To prove something is transcendental we would need to know how to compute it exactly, and I’m struggling to see how that would come up frequently in a physics context. In physics most constants are not arbitrary real numbers derived from a formula, they’re a measured relationship, which sort of inherently can’t be proved to be transcendental
It's probably possible to use timestamps, but I suppose you would have to handle ties in more places, with sequence numbers you only break ties once. It appears that the FIX specifications allows up to microsecond precision, but given the volume of messages it's still likely a problem. It's also easier to work with integer sequence numbers than timestamps, but that's also a small consideration.
I'm almost surprised that Gemini 3 uniquely has this problem. I would have expected that responses from any LLM that require complex math notation would almost certainly be LaTeX heavy, given the abundance of LaTeX source material in the training data. I suppose it is a flaw if a model can't avoid LaTeX, but given that it is the standard (and for the foreseeable future too) I don't know what appropriate output would look like. For "pure" mathematics or similar topics I think LaTeX (or system that represents a superset of LaTeX) is the only acceptable option.
I get that the author wanted to explore constraint solvers, but why can't you use a greedy algorithm for this problem? Sort the inventory slots by how much bundle space they consume, and insert the cheapest slots. The only way I see this failing is with multiple bundles, but in practice in Minecraft (which is admittedly not really part of the constraint problem) bundles only help when you have many distinct items but a large number of items occur only a few items. In that case it isn't hard to find combinations that fill each bundle completely by only inserting all of a given item (as opposed to inserting only part of an inventory slot) since many items will have only 1 or 2 copies.
I opt for the greedy strategy in most game play scenarios for pretty much the reasons you described here. I was considering making a mod to perform this action for me and was looking for a more "correct" solution but greedy is way simpler and just as effective for most cases.
If you greedily fill bundles by first inserting all weight-4 items (pearls, etc.) in any order into a single bundle, moving to a new bundle each time the current one gets full, then inserting all weight-1 items (sticks, etc.) in any order in the same way, the solution you get will use an optimal number of bundles, and also leave an optimal amount of free capacity in the final bundle. (It helps to notice that every bundle except the last must be completely full with no wasted space, since both 4 and 1 divide 64.)
If you do the same, but add all weight-1 items before adding all weight-4 items, you'll still get a solution using the same (optimal) number of bundles, but you may use more capacity in the final bundle than needed -- e.g., if you have 61 sticks and 1 pearl, and add them in that order, the first bundle wastes 3 slots and the second uses 4 slots (vs. no wasted space in the first bundle and just 1 slot used in the second if adding in the reverse order).
OTOH, if you mix adding items of different weights (while staying with the approach of only ever adding to the current bundle if there's room, and if not, moving to a fresh bundle) then you can arrive at a suboptimal number of bundles. E.g., adding 61 sticks, 1 pearl and 3 dirt in that order will require 3 bundles instead of the optimal 2.
There's enough places where em-dashes are inconvenient to type that I find it to be a reasonable indicator, particularly on the web. I don't think most people know how to generate an em-dash with a hotkey, so if I see one in a Reddit comment for example there's a high likelihood that the comment was either LLM generated or at least copy-pasted from somewhere else. Generally speaking in the past I observed a low prevalence of em-dashes on the internet except in more formal writing, so if I see an em-dash in a context where I ordinarily wouldn't expect one I do get suspicious. It's the same thing with the green check emoji, it's possible that a regular user typed it, but pre-LLM I can't recall ever seeing them, so these days I automatically assume it's AI generated content
I'd be interested to hear someone with more experience talk about this or if there's more recent research, but in school I read this paper: <https://research.cs.wisc.edu/vertical/papers/2013/hpca13-isa...> that seems to agree that x86 and ARM as instruction sets do not differ greatly in power consumption. They also found that GCC picks RISC-like instructions when compiling for x86 which meant the number of micro-ops was similar between ARM and x86, and that the x86 chips were optimized well for those RISC-like instructions and so were similarly efficient to ARM chips. They have a quote that "The microarchitecture, not the ISA, is responsible for performance differences."
`lea` is a very common x86 instruction that isn't RISC-like. (Actually I don't think any x86 operations are RISC-like since they're variable length and overwrite their inputs.)
It's just that the most complicated of all x86 instructions are so specific that they're too irrelevant to use. Or were straight up removed in x86-64.
I think what they meant is that the platforms are being performative by attempting to crack down on those specific words. If saying "killed" is not allowed but "unalived" is permitted and the users all agree that they mean the same thing, then the ban on the word "killed" doesn't accomplish anything.
What does using the grape emoji when talking about sexual assault accomplish? I see videos, compassionate, kind people who make videos speaking to victims in a completely serious tone use this emoji.
People talk about tiktok algorithm on tiktok. I don't even know...
I suppose it accomplishes being able to talk about sexual assault without having the video removed or demonetised by a regex that (fortunately?) doesn't get updated.
From a summary on HHS.gov it says "De-Identified Health Information. There are no restrictions on the use or disclosure of de-identified health information." Maybe someone with more knowledge could expand on the limitations of what counts as "De-Identified" but I think that might work. I followed the reference and nothing in the CFR jumps out at me, but I'm not a lawyer so who knows.
I thought the section on finding bugs was interesting. I’d be curious how many false positives the LLM identified to get the true positive rate that high. My experience with LLMs is that they will find “bugs” if you ask them too, even if there isn’t one.
This specific case each file had a single bug in it, and the bot was instructed to find exactly one bug. The wrong cases were all false positives, in that it made up a bug
I think this is mostly the fault of RLHF over-indexing on pleasing the user rather than being right.
You can system prompt them to mitigate this to some degree. Explicitly tell it that it is the coding expert and to push back if it thinks the user is wrong or the task is flawed, it is better to be unsure than to bullshit, etc.
Absolutely agree with this, I use ChatGPT to ask about how best to do something, if I say "I'm not sure about that" in response to some proposal the tool will basically always back down and change something even if it was totally right the first time. It's a real problem because it makes it very difficult to interrogate the tool when you're unsure if it's answer is correct.
In my experience it would not be typical to use a wedge to represent a cross product. Typically a wedge is used to refer to the outer/exterior product, which in three dimensions would correspond to a bivector as opposed to the vector you get from a cross product.
Wikipedia says it’s more common in physics, and we mostly used it in that context (e.g. fluid mechanics) rather than pure math. It was pronounced “veck”, IIRC.
reply