- This is great.
Since you've asked about bugs, I tried pushing the limits and found the following:
A2 can be successfully set to anything reasonable (up to 2500)A1: 100 B1: =100-A1 A2: =A1*(100-A1) A3: =A1*B1However, setting A3 to exactly 100 doesn't work, even though setting it to 101 or 99 (or even 100.000001) does work.
Another limit:
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.A1: 100 B1: 100 A2: =A1+B1 A3: =A1*B1 A4: =abs(A2-100) + abs(A3-100)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)?
- > 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.
- 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...
- 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...
- 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).
- I agree, but I believe the reason for the errors is because people intuitively have a pretty good grasp of the game theory for the situation where someone is trying not to give you something they promised (and it's the sort of thing where IRL you shouldn't believe somebody trying to convince you to change your mind, so it's a useful bias to ignore parts of the problem even when it is fully specified). I believe that the statisticians then try to justify that, and end up making incorrect arguments.
- Yes, I am discussing a different problem, and I don't think the original problem formulation gives enough information to distinguish between the 2 problems.
The answer can add assumptions, which is fine. I'm not passing judgement on Marilyn vos Savant. I do object to claims that the problem statement is sufficient to have a single answer, and based on that, I'd object to claims that somebody in that situation would be wrong not to switch doors. I would object on exactly the same grounds to anyone who tells you "you're wrong, there's a 50% chance of getting a car" (I might object further, on the grounds that the most obvious interpretation which gives that answer is inconsistent with this form of the problem statement).
- I think we're disagreeing about how much it's reasonable to assume. I'm happier treating it as a self contained problem (in which case I'd say that the form quoted by CrazyStat is underspecified); but if you're familiar with the TV show it's based on, you can reasonably assume that he always opens a door with a goat and gives you a chance to switch.
My objection is to the claim that "most people get it wrong", if most people are being fed the underspecified problem. I think the gut reaction is not to switch, because in most comparable situations across human experience it would be a mistake (imagine a similar situation at a sketchy-looking carnival game rather than a TV show). They then try to justify that formally and make mistakes in their justification, but the initial reaction not to swap is reasonable unless they've been convinced that Monty Hall always opens a door with a goat and gives a chance to switch.
- You might live in a world where the host doesn't want to give you the car, and only opens a door and offers you the option of switching if your first choice was the door with the car behind it. In that world, you shouldn't switch. I don't think this form of the problem statement gives you any reason to believe that you aren't in that world.
- Diagonal player movement isn't allowed (from the looks of the article), but wall connections can be diagonal. There's a duality here - if players and enemies could move diagonally, the algorithm could be adapted by only considering horizontal and vertical wall adjacencies (although still looking at the surrounding 8 squares to determine separation of adjacent walls). We're relying on the property "if adding a wall creates an enclosed region, one of the enclosed squares must be move-adjacent to the new wall".
"separated" = "not connected when considering only the 8 neighbors of where you intend to place the new wall; diagonals do count as connections between walls".
In the following example, the walls adjacent to the + are not separated:
In the next example, the walls are adjacent to the + are separated:+X X.
> There was something else in the article that bothered meX.. .+. ..XRegarding your second point, I think the article changed half way through from assuming the play area is surrounded by a wall to assuming the play area is surrounded by empty space, which I agree is confusing. Either case could be covered by this algorithm - just start with a connected component of wall at the edge of the play area.
- Unless I'm missing something, this can be done in O(n) time by tracking the connected components of wall (diagonally touching walls are connected). Placing a new wall creates an enclosed region if and only if it touches 2 separated sections of wall that are part of the same component.
The union-find disjoint sets algorithm can find whether they're in the same component. If a wall is added, it should be unioned with all adjacent walls. If a wall piece is removed, the components it was part of need to be recalculated, but it looks like that shouldn't happen more than once per frame.
In this case, the lookups of the union find algorithm will never take more than O(n) overhead per frame while checking all of up to n possible wall positions.
- Your conclusion is right, but in bees, sex is determined by Haplodiploidy ( https://en.wikipedia.org/wiki/Haplodiploidy ), not X0. Also, the daughters have the same number of chromosomes as the mother so they share 50%, not 75% of their genes with their mother (they do share an average of 75% of their genes with their sisters).
- Here's how to formulate the question in continuous space/time:
Random walks can be defined on continuous space and time as a probability distribution on functions R -> R^n (Brownian motion in n dimensions).
We can then ask whether Brownian motion beginning at the origin will ever revisit it i.e.
Given 2D Brownian motion X such that X(0)=(0,0), the probability that there exists t>0 such that X(t)=(0,0) is 1.
Given 3D Brownian motion X such that X(0)=(0,0,0), the probability that there exists t>0 such that X(t)=(0,0,0) is 0. (This is more clearly true when it doesn't begin at the origin, but it's almost certainly not at the origin at t=1, and you can divide the half open interval (0,1] into a countable number of intervals, each of which have 0 probability of passing through the origin.)
Random walks in 2D are space filling curves; random walks in 3D are not.
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.