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24 Jul 14:50

Greece finds 'Neko', a noblewoman buried in her jewelry 1,800 years ago

Greek archaeologists have discovered a virtually intact grave of an ancient noblewoman buried with her golden jewelry at a Roman burial monument in the island of Sikinos.
05 Dec 22:42

V Jemenu zabili bývalého prezidenta. Občanská válka vstupuje do nové fáze

Smrt bývalého jemenského prezidenta Alího Abdalláha Sáliha je začátkem nové fáze občanské války v Jemenu - tak to alespoň vidí katarská televize Al Džazíra. Sáliha v pondělí zabili jeho bývalí spojenci - šíitští Húsiové.
18 Dec 16:38

End of the Line: A Tube Map of Tube Maps

by Jonathan Crowe

Well, this is meta. Kenneth Field, whose map of Mars I told you about earlier this year, has created a tube map of tube maps.

End of the Line is an attempt to be the last word in tube map pastiche. […]

While Beck himself likely ‘copied’ a number of aspects that ended up on his map he did so with consummate skill to create something unique, innovative and functional. Most subsequent schematic maps are pale imitations. We wrote a semi-academic paper about it which you can access from my blog here.

All too often we see transit map templates used as a short-cut to recognition and success. With no hint of irony whatsoever (!) we’ve done exactly the same and mapped the weird and wonderful world of Becksploited maps onto some tube lines and stations.

Becksploitation. There’s a term for you. It’s not like there’s no use for it.

14 May 20:41

This Is the Greatest Get-Out-the-Vote Video Ever Made

by Elias Groll

He interrupts couples having sex and throws people into voting booths. He has a terrible mustache and even worse teeth. He is Voteman, and, for whatever reason, Danish parliamentary officials thought he was the perfect mascot for the country's get-out-the-vote campaign ahead of European parliamentary elections. He's probably the world's first get-out-the-vote mascot to be introduced to his audience while receiving fellatio from a handful of voluptuous women.

In a NSFW video released earlier this week, the people of Denmark received their first introduction to Voteman and his turbulent life story. As a young man, he forgot to vote in European Union parliamentary elections -- robbing him of a chance to weigh in on hot-button issues like agricultural subsidies -- and ever since he has dedicated his life to ensuring that people go to the polls. He typically does so via random acts of violence, including, but not limited to, randomly beheading Danes, throwing couples who are having sex through their bedroom windows, and punching passersby in the mouth.

It's difficult to do justice to the video, which also features Voteman cruising into action while strapped to the blowholes of a pair of dolphins. (Depending on how permissive your workplace is on the subject of animated nudity, it's probably not safe for the office).

Alas, we barely got to know Voteman before his time with us came to an end. On Tuesday, the Danish parliament pulled the video after coming under a halestorm of criticism for a video many viewed as disrespectful of women. "Many whose opinions I deeply respect took the E.U. information cartoon as more serious and offensive than it was meant," Morgen Lykketoft, the speaker of Folketinget, the Danish parliament, said. "I recognize that parliament as an institution shall be more circumspect about what we put our name to."

Just a day earlier Lykketoft had defended the video as a harmless, well-intentioned effort to get out the youth vote: "We are trying to inspire the very young to go out and vote. It is important we get a higher turnout, especially among the young. You have to use all sorts of methods."

Voteman, the world just wasn't ready for you. But we'll never forget you.    


14 Oct 19:17

There Is No Nanotechnology Equivalent to the Digital Divide

by Dexter Johnson

The world may be witnessing one of the most egalatarian introductions of a new technology in history
19 Sep 09:15

World of Equal Districts

by Jonathan Crowe

World of Equal Districts

I've seen a lot of maps that redraw national or subnational boundaries in the name of equal population (here's a recent example) but the World of Equal Districts is the first I've seen to do it for the entire planet: it divides the world into 665 districts, each of which has around 10 to 11 million inhabitants. This is the electoral district map for a planetary parliament. Via Boing Boing and MetaFilter.

05 Aug 19:05

looking at mushrooms


Než přestaneme používat sdílení, doufám, že máte subsribe na una.

looking at mushrooms

29 Jun 07:22

Is There Any Point to the 12 Times Table?

by Jon McLoone

My government (I’m in the UK) recently said that children here should learn up to their 12 times table by the age of 9. Now, I always believed that the reason why I learned my 12 times table was because of the money system that the UK used to have—12 pennies in a shilling. Since that madness ended with decimalization the year after I was born, by the late 1970s when I had to learn my 12 times table, it already seemed to be an anachronistic waste of time.

12 times table

To find it being given new emphasis nearly 40 years later struck me as so odd that I thought I should investigate it a little more mathematically. Here is what I concluded.

Let’s start with a basic question: exactly why do we use times tables at all? (This is the kind of question my work on has me asking a lot!)

I am going to claim that there are three basic reasons:

1) To directly know the answer to common multiplication questions.
2) To enable multiplication algorithms.
3) To enable approximate multiplication.

Let’s look at those in turn.

1) This reason is important. There are lots of small multiplication problems in day-to-day life, and there is no doubt that knowing the answer to these is useful. But knowing ANY answer to ANY question is useful. What’s so special about multiplying 1 to 12? Why stop at the 12 times table—why not learn 13, 14, 15, 16, and 17 times tables? Why not learn your 39 times table? As the table number goes up, the amount to learn increases as a square of the number while the commonality of encountering a problem that uses that table goes down. “Knowing” the answer to all possible questions is a big task and not worth the effort. This, after all, is why math was invented, so that we don’t have to know the answers to all possible calculations, but instead have a way to work them out when needed. We must draw a line somewhere and then move to a more algorithmic approach. The question is where.

2) There are many fancy computation algorithms, but most of us learn “multiplying in columns,” which involves operating on one digit at a time while managing number place and carrying overflows on to the next column. I still use it sometimes myself. By definition it needs the 0–9 times tables (and implicitly understanding the 10 times table), since it only takes one digit at a time, but any single digit could come up. Knowledge of 11 and 12 times tables is completely irrelevant. If this was the only consideration, we have a clear argument for where to draw our line—at the 10 times table. You can’t manage on less, and more is of no use.

3) But there is another useful algorithm, which is approximating numbers to a few significant digits. This might make a case for drawing the line higher.

Take as an example 7,203 x 6,892. If I want to know that exactly, then I reach for Mathematica (or if I absolutely have to, I reach for pencil and paper to apply multiplication in columns). But often I just need a rough answer, so I mentally convert this to 7,000 x 7,000 = 7 x 7 x 1,000 x 1,000 = 49,000,000. More formally I am converting the numbers the nearest approximation of the form k x 10n where k ∈ {the set of numbers for which I know times tables}. Then I use the times tables on the remaining significant digits and implicitly use the 10 times table to get the magnitude right. In this case the real answer is:



Giving me an error of 1.2%—good enough for lots of applications. Now if I knew my 72 times table, I could have made this 7,200 x 6,900 = 49,680,000. Only a 0.07% error.

So, now our “where do I draw the line” question becomes “how much better is a typical approximate calculation if I know up to the 12 times table compared to only knowing my 10 times table?” Let’s investigate. First I need to automate the process of approximating using a given lead number.

approximate[number_, lead_] := lead*10^Round[Log10[number/lead]] approximate[12345, 9] 9000

And extend that to finding the best approximation, if we have a choice of lead numbers.

approximate[number_, choices_List] :=    approximate[number, choices] = Nearest[approximate[number, #] & /@ choices, number][[1]];

For example, if I know only up to my 4 times table, then the best approximation for 18,345 is 20,000.

approximate[18345, {1, 2, 3, 4}]

Now our approximate product is just the product of the best approximations of each number.

approximateProduct[a_, b_, choices_List] := approximate[a, choices]*approximate[b, choices]

And the relative error can be found from the difference compared to the accurate answer.

relativeError[a_, b_, choices_] := Abs[approximateProduct[a, b, choices]/(a b) - 1.]

For example, working out 549 x 999 when you only know up to your 10 times table will give you a little over an 8% error.

relativeError[545, 999, Range[10]]

Now, let’s take “typical calculation” to mean a calculation involving uniformly distributed numbers between 1 and 1 million and take the “typical” error to be the average of 100,000 such calculations.

meanErrorUniform[n_] :=   meanErrorUniform[n] =    Mean[Table[     relativeError[RandomInteger[{1, 10^6}], RandomInteger[{1, 10^6}], Range[1., n]], {100000}]]

The typical error if you know up to your 10 times table is 9.4%.


But if you know up to your 12 times table, it is only 8.2%.


Here is the error as a function of how many of your times tables you have learned.

ListLinePlot of the error as a function

Interestingly, most of the improvement happens by the time you know your 7 times table. The odd bump at 10 is because the ability to approximate relies implicitly on knowing your 10 times table already (to be able to handle the trailing zeros).

We can work out how much relative improvement there is in the typical error for each extra table learned.

ListLinePlot of relative improvement

So the relative benefit gradually drops, in a cyclic way.

But the improvement in error from 9% to 8% comes at a price. Knowing up to your 10 times table requires recollection of 100 facts (OK, 55, if you assume symmetry). But knowing up to your 12 times table is 144 facts. Improving the error from 9.3% of the result to 8.1% is a relative improvement of 12% in the size of the error. But to achieve that you need to memorize 40% more information. That seems like a losing proposition.

Let’s look at the relative improvement in outcome, per extra fact memorized.

ListLinePlot per extra fact memorized

The “return on effort” drops very rapidly toward the 10 times table and then barely improves. It seems like a fairly compelling case for stopping our rote learning at 10. Indeed, if times tables were only for estimating, we would get the best return per effort by just looking at the orders of magnitude and using only the 1 and 10 times tables!

Of course numbers are not uniformly distributed. If you are in egg production, 6s and 12s probably come up a lot, just as they will if you happen to be a dealer in pre-decimal British coins! Context issues like these are hard to quantify, but one issue that is general is Benford’s law, which occurs in many real-world datasets. It says that if you look at real-life datasets that cover several orders of magnitude (e.g. populations of communities, or people’s debts, or file sizes on your computer), then the numbers are more likely to start with a 1 than with a 2, and more likely to start with a 2 than a 3, and so on. I don’t know if anyone has studied the distribution of second digits, so I will assume that is uniform. So here is a function that generates “real-world” numbers.

Function that generates real-world numbers

We can now repeat our analysis on these more realistic numbers.

meanErrorBenford[n_] :=   meanErrorBenford[n] =    Mean[Table[     relativeError[randomBenfordNumber[6], randomBenfordNumber[6], Range[1., n]], {100000}]]

ListLinePlot meanErrorBenford

Using these less uniform numbers gives poorer performance (making you more likely to need accurate computation rather than approximation). Improvement can still be achieved by knowing more tables, and this could be taken as an argument for learning beyond 12, but not when you take into account the return per extra fact learned, which makes an even stronger argument for stopping at 10.

Argument for stopping at 10

If you really are intent on some extra rote learning, there are better ways to spend your effort than learning 11 and 12 times tables. Learning all permutations of 1 to 10 together with 15 and 25 gives a better average result than 1 to 12 (since they more evenly approximate the numbers with a lead digit of 1 or 2).

Mean[Table[   relativeError[randomBenfordNumber[6], randomBenfordNumber[6], Range[1., 12]], {100000}]]

Mean[Table[   relativeError[randomBenfordNumber[6], randomBenfordNumber[6], Join[Range[1., 12], {15, 25}]], {100000}]]

Or, as Chris Carlson suggested to me, learn the near reciprocals of 100 (2 x 50 = 100, 3 x 33 = 99, 4 x 25 = 100, 5 x 20 = 100, 6 x 17 = 102, etc.), as they come up a lot. I would expect that learning squares and powers of 2 is also probably more useful than 11 and 12 times tables.

With no prospect of the pre-decimal money system returning, I can only conclude that the logic behind this new priority is simply, “If learning tables up to 10 is good, then learning them up to 12 is better.” And when you want to raise standards in math, then who could argue with that? Unless you actually apply some math to the question!

Download this post as a Computable Document Format (CDF) file.

04 Jun 10:19

Cheer up: The world has plenty of long words beyond rindfleischetikettierungsüberwachungsaufgabenübertragungsgesetz

by Peter Sullivan

Monday brought unexpected news (news, as you'll notice above, that's difficult to squeeze into a standard headline): In scrapping a requirement to test healthy cattle for mad cow disease, the European Union also set in motion the demise of Germany's longest word.

The story goes something like this: In 1999, a regional government in Germany implemented "the law concerning the delegation of duties for the supervision of cattle marking and the labelling of beef" as a measure to protect against mad cow disease. In German, the legislation was known as rindfleischetikettierungsüberwachungsaufgabenübertragungsgesetz, or RkReÜAÜG for short. But local officials have since decided that the 63-letter word is no longer needed now that the EU has tweaked its regulations concerning cattle testing. And just like that, Germany's longest word vanished. Fortunately, GlobalPost has preserved its pronunciation for posterity's sake:



But despair not! The world is still full of extremely long words. What language has the longest? It's difficult to crown a clear champion because what qualifies is open to debate. Do people have to actually use the word? Do technical and scientific terms count? For example, according to the most liberal interpretation, the longest word in English, consisting of all the chemicals that make up the protein Titin, has 189,819 letters and takes 213 minutes to say. Here are some lengthy words from around the planet that can still fit on the page.


The longest word in the Oxford English Dictionary is pneumonoultramicroscopicsilicovolcanoconiosis (45 letters), "a lung disease caused by the inhalation of very fine sand and ash dust." But its claim to the title is dubious because, as the dictionary notes, it was invented by the president of the National Puzzlers' League in 1935 for the express purpose of being a long word.

The longest not-made-up word is antidisestablishmentarianism (28 letters) -- "opposition to the disestablishment of the Church of England." Given that the movement died awhile back, it is now just known as a long word.


Kolmivaihekilowattituntimittari (31 letters) is an electricity meter.


Vervoerdersaansprakelijkheidsverzekering (40 letters) is "carrier's liability insurance." It is advertised in its full, glorious form on this Dutch website.


Anticonstitutionnellement (25 letters) means, as you can probably tell, "unconstitutionally." 


Minoritetsladningsbærerdiffusjonskoeffisientmålingsapparatur (60 letters) is a device used to measure the distance between particles in a crystalline substance. 


This indigenous New Zealand language names a hill on the North Island Taumatawhakatangihangakoauauotamateapokaiwhenuakitanatahu (57 letters). If you want to visit, here are the coordinates. It might take a while to ask for directions.


A journey back to the beginnings of Western civilization uncovers the word lopado­­temacho­­selacho­­galeo­­kranio­­leipsano­­drim­­hypo­­trimmato­­silphio­­parao­­melito­­katakechy­­meno­­kichl­­epi­­kossypho­­phatto­­perister­­alektryon­­opte­­kephallio­­kigklo­­peleio­­lagoio­­siraio­­baphe­­tragano­­pterygon (184 letters), a dish made up by the playwright Aristophanes in his 391 B.C. play, Assemblywomen. One translation describes the dish as "oysters-saltfish-skate-sharks'-heads-left-over-vinegar-dressing-laserpitium-leek-with-honey-sauce-thrush-blackbird-pigeon-dove-roast-cock's-brains-wagtail-cushat-hare-stewed-in-new-wine-gristle-of-veal-pullet's-wings." Yum.

German's now-deceased longest word does pretty well in comparison. And there's a reason. German has agglutinative qualities, meaning parts of words with different meanings are joined together to make longer words that string the meanings together. In theory, you could keep adding to a word forever. At least, that is, until the government gets involved.

09 May 06:51

The 'Onion' latest victim of Syrian Electronic Army's fat jokes

This afternoon, the Syrian Electronic Army, a group of hackers supportive of Bashar al-Assad's regime, appeared to briefly hack into the Onion's Twitter feed. Over the course of about an hour, the SEA tweeted seven times from @TheOnion, and claimed responsibility for the attack on the Onion's @ONN account (the satirical newspaper's parody of 24-hour news networks) before the messages were deleted.

You could say the SEA's attacks have been a bit hit or miss over the past several months. The group's members promoted an alternate narrative of the Syrian civil war when they hacked into @60Minutes last month, but also tweeted fat jokes about the emir of Qatar, a backer of the opposition, when they hacked the BBC's weather account ("Earthquake warning for Qatar: Hamad Bin Khalifah about to exit vehicle").

In one of their strangest strikes yet, the SEA broke into the Twitter feed of the television channel E! on Sunday to "out" Justin Bieber and then to tweet, "Angelina Jolie admits, in E! latest issue, that Jordan is to blame for the Syrian refugees' atrocious conditions" -- a sentence that  under no circumstances would ever appear on E!

Today, the SEA fell back on fat jokes about Qatar's ruler ("NASA: 9th planet discovered and identified as the Qatari Emir") and also took a few jabs at Israel -- "UN's Ban Ki Moon condemns Syria for being struck by Israel: 'It was in the way of Jewish missiles;'" "The #Onion CEO: 'We regret taking zionist money to defame Syria. now the hackers are up our ass;'" "Poland to double flights from the Middle East, anticipating Israeli mass exodus. 'The bagel bakery ovens are working over time' ~ Larry" -- after the Israelis reportedly launched two airstrikes against weapons depots in Damascus in the past week.

Whoever was behind the hacking demonstrated a fairly proficient knowledge of the Onion's style (for example, attributing a quote without context to "Larry") and included a well-timed "Futurama Fry" meme as Twitter followers wondered if @TheOnion had been hacked, or if the tweets were simply more satire:


Though the Onion is first and foremost a satirical site, it has also hosted some of the most trenchant commentary on the Syrian civil war, leaving little doubt about why it was targeted. Darkly humorous articles from the past year and a half have included titles such as, "'Help Has To Be On The Way Now,' Thinks Syrian Man Currently Being Gassed,"  "Having Gone This Far Without Caring About Syria, Nation To Finish What It Started," "Target Pulls All Sponsorship From Publicly Ignored Syrian Conflict," "Alien World To Help Out Syria Since This One Refuses To," and an op-ed by Bashar al-Assad titled, "Hi, In The Past 2 Years, You Have Allowed Me To Kill 70,000 People."

So perhaps it's not a surprise that when the news outlet finally regained control over its Twitter feed, it had this to say:


Syrian Electronic Army Has A Little Fun Before Inevitable Upcoming Deaths At Hands Of Rebels

— The Onion (@TheOnion) May 6, 2013