4denthusiast

[4denthusiast]

Boop the fact that someone deactivated. Blaze someone following you. Block a profile sticker. Enqueue a setting change for a later date.

they should add a separate like button for tags

[4denthusiast]

These solve separate problems, at least going by what I remember of reading that article a while ago. The article describes a reduction from arbitrary glider syntheses to syntheses by 15 gliders, whereas the video is about finding precursors to a pattern without a known glider synthesis.

[4denthusiast]

they should add a separate like button for tags

[4denthusiast]

Rule by LLM might not be a good idea per se, but it's at least an interesting variant on representative democracy. Rather than asking all the voters to individually decide every legislative issue (impractically bothersome) or asking them to select rulers who then make decision in their place (risks polarization, ignoring small groups, corruption, etc.), just amalgamate all the voters' opinions into an artificial ruler instead.

Of course, you wouldn't want to just use an off-the-shelf LLM. That would be far too much power for one company. The government department in charge of elections would have to be re-purposed to make the ruler. And you wouldn't want to use arbitrary web scraped data either. That would give disproportionate power to people who say things online, and have you seen online? Perhaps, instead of a normal vote, you'd be allowed to submit an essay of up to 1000 words describing your political preferences. Perhaps you answer questions, like in referenda, except on any questions where you don't answer directly your preferences are instead extrapolated algorithmically.

That latter option, with the AI answering questions rather than generating entire rulings, would probably do a better job of coping with the limited amount of training data available if you're being picky about only using training data from official, fair sources. It does have an issue though that it relies on some additional legal structure to determine what questions to ask the AI in the first place, and how to make laws if the ruler is incapable of writing.

Another possibility then would be to have two AIs. One is trained on carefully curated data submitted through official channels as part of the democratic process. It may not be able to write laws, but it can answer questions about popular opinion on political topics. The other is based on Internet data until it is able to write coherently, then post-trained on the opinions of the other AI. The limited, pure AI still gets veto power on all legislation, but the larger one is the one generating the legislation, and tries to do so in a way that will please the other.

There, democracy solved. When this flawless system is implemented, I am sure everyone will welcome their new AI president with open arms.

even the most ardent AI hater has to admit that replacing every current federal official with ChatGPT would be a step up

[4denthusiast]

Also on the topic of Strong Female Protagonist, the doctor was kind of crazy to be so dismissive of Alison taking an interest in the murder she witnessed, right? She personally witnessed a murder being committed by a friend, in response to an incident she had been involved in. Taking an interest is totally reasonable. I don't get where the author was going with that. Maybe the doctor secretly supported the murders, and didn't want Alison to interfere. I guess it's also an opportunity to demonstrate Alison's characterization is kind of a pushover.

[4denthusiast]

I just read Strong Female Protagonist. I mostly enjoyed it, but the apparent resolution of the central question the plot poses, "How do you use superpowers to actually make a positive difference in the world?", made me laugh and not in a good way. (Spoilers follow.)

We're presented with various contrasting possibilities: Feral's self-sacrifice, Menace's tyrrany, Pintsize's crime-fighting and later Moonshadow's vigilantism and Max's selfishness. Alison struggles to find her way, and work out what solution is right for her. Then after a while, she finds the solution, and is finally excited about the possibilities of making the world better, and it's just... fighting petty crime again, an answer she already rejected, only this time with a focus on one particular category of crime and a sprinkling of female solidarity.

The bit that's meant to make it different for her is the cooperation, but that just means she's partially giving up on actually doing something where her powers give her a comparative advantage. In the Valkyries, and especially in the other organizations she plans to found in the future, she's just acting as a manager and funder. Don't get me wrong, creating charities is a perfectly reasonable vocation, it just feels like an awkward departure from the theme of using superpowers for good.

I guess it kind of makes sense to interpret it as meaning in order to use superpowers for good, the people with powers need to be organized, and if nobody is doing the organizing then Alison has to do that as a pre-requisite. Still, the fact that what she's organizing them to do is just crime-fighting seems pretty silly in the context.

Alison repeatedly makes the point that apart from certain extreme cases of supervillainy, there's not much of a reson to prefer superheroes over normal police. The great majority of superheroes aren't actually invincible so they're not in much less danger fighting crime than normal police would be. The same logic applies to the Valkyries. This is America; I don't think there's anything stopping them just equipping volunteers with guns.

[4denthusiast]

In This Used To Be About Dungeons, one of the gods (Garos) is the god of symmetry, and it's mentioned that there's a picture called "Portrait of 20 Symmetries" which is a religious thing, described as "intensely symmetrical", meant to be contemplated by clerics in training to bring them closer to Garos, and it just struck me as a kind of strange number of symmetries to use, assuming they're counting symmetries in-character the same way as it's usually done in real life (as the order of the symmetry group).

For one thing, that's just not very many symmetries. Even just the platonic solids have more than that. A tetrahedron has 24, a cube or octahedron has 48, and a dodecahedron or icosahedron has 120. You can depict some of the 4D regular polytopes at least somewhat clearly as a 2D picture, and a 24-cell (my favourite for multiple reasons, but partially because of its interesting symmetries) has 1152 symmetries.

The other thing is that the order (size) of a finite group has a tendency to be a number with a lot of factors. This is illustrated in all of the numbers given above. Every positive integer has at least one group with that order, the cyclic group, but more divisible numbers tend to have more groups associated with them.

The only groups with 20 elements are the cyclic group C₂₀ (the symmetries of a 20-gon with no reflectional symmetry), C₁₀ × C₂ (the symmetries of a decagonal prism where the reflections within the plane of the decagon faces are disallowed) the dihedral group D₂₀ (the symmetries of a decagon, pentagonal prism or pentagonal antiprism), and the dicyclic group Dic₂₀ and semidirect product C₅ ⋊ C₄, neither of which (I'm reasonably sure) has a geometric representation in less than 4 dimensions*. Of these, all but the last two seem pretty boring. I guess if C₂₀ is depicted in the form C₅ × C₄, then the fact that that's isomorphic to C₂₀ makes it slightly more interesting, but not much. I would guess, for this reason, that Portrait of 20 Symmetries depicts either Dic₂₀ or C₅ ⋊ C₄ somehow, with the latter being a somewhat nicer option in my opinion.

*C₅ ⋊ C₄ is a subgroup of the symmetric group S₅, which is the group of symmetries of a 4D simplex, so if you just pick some arbitrary completely unsymmetrical 4D shape and a subgroup of the symmetries of the simplex isomorphic to C₅ ⋊ C₄, and combine together the shape's 20 images under thr group, then in general you'll get a shape whose symmetry group is C₅ ⋊ C₄.

[4denthusiast]

neurospicy was an activity enjoyed by much of the 21st century usamerican middle class, related to the contemporary practices of "astrology," "psychiatry," and "phrenology." Practitioners, known as "neurospices" (singular neurospex) would attempt to categorize people through observation and consultation with the "Diesemfive," their holy book. It is said a particularly skilled neurospex could perfectly and accurately divine the conditions of another person from a single tumblr post.

[4denthusiast]

A backwards temperature scale, thermodynamic beta, does have certain advantages. The temperature is 1/(dS/dE) (and it doesn't make much sense to make the entropy the independent variable in statistical mechanics). The probability of a microstate with energy E in the canonical ensemble is proportional to e^(-E/kT). A negative temperature is hotter than a positive one. If you use the variable β=1/kT instead of T, these all simplify.

Entropy also is defined as -kΣ p ln(p), i.e. the negative of something, so from that point of view using negentropy would be simpler. Of course it's also easier to conceptualize negentropy as a resource that gets consumed than entropy as something that builds up to a limit. Absolute entropy is always non-negative though, so negentropy is non-positive, which would be rather awkward.

i think it's funny how ol ben frank got it backwards when he electrocuted himself and now generations of students are stuck getting over the unnecessary confusion of electrons contributing negative charge and positive ions being down one electron and generally positive charges being lack of electrons.

it's as if we historically happened to have considered cold to be "more" and hot to be "less" and the terminology had persisted past the discovery of thermodynamics, such that we were all stuck with talking about contributing negative heat energy

[4denthusiast]

Perhaps it's a sign of me spending too much time on Tumblr that it sometimes surprises me when people I meet offline are normal about Harry Potter. It makes me wonder to what extent the extreme anti-HP stance is even representative here on Tumblr, and to what extent it is just more visible.

[4denthusiast]

I had been assuming the pro-ana people were using leetspeak-ish tags, and therefore annoyingly circumventing my personal blocked tags list, as a way of avoiding globally blocked tags to connect with each other. Just now though, I decided to check whether this is in fact the case and no, neither "#ana" nor "#pro ana" is actually globally blocked like some other tags are*, the leetspeak tags aren't even necessary. Were they necessary at some point in the past perhaps, such that people continue to use them without realising it has changed? If these people are just avoiding the plain tags for no good reason, that makes me much less sympathetic and more just annoyed at them. There are plenty of aspects of how to tag usefully that may not be obvious if you aren't coming from a certain point of view, but I would have thought this one would be pretty obvious.

*For some vaguely sexual tags, Tumblr refuses to show anything in the tag search at all, but for "#ana" it first redirects you to a page offering help with eating disorders then allows you to continue to the actual results if you still want to.

[4denthusiast]

Things are looking dire in the "4D" tag. Some of us are looking for actual maths content, not superstitious nonsense.

[4denthusiast]

I made a little graphics demo which I'm quite proud of so I felt like sharing. It generates a 4D mesh from 4D voxel data using the dual contouring method, then renders a rotating 3D slice. The live version is animated, but here's a screenshot of what it looks like.

[4denthusiast]

New theory of consciousness: panpsychism used to be true, but sapient brains are so much more attractive to souls than any other sort of matter that everything else stopped having conscious experiences when humans evolved, at least in the vicinity of Earth. Fresh souls continue to slowly accrete onto the planet from ever more distant regions of the universe, allowing us to keep up with population growth.

[4denthusiast]

older lesbian at a bar: [lights cigarete] i was your age when you were your age isnt that weird

other lesbian the same age as her: can yuo put that out on me

her: i just lit it though

[4denthusiast]

To elaborate on why every homeomorphism is given by the right action of some element: Take a finite boring space S of size n. There are n homeomorphisms given by the right action of elements of S on the space. This gives an injection S -> Aut(S) (where Aut here is topological automorphisms, not just topological group automorphisms). A and Aut(S) are finite and equinumerous (because S is boring), therefore this is a bijection, i.e. every homeomorphism on S is given by the right action of some element of S.

For abelianness, let the identity be e and take some element g. The left action of g on S is a homeomorphism, therefore it is the right action of some element h on S. eh = ge, therefore h=g, and the right action of g is equal to its left action. Since g was arbitrary, S is abelian.

I don't think the automorphism group of a circle can be O(2), right? Either you mean topological automorphisms, in which case the automorphism group is infinite-dimensional (I think homeomorphic to (ℝ/ℤ) × (0,1)^ℕ or something like that), or topological group automorphisms of SO(2), in which case it's the group of order 2.

I suspect that SO(2n+1) is isomorphic (via the conjugation map) to its (topological group) isomorphism group. The proof seems kind of fiddly though, so I don't feel like doing it. That still wouldn't make it boring or course, because the topological automorphism group is much larger. For some other Lie groups the symmetries of the Dynkin diagram give outer automorphisms, but the Dynkin diagram for SO(2n+1) has no non-trivial symmetries, as don't Cn, F4, G2, E7 and E8.

Call a space boring if it's homeomorphic to its homeomorphism group. Call it whoring if it's homotopy equivalent to its homeomorphism group.

(Easy hopefully?) Classify all the boring spaces.

(Probably incredibly hard) Classify all the whoring spaces.

I don't really have an instinct for how many whoring spaces there should be. Probably not many?

[4denthusiast]

Some thoughts on boring spaces:

They're homeomorphic to a group, so we may as well consider them to be equipped with that group structure. The left and right actions of this group's elements on itself are all homeomorphisms, and there are as many homeomorphisms given by the right action of some element on the set as there are elements. Assuming for now the set is finite, every homeomorphism is therefore given by the right action of some element (and similarly for left action, which implies it's abelian, but this fact won't be necessary).

If it can be partitioned into 3 or more non-empty clopen subsets, it can be partitioned into 3 or more non-empty clopen subsets which are homeomorphic to each other, and a homeomorphism of the space as a whole can be constructed swapping two of the subsets which don't contain the identity, therefore there is a homeomorphism not given by the group action, which is a contradiction, therefore the space can be partitioned into at most 2 non-empty clopen subsets.

If there is a partition into 2 non-trivial clopen subsets, each containing more than one element, then applying a non-identity element of the identity component to only the identity component, and leaving the other one unchanged, gives a homeomorphism other than the group action, which is a contradiction, therefore if the space has 2 non-trivial clopen subsets, each of them contains only a single element. The only disconnected finite boring space is therefore the discrete topology on 2 points.

If on the other hand the space is connected, take the intersection X of all the open sets containing the identity. Assume there is an element g not in X, and further assume there is h∈X ∩ gX, then X ∩h⁻¹gX is smaller than X and still contains the identity, which is a contradiction. X ∩ gX is therefore empty for all g ∉X, therefore the space is not connected, another contradiction, so there is no such g and the space is indiscrete. Every bijection from an indiscrete space to itself is a homeomorphism, therefore if the space is indiscrete it has at most 2 elements (because n! > n for n > 2).

There are only 3 spaces meeting these constraints, and all of them are indeed boring: the singleton, the discrete space of 2 points, and the indiscrete space of 2 points. These are therefore all of the finite boring spaces.

As for infinite boring spaces, I don't have a classification but I do have a few examples. ℤ, with [n,∞) as its open sets, is a boring space, as are I believe at least all finite powers of this space. These are abelian topological groups all of whose homeomorphisms are given by the group action, but the proof used for the finite case fails because the fact that X was finite was implicitly used to prove that X ∩h⁻¹gX was smaller than it.

I haven't found any more boring spaces yet, but I suspect they exist. As for whether there are any infinite boring spaces that are actually Hausdorff (let alone CW complexes) I wouldn't be surprised if not. It seems like it would be hard to make the points distinguishable enough for an infinite space to be boring without the asymmetry non-T1ness allows.

Call a space boring if it's homeomorphic to its homeomorphism group. Call it whoring if it's homotopy equivalent to its homeomorphism group.

(Easy hopefully?) Classify all the boring spaces.

(Probably incredibly hard) Classify all the whoring spaces.

I don't really have an instinct for how many whoring spaces there should be. Probably not many?