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We live in networks, although they are almost always very hard to see with our eyes.\u00a0 The most easily visible networks are probably our transportation networks, especially networks of roads. You can see roads branching and intersecting. \u00a0And you can form a mental map of road networks.\u00a0 Your mental map (if it\u2019s accurate) corresponds to an objectively existing networks of roads and points they connect.\u00a0 Think of the network of interstate highways connecting cities in the United States.\u00a0 These cities are objectively existing physical wholes.\u00a0 Each city is one whole, a single thing, a unit, a network node.\u00a0 The roads that connect them are objectively existing lines between the nodes. \u00a0The network of American cities and interstates is an enormous connect-the-dots network.\u00a0 The cities and the highways are located in space.\u00a0 And so the network is also located in space.\u00a0 Put a dot, a spatial point, in the center of every city.\u00a0 Link two urban dots with a line if they their two cities are joined by a road.\u00a0 You have a network of points and lines, a purely geometrical network, a purely mathematical network.\u00a0 But this network is located in space.<\/p>\n
Parts of our electrical and communications networks are also pretty easy to see.\u00a0 They appear as wires, strung from pole to pole along our roads.\u00a0 These networks carry electrical energy, and signals for telephones and computers.\u00a0 While you can see parts of the electrical network, the entire electrical grid is impossible to visualize without using advanced mapping technologies.\u00a0 Likewise for, say, the main lines of the internet.\u00a0 The cables that carry internet signals span the entire globe, making a network at planetary scale.\u00a0 These networks are physical structures, made of material atoms.\u00a0 But the nodes in these networks also occupy regions of space, and the links occupy regions of space as well.\u00a0 Those regions make a geometrical network of points and lines.\u00a0 This geometrical network of points and lines exists in the same space as the material network of wires and cables.\u00a0 It is a purely mathematical network that is located in space.\u00a0 Given any two points in the electrical network, they probably aren\u2019t connected by a wire that traces out a straight line.\u00a0 But there does exist a straight line that runs between those two points. \u00a0So there is another electrical network, made of points and straight lines, that is spatially overlaid onto (or that supervenes on) the visible electrical network with its bent wires and cables.<\/p>\n
Our bodies contain networks which are visible, but which remain essentially hidden.\u00a0 Your body has a network of blood vessels, but you\u2019ll never see it. \u00a0Staying alive requires that you don\u2019t see it, that it remains hidden, working beneath the visible surface of your skin. Your lymphatic network, the network of lymph nodes and lymph vessels, is even harder to see. During surgery, a surgeon will see some of the network of your blood vessels, or some of your lymphatic network, but not the entire system. \u00a0To see these networks, you need to dissect a corpse.\u00a0 Or you can look at pictures in medical books.\u00a0 Of course, a picture of the network isn\u2019t the network.\u00a0 These networks are transvisible, that is, they are not visible to the naked eye, but visible only with technological assistance. \u00a0Your blood vessels carry oxygen and glucose (along with other molecules), and your cells use oxygen and glucose to generate energy. \u00a0Energetic stuff flows through your blood network.\u00a0 Here too, in your own body, there are purely geometrical networks, purely mathematical networks, that exist in the space inside your body.\u00a0 They exist whether or not any human thinks about them.\u00a0 Space exists whether or not you think about it.\u00a0 So do points and lines in space.<\/p>\n
Likewise, consider the neural network inside your brain, or the network of nerves that spreads through your entire body. \u00a0Staying alive requires that you don\u2019t see it, that it remains invisible.\u00a0 To observe a neural network requires dissecting a brain, and looking at some neural tissue under a microscope.\u00a0 It requires even more: you have to stain the cells to make them visible.\u00a0 A lot of technology is required to reveal the living networks in human bodies, or other animal bodies.\u00a0 \u00a0These networks are also transvisible.\u00a0 Like your network of blood vessels, energy flows through your neural networks. \u00a0Charged ions flow through your nerve cells, generating electrical currents.\u00a0 These electrical currents, flowing through your nerves, generate your whole mental life.\u00a0 And technologists have built artificial neural networks, which power artificial intelligences.\u00a0 Electrical energy, flowing through these networks, also gives rise to something like mind.<\/p>\n
Our bodies, since we are social animals, live in social networks.\u00a0 You can\u2019t easily see these networks either.\u00a0 You know who your friends (and enemies) are, and you might map out your social network by drawing it on some paper.\u00a0 But you can\u2019t directly see it.\u00a0 Social networks are actually pretty abstract.\u00a0 All sorts of social signals flow through these social networks.\u00a0 These include linguistic signals, vibrations in the air.\u00a0 But microorganisms flow through social networks.\u00a0 These include bacteria and viruses, both those that cause disease, and those that are beneficial.\u00a0 Our bodies exchange invisible cells, or, at least, cells that become visible only when observed through microscopes.\u00a0 And most of us are not aware that, even when we sit around talking with friends, our bodies are exchanging lots of beneficial microorganisms, like bacteria that colonize our skin and guts.\u00a0 Our microbiomes are social constructions, parts of the social network of microbial life. \u00a0Obviously, during sex, bodies exchange genetic materials.\u00a0 DNA, energized by chemical reactions, passes from body to body.\u00a0 Social networks are transvisible systems, carrying transvisible energies and signals, generating complex self-organizing societies.\u00a0 Some philosophers say these social networks, like neural networks, give rise to hive minds.<\/p>\n
Besides socializing with other humans, we also socialize with non-human animals.\u00a0 Our most obvious animal partners are domesticated animals, like cats and dogs. \u00a0But farm animals are also members of our extended social networks.\u00a0 And so are the commensals, animals that are often parasitic on our bodies, our food, our garbage.\u00a0 These include animals like rats, cockroaches, and other unfriendly parasites.\u00a0 Our larger ecological networks include the synanthropes, animals that have learned to live in human cities and suburbs.\u00a0 The list of synanthropes is very long, including many types of birds, and many mammals.\u00a0 Think of deer, squirrels, foxes, coyotes, raccoons, bears, even cougars, and, in some places, monkeys and other tropical animals.\u00a0 Synanthropes form large-scale ecological networks in human cities.\u00a0\u00a0 Complex urban ecologies emerge from these networks.<\/p>\n
Like most other networks, these synanthropic networks are transvisible.\u00a0 You can\u2019t directly see the predator-prey networks involving hawks, rats, coyotes, squirrels, and so on. \u00a0You have to map them out scientifically.\u00a0 They are visible to the eye of the mind, that is, to the eye of the brain, an eye which can visualize more abstract relationships.\u00a0 But these transvisible networks also exist in space and time.\u00a0 Say the Great New York Coyote is the whole composed of all the coyotes in New York City. \u00a0The Great Coyote change its shape as coyotes move around, as old ones die, and new ones are born. \u00a0The Great Coyote sits beside the Great New York Squirrel, which is the whole composed of all the squirrels in New York.\u00a0 The Great Coyote and the Great Squirrel meet at various places and times, such as when a particular coyote eats a particular squirrel.\u00a0 All these meetings make a link between the Great Coyote and the Great Squirrel, namely, a predator-prey link.\u00a0\u00a0 This link exists in a high-dimensional ecological space, overlaid on ordinary physical space.\u00a0 Ecological food webs are connect-the-dots networks in ecological space.\u00a0 Coyotes and squirrels exist, and coyotes eat squirrels, whether or not any humans exist.\u00a0 Ecological food webs are not created by human minds.\u00a0 They are purely geometrical networks, that is, purely mathematical networks, that exist in ecological space-time.\u00a0 Ecological space-time is a physical space, which is also a purely geometrical and mathematical space.<\/p>\n
Other examples of networks are easy to find.\u00a0 There are networks of roots and fungal fibers (mycelia) in forests, and there are genetic networks in cells.\u00a0 There are networks among stars and planets.\u00a0 The planets in our solar system exchange rocks.\u00a0\u00a0 And there are very large-scale galactic networks in space.\u00a0 These networks are also transvisible.\u00a0 At the largest cosmic scales, they are ultravisible, visible only as computer simulations.\u00a0 Even more deeply, many of our best current physical theories say that space and time themselves emerge from deeper networks, networks which are not in space or time at all.\u00a0 These theories of emergent space-time are still hypothetical, but they are supported by lots of evidence.\u00a0 If they are right, then space and time are not basic. \u00a0Loop quantum gravity says space and time emerge from structures called spin networks.\u00a0 Various \u201cit from qubit\u201d theories say space and time (and quantum fields and particles) emerge from networks of entangled quantum bits of information. \u00a0The networks posited by these theories do not exist in space or time.\u00a0 Rather, they define space and time.\u00a0 Space and time emerge from deeper networks which are both physical and purely mathematical.<\/p>\n
Ultimately, these deep physical networks emerge from set-theoretic networks.\u00a0 In these set-theoretic networks, the dots are sets and the connections are instance of the membership relation.\u00a0 At some places, basic quantum mechanical networks emerge within these set-theoretic networks. \u00a0For instance, the spin networks of loop quantum gravity emerge, or networks of entangled qubits emerge, or networks of nodes in causal dynamical triangles emerge. \u00a0These networks aren\u2019t made out of any material stuff.\u00a0 They are neither material nor mental.\u00a0 They aren\u2019t made out of any stuff at all.\u00a0 They just exist, and their existence is both physical and mathematical. \u00a0From those networks, space and time emerge, along with their quantum fields and particles, then atoms and molecules and planets and people.\u00a0 Our own bodies emerge from the regularities of flows of energy in these networks.\u00a0 What are these flows of energy?\u00a0 They are merely ways the networks transform themselves into new networks. \u00a0But these ways just make a bigger network.<\/p>\n
Beneath all the visible networks, and the transvisible networks, there are ultravisible networks.\u00a0 These are deeply hidden networks, networks pulsing with their own energies and signals. \u00a0The deepest network of all is the purely set-theoretic network, the basement level connect-the-dots network from which all other networks emerge. \u00a0All the other networks exist inside of the set-theoretic network.\u00a0 Our bodies, our atoms, our quantum mechanical fields, our spin networks, and any other physical networks, exist inside of this purely mathematical network.\u00a0 All the relations in which our bodies participate are links within that network. \u00a0Nature is an infinite set-theoretic network, an ultravisible network which contains all the transvisible and visible networks, like an opal filled with flames.\u00a0 And this ultimate natural network is that in which we live, move, and have our being.<\/p>\n<\/div>\n<\/body><\/html>\n","protected":false},"excerpt":{"rendered":"
\u00a0by\u00a0Eric Steinhart We live in networks, although they are almost always very hard to see with our eyes.\u00a0 The most easily visible networks are probably our transportation networks, especially networks of roads. You can see roads branching and intersecting. \u00a0And you can form a mental map of road networks.\u00a0 Your mental map (if it\u2019s accurate) […]<\/p>\n","protected":false},"author":1269,"featured_media":499,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[723,720],"class_list":["post-1842","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-spiritual-naturalism","tag-connection","tag-network"],"yoast_head":"\n