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I'm not a physicist, nor a philosopher, and certainly not a mathematician - so maybe what I'm going to write will seem both naive and probably wrong, but I'm do

by cr0sh 7y ago

I'm not a physicist, nor a philosopher, and certainly not a mathematician - so maybe what I'm going to write will seem both naive and probably wrong, but I'm doing it anyhow. In this Quanta interview, Amanda Gefter writes: "Leibniz argued (against Newton) that there’s no fixed backdrop to the universe, no “stuff” of space; space is just a handy way of describing relationships. This relational framework captured Smolin’s imagination, as did Leibniz’s enigmatic text The Monadology, in which Leibniz suggests that the world’s fundamental ingredient is the “monad,” a kind of atom of reality, with each monad representing a unique view of the whole universe. It’s a concept that informs Smolin’s latest work as he attempts to build reality out of viewpoints, each one a partial perspective on a dynamically evolving universe. A universe as seen from the inside." For some reason, my mind went to the idea of "nodes and edges" of a graph; with the nodes being these "monads" and their relationships being the "edges", and then later in the interview...Smolin notes: "The event has relations with the rest of the universe, and that set of relations constitutes its “view” of the universe. Rather than describing an isolated system in terms of things that are measured from the outside, we’re taking the universe as constituted of relations among events." I don't know for sure if what I was thinking is the same thing as what he expresses here, but I think I might be close. Regardless, I now wonder something else: Could the colloquial concept/idea of "6 degrees of separation" apply here? If so, what implications might that have for Smolin's theory? https://en.wikipedia.org/wiki/Six_degrees_of_separation#Mathematics https://en.wikipedia.org/wiki/Six_degrees_of_separation#Math... I won't pretend to have any answers here (again, assuming anything I wrote above means anything)...

jerf 7y ago
The "six degrees of separation" arises because the graph has a particular shape that gives it that property, such as the mostly-power-lawish shape that human relationships have. It is not a general characteristic of graphs. While we know this model is too stupid-simple to be the whole story, if you imagine the universe as a naive 3d grid graph with nodes at evenly-space intervals where everything takes place, there is no "six degrees of separation" effect; distances between one node and another would be the Manhattan distance, with no N-node shortcut to another point available on average. (Already we see why this graph can't be our universe; our universe does not use the Manhattan distance metric for distance.)
the8472 7y ago
That sounds like the configuration-spaces in barbour's timeless physics
danbruc 7y ago
There is a very good introduction - 20 lectures of 45 minutes - to loop quantum gravity by Carlo Rovelli [1] who worked together with Lee Smolin on that topic. In a nutshell loop quantum gravity is about triangulating space with tetrahedra, then representing this triangulation as a graph - one vertex per tetrahedron, one edge between every two tetrahedra sharing a face - with the edges labeled with SU(2) transformations describing the change in orientation due to spacetime curvature as one moves from one tetrahedron to a neighboring one, and of course the dynamics of this description. I hope I got this right, I am totally not a physicist. There is also a very good talk for the general public focusing on the nature of time by Rovelli [2] in case the lecture series is to long or technical. Well, I initially started writing this comment because of the quote »Leibniz argued (against Newton) that there’s no fixed backdrop to the universe, no “stuff” of space; space is just a handy way of describing relationships.«. According to Rovelli - he talks about this in the lecture series mentioned above - Newton was fully aware [3] that his notion of space and time are just abstract notions and that space and time are fundamentally relational. But due to the success of using abstract space and time in science and engineering this got somewhat forgotten and those abstract notions were and are considered much more fundamental than they are. This in lectures two (space) and ten (time) which both provide an overview about the philosophical evolution of the concepts and should be - at least the first part of the lectures - accessible without [almost] any background. [1] https://www.youtube.com/watch?v=Mp4fpwl9loQ&list=PLwLvxaPjGHxR6zr421tXXlaDGbq8S36Un https://www.youtube.com/watch?v=Mp4fpwl9loQ&list=PLwLvxaPjGH... [2] https://www.youtube.com/watch?v=-6rWqJhDv7M https://www.youtube.com/watch?v=-6rWqJhDv7M [3] I just skipped a bit through the second lecture on space and I may have somewhat overstated Newton's awareness but I will leave this as first written. It is more like he was aware that we only have access to relational space and time but we can infer from that a true abstract notion of space and time. I really recommend to just watch the lecture for a more nuanced picture, it starts out very non-technical and this very discussion.
KingFelix 7y ago
Didn't Leibniz also say something about our brains/consciousness encompass a special type of Monad?

by cr0sh 7y ago

jerf 7y ago

The "six degrees of separation" arises because the graph has a particular shape that gives it that property, such as the mostly-power-lawish shape that human relationships have. It is not a general characteristic of graphs. While we know this model is too stupid-simple to be the whole story, if you imagine the universe as a naive 3d grid graph with nodes at evenly-space intervals where everything takes place, there is no "six degrees of separation" effect; distances between one node and another would be the Manhattan distance, with no N-node shortcut to another point available on average. (Already we see why this graph can't be our universe; our universe does not use the Manhattan distance metric for distance.)

the8472 7y ago

That sounds like the configuration-spaces in barbour's timeless physics

danbruc 7y ago

There is a very good introduction - 20 lectures of 45 minutes - to loop quantum gravity by Carlo Rovelli [1] who worked together with Lee Smolin on that topic. In a nutshell loop quantum gravity is about triangulating space with tetrahedra, then representing this triangulation as a graph - one vertex per tetrahedron, one edge between every two tetrahedra sharing a face - with the edges labeled with SU(2) transformations describing the change in orientation due to spacetime curvature as one moves from one tetrahedron to a neighboring one, and of course the dynamics of this description. I hope I got this right, I am totally not a physicist. There is also a very good talk for the general public focusing on the nature of time by Rovelli [2] in case the lecture series is to long or technical. Well, I initially started writing this comment because of the quote »Leibniz argued (against Newton) that there’s no fixed backdrop to the universe, no “stuff” of space; space is just a handy way of describing relationships.«. According to Rovelli - he talks about this in the lecture series mentioned above - Newton was fully aware [3] that his notion of space and time are just abstract notions and that space and time are fundamentally relational. But due to the success of using abstract space and time in science and engineering this got somewhat forgotten and those abstract notions were and are considered much more fundamental than they are. This in lectures two (space) and ten (time) which both provide an overview about the philosophical evolution of the concepts and should be - at least the first part of the lectures - accessible without [almost] any background. [1] https://www.youtube.com/watch?v=Mp4fpwl9loQ&list=PLwLvxaPjGHxR6zr421tXXlaDGbq8S36Un https://www.youtube.com/watch?v=Mp4fpwl9loQ&list=PLwLvxaPjGH... [2] https://www.youtube.com/watch?v=-6rWqJhDv7M https://www.youtube.com/watch?v=-6rWqJhDv7M [3] I just skipped a bit through the second lecture on space and I may have somewhat overstated Newton's awareness but I will leave this as first written. It is more like he was aware that we only have access to relational space and time but we can infer from that a true abstract notion of space and time. I really recommend to just watch the lecture for a more nuanced picture, it starts out very non-technical and this very discussion.

KingFelix 7y ago

Didn't Leibniz also say something about our brains/consciousness encompass a special type of Monad?