penteract

I'm a bit more interested in what it teaches about the hyperbolic plane than I am in it's effectiveness as a note taking app (although the way it supports an exponentially growing tree does seem appropriate for depicting knowledge - I'd be interested to see something like a force directed graph of Wikipedia plotted on the hyperbolic plane).

The points and arrows do move and change shape appropriately while panning, but the images and text do not. It might be possible to use feDisplacementMap (an SVG filter effect) cleverly to get the deformations right. This would probably make performance worse, and I'm not sure how readable the text would be, but it would mean that things wouldn't start overlapping each other while panning.

> As seen after the Black Death, a scarcity of labor drives real wages up and lower the cost of basic goods and rent.

Does this still hold when the majority of labor is no longer closely tied to a finite supply of land? At the time of the Black Death, the majority of men's labor was farming, and having more land directly made labor much more productive[1]. The modern economy feels much more complicated (e.g. if your job involves transporting things/people from A to B, it probably decreases in efficiency as the density of people decreases).

[1] https://acoup.blog/2025/09/12/collections-life-work-death-an...

I'm open to the possibilty of AI conciousness, and there is some desparation related to the concept of a higher being:

There are many people who will categorically rule out the posibility of AI consciousness due to near-unshakable belief in a higher being. This argument resembles "Christians should not be worried about our climate since God is ultimately in control." Such views make it harder to collectively prevent dangers from a sentient AI, or harm to a sentient AI.

I do not claim that everyone who believes in a higher power believes concious AI to be impossible, or vice versa; just that it would be very hard to change the minds of those who adhere to this reasoning.

Very cool. I was expecting it to make circles bigger rather than making needles smaller. Take a near-circle consisting of N lines. As N tends to infinity, the near-circle would have a diameter close to N*L/π, so would touch N*L/πW + O(1) lines twice each.

Many people move to London when they want to make money, and move out when they want to do anything else. Pretending that London is independent of the rest of the country's children and retirees is misleading.

https://trustforlondon.org.uk/data/population-age-groups/

Lena isn't about uploading. https://qntm.org/uploading

> I don't think it's possible to tile the sphere using more than 20 exactly identical pieces.

I was wrong about this (e.g. https://en.wikipedia.org/wiki/Rhombic_triacontahedron). It still seems possible to me that there's a limit to the smallest tile that can tile a unit sphere on its own. (Smallest by diameter as a set of points in R^3).

Not quite - you need 12 pentagons in a mostly hexagonal tiling of the sphere (and if you're keeping them similar sizes, Gosper-islands force hexagon-like adjacency). I don't think it's possible to tile the sphere using more than 20 exactly identical pieces.

You could get a Gosper-island like tiling starting from H3 by saying that each "Hex" is defined recursively to be the union of its 6/7 parts (stopping at some small enough hexagons/pentagons if you really want). Away from the pentagons, these tiles would be very close to Gosper islands.

No idea if they are doing this, but you can use Gosper islands (https://en.wikipedia.org/wiki/Gosper_curve) which are close to hexagons, but can be exactly decomposed into 7 smaller copies.

Your other points are more relevant to the content of the article, but point 2. relates the practical consequences of undecidable type-checking, so I'll reply to that.

I don't have a problem with compile time code execution potentially not terminating, since it's clear to the programmer why that may happen. However, conventional type checking/inference is more like solving a system of constraints, and the programmer should understand what the constraints mean, but not need to know how the constraint solver (type checker) operates. If it's undecidable, that means there is a program that a programmer knows should type check, but the implementation won't be happy with; ruining the programmer's blissful ignorance of the internals.

Decidability of a type system is like well-typedness of a program. It doesn't guarantee it's sensible, but not having the property is an indicator of problems.

No. Being well typed is not a semantic property of of a program - in a language where it makes sense to talk about running badly typed code, a piece of code that starts with an infinite loop may be well or badly typed after that point with no observable difference in program behaviour.

There are decidable type systems for Turing complete languages (many try to have this property), and there are languages in which all well typed programs terminate for which type checking is undecidable (System F without all type annotations).

For many publications you could be critisizing, I'd agree with you, but Quanta usually reaches a higher standard that I feel they deserve credit for. Here's the Quanta article on the same thing [1]. It goes into much more detail, it shows a picture of the perfect sofa, and links to the actual research paper. They're aimed at a level above "finished high school", and I appreciate that; it gives me a chance to learn from the solution to a problem, and encourages me to think about it independently.

I agree with you that Quanta doesn't always "allow specialists to understand exactly what's being claimed", which is a problem; but linking to the research papers greatly mitigates that sin.

[1] https://www.quantamagazine.org/the-largest-sofa-you-can-move...

And here's how they clearly explain the proof strategy.

> First, he showed that for any sofa in his space, the output of Q would be at least as big as the sofa’s area. It essentially measured the area of a shape that contained the sofa. That meant that if Baek could find the maximum value of Q, it would give him a good upper bound on the area of the optimal sofa.

> This alone wasn’t enough to resolve the moving sofa problem. But Baek also defined Q so that for Gerver’s sofa, the function didn’t just give an upper bound. Its output was exactly equal to the sofa’s area. Baek therefore just had to prove that Q hit its maximum value when its input was Gerver’s sofa. That would mean that Gerver’s sofa had the biggest area of all the potential sofas, making it the solution to the moving sofa problem.

This is great.

Since you've asked about bugs, I tried pushing the limits and found the following:

    A1: 100          B1: =100-A1
    A2: =A1*(100-A1)
    A3: =A1*B1

A2 can be successfully set to anything reasonable (up to 2500)

However, setting A3 to exactly 100 doesn't work, even though setting it to 101 or 99 (or even 100.000001) does work.

Another limit:

    A1: 100          B1: 100
    A2: =A1+B1
    A3: =A1*B1
    A4: =abs(A2-100) + abs(A3-100)

Setting A4 to zero (or anything below 80) doesn't work. This doesn't improve if the constants in the A4 formula are moved a short distance away from 100.

In case you can't tell from that last example, I think being able to fix the intended values of multiple outputs simultaneously would be interesting. If you were to give more details about the solver's internals, I'd be keen to hear them.

I believe that the important part of a brain is the computation it's carrying out. I would call this computation thinking and say it's responsible for consciousness. I think we agree that this computation would be identical if it were simulated on a computer or paper. If you pushed me on what exactly it means for a computation to physically happen and create consciousness, I would have to move to statements I'd call dubious conjectures rather than beliefs - your points in other threads about relying on interpretation have made me think more carefully about this.

Thanks for stating your views clearly. I have some questions to try and understand them better:

Would you say you're sure that you aren't in a simulation while acknowledging that a simulated version of you would say the same?

What do you think happens to someone whose neurons get replaced by small computers one by one (if you're happy to assume for the sake of argument that such a thing is possible without changing the person's behavior)?

My objection to that is that there isn't a particularly natural reason not to say

       (-1)ˣ = cos(πx) - i sin(πx)

As a formula about e^iπx, there is no such conflict.

> Why would anyone pick the flexible/potentially-insecure option?

Because having a connection that's encrypted between a user and Cloudflare, then unencrypted between Cloudflare and your server is often better than unencrypted all the way. Sketchy ISPs could insert/replace ads, and anyone hosting a free wifi hotspot could learn things your users wouldn't want them to know (e.g. their address if they order a delivery).

Setting up TLS properly on your server is harder than using Cloudflare (disclaimer: I have not used Cloudflare, though I have sorted out a certificate for an https server).

The problem is that users can't tell if their connection is encrypted all the way to your server. Visiting an https url might lead someone to assume that no-one can eavesdrop on their connection by tapping a cross-ocean cable (TLS can deliver this property). Cloudflare breaks that assumption.

Cloudflare's marketing on this is deceptive: https://www.cloudflare.com/application-services/products/ssl... says "TLS ensures data passing between users and servers is encrypted". This is true, but the servers it's talking about are Cloudflare's, not the website owner's.

Going through to "compare plans", the description of "Universal SSL Certificate" says "If you do not currently use SSL, Cloudflare can provide you with SSL capabilities — no configuration required." This could mislead users and server operators into thinking that they are more secure than they actually are. You cannot get the full benefits of TLS without a private key on your web server.

Despite this, I would guess that Cloudflare's "encryption remover" improves security compared to a world where Cloudflare did not offer this. I might feel differently about this if I knew more about people who interact with traffic between Cloudflare's servers and the servers of Cloudflare's customers.

To me it reads like there was a gradual rollout of the faulty software responsible for generating the config files, but those files are generated on approximately one machine, then propogated across the whole network every 5 minutes.

> Bad data was only generated if the query ran on a part of the cluster which had been updated. As a result, every five minutes there was a chance of either a good or a bad set of configuration files being generated and rapidly propagated across the network.

There's a whole paragraph in the article which says basically the same as your point 3 ( "glass bouncing, instead of shattering, and ropes defying physics" is literally a quote from the article). I don't see how you can claim the article missed it.

From the article, it looks like the problem is partially caused by significant parts of the transmission network being temporarily shut down due to ongoing upgrades. These could probably have been started slightly sooner, but they are already underway, so I don't think your point is weel supported.

Fonts can be complicated. Using nonsense like [1] (specifically contextual alternates), you could have the glyph for the first letter of a word depend on the last letter. I don't think you could get that to work for all letters in an arbitrary length word, but making a font that works for all words shorter than say 20 characters should be doable.

[1] https://blog.glyphdrawing.club/font-with-built-in-syntax-hig...

Angular size is proportional to size/distance, so the calculation you're trying to do is correct; however, 50700 km is more than 1e7 meters so the angular sizes differ by about 3 orders of magnitude.

2.2 × 10⁻⁸ radians is 0.0045 arcseconds [1]. That answer is off by 3 orders of magnitude.

[1] https://frinklang.org/fsp/frink.fsp?fromVal=2.2*10%5E-8+radi...

From the report:

> To calculate the energy consumption for the median Gemini Apps text prompt on a given day, we first determine the average energy/prompt for each model, and then rank these models by their energy/prompt values. We then construct a cumulative distribution of text prompts along this energy-ranked list to identify the model that serves the 50-th percentile prompt.

They are measuring more than one model. I assume this statement describes how they chose which model to report the LM arena score for, and it's a ridiculous way to do so - the LM arena score calculated this way could change dramatically day-to-day.

Could you explain your claim that ANNs are nothing like real neural networks beyond their initial inspiration (if you'll accept my paraphrasing). I've seen it a few times on HN, and I'm not sure what people mean by it.

By my very limited understanding of neural biology, neurons activate according to inputs that are mostly activations of other neurons. A dot product of weights and inputs (i.e. one part of matrix multiplication) together with a threshold-like function doesn't seem like a horrible way to model this. On the other hand, neurons can get a bit fancier than a linear combination of inputs, and I haven't heard anything about biological systems doing something comparable to backpropogation, but I'd like to know whether we understand enough to say for sure that they don't.

If you account for the fact that biological neurons operate at a much lower frequency than silicon processors, then the raw performance gets much closer. From what I can find, neuron membrane time constant is around 10ms [1], meaning 10 billion neurons could have 1 trillion activations per second, which is in the realm of modern hardware.

People mentioned in [2] have done the calculations from a more informed position than I have, and reach numbers like 10^17 FLOPS when doing a calculation that resembles this one.

[1] https://spectrum.ieee.org/fast-efficient-neural-networks-cop...

[2] https://aiimpacts.org/brain-performance-in-flops/

You have a very strong definition of AGI. "Never being wrong" is something that humans fall far short of.

I disagree. Any particular descision problem can be seen as an instance of an NP-hard problem. If you know you're looking at a subset of some NP-complete family, you should try to work out whether that subset is NP-hard (which you could show by finding an NP-hard problem such that any instance can be converted to an instance of your problem).

See entanglement chess ( https://entanglement-chess.netlify.app/help.html ) for an example of a problem that is not NP-hard despite looking that way at first glance.

If we assume that the stars of one galaxy (A) are distributed uniformly at random within a circular area in the galactic plane, and the other galaxy (B) is moving perpendicular to the plane of A and passes entirely through the circle containing stars, and assume that stars in galaxy B are point-like, then:

Expected Number of collisions = Number of stars in galaxy B * cross sectional area of star in A / average area of galactic circle per star in A.

https://www.wolframalpha.com/input?i=%28number+of+stars+in+m...

says it comes to 0.5 - 1.0 (the uncertainty comes from number of stars in the milky way)

My assumptions are bad enough that it could be off by a factor of 100 one way or the other (there should be a few factors of 4/pi, it looks like Andromeda is about twice the size of the Milky Way, the average star is smaller than the sun, no stars are point like, gravity probably does something, stars are much more densely packed towards the galactic center, I'm calculating the result one galaxy passing through another, not a merger in which they might partially intersect more than once).

Given a dimension, n; a collection of n-dimensional vectors of integers v_1,..,v_k; and a target n-dimensional vector u: Is there a sequence of vectors from the collection which sums to u, such that no partial sum(of an initial segment of the sequence) has any negative components?