As some of you may know, my thesis advisor was in a Hungarian rock band called Panta Rhei. If you haven't already, go sample some of their music on his website! (I can attest that he is still capable of rocking out, and he looks about the same as he did 30 years ago.) In addition, which I found out recently, Panta Rhei is both the name of a boat in Switzerland and Greek for "everything flows", an aphorism attributed to Heraclitus. So, my advisor's Hungarian band that plays progressive rock and adaptations of Grieg also has a philosophical name! Can't get better.
The idea behind Panta Rhei is often expressed as: "You can't cross the same river twice." This is meant to be paradoxical. Assuming you haven't heard this before and don't know the "solution," you might say, "Of course I can! See, there is a river. I can cross the bridge and come back. I can cross the same river as many times as I like! Naa naaa naaaa!!"
First of all, you would be very annoying. There's no need to use that tone.
But more importantly, what "river" are you talking about having crossed? That long body of flowing water called The Mississippi, for example? But that is just a name. You aren't crossing a name - an abstraction of nature into an idea called "river" - you are crossing the long body of flowing water itself. That is the first insight.
The second insight is that the thing we call "river" is in constant flux as the water flows along, so it can never be the same river. You can't cross the same river twice because the river is always changing. In some sense you are also always changing, as the cells in your body constantly replicate and die, as your brain activity responds to your thoughts about rivers, and so on. Not just people and rivers, but everything is in constant flux. Everything flows.
A further insight is that this is a result of Time. Everything flows because everything exists in time, and in our Universe time always moves forward. If there were no time, then nothing would change. In physics, this idea is expressed in terms of entropy, which is a measure of the amount of disorder in a system. Smooth, flat, homogeneous, boring things have low entropy. It is a fundamental law that entropy always increases with time - smooth things become rough (or cosmologically, smooth density fields grow into galaxy clusters, planets, and people) - and this is often expressed as the destruction of order, as in this cute TED talk by physicist Andreas Albrecht. Watch it right now!
