Category - Revision history

Tom: /* Category Theory */

2024-12-08T03:42:44Z

‎Category Theory

2024-12-08T03:39:53Z

‎Categorical Imperative

2024-12-08T03:14:17Z

‎Quantum Theory

2024-12-08T03:11:04Z

‎Quantum Theory

2024-12-08T03:07:57Z

‎Quantum Theory

2024-11-27T02:27:54Z

‎Quantum Theory

2024-11-27T02:27:14Z

‎Quantum Theory

2024-11-27T02:24:57Z

‎Quantum Theory

2024-11-27T02:23:42Z

‎Quantum Theory

2024-11-27T02:22:43Z

‎Quantum Theory

@@ Line 16: / Line 16: @@
 A Categorical Statement that is taken as maxim that you would like all others to use as a basis for all of their actions, and perhaps even the basis for all of your actions as well.
 ===Category Theory===
 http://boole.stanford.edu/cs353/handouts/book4.pdf

@@ Line 15: / Line 15: @@
 ===Categorical Imperative===
 A Categorical Statement that is taken as maxim that you would like all others to use as a basis for all of their actions, and perhaps even the basis for all of your actions as well.
 ==Problems==

@@ Line 33: / Line 33: @@
 ** expectation values defined as statistical averages of measurement outcomes weighted by measurement outcome probabilities
 * So the only outputs are narrowly about measurement outcomes alone, NOT about general phenomena happening.
-* Unless one changes the axioms, there is a conceptual gap here between one category (phenomena happening, birds foraging, early-universe-cosmology gases mixing) and another (sub?)category of measurement outcomes. And its simply a category error to contuse these two things. * This dilemma is the category problem. In particular, it would be a category error to confuse 'happening averages' with 'measurement-outcome averages' - i.e. quantum-theoretic expectation values.
+* Unless one changes the axioms, there is a conceptual gap here between one category (phenomena happening, birds foraging, early-universe-cosmology gases mixing) and another (sub?)category of measurement outcomes. And its simply a category error to contuse these two things.
 *The Category Problem and Expectation Values

@@ Line 22: / Line 22: @@
 ===Quantum Theory===
 The Category Problem <ref>Jacob Barandes, ''New Foundations for Quantum Theory'' 2024-03-04 https://www.youtube.com/watch?v=dB16TzHFvj0</ref>
-* The textbook axioms contain yet another profound problem
+* The textbook axioms contain a profound problem. On the one hand, scientists talk about various phenomena physically happening, perhaps according to probabilistic laws
 ** Ornithologists talk about birds exhibiting foraging behavior
 ** Early-universe cosmologists talk about primordial gases mixing

@@ Line 28: / Line 28: @@
 ** Microbiologists talk about DNA replicating, etc.
 ** Often one works with statistical averages over such phenomena happening as in classical physics.
-** For example if you can assign exact trajectories of a particle undergoing Brownian motion in a fluid, then one can computer the statistical avers over the trajectory.
+** For example if you can assign exact trajectories of a particle undergoing Brownian motion in a fluid, then one can compute the statistical averages over the trajectory.
 * On the other hand, according to the textbook axioms, quantum theory is an instrumentalist recipe that narrowly predict only:
 ** measurement outcomes

@@ Line 41: / Line 41: @@
 ** And yet this elision between (X happening) and (X measurement) is implicit and pervasive in textbooks and the research literature, from condensed-matter physics to quantum gravity.
-*The Measurement Problem
+The Measurement Problem
-**Activating the theory's measurement-outcome predictions requires saying "poof" at some point and magically invoking a 'measurement,' which the textbook axioms don't define
+*Activating the theory's measurement-outcome predictions requires saying "poof" at some point and magically invoking a 'measurement,' which the textbook axioms don't define
-**On the one hand, if one doesn't invoke the measurement axioms, then there is no connection with physical reality
+*On the one hand, if one doesn't invoke the measurement axioms, then there is no connection with physical reality
 ** Mathematical symbols written on paper are no more physically real than Magritte's famous "pipe" or Korzybski's '"maps"!
-** On the other hand, choosing to invoke the measurement axioms depends on making a subjective decision about when a 'measurement' has happened, meaning that one outcome is singled ;out for collapse, with in-principle empirical consequences
+* On the other hand, choosing to invoke the measurement axioms depends on making a subjective decision about when a 'measurement' has happened, meaning that one outcome is singled ;out for collapse, with in-principle empirical consequences
 ==References==

@@ Line 38: / Line 38: @@
 *The Category Problem and Expectation Values
 ** In particular, it would be a category error to confuse 'happening averages' (X happening) with 'measurement-outcome averages' (X measurement) — i.e., quantum-theoretic expectation values
-** In other words, just because these two quantities are both in (brackets), and may sometimes have approximately the same
+** In other words, just because these two quantities are both in (brackets), and may sometimes have approximately the same numerical value for certain choices of the symbol X, that doesn't mean they're physically the same categorical kind of thing!
-numerical value for certain choices of the symbol X, that doesn't
+** And yet this elision between (X happening) and (X measurement) is implicit and pervasive in textbooks and the research literature, from condensed-matter physics to quantum gravity.
 *The Measurement Problem