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Curvature is encoded in second derivatives of metric. So, any tensor that depends on second derivatives of metric, describes curvature in some way. Einstein tensor describes curvature in a way that can be related to the spacetime's physical contents.

Donald Trump has just been kicked off the GOP primary ballot in Colorado by the Colorado Supreme Court. https://edition.cnn.com/politics/live-news/colorado-trump-14th-amendment-12-19-23/index.html This reverses a finding by a Colorado District Court just a couple of weeks ago, where the judge reached the baffling conclusion that Donald Trump *had* engaged in insurrection, but should *not* be disqualified under section III of the 14th Amendment to the US Constitution, because even though he was the POTUS at the time, he wasn’t technically deemed to be an ‘Officer of the United States Government” in the sense referred to by the 14th Amendment. The Colorado Supreme Court made it clear in a 217 page ruling that they regarded this finding by the lower District Court to be a clear and reversible legal error. They also made it clear that the earlier finding that Trump had engaged in an insurrection was correct and factually based on evidence of record, and that Trump’s inflammatory speech which provoked the riot and breach of the Capitol was not protected political speech under the First Amendment. This latest ruling will undoubtedly be appealed immediately to the SCOTUS by Trump and his lawyers. In reality the Colorado decision by itself will make little difference to the calculus of the electoral college in the 2024 Presidential election, because Trump probably wouldn’t have have won any EC votes in Colorado to start with - but the new ruling does set a very interesting legal precedent. https://www.youtube.com/watch?v=N1PySqGo4L0

At least mathematical infinity is abstract https://en.wikipedia.org/wiki/Actual_infinity Okay, wait. It's abstract, period. https://bigthink.com/articles/infinity-is-not-real/

The mathematical description of the Einstein tensor is actually quite complicated: where: Actually, the above contains somewhat esoteric simplifying notation without which the expression would be even more complicated. The above images were sourced from https://en.wikipedia.org/wiki/Einstein_tensor#Explicit_form

Let me try to explain it with a bit of algebra. In an expanding homogeneous isotropic universe, a distance between any two points - let's call them, galaxies - is proportional to a number, \(a(t)\), called scale factor, which increases with time, \(t\). So, for example, if a distance between some two galaxies at some moment is \(D\) then later, when \(a(t)\) is twice as large, the distance between these two galaxies is \(2D\). Thus, this distance increases with time as \(a(t)D\). If the universe is finite, then there is a largest distance in it, which, just like any other distance, is proportional to \(a(t)\). Let's call it, \(a(t)L\). The only way for the \(a(t)L\) to become infinitely large is that \(a(t)\) becomes infinitely large. But, if \(a(t)\) becomes infinitely large, then distance between any two galaxies, \(a(t)D\), becomes infinitely large. IOW, all galaxies become infinitely far from each other. We of course know that it isn't so. Thus, either the universe was finite and remains finite, or it was infinite to start with.

Even a dying ember can reignite as it burns through the last of its fuel. As a dying sun can increase in light emissions (nova) when it burns throught its remaining fuel, our brain can experience an energetic surge of connectivity as its neural components near the end of functionality. For our brain, increased lucidity as it nears death infers increased functionality, which infers increased neural connectivity. We find explanations for terminal lucidity, when we consider what metabolic activities are more acutely engaged as our brain pursues its functional imperative amid its dying moments. In those moments, the functional imperative of our brain is not to produce lucidity, consciousness, or mind. Our brain's functional imperative is to maintain its metabolic stability (homeostasis), which is what it has been our entire life. As our brain dies, increased functionality and lucidity of mind is merely a byproduct of its metabolic imperative, which is to maintain functional stability against the degradation of its dying components.

I remember my grandad presenting that argument. I didn't like it then and I don't like it now. It's like saying: "You are a crap driver, I think I deserve your Bugatti more than you"

Over-confidence is antithetical to a good scientific approach.

He’s been soapboxxing for a long time now. Chip on shoulder. Axe to grind. Seems to have an agenda…

I think the Hamas part is very much implied, but perhaps too implied. That being said, the rest mostly referred to the otherwise hard to understand situation why Hamas has come to power in the first place. I think it is pretty obvious that Hamas has no intention to make lives better for Gazans (though potentially at the beginning some might have thought that). As mentioned, the issue is the ongoing campaign, and basically as some analysts and also Barak have mentioned, the issue is that the the suffering heaped on civilians (not Hamas) is depleting the goodwill that Israel had from suffering the violent attack by Hamas. They were therefore saying that Israel needs a targeted and timed action, but so far it is no unclear where things are going to end up. It does not help that some officials have floated the permanent displacement of Gazans and I think the original 24h deadline for Gazans to leave the North Gaza, without any assurance of a safe path (that came later, but the damage was done). That is a fair assessment . I think the issue I had with some justifications is the lack of a scope (I have mentioned commando-style actions as suggested by the US for example). But lack of announcements in that regard and again and in some cases pushing the likelihood of permanent displacement (with others contradicting those statements) does not really inspire confidence. As I said, I have simple thoughts and the thoughts said that at least we should spare the children (and then perhaps move up the morality ladder a bit if we hadn't failed that step already. And again, it does not matter whose child it was). I know you are trying to find policies that contradict this particular moral stance but as we have discussed in threads on abortion, it depends on the developmental stage of the fetus and its likelihood of survival, but also the risk to the mother. And in this context, late term abortion is a conservative talking point that misses its mark entirely. Medically, late term refers to pregnancies past 41 week gestation. I.e. if birth happens later than expected (40 weeks). Of course there is no abortion in that time frame. Moreover, fewer than 1% of abortions happen after the 21st week and I am not sure whether any of those are without some medical indication. But I suspect that it was more a jab at my simple moralism rather than a serious argument.

I think it's English with ð=th There's been a 2-year hiatus, so I must I remind myself of what all of this was about...

Not typical of my music tastes, but it's interesting to learn that a mystery regarding a background song on The X-Files has finally been solved after 25 years. I remember the episode, but hadn't the slightest idea that a background song in a bar scene was specifically composed for the episode. Or that it had an ET theme (the second video, at the end of the article, has the full track minus bar noise). https://www.npr.org/2023/12/13/1219137444/x-files-missing-song-mystery-music-lost-media

There has been one correction to my article published on Towards Data Science as a result of my activity on this board (I tried getting Mindmatters to make the change to their republication but they didn't): Original sentence: Corrected sentence: As I have previously stated, that doesn't change the point because models never reflect the actual. This has been a common observation, as seen through various related aphorisms: Correlation does not imply causation https://en.wikipedia.org/wiki/Correlation_does_not_imply_causation All models are wrong, some are useful https://stats.stackexchange.com/questions/57407/what-is-the-meaning-of-all-models-are-wrong-but-some-are-useful The map is not the territory https://en.wikipedia.org/wiki/Alfred_Korzybski Also, as I have previously stated in the thread, at least 50% of my article came from discussions on public forums, namely the entire section "Responses to counterarguments" This contrasts to utterly useless quips from certain users like iNow and StringJunky above. They are evidently only interested in the "meta." (e.g. "You are wasting your time," "He has chip on his shoulder," "He is overconfident," and other junk remarks) Please remind them to focus on the points, not on some pseudopsychoanalytic prods on perceived modus operandi. Sure, people on Reddit did that quite a bit, but at least even they coughed up useful items to add (re: exhaustive modeling, answering to accusations of intuition pumping from Dennett fanboys, etc), in this sense, iNow/StringJunky are being less than useless, worse than Reddit. Heck, even the idiot moderator on Ars(e) Technica gave me the lone "gift" of special pleading accusation before he banned me without allowing me to even reply once (because he thought that was the last word or something) Did I mention that he even deleted my post (yes, the article I wrote) after banning me? p.s. if they even bothered reading the thread, they'd already SEEN what exactly the "agenda" is. I've already mentioned the 2021 UN agency ban on AI legal personhood multiple times Bad analogy when it comes to machine consciousness since anyone who has digested the points of the argument would see that intentionality has nothing to do with any kind of machine performance. Well, iNow sure didn't read it- Doubt anyone else besides us would read it. Believe me, loads of people on my LinkedIn are also saying that the LLM approach to AI is a dead end. Chomsky mentioned GOFAI and guess what? There are talks of going back to it. Not entirely, but incorporation. That's one way to get any semblance of grounding. I saw a recording of a debate/discussion that occurred at the start of this year, and Chomsky said similar things as far as I could remember. Let me see if I can go find a link to it. It's chock full of today's authorities on AI.

Based on that analogy you made, evidently you didn't. Chomsky referred to looking at the wrong thing as barking up the wrong tree. To me, that wrong tree is really the entire reverse-engineering paradigm. The mind isn't a tool to be reverse engineered, because it isn't a designed artifact in the first place. To make progress, performance in any form should be persued, and not "reverse engineering" perceived anthropomorphisms. I've said to other people that the "optimizations" of the evolved mind isn't of the same kind possessed by engineered tools. In fact, these mental optimizations are even looked at as deficiencies, so are those going to be all "reverse engineered"? See this list https://en.wikipedia.org/wiki/List_of_cognitive_biases As for personalities, I like following Marcus's blog for the drama between him and the other AI experts, it's actually pretty hilarious.

Is that an extract from mien kampf? If history teaches us anything, it's that every war ends with excessive pacifism. Watch from 25 minutes https://www.youtube.com/watch?v=VM3Pb3ejA54