Kennen Sie diese Sorte von Mathematik-Aufgabe aus sozialen Medien? Oft sind es extrem einfache Rechnungen, zum Beispiel:

Was ergibt 8/2*(2+2)?

Und drunter stehen hunderte falscher Antworten.

Das Zeug geistert immer wieder durch Facebook und Twitter, und es erscheint unerklärlich, bei einer doch vermeintlich exakten Lehre wie der Mathematik, dass es da immer wieder so große Meinungsverschiedenheiten geben kann. In diesem Fall berechnen die zwei größten Löse-Lager 16 beziehungsweise 1. Zu welchem der Lager gehören Sie? Was halten Sie von den Rechenkünsten der Leute im anderen Lager? Und wieso sind solche Aufgaben im englischen Sprachraum noch viel beliebter als bei uns?

Klären wir erstmal, wie es überhaupt zur Meinungsverschiedenheit kommen kann. Mathematische Formeln sind ja nichts als aufgeschriebene Rezepte für Berechnungen. Nimm eine 2, pack noch eine 2 dazu, dann multipliziere das Ergebnis mit…, und so weiter, bis zum Ergebnis.

Das funktioniert nur, weil die Übersetzung der Zeichen ins Rezept eindeutig (1) ist. Weil man sich auf Regeln für diese Übersetzung geeinigt hat. Die Faustregel, die Schulkinder bei uns lernen ist: Zuerst Klammen, dann Potenzen, dann Punkt vor Strich, alles von links nach rechts. Das ist die globale Konvention, und mit dieser Konvention berechnet man oben eine 16.

In den USA handelt die entsprechende Eselsbrücke aber nicht von Punkten und Strichen, sondern von der lieben Tante Sally, der man bitte verzeihen soll: Please Excuse My Dear Aunt Sally, PEMDAS. Das steht für: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. Und erweckt leider den Eindruck, Multiplikation müsste vor der Division ausgeführt werden und die Addition vor der Subtraktion.

Daran wäre gar nichts falsch, das könnte man so machen. Dann würden wir hier eben erst die Klammer berechnen, dann das Ergebnis 4 mit der 2 multiplizieren, und dann die 8 durch dieses Zwischenergebnis 8 teilen. Ergebnis 1.

Ob man es so oder so macht, hat mit Mathematik, und mit richtigem oder falschem Rechnen nichts zu tun. Es handelt sich um reine Konvention. Man kann auch in beiden Konventionen die jeweils andere Berechnung aufschreiben. Man braucht nur zusätzliche Klammern. Also 8/(2*(2+2)) um trotz Punkt-vor-Strich eine 1 zu berechnen, beziehungsweise (8/2)*(2+2), wenn man Tante Sally weiterhin falsch verstehen will und trotzdem 16 als Antwort möchte. Falsches Rechnen wäre, nach 4 mal 4 gefragt zu werden und 15 zu antworten. Hier passiert etwas ganz anderes.

Denn das eigentliche Problem hier ist nicht, dass die Leute im anderen Lager nicht rechnen können (geben Sie ruhig zu, dass sie das oben gedacht haben), sondern dass die Regel der Tante Sally zu diesem Missverständnis einlädt. Das Problem ist eine lausige Eselsbrücke, und der Fehler liegt eigentlich nicht bei dem, der sich da verrechnet, sondern bei dem, der es ihm irreführend beigebracht hat.

Übrigens, wo wir grade beim Thema sind: was ergibt 230-220*0,5?
Sie werdens vermutlich nicht glauben, aber die Antwort ist 5!

(1) Für die Mathe-Freaks: ein-eindeutig ist diese Übersetzung nicht, weil man ja jeder Formel jederzeit noch Klammern zufügen kann, die an den Berechnungen gar nichts ändern.

English, Geekstuffs, Misc, Philosophy, Science | No Comments »

Tipp für alle, die des Englischen mächtig genug sind, mit einem flott auf Niveau dahergeplauderten Gespräch fertig zu werden. Der Podcast von Sam Harris ist regelmäßig großartig und inspirierend, aber diese Woche schlägt er selbst für seine Verhältnisse besondere Funken. Er hat Ricky Gervais zu Gast (beziehungsweise hat er ihn in London besucht), und das ist für mich nicht nur großartig, weil hier zwei sehr kluge und lustige Köpfe aufeinandertreffen (es klingt nach Buch, Herr Lichtenberg), sondern auch weil ich meine Bewunderung für die beiden Herren bislang in recht unterschiedlichen Schubladen aufbewahrt hatte und jetzt gewissermaßen den Inhalt der einen in die andere schütten kann. Provokanter Humor und besonnene Rationalität, zwei Seiten einer extrem wichtigen Medaille.

Und dann reden sie am Ende auch noch über die Rückkehr von Christopher “Hitch” Hitchens, der auf einem von Richard Dawkins geklonten T-Rex in die Stadt reiten soll, wenn ich das recht verstanden habe.

Den Podcast findet man hier auf der Webseite von Sam Harris.

Comedy, English, Geekstuffs, Misc, Nonfiction, Philosophy, Psychology, Satire | No Comments »

always sure of life on Mars
reading into lines carved into red face
messages of friendliness and welcome
tracing them, a wavering pen,
the intelligence that made them
flooding, mimesis, through me,
gladly constructed
the capsule
that would
take me
there

and
bang
oh
how
it
flew

now, amid the sands
water’s distant memory a noise in the wind
life but shadows cast by Phobos and Deimos
slowly dry to become sand, become wind,
pondering the mistake
wondering who made it
and wondering why
–
wandering sands
digging fresh canals
scratching red death
fading like those
whose long abandoned craft
litter the sand
about mine

English, Poetry, Science Fiction | No Comments »

He is one of the Clueless, an ancient family of mysteriously inept entities that think they rule the multiverse. When his sister Futility goes missing during her summer project to square the circles of hell, the distraught Fanboy assembles an imaginary team of his greatest heroes, and leads this Fellowship on the quest to try and save Futility from, like, whatever.

Fanboy starts the quest in a bar, planning to make friends and thus collect information about Futility. Things seem to be going comparatively well, until Fanboy’s younger twin brothers Fart and Fondle show up unexpectedly, and the evening quickly deteriorates.

The following morning, when Fanboy wakes up in an unfamiliar apartment clearly belonging to a female, he knows he really is in trouble. Then strange noises are coming from the kitchen.

And so it begins.

Comics, English, Satire, Science Fiction | No Comments »

Inception blatantly invites comparisons. The zero-g simulation and the center room of the dream heist evoke the mystery of 2001, the cityscape of Limbo wants to look like Brazil, and the gimmicky plot screams “this is what Matrix 2 and 3 should have been like”. Failed ambition.

If I were in want of stunning visuals lacking in emotional and logical depth, Avatar would be a much better fit than this and do the job much more nicely and honestly, without leaving the tinny taste of being taken for a sucker in the mouth. For all its technical glory, Inception makes almost no sense as story or metaphor, and it’s sad to imagine the movie this could have been, in the hands of a writer/director taking the mind seriously. Diving down into somebodies subconscious ought to be unsettling and intense, but instead there is just stuff being blown up and secret agents shooting blanks: mind as submachine gun. Yawn.

Additionally, the only way Inception can keep you from falling through the cracks in the plot is by keeping everything in frenzied motion. But once the action stops, everything crumbles. The crumbling is pretty to look at, no doubt, but what remains in the end is still only technorubble.

All Right, English, Movies, Must See, Neuroscience, Science, Science Fiction | No Comments »

Hard to say what the source of the particular power of Rebney’s rant is. Somehow, the mixture of frustrated anger and self deprecation, contrasting with the mindless task of praising a Winnebago – itself the perfect image of a thwarted desire to escape, of resistance domesticated – rises above the heat, the flies and the adversities of the daily grind, and manages to inspire.

Rebney’s story, which the documentary Winnebago Man set out to find and tell, is one of media transition, first from the austere news machine of the middle of the 20th century into the entertainment complex of its end, then on into the fragmented world of me-media. Rebney, a veteran of CBS, does Winnebago spots to escape the Stahlbad of entertainment, and then finds himself being the viral harbinger of the next wave, before the term viral has even been coined. He finally understands that he is not used as a distraction, when he first faces his audience in San Francisco, in a sequence that is both tense and moving.

The movie’s premiere last Friday was supported by the presence of Michael Moore and Jeff Garlin, who threw the audience a bone by claiming that Curb Your Enthusiasm’s very concept was inspired by Rebney’s outbreaks. But the biggest thrill was seeing the man himself, pushing 80, kneeling down in the hope for a publishing deal, increasing the punishment on Bush Jr. from a hot poker up his ass to “being hanged like Goering”, flirting with the ladies, and just being a complete fucking delight.

A little earlier, during the movie, my mood was dampened a little, when Rebney and Steinbauer walk into Golden Gate park, and a sudden wave of melancholy sadness washed over me: I used to live there. I don’t any more. In fact, most of the things I love are in the past and far away. I’m old. Boo hoo. But then that made me angry, and I gave myself a clue from Jack’s book: I don’t want any more sentimental bullshit anytime during this post, from anyone, and that includes me.

There. Now go, see the movie.

English, Geekstuffs | No Comments »

the matter is
what the mind
is fighting
against

Aphorism, English, Poetry | No Comments »

the thoughts
I think I think
are really just
thoughts thought
by the cat
thought
the cat

Animals, Copyright, English, Poetry | 2 Comments »

This plot is from chapter 4 of Michael Shermer’s book “Why People Believe Weird Things”, and it’s quite amusing.

The section of the book this is from concerns ESP experiments. Participants in these experiments have to predict one of five symbols on an unseen card, and the plot is meant to show the chance of a participant getting x of the answers right when being asked 25 times. Predictably, getting 5 right out of 25 is the most likely, but higher numbers of hits are entirely expected, and their occurence alone does not mean much. Shermer stops with the negative statement – high performance doesn’t mean ESP – and doesn’t spell out what a correct analysis would look like – not looking at a single result, but comparing a distribution of results to that predicted from chance – but this unfortunate focus on gleeful debunking rather than the education of the reader isn’t my concern. It’s the plot itself. Look at it.

Its x axis runs from -2.5 to 12.5. Bars of unit width indicate the probabilities of getting a certain number of answers right, and a Gaussian curve (Shermer calls it a Bell curve in the legend, and a normal distribution in the chapter text) to fit the bar data. Pretty much all of this is awful. First of all, fractions of x make no sense. The number of correct answers can only be a whole number, therefore probabilities should be plotted for whole numbers alone. If you want to use bars, make them discontinuous to emphasize their discrete character. Additionally, both the Gaussian and the leftmost bar extend into negative values, which also do not make sense for x. Negative values shouldn’t be on this plot at all. All this could be simply due to sloppy graphical design, of course, but the Gaussian extending into the negative is in fact a hint of the biggest error here: this distribution is not a normal distribution at all. To show a Gaussian here is a blatant statistical and conceptual error.

Random answering in a task like this in fact follows a binomial distribution. Interestingly, the numbers on the bars are from the correct binomial (except for 0.0238, which should have read 0.0236), meaning that whoever prepared the data knew what they were doing. But Shermer, fitting a Bell curve to them, clearly does not. You can even see it’s a bad fit. The bars don’t look symmetrical at all. Furthermore, the claim in the legend that “in a group of 25 several scores [above 7] will always occur purely by chance” is also quite false. He himself provides the probability for scoring below 8, which is 89.1%. Thus, in a group of 25, the chance of everybody scoring below 8 is 89.9% to the 25th power, or 5.56%. In other words, roughly one in eighteen such groups will have nobody scoring 8 or higher. There are lies, damn lies, and statistics done by fools.

Claims of the paranormal are emotionally and spiritually appealing, and it is important to counter them both on their own grounds by providing equally appealing stories about the world, and also by clearly showing where their purported proofs are untenable. Michael Shermer is the founder of the Skeptics Society, who claims this as their task, and he adopts a smug tone of intellectual superiority over the misled and uneducated foolish masses throughout this book. Yet apparently he doesn’t know what he’s talking about himself. He even told me so at the end of his foreword: “why should [you] believe anything [I] say? […] You shouldn’t.”

In the end, the whole thing is probably just a clever lesson in scepticisim. Or is it?

English, Geekstuffs, Philosophy, Psychology, Science | No Comments »

There is something odd, I feel, about the outrage over BP’s role in the current monstrosity unfolding in the gulf, and it’s this: in a situation where enormous profits were to be made by retrieving a natural resource and selling it back to the public who rightfully ought to own it, and where there is no real oversight or control of the way this business is conducted and risks are handled, what in the world did we expect this company to do? It’s all good and well to get irate about these people, for being disgustingly disconnected rich fools, but to punish them because they cut corners and neglected enormous risks, is a bit like leaving a little kid alone in a candy store and then punishing him for taking candy and breaking the jar. Yes, it’s wrong, but how could they possibly not have done it? And who in his right mind leaves a kid alone in a candy store?

The basic capitalist assumption, that providing monetary incentives will make companies do what’s best for everybody, is probably fundamentally flawed, but it very clearly is in areas where companies can reap profits while deferring risks and costs to the general public, or where there is an intrinsic conflict of interest. Take the pharmaceutical industry, which is selling products meant to cure people, and who has a clear interest in both new treatable conditions being invented, and ambiguous ones being solidified (cholesterol, anyone? Or do you have too much ADHD to focus on it?) and existing ones not being eradicated or improved. They are reaping astronomical profits on this flawed process through a monopoly enforced by our own governments, claiming that they need such protection in order to be able to operate and innovate in the public good. This from one of the most profitable industries on the planet. It completely baffles me that this is allowed to continue basically unchallenged. But I digress.

This disaster is at it’s heart not a failure of BP, for all the ways BP has failed, as much as it is a failure of a system of letting third parties with particular interests be responsible for the general and public good. Add the inability of humans to properly assess and weigh risks and to handle large numbers, especially under personal incentives, and you get an explosive mix, where corporation executives are asked to do two opposing and very disparate things – maximizing profit and minimizing a detrimental impact that is very difficult to properly assess, with asymmetrical payouts. Like in the banking industry, being successful nets you vast personal gains, but failure gets spread over the whole of society and only affects you personally if it is so humongous as to be inconceivable. And even then, you might be fine, as we are seeing in the recent banking debacle’s profit and bonus fallout. Do we truly expect somebody given the chance of vast personal enrichment under a widely distributed risk to not take that chance? Are we, then, the very idiots we must think that person to be?

Yes, we can rail against factory farmers polluting entire watersheds with runoff urine, and BP destroying entire marine ecosystems, for their unconscionable behavior, and there definitely should be punishment fitting the crime. But more importantly, I feel, we should think about the changes necessary to prevent massively powerful and dangerous industries from shitting golden bricks all over the public good, and figure out how to not allow corporations to sell the welfare of others to their own profit.

English, Nature, Politics, Technology | No Comments »