3 ms·
Mutation is just how you cut up time. If I pick up a coin and place is 6 inches to the left I've mentally cut the world into three epochs, the prior, the mutat
by tel 12y ago
Mutation is just how you cut up time.
If I pick up a coin and place is 6 inches to the left I've mentally cut the world into three epochs, the prior, the mutation, and the posterior. Thus I feel I mutated it.
If I drop a ball, I can do the same trick and cut the world into the before and after of my releasing the ball, but for the duration of it falling I think of physics just happening. This is smooth, continuous, and not a set of discrete mutations.
The math backs this up as well in the sense that integration is exactly what lets us convert the world of mutation into the world of constant physics (FRP from the "continuous time denotational semantics" perspective of Conal Elliott not the usual way the term is abused).
So to claim that "everyday objects" are beholden to mutation or immutability I think is a game of confusing the map with the terrain.
- seanmcdirmid 12y agoMutation is a function over time, for sure. Most people understand the change and not the continuous function behind the change, and many processes are too chaotic to be described by nice clean continuous functions (a physical simulation with instantaneous collisions...). I believe even FRP uses steppers for those kinds of things. Most people think in terms of mutation, not in terms of the abstract functions that cause values to change over time.
- tel 12y agoI think this is just a vocabulary difference, not a genuine mental one. When I see a ball falling I don't think of it moving forward and accelerating in an infinite number of infinitesimal mutations---I see it as being in the state of falling and recognize the space of actions I could perform in time with it. There's mutation in the sense that I cannot arbitrarily go back in time. There's immutability in the sense that the rules governing that motion are not "staged" in any way outside of the interference of my hand. A better example is perhaps catching a fly ball as an outfielder in baseball. I absolutely cannot be processing that motion as a set of mutations in order to function---instead, I predict according to a "mathematical pattern" if not a formula, where it will land based on scant observation of segments of its space-time trajectory. And that's all more or less instinctual, I believe. It must be in order for me as an outfielder to execute my task. That stuff needs to just be built in to my brain. So while ultimately FRP and physics might be "implemented" (ha, ha, philosophers forgive me) in discrete steps, there's a vital model of each which is continuous.
- seanmcdirmid 12y agoMany behaviors are continuous, it is just that many are not. I am here today and gone tomorrow, why? It doesn't matter, it just is! If all I had to worry about in a physics engine was F = ma, life would be a simple continuous function, but it turns out collisions just ruin that. If you really want to get in the thick of it, take Conway's game of life (or NKOS if you can stomache wolfram): there is quickly in a point in a physical process where you don't know what happens next without the previous state.
- tel 12y agoTo be clear, I'm not arguing that either mechanism describes all things—actually the exact opposite, that neither is sufficient.
- asQuirreL 12y agoThe issue with arguments of the form "Mutation is..." is that all these things are models of mutation: merely representations. Different models help us elucidate different properties of the same underlying phenomena. This does not mean that either one is "correct" or the one true representation of mutation.