A friend of mine just told me that he had it on good authority that if you cut a cake in half, and that half in half (to quarters), and so on that around the 64th cut you would be at the one atom stage. This seems like an surprisingly small number of cuts the get to the atomic level. I could’nt find anything with a search - anyone got a line on this?
It sounds plausible to me; You could calculate this the other way around and start with an atom, then double it 64 times and see what you end up with (I’ve seen a similar thing with a chessboard (64 squares) and grains of rice - one grain on the first square, two on the next, then four, eight etc - the total number of rice grains required is 1.845*10[sup]19[/sup])
That could work, Mangetout, how many atoms did you say there were in a cake? 
I got five bucks that says Son of Dex is gonna give us the definitive answer, but this might provide a stopgap, and, if I’m wrong, will humiliate me in the process.
I was inclined to believe this is true. Cutting the cake 64 times would leave you with approximately 18,446,744,070,000,000,000 slices of cake, which strikes me as probably more atoms then there are in said cake. I arrived at this number by multiplying two times two 64 times on my calculator, because I can’t figure out how to use the exponent function. My degrees are in Theatre Arts and Hospitality Management. So sue me.
HOWEVER…
The recent article by Son of Dex, http://www.straightdope.com/mailbag/mavogadro.html , is pretty clear that a Mole of a given substance would contain about 4000 times as many MOLECULES of that substance as you would have of pieces of your cake, and at a considerably lesser weight, no matter what your cake is made of. Mind you, these are molecules, and you’re trying to get to the atomic level. To get to the atomic level for just a one-kilogram cake, I’m guessing that you’re gonna need in excess of 80 cuts or more.
Son of Dex (or anybody else who understands this better): Please give us the definitive answer, and try not to flame me TOO badly for my admittedly ameteurish answer.
… whether we are talking about a cup-cake or a five-tier wedding cake.
Okay, a pound cake traditionally contained a “pound each of butter, sugar, and flour”. I assume even the traditional recipe had a few other ingredients–eggs, for one–so let’s call it 1.5 kilograms (3.3 pounds). A cake is basically made of carbohydrates, which have a general formula C[sub]6[/sub]H[sub]12[/sub]O[sub]6[/sub]. A mole of carbohydrate contains Avogadro’s number of molecules, natch–6.022x10[sup]23[/sup] molecules–and would weigh about 180 grams ([6 x 12] + [12 x 1] + [6 x 16]). Each molecule in this case contains 24 atoms. So, a 1500 gram cake contains 8.33 moles of carbohydrate, or 8.33 x 24 x 6.022x10[sup]23[/sup] atoms, or about 1.2x10[sup]26[/sup] atoms. If we cut something in half 64 times, we get 2[sup]64[/sup] pieces, or about 1.8 x 10[sup]19[/sup] pieces. So, assuming I haven’t made some horrendous arithmetical or conceptual error (and how much does a damn cake weigh, anyhow?), we’re still way off. 87 cuts (2[sup]87[/sup]) gets you 1.55 x 10[sup]26[/sup] pieces, which is in the same ballpark as 1.2 x 10[sup]26[/sup] atoms.
Not really, Mangetout. Let’s say you’ve got the smallest possible cake, say 100 grams. If I understood Son of Dex correctly, no matter what the cake is made of (even uranium) this tiny little cake is going to contain at LEAST one Mole, or 6.022X10E23 molecules, which is thousands of times the number of slices you get after your 64 cuts, as I noted above.
Again, my grasp of this is tenuous. I could be very, VERY wrong here.
That article FarmerOak quoted has all the necessary information. If you have one mole (6x10^23) of carbon atoms (which I’m going to assume is the main ingredient of cake), it would weigh 12 grams. 6x10^23 is approximately 2^79, so you have to cut a 12-gram cake 79 times to get a single-atom slice.
Actually there are a lot of hydrogen atoms in a cake too, so the average molecular weight is probably closer to 8 than 12. And a decent sized cake weighs a bit more than 12 grams. So you’d need to cut it about 81 or 82 times.
THANK you, MEBuckner. If I read you correctly, you said the same thing I did, only MUCH more coherently and smarter-sounding.
[Homer Simpson Voice]
Mmmmm… Carbohydrate Cake… Mmmmmmm
[/Homer Simpson Voice]
Well, we all seem to be independently getting in about the same ballpark, which is reassuring (“in excess of 80 cuts or more”, “87 cuts”, “about 81 or 82 times”). And me a history major and all! My Nat. Sci. professors would be so proud!
Ahhh, the independently reproducible results! Even I can see the significance of that!
Shhhh!!!, you made me lose count.
Where is the cake at the ‘one atom’ stage? Towards the center of the cut or out at the edge (the thin part or thick part of the wedge)?
So as per the OP, I think we can safely say that your so-called “friend” is actually a lying sack of shit and cannot be trusted let alone allowed to live. I trust you’ll take the appropriate action immediately.
You are right, Kaje, I took my friend to task armed with all this new found data and pressed him harder to remember his “good authority”. He did. He says this info is from the mouth of Carl Sagen taken from the ‘Cosmos’ series. I have not re-watched to verify this but were it to be true would that mean that Dopers are smarter than Sagen himself?
Similar to what I was thinking - conceptually, we’re talking about a slice that is less than one atom thick but has the same height as the original cake, and a depth of half the radius of the cake (presuming a round cake). I don’t think the original questions is about cutting until every piece of cake is less than the size of an atom. And of course if we’re talking about a round cake, the slice is thicker on one end.
ummm… make that 1/2 the diameter.
ummm…also, make that ‘Sagan’. (humble apologies)
We’re not talking about making radial (or diametrical) cuts here. Each cut doubles the number of pieces of cake, regardless of shape. IRL, you might need to rearrange the existing pieces to accomplish this; for that matter, you would need a knife of incredibly exceeding keenness. So what? This is a hypothetical, mathematical cake. It therefore does not matter whether we’er talking about a piece near the center or the edge, because, IRL, it’s an impossible experiment.
So, the honor of Carl Sagan is preserved. And, ah, “87” is pretty close to “about ninety”, no?