Fun

The Best Math-Related Memes

61c642b2d3333629df39b91f31e48fdd

a-guide-to-succeed-in-math_c_1374041

chair-math_o_130887

0cb

doing-math-instead-of-girls_c_876701

duckulator_c_2455921

happy-birthday_o_698353

hFF1C974B

i-8-sum-pi_c_1488893

(Explanation to the image above: the square root of minus one is the imaginary unit, usually abbreviated by i, 2 to the power of 3 is 8, the third symbol is the summation sign, the last one of course is pi … so it reads: “i 8 sum pi” = “I ate some pie”)

i-still-hate-math_o_2225991

just-math-being-math_o_870323

just-who_o_163263

le-test_o_180697

math_c_850076

Math-Jokes_c_91573

math-not-even-once_o_935204

math-porn_o_175037

math-reaction_o_258488

math-test_o_184666

matrix_o_262494

nice-try-math_o_178094

pirates_c_345991

staph_o_859913

there-is-only-one-theory-in-maths_c_643017

e2c

ee6

true-story_o_829612

yo-dawg_o_567211

The Problem With Antimatter Rockets

The distance to our neighboring star Alpha Centauri is roughly 4.3 lightyears or 25.6 trillion km. This is an enormous distance. It would take the Space Shuttle 165,000 years to cover this distance. That’s 6,600 generations of humans who’d know nothing but the darkness of space. Obviously, this is not an option. Do we have the technologies to get there within the lifespan of a person? Surprisingly, yes. The concept of antimatter propulsion might sound futuristic, but all the technologies necessary to build such a rocket exist. Today.

What exactly do you need to build a antimatter rocket? You need to produce antimatter, store antimatter (remember, if it comes in contact with regular matter it explodes, so putting it in a box is certainly not a possibility) and find a way to direct the annihilation products. Large particle accelerators such as CERN routinely produce antimatter (mostly anti-electrons and anti-protons). Penning-Traps, a sophisticated arrangement of electric and magnetic fields, can store charged antimatter. And magnetic nozzles, suitable for directing the products of proton / anti-proton annihilations, have already been used in several experiments. It’s all there.

So why are we not on the way to Alpha Centauri? We should be making sweet love with green female aliens, but instead we’re still banging our regular, non-green, non-alien women. What’s the hold-up? It would be expensive. Let me rephrase that. The costs would be blasphemous, downright insane, Charlie Manson style. Making one gram of antimatter costs around 62.5 trillion $, it’s by far the most expensive material on Earth. And you’d need tons of the stuff to get to Alpha Centauri. Bummer! And even if we’d all get a second job to pay for it, we still couldn’t manufacture sufficient amounts in the near future. Currently 1.5 nanograms of antimatter are being produced every year. Even if scientists managed to increase this rate by a factor of one million, it would take 1000 years to produce one measly gram. And we need tons of it! Argh. Reality be a harsh mistress …

Want to learn German? Get ready for brain-overload …

german articles

(Note how the feminine article turns into the masculine article for absolutely no reason)

ze7ge9

Need more? Here’s how to conjugate the verb “to work” = “arbeiten” in English and German:

I work ich arbeite
you work du arbeitest
he/she/it works er/sie/es arbeitet
we work wir arbeiten
you work ihr arbeitet
they work sie/Sie arbeiten

(Just FYI: You say “du” when talking to one person and “ihr” when talking to a group. In English you use “you” in both cases)

But on the bright side, the tenses are a lot easier … no continuous forms and the perfect form is identical in meaning to the simple form … so there’s that

Two And A Half Fallacies (Statistics, Probability)

The field of statistics gives rise to a great number of fallacies (and intentional misuse for that matter). One of the most common is the Gambler’s Fallacy. It is the idea that an event can be “due” if it hasn’t appeared against all odds for quite some time.

In August 1913 an almost impossible string of events occurred in a casino in Monte Carlo. The roulette table showed black a record number of twenty-six times in a row. Since the chance for black on a single spin is about 0.474, the odds for this string are: 0.474^26 = 1 in about 270 million. For the casino, this was a lucky day. It profited greatly from players believing that once the table showed black several times in a row, the probability for another black to show up was impossibly slim. Red was due.

Unfortunately for the players, this logic failed. The chances for black remained at 0.474, no matter what colors appeared so far. Each spin is a complete reset of the game. The same goes for coins. No matter how many times a coin shows heads, the chance for this event will always stay 0.5. An unlikely string will not alter any probabilities if the events are truly independent.

Another common statistical fallacy is “correlation implies causation”. In countries with sound vaccination programmes, cancer rates are significantly elevated, whereas in countries where vaccination hardly takes place, there are only few people suffering from cancer. This seems to be a clear case against vaccination: it correlates with (and thus surely somehow must cause) cancer.

However, taking a third variable and additional knowledge about cancer into account produces a very different picture. Cancer is a disease of old age. Because it requires a string of undesired mutations to take place, it is usually not found in young people. It is thus clear that in countries with a higher life expectancy, you will find higher cancer rates. This increased life expectancy is reached via the many different tools of health care, vaccination being an important one of them. So vaccination leads to a higher life expectancy, which in turn leads to elevated rates in diseases of old age (among which is cancer). The real story behind the correlation turned out to be quite different from what could be expected at first.

Another interesting correlation was found by the parody religion FSM (Flying Spaghetti Monster). Deducting causation here would be madness. Over the 18th and 19th century, piracy, the one with the boats, not the one with the files and the sharing, slowly died out. At the same time, possibly within a natural trend and / or for reasons of increased industrial activity, the global temperature started increasing. If you plot the number of pirates and the global temperature in a coordinate system, you find a relatively strong correlation between the two. The more pirates there are, the colder the planet is. Here’s the corresponding formula:

T = 16 – 0.05 · P^0.33

with T being the average global temperature and P the number of pirates. Given enough pirates (about 3.3 million to be specific), we could even freeze Earth.

pirates global warming correlation flying spaghetti

But of course nobody in the right mind would see causality at work here, rather we have two processes, the disappearance of piracy and global warming, that happened to occur at the same time. So you shouldn’t be too surprised that the recent rise of piracy in Somalia didn’t do anything to stop global warming.

As we saw, a correlation between quantities can arise in many ways and does not always imply causation. Sometimes there is a third, unseen variable in the line of causation, other times it’s two completely independent processes happening at the same time. So be careful to draw your conclusions.

Though not a fallacy in the strict sense, combinations of low probability and a high number of trials are also a common cause for incorrect conclusions. We computed that in roulette the odds of showing black twenty-six times in a row are only 1 in 270 million. We might conclude that it is basically impossible for this to happen anywhere.

But considering there are something in the order of 3500 casinos worldwide, each playing roughly 100 rounds of roulette per day, we get about 130 million rounds per year. With this large number of trials, it would be foolish not to expect a 1 in 270 million event to occur every now and then. So when faced with a low probability for an event, always take a look at the number of trials. Maybe it’s not as unlikely to happen as suggested by the odds.

Hollywood and Physics

We’ve all seen these kinds of movies. After a fast and dramatic chase, the bad guy jumps out of the car, determined to end the good guy once and for all. His evil plans have been thwarted for the last time! In self-defense, the good guy is forced to take a shot and when the bullet hits, the evildoer is thrown violently backwards as a result of the impact and through the nearest shop window. Once the hero is reunited with the love of his life, the credits roll and we are left to wonder if that’s really how physics work.

In a previous example we calculated the momentum of a common 9 mm bullet (p = 5.4 kg m/s). Suppose the m = 75 kg evildoer gets hit by just this bullet. Since the bullet practically comes to a halt on impact, this momentum has to be transferred to the unlucky antihero for the conservation of momentum to hold true. Accordingly, this is the speed at which the bad guy is thrown back:

5.4 kg m/s = 75 kg · v’

v’ ≈ 0.07 m/s ≈ 0.26 km/h ≈ 0.16 mph

This is not even enough to topple a person, let alone make him fly dramatically through the air. From a kinematic point of view, the impact is not noticeable. The same is true for more massive and faster bullets as well as for a series of impacts. The only thing that can make a person fall instantly after getting shot is a sudden drop in blood pressure and the resulting loss of consciousness. But in this case, the evildoer would simply drop where he stands instead of being thrown backwards.

This is not the only example of Hollywood bending the laws of physics. You’ve probably heard the weak “fut” sound a Hollywood gun makes when equipped with a silencer. This way the hero can take out an entire army of bad guys without anyone noticing. But that’s not how pistol silencers work. At best, they can reduce the the sound level to about 120 dB, which is equivalent to what you hear standing near a pneumatic hammer or right in front of the speakers at a rock concert. So unless the hero is up against an army of hearing impaired seniors (which wouldn’t make him that much of a hero), his coming will be noticed.

This was an excerpt from my Kindle book: Physics! In Quantities and Examples

For more interesting physics, check out my Best of Physics selection.

Estimating Temperature Using Cricket Chirps

I stumbled upon a truly great formula on the GLOBE scientists’ blog. It allows you to compute the ambient air temperature from the number of cricket chirps in a fixed time interval and this with a surprising accuracy. The idea actually quite old, it dates back 1898 when the physicist Dalbear first analyzed this relationship, and has been revived from time to time ever since.

Here’s how it works: count the number of chirps N over 13 seconds. Add 40 to that and you got the outside temperature T in Fahrenheit.

T = N + 40

From the picture below you can see that the fit is really good. The error seems to be plus / minus 6 % at most in the range from 50 to 80 °F.

The Island – A Fun Logic Puzzle

Imagine there’s an island with two villages, the village of lies and the village of truths. The people that live in the village of lies always lie, whereas the people from the village of truths alsways tell the truth. So far so good. Arriving on this island, you are greeted by three natives: Alex, Beatrice and Christian.

Alex says something, but due to the background noise, you don’t understand him.

Beatrice says: Alex said that he’s from the village of lies.

Christian says: Beatrice is lying.

Which village is Christian from?

———————————————————————

Enlarge the image below to find out the answer.

puzzle