The next part of my seven part explanation of chaos theory to a popular audience. Chaos is a mechanism that allows deterministic objects to behave unpredictably. I will explain why this happens and what kinds of predictions we can make when something is chaotic. Part IV is about strange attractors. If you allow something to wander chaotic for a while, what kinds of patterns does it make? Surprisingly, the answer is often a fractal.
The next part of my seven part explanation of chaos theory to a popular audience. Chaos is a mechanism that allows deterministic objects to behave unpredictably. I will explain why this happens and what kinds of predictions we can make when something is chaotic. Part III will be about Lyapunov exponents. If you search for a definition of what chaos theory is, the most common result is that chaos occurs whenever there is a positive Lyapunov exponent. While I would prefer defining chaos to be anything with positive topological entropy, Lyapunov exponents are extremely important. They explain what we mean when we say that something ‘behaves unpredictably’.
I chose the name The Chaostician for this blog. To live up to this name, this blog should be about chaos, in particular, what a physicist means when referring to ‘chaos theory’. Let’s begin with an example. Something known as the logistic map is (arguably) the simplest chaotic system. We will now describe and analyze it in detail.
I chose the name The Chaostician for this blog. To live up to this name, this blog should be about chaos, in particular, what a physicist means when referring to ‘chaos theory’. This seven part series is my explanation of chaos theory to a popular audience. Chaos is a mechanism that allows deterministic objects to behave unpredictably. I will explain why this happens and what kinds of predictions we can make when something is chaotic.
Einstein’s most revolutionary idea is that gravity is geometry. The theorems of geometry are not eternal truths, but can be changed by mass and energy. This is my first longer explanation of ideas that are well established in science, but not well understood by the public. To keep this from becoming too long and overwhelming, I have split the six parts of this explanation into three blog posts. The two parts for today are about black holes and the experimental evidence of general relativity.
Einstein’s most revolutionary idea is that gravity is geometry. The theorems of geometry are not eternal truths, but can be changed by mass and energy. This is my first longer explanation of ideas that are well established in science, but not well understood by the public. To keep this from becoming too long and overwhelming, I have split the six parts of this explanation into three blog posts. The two parts for today are about how the write the Pythagorean Theorem for spacetime and how to modify it to include gravity.
Einstein’s most revolutionary idea is that gravity is geometry. The theorems of geometry are not eternal truths, but can be changed by mass and energy. This is my first longer explanation of ideas that are well established in science, but not well understood by the public. To keep this from becoming too long and overwhelming, I have split the six parts of this explanation into three blog posts. The two parts for today are the introduction and an explanation of how different geometries have different versions of the Pythagorean Theorem.
