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Comment by tambourine_man | Hacker News Reader

> They find that with a different measuring stick, emergence vanishes.

Isn’t that the case for most/all emergent behavior? If you change the scale and watch individual water molecules, you’d see them snapping into a crystal structure one by one instead of a sudden emergent block of ice.

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Not quite. The problem is that the definition is especially poorly defined in ML. I elaborate more here[0]. You are describing emergence, but not what was claimed when LLMs were said to have emergent abilities (the distinction is explained in the article fwiw)

[0] https://news.ycombinator.com/item?id=39812315

But knowing the molecule structures at 50C and 75C tells you very little about the freezing point.

Different example: If you measure the number of cases of a given virus, it will either spread across the entire globe (R0 > 1, eg. COVID-19) or fail to spread widely (R0 < 1, eg. Ebola). Even though it's not completely binary, it's emergent behaviour because it looks binary. But if you were to measure R0 directly, you'd see a gradual increase, and could predict future variants/vaccine efficiencies/etc much more easily.

"Emergent" refers to eg. sigmoids, while "gradual" refers to eg. linear or logarithmic functions.

Nobody mistakes ice for something sudden emergent though, it's obvious to naked eye that it gradually appears

I don't know what exactly "emergent" means in this context, but doesn't ice appear pretty rapidly? It appears between -1 and 1 degrees, and when cooling down from 100 to 75 to 50 to 25 water you would learn nothing about the freezing point.

Every volume of water IRL will disagree about the rapidity though, go below 0 and first it's water, then it has some ice, then more ice, and only after a while eventually it's all ice (and even then maybe it has some water underneath, who knows). I can't see how it is not common sense. But with LLMs the common sense was until now "they can't then they suddenly can"

The water usually isn't below 0 in those cases.

My thermometer says it's -5, yet water is liquid. To be more precise, covered with thin ice. And covered with (thicker) ice it shall stay all the way to -20 probably. Whatever technical correctness you throw doesn't matter to common sense logic.

And that is even if there is a technical possibility to lower the temperature of every water molecule to -0.0001 simultaneously and demonstrate that it instantly freezes the entire volume in an instant. It'd be irrelevant since none of us live in that lab.

Your water is -5C? Is it salt water?

Thanks for another example!

For what - that different liquids have different freezing points? Not sure anyone is doubting that.

What are you arguing for exactly? That there may in theory exist some abstract spherical volume of perfect water in vacuum that freezes entirely in an instant that none of us will ever encounter in our lives? But that it is exactly what we should imagine when we think of how ice forms-- humanity's mental image should be of water instantly transforming into ice? Please clarify:)

In a way - yes. Ice in nature forms usually by water cooling heterogeneously, but not by water being below 0 all the time and everywhere and the ice forming slowly in some areas then.

Not just in nature, your glass of water in the freezer also has uneven temperature throughout the volume and becomes ice gradually (though faster than a lake)

Clear water freezes exactly at 0 degrees. I guess the graduality depends on if you think about this as interpolating the water temperature, or interpolating the energy given/taken from a body of water.

> Clear water freezes exactly at 0 degrees.

Water never arrives at 0 degrees all at once, so for practical purposes no. Even if it did, you cannot measure the temperature of every water molecule simultaneously to prove it.

Not to mention, if water is pure and still enough, you can cool it below freezing point, and it still looks like a liquid, until it is disturbed and then it suddenly doesn't. Same with heating up above boiling point.

Also with heating? So all the bubbles rising up way before boiling and the visible evaporation does not happen with distilled water? Hard to believe, I have to say. You would have to do perfect even heating of all the water, to stop the movement from different temperate areas. Microwaving it?

Bingo:

https://www.animations.physics.unsw.edu.au/jw/superheating.h....

Thx. And maybe not the best idea, but now I want to try this ..

> maybe not the best idea, but now I want to try this ..

I'm going to steal this for my epitaph, thanks

Have fun with it.

Mine would currently say:

Por tu culpa!

(this is all your fault)

But depending on the circumstances, I would be also fine with the one above. But very likely I would not care that much anymore ..

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