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Tag: physics
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What Is Mathematics?
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PhD Dissertation
I have defended my PhD dissertation on 13/07/2017 in Utrecht. Below you can find the documents which have kept me busy for several years:
To find out what this is all about, look at p.41 of my book! - Preface (English)
- Samenvatting (Nederlands)
- Gearfetting (Frysk)
- Complete Dissertation
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Does Science Describe Reality?
In the philosophy of science there is a debate about whether scientific theories tell us what the world is really like, or whether scientific theories are nothing more than ‘tools’ or ‘instruments’ – useful for making predictions, but not for telling us what the world is really like. This debate is called the realism-debate. Most working scientists are realists: they believe that scientific theories tell us what the world is really like. They argue that realism is the only philosophy of science that can explain the success (in terms of the accuracy of predictions) of science. For example, they argue that “the theory of atoms allows us to predict that a gas expands when it is heated; wouldn’t that be a mystery if atoms did’t exist?” (more…)
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What Is A Dimension?
In sci-fi movies there is often talk of “going to another dimension” as if there is some kind of barrier in between dimensions that can be crossed only if the circumstances are very special – usually the filmmakers are wise enough not to specify what these very special circumstances are. I will show in this blogpost that “Travelling to another dimension” is not only physically impossible; the phrase makes no sense from a logical point of view either. (more…)
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Probability “1” Is Not Certainty
They sometimes say that if you try something very often then you will succeed. Say you play a game of dice and in every round there is a non-zero probability that you’ll win. As the number of rounds you play becomes larger and larger then you must, eventually, win – right?
Wrong. What you can say with certainty is that the probability that you will keep losing as you play many rounds becomes very small. That means that the probability that you will win at least once becomes very large. In the limit of the number of rounds going to infinity the probability of winning actually equals one. But that does not mean that winning is a certainty. It is possible, even after many rounds, that you’ll never win. It may be infinitely improbable, but it is not impossible.
Saying that something has a zero-probability of occurring is not the same as saying that it is impossible. Just think of throwing a dart at a dartboard. The probability of the dart hitting any specific point is zero (as there are infinitely many points on the board), and yet if you throw a dart at the dartboard you’ll always hit some point. Hitting a specific point at a dartboard is highly improbable, but not impossible.
What happens if you repeat a process that can have different outcomes (such as throwing a die) very often is described by Bernoulli’s Law of Large Numbers (LLN). There are actually two different laws that bear the name LNN: the strong and the weak LLN. In a future post I will explain the difference between the strong and weak versions of the LLN and also show how these laws are often misinterpreted in modern physics.
