context of your overall software development, it's probably not worth installing your software in the first place.

If you insist on inflicting your egotistical notions of how installation from source should work, the one thing you absolutely cannot do is ignore now well-established conventions about where stuff goes: absent any explicit instruction from me, you install your shit in the appropriate directories in /usr/local and nowhere else. I don't care that it's easier for you to just copy great gobs of shit into /opt/IAmSoImportant and leave all the painful configuration to me, and for the love of all that is good and right, if you install anything directly in /usr, interfering with the packaging system of my distro, I will hunt you down like a rabid dog and hammer a mechanical pencil into your eye with your detached and still-bleeding leg. I know it's hard to decide whether you should put your headers directly in /usr/local/include or in a subdirectory thereof, or your libraries in /usr/local/lib or in a subdirectory thereof, and it's often subtly debatable how “platform independent” that file really is, so whether it should go in /usr/local/share/foo or somewhere else is, in the end, a judgement call. I know. I sympathise. I really do. But if you can't decide, and you wrote the damn thing, how the hell do you expect me to?

In short, if you want your software to ever have the slightest chance of “catching on” and becoming popular, you can't just do the fun stuff, you have to suck it up, make a decision or two, and do the mundane and tedious stuff that makes installation easy for your users and packaging easy for distributions.

End of rant :o)

Rapid Charging Electric Cars

One of the things that comes up repeatedly with electric cars is how fast you can charge them. The current answer is “overnight” or, at least, on the order of hours. Some more bullish electric car proponents argue that charging stations could be built that would reasonably match gasoline filling speeds. I don't think that's plausible.

The EPA limits gasoline filling speeds to 10 gpm (gallons per minute), or 0.63 l/s (liters per second). The volumetric energy density of gasoline is about 36 MJ/l (megajoules per liter), which means that, at the gas station, energy is flowing into your tank at a rate of 36 MJ/l * 0.63 l/s = 22.7 MJ/s = 22.7 MW (megawatts).

Now, suppose that the battery-to-wheels efficiency of an electric car is five times the tank-to-wheels efficiency of a gasoline car, which is a fairly reasonable assumption. Then we only need a charging power of 22.7/5 =  4.5 MW. Generously supposing 90% efficiency from grid to battery, we need “only” draw five million watts off the power grid.

That is an absolutely vast amount of electric power: not much less than is needed to supply 4,000 American homes. This is not a plug-in device.

A reasonable rule of thumb for distribution level electricity supply is “100VA/kV” in other words, if you were to be a 10kV primary customer, you can expect to be able to draw at most 1 MVA (the difference between VA and watts is not important for the current discussion). On that basis, the 5MW charging station will need to be a 69 kV subtransmission customer of the local power utility. One charging station, not a gas station forecourt with 8 of them.

Now, let's talk about slew rate. You can't just turn on a 5 MW load (for want of a round number) like a 60W lightbulb. Call your local power company and ask them how quickly they would allow a subtransmission customer to turn on a 5 MW load. The answer cannot be faster than they can spin up a gas turbine. The slew rate of a “hot” GE gas turbine generator is, at most, 5%-per-minute. In other words, to be able to even ramp-up a 5MW charger to full power in one minute would take 100MW of spinning reserve, and only after that have you hit gas pump-equivalent power.

Let's look at that another way. Take the 85kWh (kilowatt hour) battery in the top-end Tesla Model S. 85kWh is 306MJ. Suppose you want to charge that sucker in a minute flat, which is not unreasonable given its range of 265 miles: one minute would give you ten gallons of gas, at least enough to run a modern luxury car for that distance. To supply 306 MJ in 60s is 306/60 = 5.1 MW. Pretty much the same number.

In synopsis, refuelling an electric car at the same rate as a gas pump, any way you look at it, requires something of the order of 5 MW of electric power. This is, practically speaking, impossible. Notice that I haven't mentioned cost. Economically speaking, it is utterly beyond any reason: the charger alone would cost millions. Recharging an electric car at even ten percent of gas-pump equivalent speeds (requiring “only” a half-megawatt charger), presents enormous technical challenges in electricity supply.

In short, the technical challenges of recharging an electric car on consumer-acceptable timescales is almost nothing to do with the car or its battery.

NatGeo on Biofuels

What breakthroughs do biofuels need? asks National Geographic.

The real breakthrough would be recognition that biofuels simply cannot reasonably be expected to address a significant fraction of our energy needs. The only breakthrough worth having would be a tenfold increase in the solar efficiency of photosynthesis, which would only be possible through advanced genetic engineering, is very far beyond our current capabilities, and would be vehemently opposed by environmentalists.

The basic problem is that photosynthesis is horribly inefficient in converting sunlight to usable fuel. The maximum theoretical energy conversion efficiency of sunlight to biomass, not useful fuel, is just 6% [Zhu et al., 2008]; real efficiencies are considerably lower.

Brazil's sugarcane ethanol production is the absolute gold standard for large-scale biofuel production. The Brazilians started this bandwagon in the 70's and have aggressively optimized their ethanol production for 40 years. The most bullish prediction is that — if they keep improving at the same rate as they have in the past — they'll be able to average 9,000 liters of ethanol per hectare per year by 2018 [Goldemberg, 2008].

Brazilian Ethanol Yield Over Time

What's the energy content of 9,000 liters of ethanol? The highest value I could find is 23.4 MJ/l (megajoules per liter), corresponding to the HHV (higher heating value) of anhydrous ethanol. This means that 9 kl (kiloliters) of ethanol yields at most 211 GJ (gigajoules) of thermal energy on combustion.

Now, how much sunlight falls on a hectare? In energy slang a “sun” is 1 kW/m^2 (kilowatt per square meter). That's about the peak insolation (energy density on the ground from the sun) at noon at the equator, but of course, the sun doesn't shine at night, insolation falls with latitude, and there's seasonal variation. An insolation map of Brazil suggests that a reasonable value for the sum of the insolation over a year may be up to 2,000 kWh/m^2 (kilowatt hours per square meter), so let's be super-generous to biofuels and use a stingy figure of 1,000 kWh/m^2, which is more like the correct value for Ireland than Brazil, and equates to 36,000 GJ/ha.

Yearly Sum of Global Irradiance

So, every hectare gets at least 36,000 GJ of sunlight and produces at most 211 GJ of ethanol. That's an energy conversion efficiency of, at best, 211/36000 or less than 0.6%. A fair figure (using the LHV of ethanol, production of 7kl/ha, and 1,750 kWh/m^2) would be less than half of that. I think it's fair to say that the solar-to-liquid-fuel energy conversion efficiency of sugarcane ethanol production is currently no more than one quarter of one percent, less by the time the input energy necessary to grow, harvest, ferment, and distill the ethanol (at least one tenth of the energy produced) is accounted for.

You can do far better than this generating hydrogen in your backyard using a modern solar PV panel (20% efficient) to power a commercially available electrolyser (73% efficient). Under reasonable assumptions, today you can produce hydrogen via solar panels and electrolysis with more than 50 times the efficiency of sugarcane ethanol production. I'm not arguing for hydrogen-powered cars, merely illustrating the horrible inefficiency of ethanol production.

Speaking of cars, to ram the point home, let's suppose that we could magically transform all of the vehicles in the United States into flex-fuel vehicles capable of running on 100% ethanol. Let's further suppose that we could out-do the future Brazilians at their own game and obtain fantastic yields of 10 kl/ha (or 1 l/m^2). Let's further suppose that we could substitute ethanol 1:1 for gasoline, meaning that we would need 500 billion liters of ethanol per year just for gasoline, never mind other energy needs. How much land would that require? About 50 million hectares. That's about half the total area of the United States or about three times its arable land area. If you use actual figures for US corn ethanol production (about 3,750 l/ha)? You need 8 times the arable land area of the USA.

So when I see headlines like this, I say, “So what, it's 1% efficient?”

I don't know how we can address our need for a gasoline substitute (easily transportable, high energy density, short “recharge” time, etc.), but it seems pretty clear that biofuels are merely a distraction.

Holy Fukushima: Scaremongering is Everywhere!

It seems like this kind of thing has been doing the rounds:

Bogus Fukushima Radiation Map #1

I got a message on Facebook saying “I'd really like you to do a blog piece on this”, so here it is.

The above image is, in fact, an ocean wave amplitude graphic for the April 2011 Fukushima earthquake from NOAA. It has nothing to do with the “fallout” from the Fukushima Daiichi nuclear plant. I repeat: it has nothing whatever to do with nuclear radiation of any kind — it is an ocean wave amplitude graphic. Somebody took this innocent graphic and maliciously emblazoned it with a scaremongering lie. A slew of ignorant anti-nuclear Internet Luddites then reposted this complete fabrication, which has been swallowed wholesale by some of the more gullible members of the public.

In many cases, the above graphic has been replaced by this one:

Bogus Fukushima Radiation Map #2

Now, this one is actually a particle simulation from the New Zealand based ASR Ltd., a marine consulting company. If you actually go to the original page, it says (in their block capitals): “THIS IS NOT A REPRESENTATION OF THE RADIOACTIVE PLUME CONCENTRATION”. What this graphic actually tells us — if their computer simulation is accurate and reliable — is that, in the year after Fukushima, nothing (radioactive or otherwise) in the ocean surface currents could possibly have gotten much further than about halfway across the Pacific Ocean, which is quite a different thing from what the scaremongers would have you believe, and says nothing whatsoever about dilution or concentration. This was a publicity stunt by a private company showcasing their technology; it is neither peer-reviewed science, nor the report of a competent panel of experts.

So, is radiation from Fukushima killing Americans?

If you look at similar peer-reviewed science [Behrens et al., 2012], whose graphics have also been used for scaremongering, what you find is that the radioactivity of ¹³⁷Cs — everyone's favorite radioisotope — off the coast of California (blue box IV) due to Fukushima peaks at about 1.2 Bq/m³, while further North it might peak around 2 (cyan box II). To put this in perspective, the background of ¹³⁷Cs in the Pacific is about 3 Bq/m³, and the background level of radon in the air averages 5–15 Bq/m³, depending on where you live. In other words, this kind of increase — another couple of becquerels per cubic meter — isn't going to make a whole lot of difference to anyone.

The expert consensus is similarly undramatic: by far the most pessimistic part of the WHO's assessment is that the lifetime risk of thyroid cancer for a 1 year old female in the most affected parts of Fukushima prefecture may increase by 70%. Wow! 70%. But here's the thing: the baseline lifetime risk of thyroid cancer for women is 0.75%, 70% of that, the additional lifetime risk, is just 0.5%. I'm not saying I'd like my risk of some kind of cancer to increase by 0.5%, but it's not anything that I'm going to get my knickers in a knot over either.

If you look around, you'll find out that the total Fukushima release was 900 PBq — by any standard an enormous amount of radiation — about one sixth of a Chernobyl, about equivalent to the fallout from a 2Mt nuclear warhead, or approximately bugger all compared to what the Americans, the British, the French, and the Russians were doing throughout the 50's, 60's and 70's in the Pacific, Siberia, and the Nevada desert.

You'll also find that a reasonable estimate of the total number of additional cancer-related deaths attributable to Fukushima is about 130. That's less than half the number of coal-mining deaths over the last 10 years in the US, less than a day-and-a-half's worth of road traffic fatalities, or a few weeks of coal-mining deaths in China. In other words, also bugger all.

The reality is that nuclear power plants are actually pretty safe in the grand scheme of things, it's just that when there is an accident, it's big and it makes a big splash on the news. It's a bit like the way a plane crash that kills 300 people is a major news event, but the 300 people who die on our roads every few days in an unnoticeable trickle never get on CNN.

So, to answer the question, the danger to Americans from Fukushima is essentially zero. If you're going to start washing your vegetables in filtered water — as some of the sensationalist anti-nuclear liars in the lede would have you do — think again… with a little more skepticism and balance.