hakuseki

I was surprised that I couldn't find any simple-looking solutions in this atlas. At first I was looking for Lagrange orbits, but maybe it makes sense to exclude them if zero-mass bodies aren't allowed. I think the equilateral triangle ought to be included though.

At double-digit kyu level, you should just play every day until you feel you are stuck.

After you get stuck, you should pick one thing at a time to focus on improving. But the one thing should probably be related to tesuji or life and death.

Traditionally, handicaps are usually given in the form of extra stones played on the board. This is a coarser resolution than points, with one extra stone in the opening having a strategic value of about 13 points. So he probably couldn't have won if his handicap were a full stone smaller, but he may have won if it were a few points smaller.

Leaving aside the question of whether the universe is discrete or continuous, a simulation would still have lower "resolution" than the real world, and some information can be lost with each time step. To compensate for this, it can be helpful to have simulation step t+1 depend on both the step t and step t-1 states, even if this dependency seems "unphysical."

The article is about (position, move) pairs. Why not call these objects "steps"?

In what sense is looking at a screen a failure to prepare for the world that adults navigate? Adults also look at screens.

> However, even using extra hardware wasn't enough in this case. So they pre-calculated lookup tables for sine, cosine, tangent etc. for every angle at the necessary precision.

Is this really the order of events? I imagine the pre-calculated route is what you'd try first, and only go for extra hardware if that failed somehow.

Are you planning to decelerate by crashing into the planet at relativistic speed?

I guess you mean k log k, not n log n.

What's so difficult about optical links from deep space compared to low earth orbit, where 200 gigabit throughput has been achieved? Is it just the attenuation?

I would have imagined that we could upgrade the communication equipment on a space probe much more easily than we could add fuel for a return trip.

That is not strictly true. The weather at time t0 may affect non-weather phenomena at time t1 (e.g. traffic), which in turn may affect weather at time t2.

Furthermore, a predictive model is not working with a complete picture of the weather, but rather some limited-resolution measurements. So, even ignoring non-weather, there may be local weather phenomena detected at time t0, escaping detection at time t1, but still affecting weather at time t2.

> there is nothing in principle stopping us from running this machine for BB(748) steps

How would we compute the value of BB(748)?

So to summarize, the game tree complexity is estimated by estimating the branching factor and the game length, and raising the former to the power of the latter.

I find it slightly odd that the game length is calibrated to "reasonable" games but the branching factor is not.

If the goal is to estimate the number of possible games of go, then the calculation would be dominated by the number of long games rather than the number of short games, and very long games are possible.

If the goal is to estimate the number of "reasonable" games of go, then the branching factor should also be much smaller, as most possible moves are not reasonable. Perhaps the logarithm of the branching factor could be estimated as the entropy of some policy model such at that of KataGo.

P.S. I am happy to have received a reply from the mighty Tromp!

How were these numbers arrived at?

Seems like no collision is detected if you move the ball through the cloth fast enough.

ISTM that's just an a priori feeling. The value or lack thereof of the product totally depends on how accurately it predicts human survey responses, which you can't know without looking at the data.

I think a median rating of 5 stars makes sense for a taxi service. You want the rating system to be able to express varying levels of bad. There are many levels of bad outcomes for a car ride. There are not many ways to improve on the median experience.

I am not a vision expert, but simply matching the resolution of your display to the resolution of your sensor wouldn't necessarily produce a clear image, unless the pixels are aligned to the sensing elements.

By analogy, if you resize a 1025x1025 image to 1024x1024, it's usually going to look bad.

The `find_item` example uses List for an argument. To my thinking, this indicates that the function is intended to mutate the argument. I don't think that was the author's intention, though, so I would prefer to use Sequence in this situation (or possibly Iterable, if we only need to traverse the sequence once in order).

> It seems to me all we need here is a measure of confidence for the result averaged over the entire answer. Low confidence is a guess/hallucination.

Even if the model knows the exact answer to the question, there may be many distinct ways of phrasing the answer. This would also lead to low confidence in any particular phrasing.

> Like any good mystery, the fun was in the build up and as we move towards a resolution there's a bitter sweet aspect to the slightly mundane reality of it 'merely' being an emergent property of large networks.

I would disagree with this description. An "emergent property of large networks" would be something that just appears when you wire together a large network.

To get intelligent behavior, it's not sufficient to wire together a large neural network. You also need to use an optimizer to train it on a large data set.

This is just a guess, but I don't think there's such a deep lesson here; language models and image models have simply been developed by mostly-different groups of researchers who chose different tradeoffs. In an alternate history it may very well have gone the other way around.

I'm not sold on the concept of AI-hard or AI-complete problems.

For example, the Wikipedia article on AI-completeness mentions Bongard problems and Autonomous driving as examples of problems that might be AI-complete.

OK, so if I have an AI drives autonomously, is there some known querying strategy that I can use to make it solve Bongard problems? Can a Bongard problem-solving AI be made, by some known procedure to drive a car?

Without such reductions, at least the analogy to NP-hardness is incomplete. I believe these reductions are precisely what makes NP-hardness such a useful concept; even though we still haven't proven that any of these problems are objectively "hard," we are still able to show that if one of them is hard, then the others are as well!

This seems not quite right to me. A Turing machine may always halt, but with time depending on its input size. The input can be arbitrarily large, so there's no finite bound on the state space.

A small latitude difference does not imply that you can ignore curvature.

I am just guessing, but perhaps your intuition is that the shortest path should lie along a line of latitude. An easy-to-see counterexample would be two points close to the north pole, but with 180 degrees of longitude separating them. In this case the shortest path actually goes through the north pole, rather than around it.

You can also generalize this say that within the northern hemisphere, the shortest path between two points will curve (when viewed on a flat map) towards the north pole.

I think that's not a bad summary, though? Perhaps you would say it is a probabilistic next-token chooser, but that just seems like a very minor distinction.

Assuming all values are unequal, there are n factorial (abbreviated n!) possible cases that we need to distinguish.

If we are sorting by comparison, then each comparison will eliminate at most half of the possible cases. So we need at least log_2(n!) comparisons in the worst case.

Might it have been Glory Season?

There's some older work as well. Geoffrey Hinton's team used deep belief networks in 2006 to generate "handwitten" digits: http://www.cs.toronto.edu/~hinton/digits.html

The result actually doesn't depend on any special properties of social graphs. It works for any graph that has a component with non-constant number of edges per node.