Evil Demons and Living in the Matrix

Perhaps the greatest thing about philosophy is that really crazy ideas are taken very seriously by philosophers. My favourite example is the so called Evil Demon theory (or sometimes it's called Evil Genius), which is basically a simple question - how can you be sure that you are not being deceived by an evil demon right now? That is, how can you really be sure that your senses are not deceiving you? After all, we have all had experiences when our sense fooled us at least once. This famous problem was formulated by one of the most important western philosophers Descartes. In his philosophical treatise Meditations on First Philosophy (1641) Descartes pondered the problems of truly knowing something and achieving knowledge.

So this problem seems to be extraordinary hard, but is it even possible to find an answer for such a problem? There other similar problems like the so called dream theory, which states that it is not possible to tell if you're dreaming when you're in a dream, so how can you be sure you're not dreaming right now? Or even better, how can you be sure that you're not in Matrix? All these problems share a main feature - they really on the fact that our senses can be fooled and that some times an illusion can be as realistic as reality is. So it's seems that the solution to these problems can be found only by discovering some kind of undeniable truths.  Descartes himself believed that we should base our believes only on undeniable truths. An example of such a truth would be the famous quote cogito ergo sum (I think therefore I am). But even if this tackles the problem (many believe that it's not the case, but let's leave that for the next time) it only shows that we exist and do not help us answering the question whether we are dreaming or not. Isn't it funny how the craziest questions end up being the hardest ones?

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Top 10 Greatest Physics Experiments: 8. Measurement of the Earth's Circumference by Eratosthenes

Here we have another experiment, which enhanced our knowledge about Earth. However, this experiment is very unique, as it was carried out more than 2000 years ago. 

As the title says it, this experiment was set up to measure the circumference of Earth. Eratosthenes, a Greek mathematician and the librarian of the great library at Alexandria, in Egypt came up with a brilliant idea how to geometrically calculate the circumference of Earth using shadows in two different cities.

Eratosthenes knew that in Syene (a city almost due south of Alexandria) the sun was directly overhead at noon on a particular day of the year. This meant that at noon a yardstick wouldn’t cast a shadow. Also he knew that Sun is so far away that light rays coming from it would basically be parallel. Thus light rays at the same time in Alexandria should cast a shadow (see the diagram). 

Source

Now since Eratosthenes knew that the angle between the vertical and the shadow is equal to the central angle inside the circle (diagram). He also knew that there is 360 degrees in a circle. Thus all he needed to calculate Earth’s circumference was the distance between Alexandria and Syene.

To understand this more clearly let’s look at an example. Let us say the central angle is 7.2 degrees. This is an angle between Alexandria and Syene. Thus if we divide 360 by 7.2 we get 50. This means that Earth’s circumference is 50 longer than the distance between the two cities.

So all that Eratosthenes needed to do is pay for someone to measure the distance between the two cities. In case you’re wondering how correct was Eratosthenes, depending on the units that he used, he was somewhere between 1% and 16% off, which is amazing having in mind that the experience took place 2000 years ago. 

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