Re: For those who have kabillions of dollars.

1

The only real wealth is love, and the only real love is the love of family.

So this is a population control thread?


Posted by: lw | Link to this comment | 08-30-13 2:10 PM
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Needs moar flared bottom.


Posted by: Jackmormon | Link to this comment | 08-30-13 2:12 PM
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"On the bright side ice balls supposedly don't dilute your equally expensive drink and cool it evenly"

If it cools your drink, it dilutes it.


Posted by: nosflow | Link to this comment | 08-30-13 2:13 PM
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When the least-favored, the poorest member of society no longer wants anything.


Posted by: bob mcmanus | Link to this comment | 08-30-13 2:15 PM
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A friend (with whom I have been talking about some work stuff) recently remarked that "You have to ask at some point, 'How much money is enough?' "

I replied: "Shut the hell up. I will tell you when I we have enough money."

Then I felt guilty.


Posted by: Flippanter | Link to this comment | 08-30-13 2:17 PM
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If it cools your drink, it dilutes it.

Maybe they're ice-inspired balls, but actually cold packs.


Posted by: heebie-geebie | Link to this comment | 08-30-13 2:17 PM
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3: If it's ice, which it is. Those ice-cube-substitute stones shouldn't dilute your drink.

Their horrible website claims maximum cooling for minimum dilution, but I don't see why being a sphere would cause that--shouldn't the increased surface area mean it would both cool and dilute the drink more quickly?


Posted by: dalriata | Link to this comment | 08-30-13 2:19 PM
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3 I've seen plastic covered ice balls. The problem is that the plastic acquires odors and taste pretty quickly.


Posted by: teraz kurwa my | Link to this comment | 08-30-13 2:19 PM
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Their horrible website claims maximum cooling for minimum dilution, but I don't see why being a sphere would cause that--shouldn't the increased surface area mean it would both cool and dilute the drink more quickly?

Spheres have minimal surface area.


Posted by: heebie-geebie | Link to this comment | 08-30-13 2:21 PM
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6 was An ill phrased answer to the question

Accumulated wealth is unethical until the least favored etc...

Someone who wants nothing at all is very well-favored indeed. So then we will have to look at the (apparently) second least-favored etc.

The one with the greatest unsatisfied desire is certainly the least happy, unless desiring creates their joy, in which case we should deprive them.


Posted by: bob mcmanus | Link to this comment | 08-30-13 2:23 PM
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12: You're right. Not sure why I had that backwards.

But still, aren't cooling and melting/dilution both going to be proportional to surface area? So, in this case, both cooling and dilution would be slower (relative to a similarly sized cube). So you'd need more ice spheres.


Posted by: dalriata | Link to this comment | 08-30-13 2:24 PM
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At what line do you personally believe that accumulated wealth becomes unethical?

I don't know exactly, but I'd find it hard to defend more than, oh, $200k per person per year of purely disposable income (e.g. beyond basic expenses on housing, medical, transportation, groceries, clothing, and so on).


Posted by: x.trapnel | Link to this comment | 08-30-13 2:29 PM
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maximum cooling for minimum dilution
A sphere with good thermal conductivity could negatively dilute your drink. Their claims are bunk!


Posted by: Eggplant | Link to this comment | 08-30-13 2:31 PM
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This is actually my last day at Evil For-Profit Publisher; in two weeks I start my programming bootcamp, and 12 weeks after that, hopefully, I rejoin the upper middle class. So I've been thinking a bit about this, when I'm not suffocated by terror at the thought of failing at something new.


Posted by: x.trapnel | Link to this comment | 08-30-13 2:34 PM
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Isn't 24 karat gold really soft? I guess you wouldn't want to get too rough with that one.
We have a relative who sent us a sterling silver spoon as a birth present for each kid. What a fucking waste of money, custom engraved so you can't even return in. Once they sent a silver rattle instead which at least the baby liked playing with.
We also got a wedding present of a Stuben crystal cat. We managed to convince a Neiman Marcus near us that to take it back even though I'm sure it wasn't bought there, and they even paid us in cash (like $250) instead of store credit.
I can understand expensive presents, and I can understand useless presents, but why do people give expensive useless presents?


Posted by: SP | Link to this comment | 08-30-13 2:37 PM
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Since ice does conduct some heat, the volume isn't totally useless in terms of cooling. That is, a spherical shell of ice would melt faster than a solid sphere of ice while providing the same amount of cooling. So it seems to me that spherical ice should have a somewhat better cooling/melting ratio than other shapes. I'm not quite sure how to even estimate how much better though.


Posted by: Unfoggetarian: "Pause endlessly, then go in." (9) | Link to this comment | 08-30-13 2:38 PM
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In the long run, every shape cools equally.


Posted by: Eggplant | Link to this comment | 08-30-13 2:41 PM
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16: But what if you live someplace very expensive? Like a secret base at the bottom of the ocean?


Posted by: Walt Someguy | Link to this comment | 08-30-13 2:51 PM
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You know what's super-confusing? Objects with negative specific heat. Try putting one of those in your glass of water.


Posted by: essear | Link to this comment | 08-30-13 2:51 PM
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Once it gets to 0 degrees, which I think should happen really fast, all cooling comes from melting.

Still, the enormous spherical and cubical pieces of ice they put in fancy cocktail places do look cool.


Posted by: F | Link to this comment | 08-30-13 3:07 PM
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You know what's super-confusing? Objects with negative specific heat.

Weird. Didn't realize that could happen. I'm still going to avoid putting any stars or black holes in my drinks, though.


Posted by: dalriata | Link to this comment | 08-30-13 3:07 PM
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Wikipedia has the surface area to volume curves for different platonic solids:

http://en.wikipedia.org/wiki/Surface-area-to-volume_ratio


Posted by: lemmy caution | Link to this comment | 08-30-13 3:15 PM
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If anyone is actually looking for a way to cool their drink without diluting it, these rocks work well for the low low price of $34.


Posted by: LizSpigot | Link to this comment | 08-30-13 3:22 PM
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My bet is that the sphere has the lowest surface area to volume ratio of any shape but I bet that would be crazy hard to prove.


Posted by: lemmy caution | Link to this comment | 08-30-13 3:27 PM
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How many dimension are we assuming?


Posted by: Moby Hick | Link to this comment | 08-30-13 3:30 PM
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I bet it's not too hard to prove.


Posted by: heebie-geebie | Link to this comment | 08-30-13 3:38 PM
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I bet it is hard to prove.

(I mean, it's a well-known result, but I don't think it's easy to prove, especially once you go beyond the plane case. Maybe I have the wrong standard for "easy".)

Proving it locally would be easy.


Posted by: essear | Link to this comment | 08-30-13 3:39 PM
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I don't actually get what you mean by proving it locally. That local perturbations of a sphere would have increased surface area? I'm sure I'm forgetting pathological cases, but it doesn't seem too hard to think it through for compact objects.

Or were you saying it wouldn't be too hard for local undergrads, but undergrads at my institution would struggle? How rude!


Posted by: heebie-geebie | Link to this comment | 08-30-13 3:54 PM
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Dammit, now I'm actually thinking about it, which is bad because I'm pretty sure I could spend the whole weekend thinking about it and not actually get very close to a proof.


Posted by: essear | Link to this comment | 08-30-13 3:54 PM
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29: I mean, if I make a small volume-preserving perturbation of the sphere, I think I could show it always increases the surface area. The sphere maximizes surface area among almost-spheres. Showing it for arbitrary shapes seems much more difficult.


Posted by: essear | Link to this comment | 08-30-13 3:56 PM
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I feel like there should be some simple argument to dismiss shapes that aren't convex as a first step, but even that seems non-obvious.


Posted by: essear | Link to this comment | 08-30-13 3:57 PM
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Could this be expressed as a calculus of variations problem? I think you can show, by phrasing it that way, that the sphere is optimal among those shapes with rotational symmetry.


Posted by: dalriata | Link to this comment | 08-30-13 4:02 PM
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Surface area is going to have to do with the ratio of the mean length of lines from the centroid (whatever shape that is) to the mean gradient w/r/t the centroid between two adjacent points on the surface, right? Why can't you start from there and then just, like, you know, just do the other part.


Posted by: Sifu Tweety | Link to this comment | 08-30-13 4:04 PM
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If you have enough rotational symmetry the sphere is the only shape. Are you talking about preserving one SO(2) inside the full SO(3)?


Posted by: essear | Link to this comment | 08-30-13 4:04 PM
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I can prove it with bubbles.


Posted by: SP | Link to this comment | 08-30-13 4:05 PM
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I wasn't thinking anything that deep, just rotational symmetry along a single axis.


Posted by: dalriata | Link to this comment | 08-30-13 4:07 PM
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just rotational symmetry along a single axis.

Sorry, yeah, that's what I said, I was just using uglier words.


Posted by: essear | Link to this comment | 08-30-13 4:09 PM
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38

If you have enough rotational symmetry the sphere is the only shape.

Deep, brah.


Posted by: nosflow | Link to this comment | 08-30-13 4:09 PM
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39

Maybe you can do it in two steps? First show it has to be star convex. Then you can parametrize the shape in terms of a point on the n-sphere and its distance from the origin, and turn it into a calculus of variations problem?


Posted by: Walt Someguy | Link to this comment | 08-30-13 4:09 PM
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34: That seems like a useful way to think about it, but I have no clue where'd you go from there. That ratio (well, of the magnitude of it) should be constant for a sphere, so...enh.


Posted by: dalriata | Link to this comment | 08-30-13 4:10 PM
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Guys, the proof is trivial. Just biject it to an undecidable ring whose elements are prime unbounded-fan-in circuits.


Posted by: nosflow | Link to this comment | 08-30-13 4:10 PM
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You gave away your trick, nosflow. You can no longer intimidate us into agreeing with you.


Posted by: Walt Someguy | Link to this comment | 08-30-13 4:11 PM
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40: Oops, yeah, "star convex" is what I was visualizing when I said "convex" in 32. But how do you even get that far?

Another thing I was wondering is if there's an easy argument that any shape with locally negative curvature anywhere is bad. Then once you reduce to spaces that are everywhere positively curved, maybe you can somehow try to show that locally deforming things closer to constant curvature always helps. But somehow I doubt that making purely local arguments can ever get you all the way there.


Posted by: essear | Link to this comment | 08-30-13 4:13 PM
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Another thing I was wondering is if there's an easy argument that any shape with locally negative curvature anywhere is bad

Whoa whoa whoa. Let's not go crazy.


Posted by: nosflow | Link to this comment | 08-30-13 4:14 PM
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38:Oh, gotcha. The names of the various special groups and how they work together were among the most hastily forgotten facts of my math education.


Posted by: dalriata | Link to this comment | 08-30-13 4:16 PM
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Another thing I was wondering is if there's an easy argument that any shape with locally negative curvature anywhere is bad.

I think that's what I was dopily poking at in 34.


Posted by: Sifu Tweety | Link to this comment | 08-30-13 4:19 PM
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I like how there's surely an easily available proof of this somewhere on the internet, but we're trying to figure it out the hard way.

I'm with Walt that this is somehow a calculus of variations problem, but that's not something I've studied sufficiently to be able to formulate this. You'd need to be able to express the shape as some sort of function, and if it's star convex that's easy enough but maybe more arbitrary parameterizations could also be okay.


Posted by: dalriata | Link to this comment | 08-30-13 4:20 PM
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Point, essear.

Isoperimetric inequality

"The solution to the isoperimetric problem is given by a circle and was known already in Ancient Greece. However, the first mathematically rigorous proof of this fact was obtained only in the 19th century."


Posted by: F | Link to this comment | 08-30-13 4:23 PM
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An elegant direct proof based on comparison of a smooth simple closed curve with an appropriate circle was given by E. Schmidt in 1938. It uses only the arc length formula, expression for the area of a plane region from Green's theorem, and the Cauchy-Schwarz inequality.

Of course.


Posted by: F | Link to this comment | 08-30-13 4:24 PM
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I believe F was saying that I was totally on the right track.


Posted by: Sifu Tweety | Link to this comment | 08-30-13 4:28 PM
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I guess you also have to reduce to shapes with the topology of a sphere, before you even start to worry about things like star convexity. Even that doesn't seem trivial to me.


Posted by: essear | Link to this comment | 08-30-13 4:30 PM
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I guess I don't see why you can't do a local argument plus compactness. Modulo details.


Posted by: heebie-geebie | Link to this comment | 08-30-13 4:32 PM
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Not local as was used above. I mean, take a neighborhood around each point whose radius is greater/less than the mean radius, and argue that manipulating that neighborhood to be more sphere-like improves the ratio.


Posted by: heebie-geebie | Link to this comment | 08-30-13 4:34 PM
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Maybe?

I wonder if following Ricci flow reduces surface area.


Posted by: essear | Link to this comment | 08-30-13 4:34 PM
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The reason I thought this wouldn't be too bad is that I had a student look at soap bubbles and things along these lines as an REU project. So the topic seems accessible for a bright undergrad.


Posted by: heebie-geebie | Link to this comment | 08-30-13 4:36 PM
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Soap bubbles being surface minimizers.


Posted by: heebie-geebie | Link to this comment | 08-30-13 4:38 PM
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I thought soap bubbles are surface minimizers because they maximize radius of curvature, not because they minimize surface per se (though these end up having the same solution). Is this wrong?


Posted by: F | Link to this comment | 08-30-13 4:42 PM
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Soap bubbles are assholes.


Posted by: nosflow | Link to this comment | 08-30-13 4:50 PM
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Wealth is poison. How much any given person can take without themselves becoming toxic varies.


Posted by: CharleyCarp | Link to this comment | 08-30-13 4:50 PM
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I'm changing my mind to think there's a relatively simple argument. For shapes with an axis of rotational symmetry, as dalriata said, there should be a straightforward calculus of variations argument that the sphere is best. So the goal is to reduce to that. But I think you can do it inductively in the number of dimensions. First you prove it in the plane (where I think calculus of variations suffices, maybe modulo some subtleties about convexity). To prove it for 2-spheres in 3-dimensional Euclidean space, you slice your shape up into a bunch of layers, and for each layer, replace it with a circle of the same area. In this way you get a new shape with the same volume but, by the argument in the plane, smaller surface area. Now you've replaced your original shape with something rotationally symmetric, and you use the calculus of variations. Continue to higher dimensions as desired.

Does that make sense? It seems too slick--the Wikipedia page F linked to seems to indicate the higher-dimensional case should be harder than the planar case. But I don't know where it would go wrong.


Posted by: essear | Link to this comment | 08-30-13 4:51 PM
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(Note I'm using something like Cavalieri's principle to rearrange each layer to have the same central axis.)


Posted by: essear | Link to this comment | 08-30-13 4:54 PM
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I'll leave the calculus of variations part as an exercise because it's too much like my day job.


Posted by: essear | Link to this comment | 08-30-13 4:56 PM
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Hmm. Maybe I am being too, um, cavalier in shifting everything to have the same axis, since the horizontal displacement of one slice relative to another would tend to increase the surface area. So taking the continuum limit of my slices might not be as well-defined as I want it to be? I feel like this is controllable with sufficiently small slices, but if there's a stumbling block in the argument, I bet it's lurking there.


Posted by: essear | Link to this comment | 08-30-13 5:02 PM
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But I guess it always goes in the right direction.

Shit, I killed the thread, didn't I?


Posted by: essear | Link to this comment | 08-30-13 5:05 PM
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No, you didn't. Nice explanation.


Posted by: Turgid Jacobian | Link to this comment | 08-30-13 5:10 PM
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These things in the OP are great. I like how the knife is studded with diamonds which are irrelevant to its function as a knife.

Also, being confronted with ice spheres makes me realize... ice "cubes" are a sham! Those things are trapezoidal and not even squares on a single side.


Posted by: Cryptic ned | Link to this comment | 08-30-13 5:10 PM
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||
So, for the holiday weekend, I'm driving to Alabama to go to a funeral for my cousin's 4-month-old daughter who died of SIDS completely out of the blue two days ago. What do you even say to somebody? Nothing seems remotely adequate.

Happy Labor Day.
|>


Posted by: apostropher | Link to this comment | 08-30-13 5:15 PM
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Speaking of class struggle, I'm mightily impressed by An Agreement of the Free People of England. Not only a lot of stuff that made it into the U.S. Constitution and other better-remembered documents, but plenty that took a lot longer to happen: universal male suffrage, death penalty only for crimes on the level of murder, no imprisonment for debt. Who says democracy and human rights were thought up by well-off, chin-stroking writers and statesmen? And then a guarantee against the abolition of property; I'm not sure whether that's a concession or a defense against common slanders about their aims.


Posted by: Minivet | Link to this comment | 08-30-13 5:15 PM
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I'm surprised that nobody has commented on the fact that the ice spheres are, "hand carved." That seems like an inefficient way to produce spheres (and likely to increase the surface area).


Posted by: NickS | Link to this comment | 08-30-13 5:26 PM
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68: Very sorry. Just not much you can say. My friend who lost her baby really would have preferred to be spared the "It's all God's plan" and "He's a little angel up in Heaven now" stuff, but who knows, perhaps that would be a comfort. Hug and offers of support seem to be about all you can really do.


Posted by: Natilo Paennim | Link to this comment | 08-30-13 5:28 PM
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68: Jesus. I've been on a SID call as the primary and yeah, they're pretty bad.


Posted by: gswift | Link to this comment | 08-30-13 5:28 PM
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Sitting in that room, looking at a tiny coffin with a picture and a stuffed animal on top -- there's nothing you can do to make that less awful. I hope there is nothing worse than that in this life for me or anyone.


Posted by: Natilo Paennim | Link to this comment | 08-30-13 5:36 PM
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68, That's awful. So sorry.


Posted by: ydnew | Link to this comment | 08-30-13 5:42 PM
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How unspeakably awful. I am so sorry.


Posted by: Robert Halford | Link to this comment | 08-30-13 5:54 PM
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I'm sorry for your cousin and the family Apo.


Posted by: Moby Hick | Link to this comment | 08-30-13 5:57 PM
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Sorry, apo. As others have said, that's almost unimaginably horrible.


Posted by: Von Wafer | Link to this comment | 08-30-13 5:58 PM
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Sorry, apo, that's awful.


Posted by: essear | Link to this comment | 08-30-13 6:01 PM
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I'm so sorry, apo.


Posted by: Cala | Link to this comment | 08-30-13 6:16 PM
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79

Oh god, how horrific.


Posted by: heebie-geebie | Link to this comment | 08-30-13 6:23 PM
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That's just beyond awful, Apo. IME sometimes bearing witness to grief is all there is to do.


Posted by: Witt | Link to this comment | 08-30-13 6:24 PM
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I'm very sorry, too. Terrible. Ugh.


Posted by: x.trapnel | Link to this comment | 08-30-13 6:47 PM
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Very sorry, Sifu.


Posted by: Minivet | Link to this comment | 08-30-13 6:49 PM
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Shit. apo.


Posted by: Minivet | Link to this comment | 08-30-13 6:49 PM
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Oh dear. So sorry too, Apo. You're right, nothing seems adequate.


Posted by: md 20/400 | Link to this comment | 08-30-13 6:57 PM
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Condolences, Apo.


Posted by: torrey pine | Link to this comment | 08-30-13 7:19 PM
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Sorry, apo, that's heartrending.


Posted by: NickS | Link to this comment | 08-30-13 7:44 PM
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So sorry to hear that, Apo.


Posted by: J, Robot | Link to this comment | 08-30-13 8:01 PM
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So sorry, apo. That's the tragedy that sent Mara's family into tailspin and I'm glad your relatives have loved ones coming to support them.


Posted by: Thorn | Link to this comment | 08-30-13 8:07 PM
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My sympathies, apo.


Posted by: teofilo | Link to this comment | 08-30-13 8:30 PM
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Jesus. So sorry.


Posted by: Mr. Blandings | Link to this comment | 08-30-13 9:09 PM
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Holy shit. I'm sorry, apo.


Posted by: Josh | Link to this comment | 08-30-13 9:56 PM
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68: Jesus Christ. So sorry to hear this, Apo. What a nightmare.


Posted by: AWB | Link to this comment | 08-30-13 10:33 PM
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So sorry, apo.


Posted by: fake accent | Link to this comment | 08-30-13 10:37 PM
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That is really sad. I hope your cousin and spouse have a good support system where they live.


Posted by: Britta | Link to this comment | 08-31-13 1:05 AM
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15. Silver spoons are or were traditional Christening gifts. I got one, and we gave them a lot. The tradition goes back to the 16th century.


Posted by: chris y | Link to this comment | 08-31-13 1:18 AM
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68. Dear god that's appalling. I can't advise you what to say because I don't know the people, but don't say too much and make it clear that you're available if there's any shit work that has to be done that they can't face.


Posted by: chris y | Link to this comment | 08-31-13 1:23 AM
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On what to say, that is really tough, and depends a lot on your cousin's personality. I agree to avoid platitudes like, "it was God's plan," or "she's now in heaven looking down on us." (Well, unless your cousin is religious and sentimental). Sometimes not saying anything at all and giving a meaningful hug can help.

Offering to help is good, though I've heard that sometimes offers can be a burden in and of themselves, because the person has to think of how you can help them, and possibly might be embarrassed to take you up. Instead maybe tell them that you are going to do X task for them, and if they don't want you to do it, they should say no. That way you're not making them ask you, and they're not having to think of something, but if they really don't want you to do it they still have input.


Posted by: Britta | Link to this comment | 08-31-13 3:14 AM
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Ah apo, so sorry to hear that. Very sad for everyone.


Posted by: asilon | Link to this comment | 08-31-13 3:47 AM
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Well, unless your cousin is religious and sentimental

They are very religious indeed, but they also know that it would be totally insincere coming from the godless hippie Carolina branch of the family.


Posted by: apostropher | Link to this comment | 08-31-13 7:00 AM
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We're in no position to help in any event. We're making the 8-hour drive down this afternoon, then driving back tomorrow after the service. The last time I cut my hair was when I travelled there at the beginning of 2012 for our grandfather's funeral. Not cutting it this time, but I suppose I should make an effort to get down there for something other than a burial.


Posted by: apostropher | Link to this comment | 08-31-13 7:12 AM
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95- Huh, since I'm Jewish, she's half episcopal half catholic and we don't actually practice anything, should I take the repeated silver spoon gifts as an insult instead of just thoughtlessness?


Posted by: SP | Link to this comment | 08-31-13 7:24 AM
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Sorry Apo. Awful weekend.


Posted by: CharleyCarp | Link to this comment | 08-31-13 7:36 AM
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SP, aside from tradition, I give silver spoons as sort of a nod to the phrase "born with a silver spoon in his mouth." For me, it's a wish that their kid will never know a moment of worry about money.


Posted by: ydnew | Link to this comment | 08-31-13 7:40 AM
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So terribly sorry, Apo. Your presence there will be a comfort to them.


Posted by: Penny | Link to this comment | 08-31-13 7:53 AM
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We got a spoon for Zardoz from my aunt, but it's a stainless one with a nice pattern and her birthdate engraved on it. I liked it as a sort of traditional gift but without the fanciness of silver. We'll probably feed her the first bite of food ever with it, and then relegate it to the drawer in favor of plastic.


Posted by: Blume | Link to this comment | 08-31-13 8:09 AM
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Also, not anywhere close to the same level of tragedy, but on the topic of weird things said around the topic of death and babies: When I was at my mom's visitation and funeral while five months pregnant, lots of people talked about her looking down on Zardoz from heaven. Yes, fine, I don't believe that but I'll agree because it makes everyone feel better. But I was really surprised and confused when someone tried to comfort me by saying that now actually my mom would be meeting Zardoz before any of the rest of us. Like they were hanging out in heaven, before Zardoz was born into this world? Even if you think that's how things work, we were well past the point of quickening/ensoulment. But I didn't quibble with the woman.


Posted by: Blume | Link to this comment | 08-31-13 8:18 AM
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America has done weirder things to theology than it has to cuisine.


Posted by: Moby Hick | Link to this comment | 08-31-13 8:31 AM
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Or maybe I'm not giving Hot Cheetos covered in "nacho cheese" enough credit.


Posted by: Moby Hick | Link to this comment | 08-31-13 8:54 AM
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What a terrible thing, Apo, I'm very sorry.


Posted by: Barry Freed | Link to this comment | 08-31-13 8:59 AM
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just reading this now apo and I'm really, really sorry to hear about your cousin's baby. I remember when natilo's friends were facing that and as a parent it just gives you nightmares. my family is godless...wait, well whatever, but I'm sending you "love waves" from across the world. my mom calls them that.


Posted by: alameida | Link to this comment | 09- 1-13 7:47 AM
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God, I have never witnessed anything more heartbreaking in my entire life. 72.last couldn't be more right.


Posted by: apostropher | Link to this comment | 09- 2-13 8:01 AM
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sorry to read that apo.


Posted by: text | Link to this comment | 09- 2-13 8:15 AM
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I'm terribly sorry for everyone's loss, Apo.


Posted by: rob helpy-chalk | Link to this comment | 09- 2-13 8:30 AM
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