A Node, an Edge and a Graph walk into a bar. The Graph starts running around the bar and the Edge starts telling tall stories. "What's up with y'all?" asks the barmaid. The Node shrugs its shoulders: "The Graph's hyper, the Edge's line, and me, I just don't get the point."
@@lasttheory That's a good one. I got another one but it might be a bit more inappropriate (◕w◕) A Node is sitting at the bar, and a beautiful hypergraph approaches. The Hypergraph asks the Node: "Hey handsome, want to be in a relationship with me?" and the Node replies "Here's my UUID beautiful....call me anytime. Badabing!" Node leaves the bar... A Node takes a seat at the bar. The Hypergraph asks the Node: "Hey handsome, want to be in a relationship with me?"
Almost every thing has a structure. And every structure is a bunch of things connected with relationships. Which we represent as graphs. Yes, that one was quite simple to understand
Hi there, Great video as it was insightful and unexpectedly complex yet enjoyable to learn. Could you perhaps do a video on the physics of holograms? I'm sure you will find it fascinating 😄
Thanks! Yes, holograms are weird and fascinating, aren't they? Also, they might have a role to play in the relationship between quantum entanglement and the creation of space and time. I'll keep it in mind!
Thanks for the suggestion! As I understand it, semi-graphs are graphs without self-loops. This has important applications in some fields, but disallowing self-loops seems like an arbitrary limitation. Aren't graphs more general? If there's a good reason to apply the limitation, I'd be interested to hear it. So far, as far as I know, no one at The Wolfram Physics Project has suggested that this limitation be applied. Take a look at my video _Loops and self loops in the hypergraph_ ua-cam.com/video/Wk97OLlj020/v-deo.html for more on this.
@@lasttheory no loops but the uniqueness is about multiple edges between two vertices are different from hypergraph since the vertices in any edge of a semigraph follow a particular order though the vertices in an edge of a hypergraph do not have any such order. Opening many new mindsets about dynamic nodes and new optimizing . I'm appreciated how you present hypergraph an easy way and maybe about semigraph and disemigraph too 🙏🙏
@@lasttheory I have limitation for those, for me the complete reference was from its founder E. sampathkumar : semigraphs and their applications and disemigraph from journal basis and domination of disemigraph from Hamida Aktara Hoque
Yes, you can construct undirected hypergraphs. From what Jonathan Gorard has told me, it's not that important exactly what kinds of hypergraphs you use in the Wolfram model, but completely general, directed hypergraphs have certainly proved fruitful!
Because there is no informational content in this video. It doesn't give any definition, but it does give wrong impression. Hypergraph is a generalization of graph, where an edge is any nonempty set of nodes. So and edge can connect more than one node, or consist just of one node as opposed to a regular graph. And, of course the more general definition the more things you can fit in. It's almost like saying everything is a thing.
since mentally you could average them together, one guy could come along and make a graph out of the average. what would you call a graph made of graphs? seemingly conflicted, sure but super in context implies 2 bits of info being given at once
That's a good question. You're right: most of these examples are graphs, plain and simple. But the Wolfram Physics example is definitely a hypergraph, not a graph: each of the edges is ternary, not binary. And the metabolic pathways _could_ be seen as a hypergraph, in that the chemical reactions represented involve enzymes, metabolites and cofactors, i.e. more than 2 nodes. So I used the word hypergraphs to encompass all these examples: the hypergraphs as well as the graphs. Thanks for the question!
Thanks for the comment, Łukasz. For a definition of a hypergraph, check out my earlier video, "What is a hypergraph?" ua-cam.com/video/AbPGsRdNhds/v-deo.html
expecting similarity on every scale should be expected. thinking digitally on an analog brain ignores most input and as far as i can tell, infinity has no scale. every thing can be graphed thought of as a wave and calculus is a maths that uses infinite sums to generate waves. i would like to say also that if inclined to add infinite sums see what happens when you write an attempt to balance the equation. infinity plus one, is infinity... balance it and 1=0. it is dumb or smart thinking.. i don't know
Algebra involving infinities is tricky, for sure! And it's an interesting point you make about expecting similarity on every scale. In _some_ ways, different scales look different: planets orbiting a star look very different from electrons "orbiting" an atomic nucleus.
@@lasttheory bear with me for a tick. you could understand this. infinity plus 1? still infinity. infinity plus one equals infinity.. Algerbra says to balance it. you nullify the like terms and out popps 1=0. the math gets ignored, however it is not broken. it is a fundamental hint. i would like to say more that it equates to a super position of the answer. also that all infinities have a 1=1 ratio. your insight is great my man. you kind of are getting at what i saw. the pattern you see and find interesting is a product of a finite universe within an infinite reality. maths always leave a trail and it should have stopped at as soon as quantum theories evolved. i really enjoyed the video.
but hell if i'm right.. AND you could accept the quantum uncertainty principle as right, we are Turing complete organisms. (basically an idealized machine capable of answering any question posed) and finally infinity has no preferred scale so the notion of a body goes out the window and we are the universe and reality simulating itself in the only way most could ever know. then we as chimps hold a ruler to infinity claiming to be giants, nothing is as imagined *horrible implication in itself* i hope you can model wave forms or you could be in for a trip
The crappy ending to Interstellar... where he goes through a black hole and ends up inside infinite space and can see all time at once but finds his daughter through the power of love and screaming her name draws him to her and he writes infinite messages to her through time itself... yeah, that shit can be your life if you aren't careful about this particular thought. seeing many things and making them all of a sudden just one thing frees up everything in your mind that was spread over all the patterns you have already noticed
I wasn't aware of Bruno Latour or actor-network theory, but you're right, it looks like it could be very interesting in this context. Thanks for the pointer!
Hey, thanks! And you're right, most of these are just graphs. But the first one, generated by Wolfram Physics, is a hypergraph, and the metabolic pathway, too, can be rendered as a hypergraph, since the chemical reactions (edges) involve enzymes, metabolites and cofactors (nodes). I used "hypergraph" to encompass them all: graphs are hypergraphs too! I appreciate the comment: you obviously know your hypergraphs!
@@lasttheoryThere's nothing mathematically or computationally novel about hypergraphs: the nodes are analogous to atoms in Prolog, and the links to predicates of arity > 1. So it's not surprising that you can find them everywhere in nature. Also, please note that a graph with "hyperedges" involving more than two nodes can be represented by a graph with binary edges, simply by having each "edge" be a special type of node with links to the members of the relationship.
@@eryqeryq Yes, absolutely, I'm glad you agree with the point of my video, that hypergraphs are everywhere, and that it's no surprise that they're everywhere! And yes, you can represent hypergraphs as graphs, if you're willing to take that rather arbitrary step and label nodes as "special" or "not special". It seems much simpler, though, mathematically, to represent such systems as hypergraphs.
"What I want to know is: Why? Why are hypergraphs everywhere?" They are not. This is no different than seeing animals in clouds only with something is pretty much formless in the first place. This does not mean that Wolfram's ideas are full of it but it does not support it either.
Thanks for the response! You may be right: there _are_ patterns in nature that are just like seeing animals in clouds. For example, the way we analogize from planets orbiting a star to electrons orbiting an atomic nucleus is just plain wrong. But I think there's something more basic going on with hypergraphs, because of the way we humans see the world as discrete, connected entities. I think this is compelling enough to be worth pursuing, but you're right, I might be wrong!
@@lasttheory There are two problems with this. Not one thing is testable so far, just like the String Hypothesis. The other is that it could be false and still fit the evidence, just like the String Hypothesis. Or right and not be falsifiable. Interesting is not the same as useful.
@@ethelredhardrede1838 Thanks for pushing me on this. These are real issues, and it helps me to engage in real debate about them. Again, you're right: nothing testable from Wolfram Physics so far. And yes, the possibility that "it could be false and still fit the evidence" is a real concern. You put it well. When I say nothing testable from Wolfram Physics so far, I should clarify. General Relativity and aspects of Quantum Mechanics _can_ be derived from Wolfram Physics. But that's too easy: we already know these things. And that gets to the heart of the matter. The thing is, our existing theories, specifically General Relativity and Quantum Mechanics, model reality so accurately that it's going to be hard for _any_ new theory of physics to find a corner of reality where GR & QM _don't_ predict things perfectly accurately. So it's no surprise that neither String Theory nor Wolfram Physics has failed to find such a corner of reality. But I don't think that means we should give up. Even if we found a theory that predicts nothing beyond existing GR & QM, but combines GR & QM into a single, seamless theory, I think that would be worth our attention. But I don't think that will be the case. A theory that does this will, I suspect, yield testable predications at the extremities. It's going to be hard to find such a theory, and it may take years or decades to bring any such theory to the point of testable predictions. To steal a line from JFK, we do these things not because they are easy, but because they are hard.
perhaps it is not hypergraphs that are everywhere, but everywhere that is a hypergraph
Ha! Yes, exactly!
This is perfect for the kids in my class.... Great job sir!!!
That's great, thanks!
What did the Node say to the Hypergraph at the bar?
*I like to live on the edge.*
A Node, an Edge and a Graph walk into a bar. The Graph starts running around the bar and the Edge starts telling tall stories. "What's up with y'all?" asks the barmaid. The Node shrugs its shoulders: "The Graph's hyper, the Edge's line, and me, I just don't get the point."
@@lasttheory That's a good one. I got another one but it might be a bit more inappropriate (◕w◕)
A Node is sitting at the bar, and a beautiful hypergraph approaches. The Hypergraph asks the Node: "Hey handsome, want to be in a relationship with me?" and the Node replies "Here's my UUID beautiful....call me anytime. Badabing!"
Node leaves the bar...
A Node takes a seat at the bar. The Hypergraph asks the Node: "Hey handsome, want to be in a relationship with me?"
That was an excellent presentation, good on you
Thanks, I appreciate it! I'll keep these videos coming!
Almost every thing has a structure. And every structure is a bunch of things connected with relationships. Which we represent as graphs.
Yes, that one was quite simple to understand
Yes, exactly!
Hi there, Great video as it was insightful and unexpectedly complex yet enjoyable to learn.
Could you perhaps do a video on the physics of holograms?
I'm sure you will find it fascinating 😄
Thanks! Yes, holograms are weird and fascinating, aren't they? Also, they might have a role to play in the relationship between quantum entanglement and the creation of space and time. I'll keep it in mind!
Would u please also talk on semigraph and disemigraph too ?
Thanks for the suggestion!
As I understand it, semi-graphs are graphs without self-loops. This has important applications in some fields, but disallowing self-loops seems like an arbitrary limitation. Aren't graphs more general?
If there's a good reason to apply the limitation, I'd be interested to hear it. So far, as far as I know, no one at The Wolfram Physics Project has suggested that this limitation be applied.
Take a look at my video _Loops and self loops in the hypergraph_ ua-cam.com/video/Wk97OLlj020/v-deo.html for more on this.
@@lasttheory no loops but the uniqueness is about multiple edges between two vertices are different from hypergraph since the vertices in any edge of a semigraph follow a particular order though the vertices in an edge of a hypergraph do not have any such order. Opening many new mindsets about dynamic nodes and new optimizing . I'm appreciated how you present hypergraph an easy way and maybe about semigraph and disemigraph too 🙏🙏
@@wprayudo Ah, OK, got it. I think! Do you have any good references on semigraphs and disemigraphs?
@@lasttheory I have limitation for those, for me the complete reference was from its founder E. sampathkumar : semigraphs and their applications and disemigraph from journal basis and domination of disemigraph from Hamida Aktara Hoque
@@wprayudo Thanks, I'll look it up!
is there such a thing as an undirected hyperedge. where the order of nodes within the curly brackets does not matter?
Yes, you can construct undirected hypergraphs. From what Jonathan Gorard has told me, it's not that important exactly what kinds of hypergraphs you use in the Wolfram model, but completely general, directed hypergraphs have certainly proved fruitful!
Why you call these hypergraph instead of just... Graph?
Because there is no informational content in this video. It doesn't give any definition, but it does give wrong impression.
Hypergraph is a generalization of graph, where an edge is any nonempty set of nodes. So and edge can connect more than one node, or consist just of one node as opposed to a regular graph.
And, of course the more general definition the more things you can fit in. It's almost like saying everything is a thing.
@@OmateYayami correct me if I'm wrong, but all the examples here are just normal graph?
since mentally you could average them together, one guy could come along and make a graph out of the average. what would you call a graph made of graphs? seemingly conflicted, sure but super in context implies 2 bits of info being given at once
That's a good question. You're right: most of these examples are graphs, plain and simple. But the Wolfram Physics example is definitely a hypergraph, not a graph: each of the edges is ternary, not binary. And the metabolic pathways _could_ be seen as a hypergraph, in that the chemical reactions represented involve enzymes, metabolites and cofactors, i.e. more than 2 nodes. So I used the word hypergraphs to encompass all these examples: the hypergraphs as well as the graphs. Thanks for the question!
Thanks for the comment, Łukasz. For a definition of a hypergraph, check out my earlier video, "What is a hypergraph?" ua-cam.com/video/AbPGsRdNhds/v-deo.html
Several of those are just graphs...
Yes, absolutely! But graphs are hypergraphs too!
expecting similarity on every scale should be expected. thinking digitally on an analog brain ignores most input and as far as i can tell, infinity has no scale. every thing can be graphed thought of as a wave and calculus is a maths that uses infinite sums to generate waves. i would like to say also that if inclined to add infinite sums see what happens when you write an attempt to balance the equation. infinity plus one, is infinity... balance it and 1=0. it is dumb or smart thinking.. i don't know
Algebra involving infinities is tricky, for sure! And it's an interesting point you make about expecting similarity on every scale. In _some_ ways, different scales look different: planets orbiting a star look very different from electrons "orbiting" an atomic nucleus.
@@lasttheory bear with me for a tick. you could understand this. infinity plus 1? still infinity. infinity plus one equals infinity.. Algerbra says to balance it. you nullify the like terms and out popps 1=0. the math gets ignored, however it is not broken. it is a fundamental hint.
i would like to say more that it equates to a super position of the answer. also that all infinities have a 1=1 ratio. your insight is great my man. you kind of are getting at what i saw. the pattern you see and find interesting is a product of a finite universe within an infinite reality. maths always leave a trail and it should have stopped at as soon as quantum theories evolved.
i really enjoyed the video.
but hell if i'm right.. AND you could accept the quantum uncertainty principle as right, we are Turing complete organisms. (basically an idealized machine capable of answering any question posed) and finally infinity has no preferred scale so the notion of a body goes out the window and we are the universe and reality simulating itself in the only way most could ever know. then we as chimps hold a ruler to infinity claiming to be giants, nothing is as imagined *horrible implication in itself* i hope you can model wave forms or you could be in for a trip
The crappy ending to Interstellar... where he goes through a black hole and ends up inside infinite space and can see all time at once but finds his daughter through the power of love and screaming her name draws him to her and he writes infinite messages to her through time itself... yeah, that shit can be your life if you aren't careful about this particular thought. seeing many things and making them all of a sudden just one thing frees up everything in your mind that was spread over all the patterns you have already noticed
@@rinolevesquejr2914 Thanks for these comments! We are Turing complete organisms, for sure!
The late Bruno Latour might be interesting in this context
I wasn't aware of Bruno Latour or actor-network theory, but you're right, it looks like it could be very interesting in this context. Thanks for the pointer!
💡
It's kinda enlightening, isn't it, when you start seeing hypergraphs everywhere?
Uhh These are just graphs man.. But nice Video in visualization and storytelling
Hey, thanks! And you're right, most of these are just graphs. But the first one, generated by Wolfram Physics, is a hypergraph, and the metabolic pathway, too, can be rendered as a hypergraph, since the chemical reactions (edges) involve enzymes, metabolites and cofactors (nodes). I used "hypergraph" to encompass them all: graphs are hypergraphs too! I appreciate the comment: you obviously know your hypergraphs!
@@lasttheoryThere's nothing mathematically or computationally novel about hypergraphs: the nodes are analogous to atoms in Prolog, and the links to predicates of arity > 1. So it's not surprising that you can find them everywhere in nature.
Also, please note that a graph with "hyperedges" involving more than two nodes can be represented by a graph with binary edges, simply by having each "edge" be a special type of node with links to the members of the relationship.
@@eryqeryq Yes, absolutely, I'm glad you agree with the point of my video, that hypergraphs are everywhere, and that it's no surprise that they're everywhere!
And yes, you can represent hypergraphs as graphs, if you're willing to take that rather arbitrary step and label nodes as "special" or "not special". It seems much simpler, though, mathematically, to represent such systems as hypergraphs.
"What I want to know is:
Why?
Why are hypergraphs everywhere?"
They are not. This is no different than seeing animals in clouds only with something is pretty much formless in the first place.
This does not mean that Wolfram's ideas are full of it but it does not support it either.
Thanks for the response! You may be right: there _are_ patterns in nature that are just like seeing animals in clouds. For example, the way we analogize from planets orbiting a star to electrons orbiting an atomic nucleus is just plain wrong.
But I think there's something more basic going on with hypergraphs, because of the way we humans see the world as discrete, connected entities. I think this is compelling enough to be worth pursuing, but you're right, I might be wrong!
@@lasttheory
There are two problems with this. Not one thing is testable so far, just like the String Hypothesis. The other is that it could be false and still fit the evidence, just like the String Hypothesis. Or right and not be falsifiable.
Interesting is not the same as useful.
@@ethelredhardrede1838 Thanks for pushing me on this. These are real issues, and it helps me to engage in real debate about them.
Again, you're right: nothing testable from Wolfram Physics so far. And yes, the possibility that "it could be false and still fit the evidence" is a real concern. You put it well.
When I say nothing testable from Wolfram Physics so far, I should clarify. General Relativity and aspects of Quantum Mechanics _can_ be derived from Wolfram Physics. But that's too easy: we already know these things.
And that gets to the heart of the matter. The thing is, our existing theories, specifically General Relativity and Quantum Mechanics, model reality so accurately that it's going to be hard for _any_ new theory of physics to find a corner of reality where GR & QM _don't_ predict things perfectly accurately. So it's no surprise that neither String Theory nor Wolfram Physics has failed to find such a corner of reality.
But I don't think that means we should give up. Even if we found a theory that predicts nothing beyond existing GR & QM, but combines GR & QM into a single, seamless theory, I think that would be worth our attention. But I don't think that will be the case. A theory that does this will, I suspect, yield testable predications at the extremities.
It's going to be hard to find such a theory, and it may take years or decades to bring any such theory to the point of testable predictions. To steal a line from JFK, we do these things not because they are easy, but because they are hard.