Philosophy
If you study subjects like philosophy, cosmology or mathematics, it won't be long until you find yourself deep in the contemplation of the nasty little business of infinity.
Zeno's paradoxes of motion represent some of the earliest attempts to confront this beast, and although modern tools like calculus or the idea of an infinite sum seems to resolve the problem, I can't say that we've really solved it. It's more like we've brushed it aside and agreed to pretend it's been dealt with. Although I find myself on a small minority here, I still sympathize with Zeno.
One thought-experiment I've never been able to swallow, however, is Hilbert's Infinite Hotel. From the very beginning, it seems to want to assume premises that I would not want to grant... but this is not about me. It's about you, dear reader, and it's about exposing you to interesting ideas that will be worth your while to think about, so here's a short introduction:
And if you want more, check out the Grandfather paradox or the Chinese Room thought experiment.
- What Is Zeno's Dichotomy Paradox?
When I first introduce my students to the weirdness of philosophy and how even our most deeply-entrenched beliefs might be subject to serious questioning, I usually like to begin by posing to them Zeno's attempt to refute the idea that motion is possible...
- To Infinity And Beyond
Apparently the title of this documentary also has something to do with Toy Story? Well, I haven't seen that movie, but I can tell you what this documentary is about... Infinity. The most obvious way to start thinking about infinity is through...
- The Impossibility Of Motion - Achilles And The Tortoise
There are many things most of us just take for granted as obvious or just plain common sense, and therefore as not worth wasting our time on. Philosophers, however, nit-picking bunch that we are, are insatiably curious, and in our search for some coherent...
- Everything And Nothing - Everything
You may find this hard to believe, but we've known about the true size of the universe for only about 100 years. When Copernicus proposed his revolutionary heliocentric model, for instance, he still believed in the existence of a perfect celestial...
- An Infinite Universe?
If the universe is infinite now it has always been infinite. This is the opinion of many astronomers today as can be concluded from the following series of interviews, but the opinions differ much more than I had expected. Many astronomers do not have...
Philosophy
Hilbert's Infinite Hotel
Zeno's paradoxes of motion represent some of the earliest attempts to confront this beast, and although modern tools like calculus or the idea of an infinite sum seems to resolve the problem, I can't say that we've really solved it. It's more like we've brushed it aside and agreed to pretend it's been dealt with. Although I find myself on a small minority here, I still sympathize with Zeno.
One thought-experiment I've never been able to swallow, however, is Hilbert's Infinite Hotel. From the very beginning, it seems to want to assume premises that I would not want to grant... but this is not about me. It's about you, dear reader, and it's about exposing you to interesting ideas that will be worth your while to think about, so here's a short introduction:
And if you want more, check out the Grandfather paradox or the Chinese Room thought experiment.
- What Is Zeno's Dichotomy Paradox?
When I first introduce my students to the weirdness of philosophy and how even our most deeply-entrenched beliefs might be subject to serious questioning, I usually like to begin by posing to them Zeno's attempt to refute the idea that motion is possible...
- To Infinity And Beyond
Apparently the title of this documentary also has something to do with Toy Story? Well, I haven't seen that movie, but I can tell you what this documentary is about... Infinity. The most obvious way to start thinking about infinity is through...
- The Impossibility Of Motion - Achilles And The Tortoise
There are many things most of us just take for granted as obvious or just plain common sense, and therefore as not worth wasting our time on. Philosophers, however, nit-picking bunch that we are, are insatiably curious, and in our search for some coherent...
- Everything And Nothing - Everything
You may find this hard to believe, but we've known about the true size of the universe for only about 100 years. When Copernicus proposed his revolutionary heliocentric model, for instance, he still believed in the existence of a perfect celestial...
- An Infinite Universe?
If the universe is infinite now it has always been infinite. This is the opinion of many astronomers today as can be concluded from the following series of interviews, but the opinions differ much more than I had expected. Many astronomers do not have...