While your proposed solution to not decide one vs the other seems reasonable, it clearly presents a situation where I don't see how this model can't explain anything. I understand causal invariance but don't understand how this will meaningfully reduce the ludicrously large number of potential solutions (100 iterations, for instance, will produce 1.7 x 10^198 alternatives -- how much can causal invariance reduce this number? Can you run through a hypothetical example? Unless I'm really missing something.
Yes, I share your concerns. As you say, causal invariance helps, but all it does is ensure that it's _possible_ to get from one state of the universe to another; it doesn't collapse all those different states. Stephen Wolfram has an idea that consciousness consists in the collapse of different timelines into a single timeline, i.e. the collapse of different paths through the multiway graph into a single path. I need to look into this further, and I come at it, as you do, I think, from a point of view of skepticism as to how all these states can be collapsed into something that actually happens. But I'm planning videos specifically on this issue, and will illustrate, as ever, with specific examples of how this would actually work in the multiway graph. Thanks for the astute critique!
I'm glad you covered this. It's true as you said, that the multiway graphs don't tell us which specific update order to choose. However, doesn't this mean that multiway graphs won't be useful in the (ideal) final analysis, where we want to have the specific update sequence for our universe? But, whenever I hear Wolfram talking about multiway systems, he seems to suggest that our universe is actually unfolding in a multiway fashion. He then says us observers "conflate these paths into a single thread of experience" (this sounds like "the observer collapses the wavefunction"). Is this not just an avoidance of the measurement problem, just as in QM? While multiway systems may be useful models when operating under uncertainty, I feel that Wolfram will eventually have to commit to a specific update order rather than a multiway system, if he wants to solve the measurement problem and obtain a complete model of our universe.
Thanks, Maxwell, these are really good questions. The first point I'd make is that causal invariance is crucial here. Where rules show causal invariance, the different branches of the multiway graph can come back together. And the second point I'd make is that you're absolutely right to bring up Stephen Wolfram's idea of conscious observers bringing separate branches together into a single thread of time. If this concept of consciousness works, it can avoid the measurement problem. It's not so much that the observer collapses the wavefunction, as in traditional interpretations of quantum mechanics, as that the observer creates their own interpretation of the branching of the multiway graph. So I don't think it's necessary to commit to a specific update order. Indeed, it may be that many aspects of quantum mechanics arise only if we _don't_ commit to a specific update order. There's much more I have to learn about this and there'll be much more to say about it in future videos!
@@lasttheory I see, thanks. Yes, I forgot about causal invariance, so our universe could then be a hypothesised to be causally invariant multiway system. I know that you mentioned it in your video. This then must mean that Wolfram's space nodes are interchangeable? I'm now trying (and struggling) to visualise space as a multiway hypergraph evolving over time...
@@maxwelldillon4805 Wolfram Physics _doesn't_ treat space nodes as interchangeable, but still causal invariance is possible: applying the rule in different orders can still reach exactly the same hypergraph, with all the non-interchangeable nodes in the same places. And yes, I too struggle with visualizing space through the multiway graph. Working on it!
The next story might cover rulial hyperspace in the context of the multiway hypergraph from the point of view of computational complexity. Such a computer cannot possibly be available at Best Buy.
If you're simulating the multi-way graph, one thing you want to do at each step is to prune duplicates graphs from each level. Doing this brute force, by directly comparing the graphs to each other, would be hugely expensive. Are there any known tricks or clever data structures that can reduce the work? Also, I wonder what percent of graphs can be pruned on average. Does the percentage go up as the multiway graph evolves? does pruning every begin to constrain the total number of graphs meaninfully?
These are excellent questions, thanks Patrick, but I don't know the answers yet. I'm working on my multiway graph code right now - I figure I'll understand things better if I write my own code rather than use the code from The Wolfram Physics Project - so I'm hoping I'll have answers soon. I'm tempted to guess that the answer to how much pruning you can do depends on the rule. For sure, there are some rules where no pruning will be possible, whereas for causally invariant rules some pruning will definitely be possible. I'll see when I do it!
@@lasttheory isn't the case that if if you've selected a rule or rules, such that the pruning at each steps constrains the number of graphs to roughly the same number as those of the previous levels, then you're going to get causal invariance?
One way to speed up the pruning is to define a total ordering to your graphs. each graph would be an ordered list of graph elements, instead of an unordered set. then you can compare graphs the same way you do strings, in O(n) time. @lasttheory. When you apply rules, you copy the parent graph, remove the element the rule removes, and insert the new elements in the correct order.
@@patrick_into_the_future Thanks Patrick. I don't think the same number of graphs at each level of the multiway graph corresponds to causal invariance: I think you can have a rapidly expanding number of graphs at each level and still have causal invariance. This hinges on the precise definition of causal invariance, which is not that two branches of the mutliway graph _do_ come back together, but that they _can_ come back together. I really need to make a video on this to clarify it in my own mind. I like your idea of maintaining the graph as an ordered list of edges to facilitate comparison. Again, the precise definition of what constitutes two graphs being "the same" is crucial here, and that depends on how we identify nodes. For example, we could identify nodes strictly by numbering them, in which case graphs are the same if precisely the same nodes are connected by edges, or we could say all nodes are interchangeable, in which case graphs are the same if they're isomorphic, or somewhere in between. Again, I need to make a video on this. It's crazy how quickly this gets complicated!
Another thing to consider is minimizing memory by not copying the whole graph every time. we might borrow a page from the git version contol algorithm and treat each child graph in the multi-way causal graph as a diff of its parent graph, and encode only the changes... we'd want to get to a place where we can decompose the problem and handle it in parallel, while doing the best we can to minimize overall memory growth as the universe evolves. If we can do that, then we might be able to offload it to a graphics card for a 100x speed boost. Then again, if the whole thing grows at an obscene rate, then such optimizations may not matter much as it'll grind to a halt just a few steps later no matter how efficient we make the algorithm.
In my mind, the multiway graph is just a visualization of the fact the rule can be applied at different points in the hypergraph in different orders. Could you say what specifically is wrong here?
It's interesting that you say that this is not like the many worlds interpretation of quantum mechanics, when in fact it's pretty much exactly like the many worlds interpretation of quantum mechanics. (Or rather, the simple fact of just using the Schrödinger equation to evolve the universal wave function, which, if the universe is a "superposition" of states would apply the evolution to each of the states linearly). The wave function would simply then be one level of the multiway graph, each possible universe in the graph being a base vector in Hilbert space. In fact, despite being called the "muliple worlds" interpretation it does _not_ postulate multiple worlds at all. The multiple worlds are an emergent phenomenon when the splitting of universes becomes sufficiently different (due to a process called decoherence) so that they cannot observably interact anymore. I remember an interview with Stephen Wolfram by Sean Caroll (it may have been on his podcast) where they discussed this and sort of agreed on it.
Ah, interesting, is this ruclips.net/video/0bMYtEKjHs0/видео.html the Wolfram/Carroll interview you're talking about? If so, I'll certainly watch. So maybe Stephen Wolfram will contradict me on this, but my interpretation of his idea of "consciousness" reducing multiple timelines to a single timeline is that there's only _one_ universe, and we make sense of it through our reduction of complexity to something that's manageable. In my mind, that's very different from the many-worlds interpretation of quantum mechanics.
Good questions! Where is the Earth? Well, we'd have to start with: what is matter? It may be that elementary particles are persistent tangles in the hypergraph. Think of a knot of nodes and edges that propagates through the hypergraph as the rules are applied: this could be an elementary particle propagating through space. And, of course, at a much, much larger scale, the Earth is made of elementary particles. So where is the Earth in the hypergraph? It's a collection of a very, very large number of persistent tangles in the hypergraph. I'll have much more to say on this, plus some animations to illustrate it, in future videos. And where is the Big Bang? Well, maybe it's just the early stages of the application of the rules to the hypergraph. At this point, the hypergraph, i.e. space, grows very rapidly, so it certainly _looks_ a bit like the Big Bang.
I'm not sure to understand because for exemple on the hypergraph in the website of Wolfram ou univers appears on the 10*400 steps of the multiway graph so then my question is is there what we call a Big Bang every time a new branch starts like its seem to be on the hypergraph of Wolfram and he calls the begining of the hypergraph "initial condition" but this is not what we call big bang is a thing far away "in the past" from our big bang ? (Sorry for my english)
@@RUclipslaschool Your English is good! Thanks for the further questions. I think what Stephen Wolfram is trying to say is that the universe, as it is right now, consists of maybe 10^400 nodes & edges (at a very very rough approximation). That's not to say that the universe has always been this big or that the universe wasn't the universe before it reached this size. Rather, it could have started out at the Big Bang with only, say, one node and one edge, and, through repeated application of the rule, exploded rapidly into the early universe, then more slowly into today's universe. So no, I wouldn't call every new branch a Big Bang, since new branches are being created all the time, in extremely large numbers. There was only one Big Bang, which, as you say, was a long time ago. The "initial condition" is the hypergraph we start with when we start applying the rule. For specific rules, specific initial conditions are needed to get the evolution of the hypergraph going, e.g. a few nodes and a few edges that can be matched by the rule. But if, rather than one specific rule, all possible rules may be applied in our universe, then no specific initial conditions are needed: the universe could be created out of no initial nodes or edges. I hope this makes things clearer: I'll have to do an episode on this some time!
Well, I used to think about vertices in a graph as something, that is pure inconvenience that we have to deal with, due to how mathematics work. We can't write down data about edges connected to each other without giving names to everything first. So two graphs that have same 'shape' but different names, are completely equivalent. Like, in the case of representing mathematical expression as a graph - we don't care about how each operator is uniquely named. We only care about types of operations, and how they are connected together. That's what we write down in the serialized form of a tree graph, after all ("1 + 4 - 3"). We only give stuff names when implementing algorithms that, for example, need to iterate over data multiple times, thus creating loops, resulting expression graph to turn from tree to a network.
You've hit on a real question for Wolfram Physics: whether and how to name the nodes. Jonathan Gorard has some interesting ideas about labelling nodes according to their histories. I need to dig into this deeper, but it's for sure a crucial question.
@@lasttheory In my opinion, name is just a yet another parameter assigned to the node, that makes it unique from the other nodes. We need to give everything names in order to keep track of things, to compute stuff by storing it in unique memory cells and such. But the universe doesn't do that. And even if it did do that, that wouldn't matter, as long as names don't influence the topology of the world. I mean, does it matter whether we name one of the axes X and Y, or if we choose to name them Y and X instead? Particles and beings living on that grid wouldn't be able to tell the difference. So, in their context they are equal, and they don't care whether or not we in our outsider context consider them equal or not.
@@tempname8263 You're right, it doesn't matter _what_ we name the nodes, but it does matter _whether_ we name them. Or, more specifically, it matters whether two nodes are _interchangable_ if they were arrived at through different evolutions of the hypergraph but are topologically identical. I don't know the answer to this question, but both Stephen Wolfram and Jonathan Gorard are taking the answer to be no, the two nodes are different. This has profound implications for the multiway graph.
I just bingewatched your entire series all today. You did a good job representing Wolfram Physics.
Thanks, Rick, I appreciate that.
While your proposed solution to not decide one vs the other seems reasonable, it clearly presents a situation where I don't see how this model can't explain anything. I understand causal invariance but don't understand how this will meaningfully reduce the ludicrously large number of potential solutions (100 iterations, for instance, will produce 1.7 x 10^198 alternatives -- how much can causal invariance reduce this number? Can you run through a hypothetical example? Unless I'm really missing something.
Yes, I share your concerns.
As you say, causal invariance helps, but all it does is ensure that it's _possible_ to get from one state of the universe to another; it doesn't collapse all those different states.
Stephen Wolfram has an idea that consciousness consists in the collapse of different timelines into a single timeline, i.e. the collapse of different paths through the multiway graph into a single path.
I need to look into this further, and I come at it, as you do, I think, from a point of view of skepticism as to how all these states can be collapsed into something that actually happens.
But I'm planning videos specifically on this issue, and will illustrate, as ever, with specific examples of how this would actually work in the multiway graph.
Thanks for the astute critique!
I'm glad you covered this. It's true as you said, that the multiway graphs don't tell us which specific update order to choose. However, doesn't this mean that multiway graphs won't be useful in the (ideal) final analysis, where we want to have the specific update sequence for our universe?
But, whenever I hear Wolfram talking about multiway systems, he seems to suggest that our universe is actually unfolding in a multiway fashion. He then says us observers "conflate these paths into a single thread of experience" (this sounds like "the observer collapses the wavefunction"). Is this not just an avoidance of the measurement problem, just as in QM? While multiway systems may be useful models when operating under uncertainty, I feel that Wolfram will eventually have to commit to a specific update order rather than a multiway system, if he wants to solve the measurement problem and obtain a complete model of our universe.
Thanks, Maxwell, these are really good questions.
The first point I'd make is that causal invariance is crucial here. Where rules show causal invariance, the different branches of the multiway graph can come back together.
And the second point I'd make is that you're absolutely right to bring up Stephen Wolfram's idea of conscious observers bringing separate branches together into a single thread of time.
If this concept of consciousness works, it can avoid the measurement problem. It's not so much that the observer collapses the wavefunction, as in traditional interpretations of quantum mechanics, as that the observer creates their own interpretation of the branching of the multiway graph.
So I don't think it's necessary to commit to a specific update order. Indeed, it may be that many aspects of quantum mechanics arise only if we _don't_ commit to a specific update order.
There's much more I have to learn about this and there'll be much more to say about it in future videos!
@@lasttheory I see, thanks. Yes, I forgot about causal invariance, so our universe could then be a hypothesised to be causally invariant multiway system. I know that you mentioned it in your video. This then must mean that Wolfram's space nodes are interchangeable?
I'm now trying (and struggling) to visualise space as a multiway hypergraph evolving over time...
@@maxwelldillon4805 Wolfram Physics _doesn't_ treat space nodes as interchangeable, but still causal invariance is possible: applying the rule in different orders can still reach exactly the same hypergraph, with all the non-interchangeable nodes in the same places.
And yes, I too struggle with visualizing space through the multiway graph. Working on it!
@@lasttheory Ah ok. That's clarifying, thanks
The next story might cover rulial hyperspace in the context of the multiway hypergraph from the point of view of computational complexity.
Such a computer cannot possibly be available at Best Buy.
If you're simulating the multi-way graph, one thing you want to do at each step is to prune duplicates graphs from each level. Doing this brute force, by directly comparing the graphs to each other, would be hugely expensive. Are there any known tricks or clever data structures that can reduce the work?
Also, I wonder what percent of graphs can be pruned on average. Does the percentage go up as the multiway graph evolves? does pruning every begin to constrain the total number of graphs meaninfully?
These are excellent questions, thanks Patrick, but I don't know the answers yet.
I'm working on my multiway graph code right now - I figure I'll understand things better if I write my own code rather than use the code from The Wolfram Physics Project - so I'm hoping I'll have answers soon.
I'm tempted to guess that the answer to how much pruning you can do depends on the rule. For sure, there are some rules where no pruning will be possible, whereas for causally invariant rules some pruning will definitely be possible. I'll see when I do it!
@@lasttheory isn't the case that if if you've selected a rule or rules, such that the pruning at each steps constrains the number of graphs to roughly the same number as those of the previous levels, then you're going to get causal invariance?
One way to speed up the pruning is to define a total ordering to your graphs. each graph would be an ordered list of graph elements, instead of an unordered set. then you can compare graphs the same way you do strings, in O(n) time. @lasttheory. When you apply rules, you copy the parent graph, remove the element the rule removes, and insert the new elements in the correct order.
@@patrick_into_the_future Thanks Patrick.
I don't think the same number of graphs at each level of the multiway graph corresponds to causal invariance: I think you can have a rapidly expanding number of graphs at each level and still have causal invariance. This hinges on the precise definition of causal invariance, which is not that two branches of the mutliway graph _do_ come back together, but that they _can_ come back together. I really need to make a video on this to clarify it in my own mind.
I like your idea of maintaining the graph as an ordered list of edges to facilitate comparison. Again, the precise definition of what constitutes two graphs being "the same" is crucial here, and that depends on how we identify nodes. For example, we could identify nodes strictly by numbering them, in which case graphs are the same if precisely the same nodes are connected by edges, or we could say all nodes are interchangeable, in which case graphs are the same if they're isomorphic, or somewhere in between. Again, I need to make a video on this.
It's crazy how quickly this gets complicated!
Another thing to consider is minimizing memory by not copying the whole graph every time. we might borrow a page from the git version contol algorithm and treat each child graph in the multi-way causal graph as a diff of its parent graph, and encode only the changes... we'd want to get to a place where we can decompose the problem and handle it in parallel, while doing the best we can to minimize overall memory growth as the universe evolves. If we can do that, then we might be able to offload it to a graphics card for a 100x speed boost.
Then again, if the whole thing grows at an obscene rate, then such optimizations may not matter much as it'll grind to a halt just a few steps later no matter how efficient we make the algorithm.
If there are parts of this theory that are wrong, this is one of them. Thinking about the application of rules weirdly.
In my mind, the multiway graph is just a visualization of the fact the rule can be applied at different points in the hypergraph in different orders. Could you say what specifically is wrong here?
Brilliant work...
Just Brilliant......!
Thanks so much!
It's interesting that you say that this is not like the many worlds interpretation of quantum mechanics, when in fact it's pretty much exactly like the many worlds interpretation of quantum mechanics. (Or rather, the simple fact of just using the Schrödinger equation to evolve the universal wave function, which, if the universe is a "superposition" of states would apply the evolution to each of the states linearly). The wave function would simply then be one level of the multiway graph, each possible universe in the graph being a base vector in Hilbert space.
In fact, despite being called the "muliple worlds" interpretation it does _not_ postulate multiple worlds at all. The multiple worlds are an emergent phenomenon when the splitting of universes becomes sufficiently different (due to a process called decoherence) so that they cannot observably interact anymore.
I remember an interview with Stephen Wolfram by Sean Caroll (it may have been on his podcast) where they discussed this and sort of agreed on it.
Ah, interesting, is this ruclips.net/video/0bMYtEKjHs0/видео.html the Wolfram/Carroll interview you're talking about? If so, I'll certainly watch.
So maybe Stephen Wolfram will contradict me on this, but my interpretation of his idea of "consciousness" reducing multiple timelines to a single timeline is that there's only _one_ universe, and we make sense of it through our reduction of complexity to something that's manageable. In my mind, that's very different from the many-worlds interpretation of quantum mechanics.
Amazing explanation thank you
Thanks, Ilya. Much more to come on the multiway graph!
One stupid question maybe but where is earth on a hypergraph ?
And a previous question... where is big bang ?
Good questions!
Where is the Earth? Well, we'd have to start with: what is matter? It may be that elementary particles are persistent tangles in the hypergraph. Think of a knot of nodes and edges that propagates through the hypergraph as the rules are applied: this could be an elementary particle propagating through space.
And, of course, at a much, much larger scale, the Earth is made of elementary particles. So where is the Earth in the hypergraph? It's a collection of a very, very large number of persistent tangles in the hypergraph.
I'll have much more to say on this, plus some animations to illustrate it, in future videos.
And where is the Big Bang? Well, maybe it's just the early stages of the application of the rules to the hypergraph. At this point, the hypergraph, i.e. space, grows very rapidly, so it certainly _looks_ a bit like the Big Bang.
I'm not sure to understand because for exemple on the hypergraph in the website of Wolfram ou univers appears on the 10*400 steps of the multiway graph so then my question is is there what we call a Big Bang every time a new branch starts like its seem to be on the hypergraph of Wolfram and he calls the begining of the hypergraph "initial condition" but this is not what we call big bang is a thing far away "in the past" from our big bang ? (Sorry for my english)
@@RUclipslaschool Your English is good! Thanks for the further questions.
I think what Stephen Wolfram is trying to say is that the universe, as it is right now, consists of maybe 10^400 nodes & edges (at a very very rough approximation). That's not to say that the universe has always been this big or that the universe wasn't the universe before it reached this size. Rather, it could have started out at the Big Bang with only, say, one node and one edge, and, through repeated application of the rule, exploded rapidly into the early universe, then more slowly into today's universe.
So no, I wouldn't call every new branch a Big Bang, since new branches are being created all the time, in extremely large numbers. There was only one Big Bang, which, as you say, was a long time ago.
The "initial condition" is the hypergraph we start with when we start applying the rule. For specific rules, specific initial conditions are needed to get the evolution of the hypergraph going, e.g. a few nodes and a few edges that can be matched by the rule. But if, rather than one specific rule, all possible rules may be applied in our universe, then no specific initial conditions are needed: the universe could be created out of no initial nodes or edges.
I hope this makes things clearer: I'll have to do an episode on this some time!
Ok thank you for your answers
So if it's not "big bangs" what are new branches in our univers ? New galaxies ?
Can a new branch be a baby univers ?
Well, I used to think about vertices in a graph as something, that is pure inconvenience that we have to deal with, due to how mathematics work. We can't write down data about edges connected to each other without giving names to everything first. So two graphs that have same 'shape' but different names, are completely equivalent.
Like, in the case of representing mathematical expression as a graph - we don't care about how each operator is uniquely named. We only care about types of operations, and how they are connected together. That's what we write down in the serialized form of a tree graph, after all ("1 + 4 - 3"). We only give stuff names when implementing algorithms that, for example, need to iterate over data multiple times, thus creating loops, resulting expression graph to turn from tree to a network.
You've hit on a real question for Wolfram Physics: whether and how to name the nodes. Jonathan Gorard has some interesting ideas about labelling nodes according to their histories. I need to dig into this deeper, but it's for sure a crucial question.
@@lasttheory In my opinion, name is just a yet another parameter assigned to the node, that makes it unique from the other nodes. We need to give everything names in order to keep track of things, to compute stuff by storing it in unique memory cells and such. But the universe doesn't do that.
And even if it did do that, that wouldn't matter, as long as names don't influence the topology of the world. I mean, does it matter whether we name one of the axes X and Y, or if we choose to name them Y and X instead? Particles and beings living on that grid wouldn't be able to tell the difference. So, in their context they are equal, and they don't care whether or not we in our outsider context consider them equal or not.
@@tempname8263 You're right, it doesn't matter _what_ we name the nodes, but it does matter _whether_ we name them. Or, more specifically, it matters whether two nodes are _interchangable_ if they were arrived at through different evolutions of the hypergraph but are topologically identical. I don't know the answer to this question, but both Stephen Wolfram and Jonathan Gorard are taking the answer to be no, the two nodes are different. This has profound implications for the multiway graph.
the only thing i've understanded with this video is that women and nodes are the same