(Hmm. Come to think of it, if the y-axis were in logits, the error bars might be ill-defined, since “all the predictions come true” would correspond to +inf logits.)
Optimization Process
Karma: 692
Ah—I took every prediction with p<0.50 and flipped ’em, so that every prediction had p>=0.50, since I liked the suggestion “to represent the symmetry of predicting likely things will happen vs unlikely things won’t.”
Thanks for the close attention!
I like the idea, but with n>100 points a histogram seems better, and for few points it’s hard to draw conclusions. e.g., I can’t work out an interpretation of the stdev lines that I find helpful.
Nyeeeh, I see your point. I’m a sucker for mathematical elegance, and maybe in this case the emphasis is on “sucker.”
I’d make the starting point p=0.5, and use logits for the x-axis; that’s a more natural representation of probability to me. Optionally reflect p<0.5 about the y-axis to represent the symmetry of predicting likely things will happen vs unlikely things won’t.
(same predictions from my last graph, but reflected, and logitified)
Hmm. This unflattering illuminates a deficiency of the “cumsum(prob—actual)” plot: in this plot, most of the rise happens in the 2-7dB range, not because that’s where the predictor is most overconfident, but because that’s where most of the predictions are. A problem that a normal calibration plot wouldn’t share!
(A somewhat sloppy normal calibration plot for those predictions:
Perhaps the y-axis should be be in logits too; but I wasn’t willing to figure out how to twiddle the error bars and deal with buckets where all/none of the predictions came true.)
Random numbers! Code for the last figures.
That all of physics was perfectly beautiful and symmetric except for hyperspace, artificial gravity, shields and a few weapon types.
Oh, this is genius. I love this.
Ahhh! Yes, this is very helpful! Thanks for the explanation.
Question: if I’m considering an isolated system (~= “the entire universe”), you say that I can swap between state-vector-format and matrix-format via
. But later, you say...
If is uncoupled to its environment (e.g. we are studying a carefully vacuum-isolated system), then we still have to replace the old state vector picture by a (possibly rank ) density matrix …
But if , how could it ever be rank>1?
(Perhaps more generally: what does it mean when a state is represented as a rank>1 density matrix? Or: given that the space of possible s is much larger than the space of possible s, there are sometimes (always?) multiple s that correspond to some particular ; what’s the significance of choosing one versus another to represent your system’s state?)
That is… a very interesting and attractive way of looking at it. I’ll chew on your longer post and respond there!
I have an Anki deck in which I’ve half-heartedly accumulated important quantities. Here are mine! (I keep them all as log10(value in kilogram/meter/second/dollar/whatever seems natural), to make multiplication easy.)
Quantity Value Electron mass -30 Electron charge -18.8 Gravitational constant -10.2 Reduced Planck constant -34 Black body radiation peak wavelength -2.5 Mass of the earth 24.8 Moon-Earth distance 8.6 Earth-sun distance 11.2 log10( 1 ) 0 log10( 2 ) 0.3 log10( 3 ) 0.5 log10( 4 ) 0.6 log10( 5 ) 0.7 log10( 6 ) 0.8 log10( 7 ) 0.85 log10( 8 ) 0.9 log10( 9 ) 0.95 Boltzmann constant -22.9 1 amu -26.8 1 mi 3.2 1 in -1.6 Earth radius 6.8 1 ft -0.5 1 lb -0.3 world population 10 US federal budget 2023 12.8 SWE wage (per sec) -1.4 Seattle min wage (per sec) 2024 -2.3 1 hr 3.6 1 work year 6.9 1 year 7.5 federal min wage (per sec) -2.7 1 acre 3.6
I thank you for your effort! I am currently missing a lot of the mathematical background necessary to make that post make sense, but I will revisit it if I find myself with the motivation to learn!
This is a good point! I’ll send you $20 if you send me your PayPal/Venmo/ETH/??? handle. (In my flailings, I’d stumbled upon this “fractional step” business, but I don’t think I thought about it as hard as it deserved.)
How are you defining “basically equivalent”
Nyeeeh, unfortunately, sort of “I know it when I see it.” It’s kinda neat being able to take a fractional step of a classical elementary CA, but I’m dissatisfied because… ah, because the long-run behavior of the fractional-step operator is basically indistinguishable from the long-run behavior of the corresponding classical CA.
So, tentative operationalization of “basically equivalent”: is “basically equivalent” to a classical elementary CA if the long-run behavior of is very close to the long-run behavior of some , i.e., uh,
...but I can already think of at least one flaw in this operationalization, so, uh, I’m not sure. (Sorry! This being so fuzzy in my head is why I’m asking for help!)
I was imagining the tape wraps around! (And hoping that whatever results fell out would port straightforwardly to infinite tapes.)
I’ve never been familiar enough with group-theory stuff to memorize the names (which, warning, also might mean that it will take you a lot of time to write a sufficiently-dumbed-down version), but the internet suggests is related to… the Minkowski metric? I would be flabbergasted to learn that something so specific-to-our-universe was relevant to this toy mathematical contraption.
I think compared to the literature you’re using an overly restrictive and nonstandard definition of quantum cellular automata.
That makes sense! I’m searching for the simplest cellular-automaton-like thing that’s still interesting to study. I may have gone too far in the “simple” direction; but I’d like to understand why this highly-restricted subset of QCAs is too simple.
Specifically, it only makes sense to me to write as a product of operators like you have if all of the terms are on spatially disjoint regions.
Hmm! That’s not obvious to me; if there’s some general insight like “no operator containing two ~‘partially overlapping’ terms like can be unitary,” I’d happily pay for that!
Things have coalesced near the amphitheater. When the music kicks off again, we’ll go northeast to… approximately here. 47.6309473, −122.3165802 JMJM+99F Seattle, Washington
Announcement 1: I, the organizer, will be 5-10min late. Announcement 2: apparently there’s some music thing happening at the amphitheater! I’ll set up somewhere northeast of the amphitheater when I get there, and post more precise coordinates when I have.
$10 bounty for anybody coming / passing through Capitol Hill: pick up a blind would-be attendee outside the Zeek’s Pizza by 19th and Mercer. DM me your contact information, and I’ll put you in touch, and I’ll pay you on your joint arrival.
Update: the library is unexpectedly closed due to staffing issues. The event is now at Fuel Coffee, one block south and across the street.
It sounds like you’re assuming you have access to some “true” probability for each event; do I misunderstand? How would I determine the “true” probability of e.g. Harris winning the 2028 US presidency? Is it 0⁄1 depending on the ultimate outcome?