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I've been reading Process Philosophy and the Whiteheadian conception of processes describe them to be existing in "non-spacetime" dimensions. How can it be explicated in simpler terms? "Non-spacetime" dimensions really defy my intellectual grasping of the meaning of the mode of existence of processes.

user43163
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    It would be nice if you added an extended quote, with citation, so we had some idea what you're looking at as you ask this. – Ted Wrigley Dec 30 '19 at 20:16
  • Whatever Whitehead has in mind "non-spacetime processes" shouldn't defy intellectual grasping. Quantum wave function does not evolve "in spacetime" either, it lives in a higher dimensional configuration space, spin is not "in spacetime", and even the phase space of classical mechanics includes momentum dimensions (which one can link to Aristotle's "potentiality"), and hence the Hamiltonian is also not "in spacetime". Processists talk about extra dimensions because they believe that spatiotemporal manifestations of processes are only partial projections of them, not including "experience", etc. – Conifold Dec 31 '19 at 00:30
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    In computing, a program is a list of instructions and a process is an executing program. The distinction is that the program is abstract, it is an idea. A process consumes energy and takes place over time. Is your meaning of process different? By the computing definition. a process is very much part of time and space; whereas a program -- an algorithm -- is not. – user4894 Dec 31 '19 at 07:44
  • I cannot grasp how a process can be independent of time. The concept of time is inherent to the idea of process. –  Dec 31 '19 at 12:01
  • @PeterJ It can unfold independently of physical spacetime, like the One emanating the world, for example. Whitehead, like Husserl and Bergson, thinks of some non-physical "duration" for experience/consciousness. – Conifold Dec 31 '19 at 14:10
  • @Conifold - I see the argument, but do you not find these ideas incoherent? I dismiss them,as ad hoc and incomprehensible. I also struggle with the idea of 'physical space-time' since I don't know what this could mean. Why can we not say that all processes require the same sort of time? .Having two sorts seems rather profligate. Pardon me though, shouldn't chat. . –  Dec 31 '19 at 17:38
  • @PeterJ Isn't it perennial philosophy at its finest? "Perennialism has its roots in the Renaissance interest in neo-Platonism and its idea of the One, from which all existence emanates". – Conifold Jan 01 '20 at 04:45
  • @Conifold - The philosophy predates Plotinus by many centuries but yes, the name 'perennial' is more recent. For Plotinus and the mystics time would be necessary for processes yet not fundamental. Thus getting to the bottom of time would be getting to the bottom of consciousness and Reality. The 'Perennial Now' or 'Divine Instant' would be the mystical basis for time. The OP might like a well-known book 'Abhidhamma Studies: Buddhist Exploration of Consciousness and Time' by Nyaponika Thera. . . –  Jan 01 '20 at 11:57
  • @Conifold *even the phase space of classical mechanics includes momentum dimensions ... hence the Hamiltonian is also not "in spacetime"* Are you suggesting the concept of instantaneous velocity contradicts the idea that everything in classical mechanics is "in spacetime"? If so, do you have a clear definition of what it means for something to be "in spacetime" or is it more of an intuition? This seems akin to saying that the slope/first derivative of a curve in 2D space is somehow not "in" that 2D space, since instantaneous velocity is just the time-derivative of a curve in spacetime. – Hypnosifl Jan 30 '20 at 19:08
  • @Hypnosifl Velocities and higher derivatives are trivially not in the manifold itself, they live in the tangent space and its tensor powers. "Intuitively" in physics, they are a leftover of Aristotelian potentialities that describe what is becoming rather than what is. – Conifold Jan 30 '20 at 21:33
  • @Conifold - What does "in the manifold itself" mean, exactly? Derivatives are deterministic functions of sets of points on a manifold (those points that lie on a particular curve). The volume of an extended object in space is similarly a function of multiple points, would you say the volume of a spatially extended object is not "in" space? And can you point to any mathematician or physicist who offers a clear and general definition corresponding to your notion of what it means for some property or value to be "in" a manifold, or is it your own idea? – Hypnosifl Jan 30 '20 at 22:27
  • @Hypnosifl A manifold is a set of points, of space or spacetime in physics. A volume is its subset, its numerical value is not in it, and neither are velocities or momenta. This is why we have configuration and phase spaces, a.k.a. tangent and cotangent bundles. All of this is standard terminology, you can find it in any text on differential geometry or analytic mechanics. I also recommend less prejudicial tone in your comments generally. – Conifold Jan 30 '20 at 23:27
  • @Conifold - There are different types of manifolds, if you say it is just a "set of points" you would be talking about a purely [topological manifold](https://en.wikipedia.org/wiki/Topological_manifold) with no extra structure, but you had earlier referred to something "in spacetime" which would imply you were talking about a [pseudo-riemannian manifold](https://en.wikipedia.org/wiki/Pseudo-Riemannian_manifold) with a specific metric. Are you *inferring* that since metrical concepts like volume are in addition to the basic def. of a topological manifold a mathematician would say they are not – Hypnosifl Jan 31 '20 at 03:52
  • (cont) "in the manifold", or have you seen a statement from a mathematician that says this specifically, or that defines the phrase "in the manifold"? And in addition to the terminological question, there is also the question of whether this is relevant to whether a *philosopher* would say something is or is not "in spacetime", there is no reason they would necessarily use identical definitions; perhaps they'd say any entity or property which is uniquely with a specific point (or set of points) in spacetime is "in spacetime". – Hypnosifl Jan 31 '20 at 03:55
  • @Hypnosifl The spacetime of GR is a 4D manifold with evolving metric, which, however, is not "in" it, and neither are its tangent vectors, etc. Mathematicians have symbols like ∈, ⊂ to indicate what is and is not "in". And *philosophers* are even more sensitive to velocities not being "in" since it matters in Zeno-like paradoxes. Do you have a point beyond verbal exercises? – Conifold Jan 31 '20 at 04:27
  • @Conifold - The symbols you refer to are about what is in or not in a *set*, I don't see how that's relevant to what's "in spacetime". Just checking on google books, I find multiple example of mathematical textbooks using the phrase ["metric in the manifold"](https://www.google.com/search?tbm=bks&q=%22metric+in+the+manifold%22) or ["metric in a manifold"](https://www.google.com/search?tbm=bks&q=%22metric+in+a+manifold%22). As for philosophy, I doubt very much that philosophers would say metric quantities like length or volume or time intervals are not "in" spacetime, – Hypnosifl Jan 31 '20 at 04:38
  • (cont) or that there's a consensus that instantaneous velocities aren't in it--again, sources would be appreciated if you disagree. Zeno himself could not have had an opinion on the matter since without calculus he didn't have a concept of instantaneous velocity. And this would be relevant to interpreting what Whitehead might have meant if he talked about processes not "in" ordinary spacetime, I doubt he was just talking about the evolution of a system's velocity or changes in distances in volumes or anything so conventionally physical. – Hypnosifl Jan 31 '20 at 04:39
  • @Hypnosifl The more standard expression is "metric on a manifold" or more precisely "on tangent bundle", but again, what is your point beyond loose use of prepositions in textbooks? Symbols are for expressing things more precisely, and velocities will be in TM, not in M. Whitehead et al. have a richer conception of "process", but velocities are exactly the shadows of it that allow calculus to describe dynamics using fixed sets. Zeno's arrow can move because its space location does not exhaust its state, which extends beyond it. – Conifold Jan 31 '20 at 04:55
  • @Conifold - Your statement makes sense only if you use the word "in" exclusively to refer to set membership, there's no reason for to think mathematicians exclusively use it that way, less so philosophers (also, if mathematicians *did* want to just talk this way, where would they "locate" distances and times along curves in manifolds with metrics? Not in the tangent space, since that's a vector space). And Whitehead was both a mathematician and a philosopher, so their use of english-language terminology is relevant to interpreting his statement, though we still haven't gotten his exact quote. – Hypnosifl Jan 31 '20 at 05:40
  • Also on Zeno's paradox, I found [this paper](https://philosophy.unc.edu/files/2013/10/PRarticle.pdf) which says that many philosophers would say "a body’s instantaneous velocity is ontologically parasitic on its trajectory", and implies it's a minority view that velocity has a distinct ontological status from the sets of positions constituting a trajectory (in terms of [Quine's criterion of ontological commitment](https://plato.stanford.edu/entries/ontological-commitment/#QuiCriPre), perhaps). – Hypnosifl Jan 31 '20 at 05:46
  • @Hypnosifl Distances can be identified with geodesic segments if one wants to "locate" them, although people usually do not feel the need to "locate" numbers, shapes and other abstractions. Whitehead talked of extra dimensions for processes to account for "experience", etc., in the same way that extra dimensions are added to space or spacetime to account for dynamics. Lange's view has nothing to do with Whitehead's, Quine's criterion is long out of the mainstream, even his students like Maddy disclaimed it. Can we stop now? – Conifold Jan 31 '20 at 05:47
  • @Conifold - You did not say Whitehead's statement should be interpreted exclusively in terms of "experience" originally, were your comments about mathematical tools/properties used by physicists, like phase space and momentum and such, not intended to describe what you thought Whitehead is likely to have meant? Also, though it might not involve space, I think many philosophers would say that experience intrinsically involves time, especially if they consider themselves process philosophers. – Hypnosifl Jan 31 '20 at 05:54

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In physics, "spacetime dimensions" are the familiar three spatial dimensions plus one of time (commonly written as (t,x,y,z) that provide the stage upon which all actions in the physical world that we inhabit are played out.

In non-physics contexts, "non-spacetime dimensions" can mean anything at all that the writer wants them to mean. However, please note the following:

Obviously, anything intangible cannot be assigned coordinates like (t,x,y,z) which define a specific location in the spacetime of our physical world. So if Whitehead or anyone else is dealing with intangibles, then it would be redundant to describe them as "existing in non-spacetime dimensions".

One reason someone might redundantly describe them in this way would be to put a scientistic gloss on their discourse to make it sound more rigorous, which is a misuse of a scientific term of art in a nonscientific context.

niels nielsen
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