sigh.

Are you saying it's cooling faster because the ball is bigger?

More ice, more cooling potential. That's one factor that you can model pretty safely.

If so, how would a bigger cube cool in comparison?

Double sigh.

Remember last year when I said:

I wouldn't model this with a ten foot pole

???

That was me saying "I don't fucking know." More than that, that's me saying "I don't fucking want to find out mathematically." Even more, that's me saying "Anyone with any experience in modeling and curve fits would run this three times, Look at the line, pick linear or quadratic and throw a coefficient on it and call it a day."

What I mean is "I wouldn't model this with a ten foot pole." I've pointed out all the factors I can think of that make it complicated - I do this not to say "I have the answer" but to say "all these factors preclude an easy answer." The fact that you keep asking questions about "the center where T3 is" indicates that you're just not listening. Look:

Ice cools water through phase change. While it's changing phase, it can release energy into the surrounding fluid without changing temperature. "the center where T3 is" is pretty much everywhere where ice is during a transition. That omission alone should indicate that you're underthinking this.

2. I never said that the rate of cooling for spheres vs cubes should be the same.

And I never said otherwise. You threw some math up there to indicate your thinking. I threw up some caveats to show that your thinking was over-simplified.

To be clear:

I wouldn't model this. It's heinous. I've been forced to model enough in my life to know that it's heinous.

You're trying to model this. You refuse to acknowledge the heinousness of it because you've never been forced to confront the heinousness of heat transfer in an empirical environment.

That chart does not show how much of the ice has melted, which is the key question I had posed.

Here's your key question:

It is being said that spherical ice cubes cool your drink quickly and minimize the dilution. (Humbug, I say!) I would like a proof in the purest form: by math.

Humbug all you want, yo. Pure math has no business here. I've said that five different ways. Each time it comes down to you doubting my expertise.

I'm over it.