snarkconjecture

You could say that as well. Gamma is often (usually?) defined as any radiation that originates from nuclear state transitions rather than electrons; this tends to be very high energy but can overlap the range of EM radiation from electronic transitions. Th229 is the extreme outlier.

How so? Isn't the Markov property just a consequence of basic QM?

For sufficiently large N, it's impossible to prove Halt_N correct.

(The N required depends on your axioms.)

This follows fewer of the principles on the "Brutalist Web Design" link than HN does. In particular, it's slower, has less obvious links, breaks my back button, and has (imo) distracting unnecessary decoration.

I would also bet it uses JavaScript for the "hyperlinks" but haven't checked.

"Ah yes, you wanted to know where the electro-weak mixing angle came from, didn’t you? It’s the sum of the angle of tilt of the Earth’s axis, and the angle of inclination of the Moon’s orbit. Well, not exactly, because the particle experiments are more difficult to do than the astronomical ones, but it’s pretty close."

This is absurd crackpot nonsense.

Why would a disappointingly simple explanation be a hint that there are gaps in our models? Or am I parsing that part wrong?

I disagree that it's really that simple an explanation, though. Our best theoretical prediction for dark energy is that it should be denser by dozens of orders of magnitude. It's not remotely clear why the actual value seems to be so small, especially since it's not exactly zero.

Yup. On which note, the Higgs' symmetry breaking should really have changed the vacuum energy density by something orders of magnitude larger than the density of dark energy...

Big rip scenarios are inconsistent with dark energy having a constant value of w=-1, which is what the author is discussing in that paragraph. The article is wrong.

It makes more sense if you've learned general relativity.

Both of those are pressureless, so they could be dark matter but not dark energy.

Except that primordial black holes are ruled out (as 100% of dark matter) by various observational bounds, and antimatter would be just as visible as normal matter and not "dark" at all.

Momentum is just mv, not mv².

Neither the OP nor the top answer on Reddit mentioned the Higgs boson. You're right, but I'm not sure who you're rebutting.

General Relativity is a straightforward consequence of basically any form of string theory.

> All of these terms, including the Anglo‐Saxon word “lifere,” seem to closely resemble the English verb “to live,” underscoring the relation of the liver to life in populations influenced by the Celtic culture.

Except that "liver" (etc) and "life" have no etymological relationship, so this coincidence can't have anything to do with Germanic culture, much less Celtic(?!) culture.

OP's code still only has log2(52!) different binary strings that can be encoded, but they vary in length from 52 to 1378 bits (and are the leaves of a binary tree). This is handy for easily encoding sequences drawn from a non-uniform distribution, like strings of English letters, by giving each letter a fixed-length binary codeword. It's sort of flipped from the more common method of giving symbols a varying-length binary codeword (e.g. with Huffman coding) and encoding a fixed-length binary string in a deck of cards (or anything else).

I have to admit I don't immediately see how that would work, since the proof uses properties of Penrose tilings other than aperiodicity, but if you flesh out the details I think it would be a great paper.

Yup, way off base.

There are many ways to construct an aperiodic set of points with algebraic coordinates, or even rational, or integer, coordinates.

Penrose tilings have vertices with algebraic coordinates. The new aperiodic "hat" tiling does too.

In fact, the hat tiling has an underlying periodic sub-tiling of kites, and you can use this fact to distort the hat tiling into an aperiodic tiling with integer coordinates.

The grain of truth in your argument is that algebraic numbers are more structured. Crucially, they can always be represented exactly with a finite amount of data. The Penrose vertex coordinates are particularly nice because they're rational linear combinations of 1 and sqrt(5), iirc, so you can represent them as a pair of pairs of integers.

(Edit: I'm also pretty certain the slopes of the cut-and-project plane are algebraic. You can obtain a nice one-dimensional aperiodic tiling by cutting a 2D grid at a slope of the golden ratio, which is obviously algebraic.)

A decimal "point" is called that because it's written as a dot: .

"Fixed point" arithmetic has nothing to do with "fixed point theorems", it's a name collision.

Base ten has nothing to do with the distinction between real and algebraic numbers.

If you Google "algebraic vs transcendental number" you'll find many good resources. Pi is an example of a transcendental number.

You're on the right track, especially with the last sentence.

If reality had an infinite amount of detail (i.e. matter could be arbitrarily small), we could make storage media as dense as we liked by encoding ones and zeros as the presence or absence of tiny bits of matter.

The alien's stick is a version of this, albeit an exponentially inefficient one restricted to codewords of the form 1111...0000.

In practice, if atoms are about N orders of magnitude smaller than macroscopic objects, we can fit (very roughly) 10^N bits of information in an object, and the alien's method can only fit, as you said, roughly N bits.

Of course, existing storage methods are somewhere in between, because 1 gram of storage media can hold way more than 23 bits but way less than 10^23.

(I'm handwaving past some important distinctions, like the distinction between the size of atoms and the level of detail in the physical world. In classical Newtonian physics, things can be made of particles but the particles can have perfectly continuous positions, so that there's still no ultimate limit on measurement detail. Quantum physics changes this -- although this gets complicated because of the holographic principle; many physicists think the ultimate information limit grows like the 2/3 power of volume, instead of linearly...)

As of right now, it seems to work for any song on Infinite Jukebox mode but the Autocanonizer gets stuck on loading for any song that isn't one of the presets.

General relativity has no problem with dark energy or dark matter. Singularities, yes. And nonrenormalizability is an issue (with trying to make it quantum).

Speaking as a physicist, I think you're basically on the right track! (But also, this is as much philosophy of math/science as it is physics, so I wouldn't quite call myself an authority on this.)

I definitely think of probability as something like a mental framework with a set of axioms that can be applied to anything where the axioms fit well enough, which can be "true" quantum probability or sequential frequentist dice rolls or subjective Bayesian stuff.

"Good old-fashioned AI" (GOFAI) is a term of art that refers to symbolic AI, in contrast to deep NNs.

Maybe we need to rename it if deep learning is already "old fashioned"!

(EDIT: to be clear, I have no idea what TechCrunch thinks GOFAI means.)

I rather like this collection: https://namingschemes.com/Main_Page

Nonstandard terminology warning: the author is using "autocorrelation" in a way I've never seen before. There is a much more common usage of "autocorrelation" to refer to the correlation of a timeseries with itself (shifted by some amount).

If you use autocorrelation to refer to the thing in OP, you'll probably confuse people who know statistics, and vice versa.

The great-grandparent comment was talking about an "information density limit" and black holes in our universe, so I assumed the referenced sci-fi collection had something to do with holography. I don't know of any particular emphasis on AdS in that context before 1997. Elaborate?

Obviously you can stick GR in AdS, but AFAIK nothing about that would've seemed interesting with regards to holography before Maldacena, let alone plausibly providing inspiration to a fiction author.

To be less roundabout than my previous comment: I think Baxter may have been inspired by the holographic principle in general, but I doubt AdS crossed his mind at all when he was writing these stories in the 80s and early 90s.

(EDIT: or maybe Baxter was thinking about AdS but not about holography. I haven't read his work.)

The AdS/CFT correspondence was published slightly after that collection. Are you saying Baxter scooped Maldacena?

There is of course a catch, since physics can be simulated (with an exponential slowdown) by a Turing machine.

The catch is that "macroscopic behavior" in this context includes things that are not really macroscopically observable, or require conditions that cannot easily be specified. For the spectral gap, I think the way this manifests is that you can't ever be certain that you're in the ground state, but I'm not sure this is correct.

I stand corrected.

No, multiplying the incidence by 1.05 is incorrect. The 5% figure is additive.

ICRP Publication 103 is pretty unambiguous; e.g. Table A.4.2 gives total figures of about 400-600 "cases per 10,000 persons per Sv".