I don’t think it’s quite right to say the idea of the universe being in some sense mathematical is purely a carry-over of Judeo-Christian heritage—what about the Greek atomists like Leucippus and Democritus for example? Most of their writings have been lost but we do know that Democritus made a distinction similar to the later notion of primary (quantitative) vs. secondary (qualitative) properties discussed at https://plato.stanford.edu/entries/qualities-prim-sec/ with his comment about qualitative sensations being matters of human convention: “By convention sweet and by convention bitter, by convention hot, by convention cold, by convention colours; but in reality atoms and void.” CCW Taylor’s book “The Atomists: Leucippus and Democritus” gathers together all the known fragments from the first two major atomists as well as commentary by other ancient Greek philosophers, it says that various other philosophers attributed to them the position that the only properties of atoms were geometric ones like size and shape and relative position, for example Aristotle’s “Metaphysics” says at http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0052%3Abook%3D1%3Asection%3D985b that for the atomists the “differences” between atoms and groups of atoms were the explanation for all physical reality, and that “These differences, they say, are three: shape, arrangement, and position”. Aristotle’s “On the Heavens” at http://classics.mit.edu/Aristotle/heavens.3.iii.html also says of the atomists “Now this view in a sense makes things out to be numbers or composed of numbers. The exposition is not clear, but this is its real meaning.”
Personally I’m sympathetic to certain forms of panpsychism but I don’t think it’s inconsistent with a mathematical view of nature. Ever since I read Roger Penrose’s book “Shadows of the Mind” as a teenager I’ve been interested in the notion of the three interconnected “worlds” we have to deal with in any broad philosophical account of reality: the physical world, the world of subjective experience, and the world of mathematical truth (you can see Penrose’s memorable diagram of the three worlds and their connections at https://astudentforever.wordpress.com/2015/03/13/roger-penroses-three-worlds-and-three-deep-mysteries-theory/ ). I suppose I have an instinctive monist streak because it always seemed to me philosophers should try to unify these three worlds, the way physicists seek to unify the forces of nature. The notion of “structure” might be a good starting point, since there are good cases for the structuralist perspective (where each part is defined wholly by its relation to other parts, with no purely intrinsic properties) in all three: see mathematical structuralism at https://plato.stanford.edu/entries/structuralism-mathematics/ and structural realism in physics at https://plato.stanford.edu/entries/structural-realism/ (Ladyman and Ross’ book “Every Thing Must Go” makes a good extended case for this) and the idea of a “structuralist” view of qualia at https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3957492/ (and also against the idea that this is just Judeo-Christian, the structuralist view of the mind also has some parallels with branches of Mahayana Buddhism that say that all parts of experience and reality exist only in an interdependent way, using the metaphor of “Indra’s Net”, see http://dharma-rain.org/wp-content/uploads/2016/02/Hua_Yen_Buddhism_Emptiness_Identity_Inte.pdf and note that p. 66 even cites a Buddhist text that can be interpreted as applying this view to numbers as well).
Finally, I’d say that the notion of “reductionism” at the level of predicting physical behavior (the idea that all behavior of more complex systems is in principle derivable from fundamental physical laws acting on basic physical states, whatever those turn out to be exactly) is not primarily a matter of philosophical preconceptions, but more a matter of how this has been a successful paradigm in science which continually expands the range of how many phenomenon can be explained, even if we are far from being able to predict everything in a reductionist way in practice. For example, the range of molecular/chemical behaviors that can be explained in an “ab initio” way from quantum laws has continually expanded over time, likewise the range of cell behaviors that can be explained in terms of biochemical interactions and physical forces, the range of simple brain behaviors or aspects of early embryological development that can be explained in terms of local interactions between cells with one another and with their chemical environment, etc.
I’d make a comparison here to the idea that all adaptive structures in the bodies of living organisms have developed through a process of natural selection acting on mutations that are random with respect to fitness (allowing for the possibility that some adaptive features might be side-effects of others, ‘spandrels’, like the brain’s pattern-seeking abilities being applied in new scenarios not part of an organism’s evolutionary history). We can’t hope in practice to have strong evidence this is true for every adaptive structure in every organism, but evolutionary biologists continually expand the evidence that this is true in all sorts of specific cases, which makes for a good Occam’s razor style case that this is true for all of them. I think the same can be said about the reductionist view that all physical behavior is in principle reducible to physics.
I don’t think it’s quite right to say the idea of the universe being in some sense mathematical is purely a carry-over of Judeo-Christian heritage—what about the Greek atomists like Leucippus and Democritus for example?
From what I’m aware, the teachings of Greek classics in Christian schools made the two cultures rather closely aligned; the rationalist traditions have firm roots in Greek philosophy, including standards of evidence, court as argumentation, even democracy itself. Aristotle and the likes were required reading during the hundreds of years of the evolution of the Western university education system. I’m a bit ignorant of the details there in all honesty, but I think today’s beliefs have some interesting parallels with the Pythagorean maths cult!
In today’s age, most people haven’t read Greek philosophy, they hold values that come from their peer group and an establishment that was built by Christian scientists. Specific ideas come from across all the world’s influential cultures, it’d be an absurd anglocentric view to argue they didn’t. So my point isn’t that “Christians created it all” but more “the Christian tropes that aren’t obvious enough to be challenged still remain, and are responsible for cognitive biases that we hold today.”
The notion of “structure” might be a good starting point, since there are good cases for the structuralist perspective (where each part is defined wholly by its relation to other parts, with no purely intrinsic properties) in all three
I kind of agree here, but I prefer the process and interaction framing. As with the other things like determinism, laws or objective reality, structure can naturally emerge from simple processes but the reverse needs some other aspect or doesn’t say anything. This isn’t a good analogy because it’s about objects, but take Conway’s game of life as an example. It has structures on a higher levels due to the differences between cells, but all that really exists is the bitfield. The idea of structure gives us a way to reason about it; a glider is an us thing rather than an it thing.
I think structuralism puts the map first in a similar way. I do think the differences between things shape possibilities and at higher levels these give rise to very complex structure, and yes this could be said to “exist” or even be existence itself. But the framing makes the territory a kind of map, which leads to the kind of thinking that I object to.
… more a matter of how this has been a successful paradigm in science which continually expands the range of how many phenomenon can be explained
Absolutely. Success is what gave science the authority of truth. In order to make progress in it or to teach it, it helps to have a simple memetic framework that’s compatible with it and—perhaps more importantly—is compatible with the competition. It’s got to be robust and incorruptible, accessible so it can onboard new minds, be morally acceptable so it doesn’t get suppressed and so on. And that’s what we’re left with, memes that are extremely resilient to change, shaped by history rather than built from first principles.
I think the same can be said about the reductionist view that all physical behavior is in principle reducible to physics.
I have to object to that on weak and shaky grounds of ignorance! 🙂
Firstly we can’t really hope to simulate a molecule from quantum theory, we’d need way more compute than is possible. So whatever optimizations we make in order to understand stuff will be biased by our own beliefs. Secondly, we’re hairless apes trying to fit the “laws” of nature into squiggly lines that represent mouth sounds, as tiny bags of water on the skin of an insignificant blob of molten rock, it’s kinda hubristic to assume that’s even possible. If we consider that everything may be a sea of Planck length things sloshing about, there’s potentially 30 orders of magnitude more stuff under the scale of what we can ever hope to measure. Finally, I think the idea of “laws” in general is human and based on us living in a world of solid, persistent objects, while we can only measure aggregates, and most of the universe is actually unpredictable fluids.
I think the aggregate thing is most important. Having physical laws based on average tendencies of things that we can measure, then saying that the universe “is” those laws seems like false authority. IMO stuff simply is what it is. We can try to understand it and work out rough maps of it, and we make better maps over time, but to say there exists a perfect map that all things are beholden to seems religious to me. It seems so unlikely that if it was proven to be true then I’d have to start believing in a creator!
Thanks again for the feedback, unfortunately I can only post one message a day here due to Lesswrong not liking this post. So gimme a nudge on Twitter if I don’t reply!
I don’t think it’s quite right to say the idea of the universe being in some sense mathematical is purely a carry-over of Judeo-Christian heritage—what about the Greek atomists like Leucippus and Democritus for example? Most of their writings have been lost but we do know that Democritus made a distinction similar to the later notion of primary (quantitative) vs. secondary (qualitative) properties discussed at https://plato.stanford.edu/entries/qualities-prim-sec/ with his comment about qualitative sensations being matters of human convention: “By convention sweet and by convention bitter, by convention hot, by convention cold, by convention colours; but in reality atoms and void.” CCW Taylor’s book “The Atomists: Leucippus and Democritus” gathers together all the known fragments from the first two major atomists as well as commentary by other ancient Greek philosophers, it says that various other philosophers attributed to them the position that the only properties of atoms were geometric ones like size and shape and relative position, for example Aristotle’s “Metaphysics” says at http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0052%3Abook%3D1%3Asection%3D985b that for the atomists the “differences” between atoms and groups of atoms were the explanation for all physical reality, and that “These differences, they say, are three: shape, arrangement, and position”. Aristotle’s “On the Heavens” at http://classics.mit.edu/Aristotle/heavens.3.iii.html also says of the atomists “Now this view in a sense makes things out to be numbers or composed of numbers. The exposition is not clear, but this is its real meaning.”
Personally I’m sympathetic to certain forms of panpsychism but I don’t think it’s inconsistent with a mathematical view of nature. Ever since I read Roger Penrose’s book “Shadows of the Mind” as a teenager I’ve been interested in the notion of the three interconnected “worlds” we have to deal with in any broad philosophical account of reality: the physical world, the world of subjective experience, and the world of mathematical truth (you can see Penrose’s memorable diagram of the three worlds and their connections at https://astudentforever.wordpress.com/2015/03/13/roger-penroses-three-worlds-and-three-deep-mysteries-theory/ ). I suppose I have an instinctive monist streak because it always seemed to me philosophers should try to unify these three worlds, the way physicists seek to unify the forces of nature. The notion of “structure” might be a good starting point, since there are good cases for the structuralist perspective (where each part is defined wholly by its relation to other parts, with no purely intrinsic properties) in all three: see mathematical structuralism at https://plato.stanford.edu/entries/structuralism-mathematics/ and structural realism in physics at https://plato.stanford.edu/entries/structural-realism/ (Ladyman and Ross’ book “Every Thing Must Go” makes a good extended case for this) and the idea of a “structuralist” view of qualia at https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3957492/ (and also against the idea that this is just Judeo-Christian, the structuralist view of the mind also has some parallels with branches of Mahayana Buddhism that say that all parts of experience and reality exist only in an interdependent way, using the metaphor of “Indra’s Net”, see http://dharma-rain.org/wp-content/uploads/2016/02/Hua_Yen_Buddhism_Emptiness_Identity_Inte.pdf and note that p. 66 even cites a Buddhist text that can be interpreted as applying this view to numbers as well).
Finally, I’d say that the notion of “reductionism” at the level of predicting physical behavior (the idea that all behavior of more complex systems is in principle derivable from fundamental physical laws acting on basic physical states, whatever those turn out to be exactly) is not primarily a matter of philosophical preconceptions, but more a matter of how this has been a successful paradigm in science which continually expands the range of how many phenomenon can be explained, even if we are far from being able to predict everything in a reductionist way in practice. For example, the range of molecular/chemical behaviors that can be explained in an “ab initio” way from quantum laws has continually expanded over time, likewise the range of cell behaviors that can be explained in terms of biochemical interactions and physical forces, the range of simple brain behaviors or aspects of early embryological development that can be explained in terms of local interactions between cells with one another and with their chemical environment, etc.
I’d make a comparison here to the idea that all adaptive structures in the bodies of living organisms have developed through a process of natural selection acting on mutations that are random with respect to fitness (allowing for the possibility that some adaptive features might be side-effects of others, ‘spandrels’, like the brain’s pattern-seeking abilities being applied in new scenarios not part of an organism’s evolutionary history). We can’t hope in practice to have strong evidence this is true for every adaptive structure in every organism, but evolutionary biologists continually expand the evidence that this is true in all sorts of specific cases, which makes for a good Occam’s razor style case that this is true for all of them. I think the same can be said about the reductionist view that all physical behavior is in principle reducible to physics.
Thanks for the decent criticism!
From what I’m aware, the teachings of Greek classics in Christian schools made the two cultures rather closely aligned; the rationalist traditions have firm roots in Greek philosophy, including standards of evidence, court as argumentation, even democracy itself. Aristotle and the likes were required reading during the hundreds of years of the evolution of the Western university education system. I’m a bit ignorant of the details there in all honesty, but I think today’s beliefs have some interesting parallels with the Pythagorean maths cult!
In today’s age, most people haven’t read Greek philosophy, they hold values that come from their peer group and an establishment that was built by Christian scientists. Specific ideas come from across all the world’s influential cultures, it’d be an absurd anglocentric view to argue they didn’t. So my point isn’t that “Christians created it all” but more “the Christian tropes that aren’t obvious enough to be challenged still remain, and are responsible for cognitive biases that we hold today.”
I kind of agree here, but I prefer the process and interaction framing. As with the other things like determinism, laws or objective reality, structure can naturally emerge from simple processes but the reverse needs some other aspect or doesn’t say anything. This isn’t a good analogy because it’s about objects, but take Conway’s game of life as an example. It has structures on a higher levels due to the differences between cells, but all that really exists is the bitfield. The idea of structure gives us a way to reason about it; a glider is an us thing rather than an it thing.
I think structuralism puts the map first in a similar way. I do think the differences between things shape possibilities and at higher levels these give rise to very complex structure, and yes this could be said to “exist” or even be existence itself. But the framing makes the territory a kind of map, which leads to the kind of thinking that I object to.
Absolutely. Success is what gave science the authority of truth. In order to make progress in it or to teach it, it helps to have a simple memetic framework that’s compatible with it and—perhaps more importantly—is compatible with the competition. It’s got to be robust and incorruptible, accessible so it can onboard new minds, be morally acceptable so it doesn’t get suppressed and so on. And that’s what we’re left with, memes that are extremely resilient to change, shaped by history rather than built from first principles.
I have to object to that on weak and shaky grounds of ignorance! 🙂
Firstly we can’t really hope to simulate a molecule from quantum theory, we’d need way more compute than is possible. So whatever optimizations we make in order to understand stuff will be biased by our own beliefs. Secondly, we’re hairless apes trying to fit the “laws” of nature into squiggly lines that represent mouth sounds, as tiny bags of water on the skin of an insignificant blob of molten rock, it’s kinda hubristic to assume that’s even possible. If we consider that everything may be a sea of Planck length things sloshing about, there’s potentially 30 orders of magnitude more stuff under the scale of what we can ever hope to measure. Finally, I think the idea of “laws” in general is human and based on us living in a world of solid, persistent objects, while we can only measure aggregates, and most of the universe is actually unpredictable fluids.
I think the aggregate thing is most important. Having physical laws based on average tendencies of things that we can measure, then saying that the universe “is” those laws seems like false authority. IMO stuff simply is what it is. We can try to understand it and work out rough maps of it, and we make better maps over time, but to say there exists a perfect map that all things are beholden to seems religious to me. It seems so unlikely that if it was proven to be true then I’d have to start believing in a creator!
Thanks again for the feedback, unfortunately I can only post one message a day here due to Lesswrong not liking this post. So gimme a nudge on Twitter if I don’t reply!