Math Formula

Wednesday, December 21, 2011

Nothing Is Ever What It Seems - An Alternate View To The Globe

Recently I was given an atlas as a present by good friends. May not sound too surprising - unless you take into account that this atlas does not represent the world in the way we got used to since we were kids, but in a slightly different format. Something like this (source:

Confused? Maybe even more so if you contrast it with the more traditional world map (source:, combined by the author; click to enlarge):

As you see, some areas on the traditional map (on the right side), appear bigger relative to others, when compared to the Peters map (on the left side), which presents areas exactly in the ratio they actually are. A few highlights of how areas are over-presented in the traditional map (all numbers:
  • Europe appears only slightly smaller than Africa; in fact, it's only one third (10,180,000 km2 vs. 3,221,532 km2)
  • Greenland appears similar to Brazil, whereas actually it's only a quarter (2,166,086 km2 vs. 8,514,877 km2)
  • The three Scandinavian countries Norway, Sweden and Finland combined appear even bigger than Mexico, whereas the very opposite is true (835,216 kmvs. 1,972,550  km)

So, what's wrong here? Well, the problem is, that we are apparently trying to represent a round, three-dimensional ball on a flat, two-dimensional sheet of paper. Kind of similar to squaring the circle, which is known to be rather difficult a task either.

Thus, inherently all representations of the world on a map are wrong.

Each representation is a trade-off between keeping
  • distance equality
  • angle equality
  • area equality
Unfortunately, you can only preserve two, but not all of them (for more background information, please refer to the Wikipedia article on map projection).

Since maps were originally mainly used for navigational purposes, it was rather useful to keep both distance and angle, and disregard area equality. (Just imagine where important sailors like Christopher Columbus, Vasco da Gama, Marco Polo or James Cook might have ended up on their long journeys home without proper cartographic and navigational equipment)

However, this "area inequality" is more severe the closer you come to the poles. Therefore, areas closer to the poles are more stretched and appear bigger relative to the ones around the equator. As it happens, this representation extremely favours areas like the USA and Europe - the western world, at the expense of Africa, Latin America, ...

This is not to blame "westerns" of using a "wrong" map - as I said before, all maps are wrong to some extent. Yet, I think disregarding economic power and political strength, it is fair not to draw any short-sighted conclusions based on a misleading representation of sizes.

Tuesday, December 13, 2011

Call me paraglider ... ehm, officially tested paragliding pilot!

Several weeks ago, I joined airdrenaline, a local paragliding club. During Monday's annual meeting of the club, I was awarded the "Diploma Pilot paraglajdera", rendering me an officially tested paragliding pilot!

In the weeks between, I got to know some of the guys from the club fairly well, and it's hard to describe how great a time I had. In the meantime, I
  • scared away a cow which was calmly eating when I approached it from the air
  • scared away a farmer who was taking a dump in the field
  • literally found the pretty worst landing zone on the entire hill (some coppice)
  • literally found the only tree on the entire hill
It's definitely no exaggeration to say that a big share of my amazing year 1 aftermath is due to you, dear colleagues from the club.
Admittedly, the ratio between effort and actual enjoyment is fairly high, similar to, say, surfing, or ... well, I guess you can imagine one or two more similar activities.

For those of you who are not familiar with paragliding: Basically, the only equipment used is a wing, to which you are connected with an awful lot of lines. Unfortunately, these lines have a tendency to get tangled whenever they can. This wing is made of ultra-light fabric such as polyester, and typically around 25-30 sqm. It is constructed in a way that it would fly without any external powers - as soon as it is inflated properly. Once in the air, you mainly control it via a left and a right line (brake). Pulling the left brake deflates the glider a little bit on that side, resulting in the air streaming faster through the right part of it. Consequently, you turn left.

Typically, you start by spreading your glider on a hill and turn your back to the hill, looking towards the glider. Under normal conditions, the wind blows up hill. Therefore, once you start pulling the lines, the glider inflates and, since it's constructed in a way to fly, it starts ascending above your head.
Something like that:

Useless to say, it also starts showing its own will, too. Thus, the first two days of learning how to handle a glider only consist of getting to know what the glider wants, and how to enforce what you want. Pulling it up. Glider going down. Pulling it up. Glider pulling you five meters in one direction. And pulling it up. Glider all of a sudden trying to take you off, and concerned instructor trying to hold you back. Packing glider. And again.

However, the moments where you gain control over the glider become more frequent and longer.
Until, one day, you are considered to be ready for takeoff. In order to do that, you pull up the glider until it is directly above you, turn, raise your hands in order to release the brakes ... and then you run. Remember, it's still takeoff against the wind, so you must run and pull really strong:

... until, all of a sudden, the wind just lifts you up, and you are flying .. woohooo!

Similar to some of the other activities from above, it's hard to describe it to somebody who never experienced it himself. For me, it's an awesome combination of freedom, calmness ... well, you best simply try it out yourself!

Even though I obtained the diploma now, I know there is so much and more to learn ... and I can't tell you how excited I am to spend some more time out there in the Bosnian mountains, together with some nice guys, doing something that is simply awesome...

P.S.: If you are interested in more pictures, check out the club's Facebook page. There are also some cool videos on youtube.

Wednesday, December 7, 2011

About The Freedom Of Goods

Chapter 2 of "TITLE I - Free movement of goods" of the Consolidated version of the Treaty establishing the European Community provides the basis for one of the four major pillars of what is referred to as the Single Market.

According to,
... controls on the movement of goods within the internal market have been abolished and the European Union is now a single territory without internal frontiers.
The abolition of customs tariffs promotes intra-Community trade, which accounts for a large part of the total imports and exports of the Member States.
Articles 28 and 29 of the Treaty establishing the European Community prohibit import and export restrictions between all Member States. However, if there is a threat to public health or the environment, Member States may restrict the free movement of goods.
This renders the EU a customs union, a special type of free trade area. Well, good and nice - as long as you find yourself on the lucky side of globalization, and as long as you don't happen to live in a country which is implicitly excluded from the union, by not being explicitly included. Like, say, Bosnia for example, in which case even purchasing a kindle via Amazon can become quite lengthy a process.

I will not dive into the pros and cons of free trade vs. protectionism now (oh, just found there is an entire article dedicated to the free trade debate on Wikipedia). Instead, I want to tell you how surprised I was again this week.

As some of you might remember, I bought a motorbike a while ago. Since I found that registering a vehicle can be quite complex a task for a foreigner in Bosnia (and, I assume, in most other countries too), this bike is now registered on a local friend's name. Recently, I talked to two Austrian custom experts, about me driving to Austria with 'my' BiH bike. Bang! Shake-heads, absolutely no, how can I even think about it (that's the young, naive European again), no way!

Just to be clear: Even with a written permission from the owner, I (as a citizen of an EU member state) must not 'import' any vehicle from a third-country ... and in that context, simply driving the vehicle across the border, and be it just for one hour, is 'importing' already.

I must confess, this requires me to rethink the entire idea of 'importing'. For me, that was rather permanent a thing, i.e., with the intent of using something for an extended period, or selling it. On the contrary, the liability to declare a good already arises by simply moving the good across the border, disregarding intended duration and purpose.

But, you might think, what happens if my friend rides the bike across the border, and I just use it afterwards? Well, I was informed, that's "abusive usage" then, representing a criminal act from both of us ...

Thinking the other way round, the same is true if I lend my Austrian car to a friend here - "abusive usage"! I'm neither a lawyer nor a customs expert (however I'm guilty of istism right now), and I guess there is some rationale behind that interpretation (am I also guilty of being naive now?), but my common sense simply cannot see anything wrong about it. It is my friends bike, and he is lending it to me, so why should I not drive to Austria, or any other place I want to?

I don't know whether the EU in general is too positively perceived at the moment, but giving me the freedom to lend my stuff to whomever I want, for whichever purpose I want, is clearly a great thing ... and that is what the Freedom of Goods is all about.

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