Yeah, I recently upgraded to the 9a from the 4a for $250 USD and am still really enjoying Pixels. I might just be out of the loop on what's available, but I can't imagine many other phones at this price are competitive.
The A line is still a competitive midrange (at least when on sale) and if you enjoy the pixel experience there's nothing wrong with it at all.
However the regular pixel or the pro haven't been competitive in several years. This year is particularly bad because it's very close to iPhone price for less storage, less performance, worse battery life, and less easily accessible help (tech support/warranty/repair).
The usual comeback is the the pixel is fast enough so it doesn't matter. And it's kinda true. But it doesn't change the fact that it's poor value, midrange hardware for premium price.
I'm an American mathematician and have always allowed the codomain of a random variable to be any measurable space. I haven't noticed anyone mention random elements. I don't work in probability though, so maybe people directly in the field care more.
From what I saw as a recent grad student in probability, most texts do define a random variable to necessarily map into the reals, or the extended reals or perhaps a subset thereof, or occasionally the complex numbers, and the more general concept is a "random element" (when a more specific term is called for, there are "random vectors", "random graphs", "random processes", etc.). But this is certainly not universal even within probability. In any case, I don't believe it matters much -- it's hard to see how a mix-up here might cause any real confusion, though as always it is annoying that there isn't a common convention.
Interesting way to look at it. Your description of what physicists are experts at matches my math PhD pretty closely. I focused on mathematical modeling. I now work with a bunch of physicists, so I guess that checks out.
Yeah, if you work on the applied side of math it can be very similar to what people do in physics. But I was thinking more about pure math.
Edit: I think the main difference there is that in applied math they still prove that the models are mathematically correct. In physics they just show that the model align with experiments and skip math formalism.
I was with you on the generalities, but oh do theoretical physics suffer from math envy when it comes to formalism. Basically since the invention of quantum mechanics, has physics been dominated by “proofs” and “theorems” like the physical world is assumed to be axiomatically defined by Heisenberg’s and Pauli’s principles, and everything else is just maths.
No small part of the stagnation I sense in physics today stems from too deep a faith in the ultimate truth of the mathematical models we call theories. It doesn’t help the fact that we rely on Taylor expansions and perturbation methods for most experimental predictions.
The Higgs hunt and the passivity of the (experimental) physicists in challenging this stupid theory-driven search for new physics is emblematic of this era.
If only math was seen as a modeling language and not somehow truth/consistency itself, physics would be much better off.
Yeah, I saw that as well, met some professors in grad school that started talking about physics in terms of axioms and proofs instead of experimental results and models. At that point I lost interest and just went with math instead, if it is going to be math anyway why not go with the real thing.
The article says that biking increased and walking decreased. I don't think I can explain those things simultaneously with just "well we were in a pandemic during that time."
Pedestrian fatalities are up in pretty much every metro, so this isn't a meaningful signal. It's still worth pursuing banning high-fatality vehicles from urban areas.
You don't think increasing pedestrian fatalities could be linked to people choosing to walk less? I've certainly noticed in my area that drivers have been much more aggressive since the pandemic started and I walk less because of it.
A classical universal function approximator is probably not sufficient to approximate quantum systems
(unless there is IDK a geometric breakthrough in classical-quantum correspondence similar to the Amplituhedron).
IIUC Church-Turing and Church-Turing-Deutsch say that Turing complete is enough for classical computing, and that a qubit computer can simulate the same quantum logic circuits as any qudit or qutrit computer; but is it ever shown that Quantum Logic is indeed the correct and sufficient logic for propositional calculus and also for all physical systems?
> - The rotation operators Rx(θ), Ry(θ), Rz(θ), the phase shift gate P(φ)[c] and CNOT are commonly used to form a universal quantum gate set.
> - The Clifford set {CNOT, H, S} + T gate. The Clifford set alone is not a universal quantum gate set, as it can be efficiently simulated classically according to the Gottesman–Knill theorem.
> - The Toffoli gate + Hadamard gate.[17] The Toffoli gate alone forms a set of universal gates for reversible boolean algebraic logic circuits which encompasses all classical computation.
[...]
> - The parametrized three-qubit Deutsch gate D(θ)
> A universal logic gate for reversible classical computing, the Toffoli gate, is reducible to the Deutsch gate, D(π/2), thus showing that all reversible classical logic operations can be performed on a universal quantum computer.
That's interesting. I thought it was obvious that ADHD does exist because it's just a constellation of behaviors that some people indeed do exhibit. I feel like we agree completely on the base facts and somehow have arrived at opposite conclusions.
That's more a semantic disagreement than an opposite conclusion, considering you both agree the constellation of behaviors exists.
The degree to which any medical diagnosis exists is on a spectrum. A cancerous tumor obviously exists, high blood pressure exists but is relative, schizophrenia - and psychiatric diagnoses generally - exist but can be more difficult to observe externally.
The behaviors associated with ADHD are so common and relatable to most folks that the diagnosis seems less legitimate. To my knowledge, you cannot scan the brain of someone with ADHD and point out an abnormality associated with the disorder. Yet we give 8 year old boys stimulant medication because they can't sit still in a classroom for hours a day.
Fwiw I have ADHD and take stimulant medication daily. But I also understand folks' resistance to accept ADHD as being as legitimate as other medical diagnoses.
> To my knowledge, you cannot scan the brain of someone with ADHD and point out an abnormality associated with the disorder. Yet we give 8 year old boys stimulant medication because they can't sit still in a classroom for hours a day.
I'm not well-versed in the risks of stimulants given to children so I'm not commenting on that specifically, but I want to push back on the insinuation (if I understood you correctly) that ADHD or its treatments are any less legitimate because we haven't yet figured out if we can use brain imaging to diagnose and measure treatment efficacy.
It would be great if all medical disorders could be externally measured and quantified objectively, but when they're not, we often rely on evaluating and diagnosing them based on the (often somewhat more subjective) impact of their symptoms. That's not ideal, but it seems better than nothing to me.
Full disclosure: I'm also diagnosed with ADHD and take daily stimulants. Apologies if I came off as combative, I'm relatively new to my ADHD journey and genuinely curious to learn more about the medical/scientific aspects.
> ...but I want to push back on the insinuation (if I understood you correctly) that ADHD or its treatments are any less legitimate because we haven't yet figured out if we can use brain imaging to diagnose and measure treatment efficacy.
I was playing devil's advocate to explain why someone might feel that way. My personal opinion is that every adult should have the right to assess for themselves whether they feel stimulants can improve their quality of life. The question of whether ADHD is "real" or legitimate is totally unimportant to me. And I agree with your take: if we can identify symptoms and effectively treat them, that is more important than uncovering some underlying "legitimacy" of the treated condition.
Congratulations on getting diagnosed. ADHD has the highest treatment success rate among psychiatric conditions. Be sure to keep up with all the other healthy habits for improving focus (sleep, exercise, nutrition, hydration, etc.).
It doesn't follow from the constituent behaviors being real that a concept is real. Take neurasthenia as an example; it was a popular American diagnosis in its day, and I don't think anyone argues that millions of people were faking it. But we draw different lines around these constituent symptoms today, and no longer see it as a coherent condition.
The search term "culturally-bound syndrome" makes for interesting reading in this area.
