hakuseki

I think the bigger issue (for someone hoping for P=NP) is that there's a huge gap between "polynomial" and "exponential." Even if it were the case that all NP problem classes had subexponential decision algorithms, that would not get us close to P=NP.

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?