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There's a longer land path that starts in or near Senegal and ends in China. But they miss it because it goes near the Dead Sea, and they treat anything below sea level as water.


Indeed, this route would be about 13,250 km, or about 2,000 km longer than the one TLA suggests.

http://www.gcmap.com/mapui?P=10%B0+24%27+41.4%22+N,+14%B0+31...

Or, using nearby airports: https://www.greatcirclemap.com/?routes=gucy-vmmc


Almost 7200 nautical miles from Macau, China to Conakry, Senegal, west africa, through Suez. 8253 miles.


It seems like that path crosses the Suez canal. I think it's fair that bridges and/or tunnels don't count.


The one they give also crosses numerous rivers and lakes. For the strict version of the challenge where you literally can't cross water it's likely that the best solution is across Antarctica. Guaranteed by temperature to contain no water whatsoever.


technically Antarctica is covered in (solid) water.

"technically incorrect the worst kind of incorrect".


> Guaranteed by temperature to contain no water whatsoever.

Depends on where and when.

Plenty of puddles form around the bases in summer.


I'm confident that the Land Paths need bridges to cross the numerous rivers along the route. You need a different qualifier.


That would an interesting finding!


If you are talking about the trail from Cape Town to Vladivostok, that one is not a straight line.


In passing, https://en.wikipedia.org/wiki/Paul_Salopek is walking from Ethiopia to Tierra del Fuego, tracing the path of human migration out of Africa. Walking the coast, not a straight line.


They aren't, as clicking through on a sibling's link demonstrates. Moreover, Senegal is nowhere near Cape Town.


It's also robust to errors in the mesh. Like if the triangles don't quite join up it still gives a reasonable answer. https://mathstodon.xyz/@keenancrane/109388206643166726


You could maybe determine this using a SAT solver. You would have to encode the entire QR code specification. I was thinking of doing this to find a minimalist QR code that just had as few black cells as possible.





They're trained on human data. I would expect them to emulate human biases as closely as possible.


This is where harness, and the fact that a machine can be endlessly prompted to try again comes in.

Even if an LLM starts by pursuing things that follow human bias, continuous failures and re-prompting to try something different will eventually force it to consider things outside of what ever biases it has.

You can do the same thing to a human. But most people would consider it unethical to lock someone in a box and force them to keep trying to solve the same problem over and over again until they figure it out.


Your comment stopped me in my tracks a little bit.

Is a 'bias' in a piece of writing generally a property of word to word choice and sentence to sentence construction or is it something more nebulous? Especially in terms of the appreciation of mathematics and someone's hesitance about publishing a mathematical argument they think is ugly or brute forced in some way.


> Is a 'bias' in a piece of writing generally a property of word to word choice and sentence to sentence construction or is it something more nebulous?

You might be fascinated when you read the story of Golden Gate Claude: https://www.anthropic.com/news/golden-gate-claude


Is it? I'd expect most of the training set to be synthetic data extrapolated from a small set of human authored texts.


Most of the training set is half of the Internet. LLMs are pre-trained on general set of human biases and patterns of thinking.


It's more complex than that, especially as post training is often goal based.


I wouldn't have expected that there was post training specifically on the issue of looking for proofs vs counter examples. But it might be that other post training has a side effect of making AIs better at looking for counter examples. I wonder if these agents are overall less biased and more rational than humans. Can you expand on what you mean by goal based training?


No, they are not. Specifically, this was a method based specifically on learning from scratch, like most modern AI models.

Why do you think it's called Alpha ZERO?


I think you're in the wrong thread. This one is about Claude producing counterexamples. The Go thread is next door.


Programmers love to give things names that they think sound cool


That's nice.

It's called Alpha Zero specifically because it was trained from scratch - zero, not on human data.


The AI understands context so it's able to spot typos even when they coincidentally make reel words.


One argument would be that Ozempic doesn't give your body any additional resources. It just triggers your body to behave in a different way. But if the changes it causes are universally good, why didn't evolution already make your body work that way?

I suppose the counterargument would be that modern life is different from the evolutionary environment, and so it's possible for a change to be beneficial now that wasn't beneficial then. But it would still be good to understand better the mechanism of the effect of Ozempic on things like addiction.


There are people with more or less sensitive GLP-1 receptors today, who have lesser or greater impulsivity. If some event occurs where only those with lower impulsivity survive, then the future population will have more sensitive GLP-1 receptors.

This is the only way that happen - noticeable evolution is always driven by population bottlenecks or strong selective pressure. In the absence of those, mutation just keeps expanding the gene pool so more different candidates are available for the next bottleneck.

In case an event happens where only red-haired people survive, good thing some are available, otherwise there's no reason to think everyone will have red hair in the future.


> But if the changes it causes are universally good, why didn't evolution already make your body work that way?

We evolved in an environment where every bit of food took hours of effort and food preservation was impossible, so the only logical thing to do with extra food was feast and store up as much fat as possible for lean times. We're still many generations away from evolving to compensate for the discovery of fire, let alone everything that came after that.


> But if the changes it causes are universally good, why didn't evolution already make your body work that way?

That’s not how evolution works.


John D Cook gives more technical details here: "Trying to fit a logistic curve" https://www.johndcook.com/blog/2025/12/20/fit-logistic-curve...


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