Corpus evidence — top 10 passages

Most-relevant passages from the entire indexed corpus (67,286 paragraph chunks across YouTube transcripts, PubMed, arXiv, archive.org, Stanford Encyclopedia of Philosophy, OpenAlex, and more) ranked by semantic similarity (bge-small-en-v1.5).

1. 01 · yt0.745

   But what actually happens with   the observable is, is that you have a function and  you can either measure the function at the point   and then multiply it by the quantum wave, or  you can take that function, differentiate it   to get a one form, stick it into a symplectic  form to get a vector field, throw the vector   field to a connection and use that connection to  take a directional derivative. So one of these   ends up as the position operator. One of these  sort of ends up as a momentum operator for the &nb…

   yt/ILlhFKuu3NQ-geometric-unity-unifying-all-forces-generations-eric-weinste/transcript.txt

2. 02 · yt0.733

   The fact that you need x and t, or, if you're living in three spatial dimensions, the fact that you need x, y, z and t is not new. That is not the revolution Einstein created. The fact that you need four coordinates to label an event is nothing new. What he did that is new will be clear later. So, does everyone understand what an event means? Okay? An event is something that happens and to say exactly where and when it happened, in our world of one dimension, we give it an x and we give it a t. Now, that's me, and I'm going to give my frame of reference the name S. It turns out S is not just b…

   yt/pHfFSQ6pLGU-12-introduction-to-relativity/transcript.txt

3. 03 · blog0.730

   One can think, following van Benthem (1996: 206–208), that since sets (histories) are generally considered in a particular situation and with specific purposes in mind, there is no reason to take all possible sets (histories) into account; it is preferable to circumscribe the range of the quantification over sets that is relevant to the purposes at stake. An example of this way of proceeding can be found in Stirling (1992), where interesting (first-order and second-order) closure properties are identified for the set of branches (or paths, or runs, or histories) in temporal logic for computer …

   blog/plato-stanford-edu/branching-time.md

4. 04 · blog0.723

   See the above-mentioned entry on Newton’s view of space, time, and motion as well as the entries on Leibniz’s philosophy of physics , classical theories of absolute and relational space and motion , post-Newtonian theories of absolute and relational space and motion , and the hole argument. 3. The Topology of Time It’s natural to think that time can be represented by a line. But a line has a shape. What shape should we give to the line that represents time? This is a question about the topology, or structure, of time. One natural way to answer our question is to say that time should be represe…

   blog/plato-stanford-edu/time.md

5. 05 · blog0.723

   Moments represent events that are spatially maximal and only have an instantaneous or minimal duration. Trees are commonly defined as pairs \((M,\prec\)), where \(M\) is a non-empty set of moments and the temporal precedence relation \(\prec\) is a strict partial order that complies with the principles of Connection and No backward branching (see below). As Belnap, Perloff, and Xu observe, the concept of a moment … is a Newtonian idea. It is distant from our everyday conceptions, and it is non-relativistic. It inherits from Laplace’s demon the implausible presupposition that the fundamental te…

   blog/plato-stanford-edu/branching-time.md

6. 06 · blog0.722

   Note that there is no necessity that ‘ qua ’ operators be of the form ‘ qua Y ’, where Y is a noun phrase. For example, Aristotle says ( De anima iii.4.429b25-6) that two things affect and are affected “ qua something in common belongs to both.” Similarly, as evidence that ‘ qua ’ does not in these contexts always mean ‘because’ (usually, the context is too ambiguous to precisely decide whether it means ‘because’ or ‘in the respect that’), consider Nicomachean Ethics i.3.1102b8-9, “Sleep is an inactivity of the soul qua it is called good or bad,” but certainly not because it is. With only one …

   blog/plato-stanford-edu/aristotle-and-mathematics.md

7. 07 · blog0.718

   These terms stood for positions that have little to do with the modern notion of an abstract object. Modern platonists (with a small ‘p’) need not accept any of the distinctive metaphysical and epistemological doctrines of Plato, just as modern nominalists need not accept the distinctive doctrines of the medieval nominalists. Moreover, the literature also contains mention of anti-platonists , many of whom see themselves as fictionalists about abstracta, though this doesn’t help if it turns out that the best analysis of fictions is to regard them as abstract objects. So the reader should theref…

   blog/plato-stanford-edu/abstract-objects.md

8. 08 · yt0.715

   So, continuing with the analogy, this board is going to be used for analogy, we used to have K = ½ mv^(2). Yet, we can have K = ½ Iω^(2) and I is called the moment of inertia. So, the moment of inertia is determined not only by the masses that make up the body but how far they are from the center. If all the masses just fell on top of the center, the body would have no moment of inertia. It'll weigh the same; the moment of inertia would vanish. And likewise, if the mass is spread out the moment of inertia is more. For example, if I'm standing around here, and you come along and decide to spin …

   yt/mx2P1_M-7UA-9-rotations-part-i-dynamics-of-rigid-bodies/transcript.txt

9. 09 · yt0.714

   Take a, take a   page from object oriented programming. In a class  definition, you've got member variables and you've   got bound methods. So that's like stuff and stuff  you can do and method and it's, you've got nouns,   you've got verbs, you've got stuff and you've got  things you can do with the stuff. So that's what   the observers is. It's two spaces with a fiber and  sections connecting them, and then it's bundles on   top of them. And if you wanted to talk about  like the shift in perspective from Einstein,&nbs…

   yt/ILlhFKuu3NQ-geometric-unity-unifying-all-forces-generations-eric-weinste/transcript.txt

10. 10 · blog0.712

    On this view you have a temporal part right now, which is a three-dimensional “time slice” of you. And you have a different temporal part at noon yesterday, but no temporal parts in the year 1900 (since you are not located at any time in 1900). Also on this view, the physical object that is you is a fusion of all of your many temporal parts. (Note: there is a variation on the standard four-dimensional view, which is sometimes called “the worm view”. The variation, known as “the stage view”, holds that names and personal pronouns normally refer, not to entire fusions of temporal parts but, rath…

    blog/plato-stanford-edu/time.md