The Intriguing Mr. Wolfram
Stephen Wolfram is back in the news again. In 2002 he published "A New Kind of Science", which I did not read. I'm still not going to read it, but his ideas, as reported in the media, are intriguing, so I can't help recording my musings on the subject. No one will read what I write either, so that's fair.
The idea of NKS is that fundamental physics can be explained by simple computational programs. That idea isn't particularly new. Wolfram is a former APL programmer, as am I, and in 1992 the French APLer Gerard Langlet presented a paper at an APL conference in St. Petersburg, Russia proposing a computational foundation for a "theory of everything" based on the not-equals process, which in APL is referred to "not-equals scan".
An axiom of special relativity is that there is no universal clock. It does not make sense to speak of the time in one place as being the same, or different, from the time in another. If there were a universal clock, communication between different entities could depend on when a signal was received, or how far apart the signals were. But thanks to Einstein we know it's not possible. We're left with only asynchronous communication.
And what is the simplest imaginable asynchronous communication? An entity that detects whether the incoming signal has changed.
Imagine incoming signals as a binary stream of ones and zeros. If the time of arrival of the signal and time between signals cannot possibly be meaningful, then the only information we can get is when the signal changes. Here is a possible stream of incoming bits:
0 0 0 1 1 1 1 0 1 1 1 1 0 0 0 0 0 0 1
And here is the result of applying the not-equal process to that stream:
0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 0 0 1
Evidently the not-equal process detects change.
In computer communication, the timing of a stream of bits is carefully controlled, but in the context of physics, timing is irrelevant. You get the same result no matter how the signals are spaced out in time:
0 0 0 1 1 1 1 0 1 1 1 1 0 0 0 0 0 0 1
0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 0 0 1
But what is the nature of these signals? And what is the nature of the communicating entities? We don't know, maybe can't know, and maybe it doesn't matter. Maybe if we can find mathematics that predicts everything we can observe, that would be sufficient for any human purpose. Perhaps we can call that an "explanation", particularly if everything we can observe can be predicted from it.
This approach treats the physical world as discrete rather than continuous. It's made up of discrete entities, whatever they are, and is not infinitely divisible. It's made of nuts, not butter.
It must be so, as Xeno's famous paradox proves. Xeno speculated that, before walking to a flagpole, one must first walk halfway. And before reaching that point, one must first walk halfway to that, i.e. one-fourth of the way. And so on. If that is true, we can never move, because before we move to any point, we must move halfway to that point. Evidently, at a sufficiently small scale, it is no longer true that you need to go half way to a point before going to that point.
Let's call the point you're at point A and the point you want to reach point B. At some scale, there is no point C between point A and B. You go from A to B without first passing through any point C.
But if so, where are you when you leave point A but haven't reached point B yet? If there were such as place, it would be point C, but there can't be a point C. You must instantaneously move from point A to point B with no passage of time and without being somewhere else in the meantime. Perhaps you can spend some time at point A and then some time and point B, but there can be no passage of time as you move between them. It means that, for some very short period of time at least, you must be at both point A and point B simultaneously.
And furthermore, as there's no "there" there between A and B, for some very short period of time, at least, A and B must in some sense be in the same place.
We know from relativity that two things cannot be in the same place at the same time. Ergo, for at least some very short period of time, A and B must be the same thing. To move from point A to point B at the smallest scale, A and B must merge into a single entity, at least momentarily, before separating again.
But anyway, Xeno's paradox and everything that follows from it is also proof of the discrete nature of physics. If the world were butter, where there was always something in between where you were and where you meant to go, you certainly wouldn't be able to move.
All of which leads me to agree with Wolfram, and many others by the way, that the universe can be explained by simple fundamental mathematical processes acting on discrete entities, or perhaps ultimately, by a single process, not-equals. That's not to say that Wolfram's method will produce results. That's a whole other question.
The idea of NKS is that fundamental physics can be explained by simple computational programs. That idea isn't particularly new. Wolfram is a former APL programmer, as am I, and in 1992 the French APLer Gerard Langlet presented a paper at an APL conference in St. Petersburg, Russia proposing a computational foundation for a "theory of everything" based on the not-equals process, which in APL is referred to "not-equals scan".
An axiom of special relativity is that there is no universal clock. It does not make sense to speak of the time in one place as being the same, or different, from the time in another. If there were a universal clock, communication between different entities could depend on when a signal was received, or how far apart the signals were. But thanks to Einstein we know it's not possible. We're left with only asynchronous communication.
And what is the simplest imaginable asynchronous communication? An entity that detects whether the incoming signal has changed.
Imagine incoming signals as a binary stream of ones and zeros. If the time of arrival of the signal and time between signals cannot possibly be meaningful, then the only information we can get is when the signal changes. Here is a possible stream of incoming bits:
0 0 0 1 1 1 1 0 1 1 1 1 0 0 0 0 0 0 1
And here is the result of applying the not-equal process to that stream:
0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 0 0 1
Evidently the not-equal process detects change.
In computer communication, the timing of a stream of bits is carefully controlled, but in the context of physics, timing is irrelevant. You get the same result no matter how the signals are spaced out in time:
0 0 0 1 1 1 1 0 1 1 1 1 0 0 0 0 0 0 1
0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 0 0 1
But what is the nature of these signals? And what is the nature of the communicating entities? We don't know, maybe can't know, and maybe it doesn't matter. Maybe if we can find mathematics that predicts everything we can observe, that would be sufficient for any human purpose. Perhaps we can call that an "explanation", particularly if everything we can observe can be predicted from it.
This approach treats the physical world as discrete rather than continuous. It's made up of discrete entities, whatever they are, and is not infinitely divisible. It's made of nuts, not butter.
It must be so, as Xeno's famous paradox proves. Xeno speculated that, before walking to a flagpole, one must first walk halfway. And before reaching that point, one must first walk halfway to that, i.e. one-fourth of the way. And so on. If that is true, we can never move, because before we move to any point, we must move halfway to that point. Evidently, at a sufficiently small scale, it is no longer true that you need to go half way to a point before going to that point.
Let's call the point you're at point A and the point you want to reach point B. At some scale, there is no point C between point A and B. You go from A to B without first passing through any point C.
But if so, where are you when you leave point A but haven't reached point B yet? If there were such as place, it would be point C, but there can't be a point C. You must instantaneously move from point A to point B with no passage of time and without being somewhere else in the meantime. Perhaps you can spend some time at point A and then some time and point B, but there can be no passage of time as you move between them. It means that, for some very short period of time at least, you must be at both point A and point B simultaneously.
And furthermore, as there's no "there" there between A and B, for some very short period of time, at least, A and B must in some sense be in the same place.
We know from relativity that two things cannot be in the same place at the same time. Ergo, for at least some very short period of time, A and B must be the same thing. To move from point A to point B at the smallest scale, A and B must merge into a single entity, at least momentarily, before separating again.
But anyway, Xeno's paradox and everything that follows from it is also proof of the discrete nature of physics. If the world were butter, where there was always something in between where you were and where you meant to go, you certainly wouldn't be able to move.
All of which leads me to agree with Wolfram, and many others by the way, that the universe can be explained by simple fundamental mathematical processes acting on discrete entities, or perhaps ultimately, by a single process, not-equals. That's not to say that Wolfram's method will produce results. That's a whole other question.
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