My government name is Mack Gallagher. I am an underfunded "alignment" "researcher". Crocker's Rules. DM me if you'd like to fund my posts, or my project.
Try using Marginalia [ I'm unaffiliated ] instead of Google for searches that want posts from small, independent blogs [ "the old Internet" ].
[ TBC, I know orbits can oscillate. However, most 3D shell orbits do not look like oscillating, but locally stable, 2D orbits. ]
Two physics riddles, since my last riddle has positive karma:
Why do we use the right-hand rule to calculate the Lorentz force, rather than using the left-hand rule?
Why do planetary orbits stabilize in two dimensions, rather than three dimensions [i.e. a shell] or zero [i.e. relative fixity]? [ It's clear why they don't stabilize in one dimension, at least: they would have to pass through the center of mass of the system, which the EMF usually prevents. ]
Crossposting a riddle from Twitter:
Karl Marx writes in 1859 on currency debasement and inflation:
One finds a number of occasions in the history of the debasement of currency by English and French governments when the rise in prices was not proportionate to the debasement of the silver coins. The reason was simply that the increase in the volume of currency was not proportional to its debasement; in other words, if the exchange-value of commodities was in future to be evaluated in terms of the lower standard of value and to be realised in coins corresponding to this lower standard, then an inadequate number of coins with lower metal content had been issued. This is the solution of the difficulty which was not resolved by the controversy between Locke and Lowndes. The rate at which a token of value – whether it consists of paper or bogus gold and silver is quite irrelevant – can take the place of definite quantities of gold and silver calculated according to the mint-price depends on the number of tokens in circulation and by no means on the material of which they are made. The difficulty in grasping this relation is due to the fact that the two functions of money – as a standard of value and a medium of circulation – are governed not only by conflicting laws, but by laws which appear to be at variance with the antithetical features of the two functions. As regards its function as a standard of value, when money serves solely as money of account and gold merely as nominal gold, it is the physical material used which is the crucial factor. [ . . . ] [W]hen it functions as a medium of circulation, when money is not just imaginary but must be present as a real thing side by side with other commodities, its material is irrelevant and its quantity becomes the crucial factor. Although whether it is a pound of gold, of silver or of copper is decisive for the standard measure, mere number makes the coin an adequate embodiment of any of these standard measures, quite irrespective of its own material. But it is at variance with common sense that in the case of purely imaginary money everything should depend on the physical substance, whereas in the case of the corporeal coin everything should depend on a numerical relation that is nominal.
This paradox has an explanation, which resolves everything such that it stops feeling unnatural and in fact feels neatly inevitable in retrospect. I'll post it as soon as I have a paycheck to "tell the time by" again.
Until then, I'm curious whether anyone* can give the answer.
*who hasn't already heard it from me on a Discord call - this isn't very many people and I expect none of them are commenters here
Newton's laws of motion are already laws of futurology.
"The antithesis is not so heterodox as it sounds, for every active mind will form opinions without direct evidence, else the evidence too often would never be collected."
I already know, upon reading this sentence [source] that I'm going to be quoting it constantly.
It's too perfect a rebuttal to the daily-experienced circumstance of people imagining that things - ideas, facts, heuristics, truisms - that are obvious to the people they consider politically "normal" [e.g., 2024 politically-cosmopolitan Americans, or LessWrong], must be or have been obvious to everyone of their cognitive intelligence level, at all times and in all places -
- or the converse, that what seems obvious to the people they consider politically "normal", must be true.
Separately from how pithy it is, regarding the substance of the quote: it strikes me hard that of all people remembered by history who could have said this, the one who did was R.A. Fisher. You know, the original "frequentist"? I'd associated his having originated the now-endemic tic of "testing for statistical significance" with a kind of bureaucratic indifference to unfamiliar, "fringe" ideas, which I'd assumed he'd shared.
But the meditation surrounding this quote is a paean to the mental process of "asking after the actual causes of things, without assuming that the true answers are necessarily contained within your current mental framework".
"That Charles Darwin accepted the fusion or blending theory of inheritance, just as all men accept many of the undisputed beliefs of their time, is universally admitted. [ . . . ] To modern readers [the argument from the variability within domestic species] will seem a very strange argument with which to introduce the case for Natural Selection [ . . . ] It should be remembered that, at the time of the essays, Darwin had little direct evidence on [the] point [of whether variation existed within species] [ . . . ] The antithesis is not so heterodox as it sounds, for every active mind will form opinions without direct evidence, else the evidence too often would never be collected."
This comes on the heels of me finding out that Jakob Bernoulli, the ostensible great-granddaddy of the frequentists, believed himself to be using frequencies to study probabilities, and was only cast in the light of history as having discovered that probabilities really "were" frequencies.
"This result [Jakob Bernoulli's discovery of the Law of Large Numbers in population statistics] can be viewed as a justification of the frequentist definition of probability: 'proportion of times a given event happens'. Bernoulli saw it differently: it provided a theoretical justification for using proportions in experiments to deduce the underlying probabilities. This is close to the modern axiomatic view of probability theory." [ Ian Stewart, Do Dice Play God, pg 34 ]
Bernoulli:
"Both [the] novelty [ of the Law of Large Numbers ] and its great utility combined with its equally great difficulty can add to the weight and value of all the other chapters of this theory. But before I convey its solution, let me remove a few objections that certain learned men have raised. 1. They object first that the ratio of tokens is different from the ratio of diseases or changes in the air: the former have a determinate number, the latter an indeterminate and varying one. I reply to this that both are posited to be equally uncertain and indeterminate with respect to our knowledge. On the other hand, that either is indeterminate in itself and with respect to its nature can no more be conceived by us than it can be conceived that the same thing at the same time is both created and not created by the Author of nature: for whatever God has done, God has, by that very deed, also determined at the same time." [ Jakob Bernoulli's "The Art of Conjecturing", translated by Edith Dudley Sylla ]
It makes me wonder how many great names modern "frequentism" can even accurately count among its endorsers.
Edit:
Fisher on the philosophy of probability [ PLEASE click through, it's kind of a take-your-breath-away read if you're familiar with the modern use of "p-values" ]:
"Now suppose there were knowledge a priori of the distribution of μ. Then the method of Bayes would give a probability statement, probably a different one. This would supersede the fiducial value, for a very simple reason. If there were knowledge a priori, the fiducial method of reasoning would be clearly erroneous because it would have ignored some of the data. I need give no stronger reason than that. Therefore, the first condition [of employing the frequentist definition of probability] is that there should be no knowledge a priori.
[T]here is quite a lot of continental influence in favor of regarding probability theory as a self-supporting branch of mathematics, and treating it in the traditionally abstract and, I think, fruitless way [ . . . ] Certainly there is grave confusion of thought. We are quite in danger of sending highly-trained and highly intelligent young men out into the world with tables of erroneous numbers under their arms, and with a dense fog in the place where their brains ought to be. In this century, of course, they will be working on guided missiles and advising the medical profession on the control of disease, and there is no limit to the extent to which they could impede every sort of national effort."
[ R.A. Fisher, 1957 ]
I made the Pascal's triangle smaller, good idea.
Thank you!
Thank you for your kind comment! I disagree with the johnswentworth post you linked; it's misleading to frame NN interpretability as though we started out having any graph with any labels, weird-looking labels or not. I have sent you a DM.
While writing a recent post, I had to decide whether to mention that Nicolaus Bernoulli had written his letter posing the St. Petersburg problem specifically to Pierre Raymond de Montmort, given that my audience and I probably have no other shared semantic anchor for Pierre's existence, and he doesn't visibly appear elsewhere in the story.
I decided Yes. I think the idea of awarding credit to otherwise-silent muses in general is interesting.
Ptolemaically, this looks like the ~stationary larger body, dragging the rest of spacetime with it in a 2-D fixed velocity [that is, fixed over the orbit's period] around me - with exactly one dimension, the one we see as ~Polaris vs ~anti-Polaris, fixed in place, relative to the me/larger-body system. That is, the universe begins rotating around me cylindrically. The major diameter and minor diameter of the cylinder are dependent on the linear velocity I entered at [ adding in my mass and the mass of the heavy body, you get the period ] - but, assuming the larger body is stationary, nothing else about my fate in the capturing orbit appears dependent on anything else about my previous history - the rest is ~erased - even though generally-relative spacetime doesn't seem to preclude more, or fewer, dependencies surviving. My question is, why is this? Why don't more, or fewer, dependencies on my past momenta ["angular" or otherwise] survive?