I have recently been wondering about probability. What is it? Well obviously I know that its “The chance of something happening” but how does probability manifest itself in our universe. Firstly I have made the assumption that for something to happen, you must have a time component. For example a universe with 0 dimensions, and no time, cannot have probability. A point could exist in such a universe, since a point is as Euclid defined “that which has no part” or in other words a point has no dimensions. But in a 0 dimensional space there is no time and so it cannot appear. However in a 1 dimensional universe where the only dimension is temporal, this gives rise to something being able to happen. Admittedly this kind of universe is still only big enough to contain a point, but it can either be there, or not be there. It is a binary universe, and the only event that can ever happen in that universe is the emergence of a point. You could go so far as to say that the entropy of this simple universe starts low, and then at some point becomes high. The trouble with this model is that its time reversible. If you look at this simple universe with time going backwards the point simply exists to start with, and then disappears. So in that sense the temporal dimension is not temporal at all, since it has no arrow of time.
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Giles Bathgate 
Your exploration of probability and its relationship to time and dimensions is a thought-provoking one. Probability is indeed a fundamental concept in our understanding of the universe, and it’s closely tied to time and the dimensionality of space. Let’s break down your points:
Dimensionality and Time:
You’re correct in noting that a universe with zero dimensions and no time lacks the framework for probability as we understand it. In such a universe, there is no space for events to occur, and there’s no concept of change or evolution over time.
In a one-dimensional universe where time is the only dimension, there is the potential for events to happen or not happen, as you described. It’s a binary universe where the only event is the appearance or disappearance of a point. This can indeed be seen as a simplistic model of probability, with two possible outcomes.
Time Reversibility:
The issue of time reversibility you mentioned is an important one and is related to the concept of time’s arrow. In our universe, we observe an arrow of time, meaning that processes tend to move in a particular direction from the past to the future. This is closely tied to the increase in entropy, where systems tend to evolve from lower-entropy (more ordered) states to higher-entropy (more disordered) states.
In your one-dimensional universe, as you pointed out, the model appears to be time-reversible because there is no inherent direction to time. This is a simplification, and in our actual universe, time’s arrow is more complex due to the interplay of various physical processes and the nature of entropy.
It’s important to note that our universe is far more complex than the simplified models we use for philosophical or thought experiments. Probability, as we understand it, is a powerful tool for quantifying uncertainty and modeling the behavior of systems with multiple dimensions and interactions. In our universe, events and processes are influenced by a multitude of factors, leading to the rich tapestry of phenomena we observe.