Sida Liu

Stephen Wolfram recently posted an essay ‘On the Nature of Time’: https://writings.stephenwolfram.com/2024/10/on-the-nature-of-time/

There are five sections: (1) The Computational View of Time, (2) The Role of the Observer, (3) Multiple Threads of Time, (4) Time in the Ruliad, and (5) So What in the End Is Time?

In order to understand it more thoroughly, I tried to rephrase most of the paragraphs in a more concise way with some of my own thought. So here it goes:

The Computational View of Time

1. Traditional science views time as a dimension of spacetime, but this doesn’t explain what time is.
2. Time is the “progressive doing of computation by the universe.”
3. Time can’t be “set to any value” to determine a system’s state, due to computational irreducibility, the system must progress step by step from the start.
4. Several CA examples illustrate what computational irreducibility means.
5. Time might not progress robustly in computation-reducible systems, but our universe is full of computation irreducibility.

The Role of the Observer

1. If the universe is deterministic, why do we experience the future only as it unfolds?
2. Because we are observers within the computationally irreducible system, we are computationally bounded by it, meaning we can’t compute the future in advance and can only unfold with it.
3. As a result of the interplay between computational irreducibility and our computational boundedness, we observe the Second Law and we perceive time as flowing in one direction.
4. It appears to an inner observer that irreducible computation usually turns states with orderly structure to disorder. By symmetry, it’s possible to construct a system with backward rules that appears to evolve from disorder to order, but we can’t compute the initial state due to computation boundedness.
5. Since relativity, we’ve started talking about space and time as if they are bundled together.
6. But in Wolfram’s Physics Project, space is represented as a hypergraph with node as the “atoms of space”, and time corresponds to the progressive rewriting of the hypergraph.
7. “Atoms of time” are elementary rewriting events, where early events feeding information to later ones. All events together from a causal graph.
8. In everyday experience, we tend to parse events into slices of successive times. As in relativity, there are multiple ways of parsing, leading to different reference frames.
9. The causal graph bundles together space with time, with one event leading to different successive events (hinting at the parallel universe). “Time represents ‘computational progress’ in the universe, while space represents the ‘layout of its data structure’.”
10. Because we are computationally bounded observers, we can derive Einsten’s equations for the large-scale behavior of spacetime from the causal graph of hypergraph rewriting. And we internally record the progress of time (hinting at memory).
11. An extreme situation occurs when a part of the hypergraph has too much activity (roughly corresponds to too much energy-momentum), resulting no more rewrites being possible, and time stopping there.

Multiple Threads of Time

1. Time progresses in multiple threads, but we experience time as a single thread.
2. When updating a hypergraph based on a set of rules, events can occur in different orders, leading to different paths of history.
3. We observers perceive just one path, which is linked to the phenomenon of measurement in quantum mechanics.
4. A brachial space is a brachial graph where each node represents a hypergraph of entire space. It is an instantaneous slice of the multiway causal graph.
5. An edge in the hypergraph of ordinary space represents the proximity of “atoms of space,” and an update event at a node can only affect its immediate neighbors. In contrast, an edge in brachial space means the nodes it connects share the common ancestors in the causal graph.
6. (Entanglement cones in branchial space is analogous to light cone in ordinary space.)
7. There are lots of branches, and we observers within the system are also branching, which allows us to observe and store part of the information.
8. It’s similar to how we can only perceive the macroscopic fluid-dynamics-level behavior of a gas.
9. Similarly, we perceive ordinary space as continuous and describe it in computational reducible ways.
10. Our minds are “big” and occupy many similar branches, but we ignore the details and perceive only at a high-level aggregated thread of history (until significant branching occurs).
11. Sometimes we can observe quantum effects that reveal multiple threads, but we generally perceive them in the aggregate way.
12. Since we are computationally bounded, we can only pick out features that are simple enough to describe.
13. We assume that, though we are made of different atoms of space and different branches in the causal graph, we believe we are still “the same us”.
14. But do different human minds or different measuring devices share an “objective reality”? 
15. Wolfram believes we perceive a shared “objective reality” because we are sufficiently nearby in some small patch of branchial space.
16. Just as there’s the speed of light, there would be the maximum entanglement speed (whose value we don’t know yet). If two observers go in different directions at the speed of light, they would probably perceive different realities.
17. The Physics Project suggests that the density of events in the hypergraph of space determines the energy (and mass), and the density of events in the multiway graph (or in branchial graph slices) determines the energy-like action in branchial space.
18. For us to perceive time as a single thread, we need to stay at the same place, believe we’re persistent, and be computational bounded—and we meet these conditions.

Time in the Ruliad

1. The ruliad is the entangled limit of all possible computations across all possible rules.
2. As observers within the ruliad, with just a few assumptions about ourselves, we can derive our laws of physics, including the Second Law, the Einstein equations for spacetime, and (possibly) the path integral in quantum mechanics.
3. The ruliad is unique and abstract. If we could view it from outside, it would be a single timeless object. But we exist within it.
4. If we were not computationally bounded, we could compute the entire ruliad. But we’re computationally bounded.
5. So we can only explore the ruliad step by step as the computation progresses, which gives rise the concept of time.
6. We are very close in ruliad space (just like in branchial space), which is why we have a shared objective reality.
7. The ruliad contains not just all possible physics but also all possible mathematics.
8. When we explore mathematics within the ruliad, we only carve out some domain of theorems we assume are true. It’s a different way of exploring the ruliad, when do math, we usually don’t need time.
9. So, a physical process is like motion, where we translate between rule sets. A mathematical process, on the other hand, is like expansion. The former requires moving between computational rules over time, while the latter is understanding the rules without the notion of time. (Sorry, I’m not very sure about the last paragraph in this section.)

So What in the End Is Time?

1. Time is what progresses when one applies computational rules. It can be defined abstractly, independent of the details of those rules.
2. We can’t jump ahead; instead, we have to follow a linear chain of steps, leading to our perception of time progressing.
3. Different systems following different irreducible computational rules accumulate computational effects in the same way and thus progress through time in the same way.
4. There’s an analogy between time and heat: heat is abstract and can describe different materials, time can describe the progresses of different systems with different rules.
5. This is more than an analogy—heat is abstract due to the universality of computational irreducibility.
6. If we were not computationally bounded, we could break the Second Law and wouldn’t just describe things in terms of randomness and heat. Also, we’d be able to jump ahead or following different threads of time.
7. But we are computationally bounded, so we approximately view time as a single one-dimensional thread.
8. Even with science, we can’t outrun time and predict the future. (I think here Wolfram means the perfect, entire future, but we can still approximately predict parts of the future.)
9. Next is the implications for classic issues.
10. First is the reversibility question. The ruliad is symmetric, but why we don’t experience the other direction?
11. We remember the past, but only certain filtered features of past that fit in our finite minds. And we can’t “outrun” time to know the detailed future.
12. (Here, Wolfram says we are requiring the past to be simpler, but I don’t agree. I think the reason is that, even in the part of the ruliad where the set of rules and the flow of states are reversed compared to our part, we would still only remember our “past”, which would actually be the future if we observed the time progress externally, because our memory is materialized as part of the state, which is identical with our current part.)
13. The second is the time travel question. If we view time as a process of applying computational rules, time travel is much less natural.
14. For example, even if we were in a loop in our causal graph, since us are within the system, our state would be identical and we wouldn’t consider it as time travel.
15. Basically, we as computational bounded observers can’t make time travel happen.
16. But we can still have time dilation.
17. Based on Wolfram’s Physics Project, if an object moves, it has to be re-created at a difference place in space, which takes up a certain amount of computation, leaving fewer computations for the intrinsic rewriting of the object itself, causing time to run slower for it.
18. (For the case of gravitational fields, I thought it was that more energy-momentum requires more rewriting, leaving fewer computations for the rewriting of the object itself, causing time to run slower for it. At least this is analogous to the situation of a moving object.)
19. The last issue is the perception of time. In our everyday life, we tend to parse the world into a sequence of states of space at successive moments in time. It takes our brains milliseconds to register what we’ve seen, but the difference in the time for photons from different objects to arrive is less then a microsecond. If our brains could run a million times faster, we’d perceive relativity directly. Alternatively, we could keep our brains the same, but observe objects from afar.
20. But this is our perception of time. Time itself remains as the computational progression of the entire system.

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Here, I also add a quick reminder of the different types of graphs.

A multiway graph:

A multiway causal graph:

Four succesive branchial graphs: