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An Upper Bound on the Probability of a Macroscopic Food Object (a “Kraft Single”) Arising as a Boltzmann Fluctuation
We bound the probability that thermal fluctuations in the observable universe have ever produced, for any nonzero duration, a specific macroscopic object: a ~20 g processed cheese slice (“Kraft Single”). Modeling the event as a large negative entropy fluctuation out of near-equilibrium matter, we combine (i) a conservative lower bound on the entropy decrease required for coarse localization of ~10²⁴ atoms into a fixed 10⁻⁵ m³ volume with (ii) an extremely generous upper bound on the total number of statistically independent spacetime trials (Planck-scale 4-cells across the observable universe and its age). The resulting expectation ( \mathbb E[N] ) and total probability (P) obey
[ \mathbb E[N];\lesssim;P;\lesssim;10^{-4.34\times 10^{24}}, ]
i.e., effectively zero for any physical purpose. Tighter (more realistic) modeling only decreases (P).
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Classical Ontological Options
- Substratum (Substance) Theory: Objects are "bare particulars" which have attributes, but the identity of the object is independent of the attributes.
- Bundle Theory: Objects are nothing over and above their attributes; what individuates an object is the collection of its properties.
- Problems: Substrata are metaphysically mysterious; bundles have difficulty with individuation, especially when two objects share all attributes.
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Dipert's Graph-Based Structural Ontology
- Randall R. Dipert in "The Mathematical Structure of the World: The World as Graph" argues that the world is a single, large graph.
(https://philpapers.org/rec/DIPTMS?utm_source=chatgpt.com)
- Randall R. Dipert in "The Mathematical Structure of the World: The World as Graph" argues that the world is a single, large graph.
(defun find-terms (num-terms max-size | |
&optional (desired-sum 0) | |
&aux (iterations 0)) | |
"Returns a list of terms in the range -max-size ... +max-size, | |
inclusive, that sum to desired-sum. | |
Has strange properties. Likelier to blow the stack as max-size | |
increases. Seems to spend most time backtracking on the last few | |
terms. |
The following was sent to the JACL e-mail announcement list on 2021-02-26.
Hello everyone, and a belated happy 2021 to you! I hope your year has been off to a good start.
It's been almost a year since JACL became public, and nearly as long since any other announcement or release, so I thought to share three major related educational and design developments. The project is very much alive, just mostly in my head :-)
First, while I haven't made significant tangible progress on the JACL compiler or runtime since last year, I have continued to research and study implementation techniques. I have prototyped several schemes for efficient and JavaScript-friendly multiple-value returns, consuming relevant literature (mostly from the Scheme community) along the way. I have also studied and experimented with CLOS, and to speculate about how best to support a maximum of CLOS functionality without compromising JACL's calculated relationship with the JavaScript platform. One interes
(defconstant mv-limit 20) | |
(defparameter *mv-expected* 1) | |
(defparameter *mv* (make-array mv-limit)) | |
(defun mv (&rest vals) | |
(do ((i 0 (1+ i)) | |
(vs vals (cdr vs))) | |
((or (eql i *mv-expected*) (null vs)) |
(defn fizzbuzz [n] | |
(let [fb (str ({0 "fizz"} (mod n 3)) | |
({0 "buzz"} (mod n 5)))] | |
({"" (str n)} fb fb))) |
const removeAt = (xs, i) => xs.filter((x, j) => j !== i); | |
const permute = xs => xs.length | |
? xs.flatMap((x, i) => permute(removeAt(xs, i)).map(ys => [x, ...ys])) | |
: [[]]; |
(defconstant mv-limit 20) | |
(defparameter *mv-expected* 1) | |
(defparameter *mv* (make-array mv-limit)) | |
(defun mv (&rest vals) | |
(do ((i 0 (1+ i)) | |
(vs vals (cdr vs))) | |
((or (eql i *mv-expected*) (null vs)) |
(def mv-limit 20) | |
(def ^:dynamic *mv-arr*) | |
(def ^:dynamic *values-expected* 1) | |
(defn values [& vals] | |
(when (thread-bound? #'*values-expected*) | |
(dotimes [i (set! *values-expected* | |
(min *values-expected* (count vals)))] |