Abstract: "We show that motion with as few as three degrees of freedom (for instance, a particle moving in a three-dimensional potential) can be equivalent to a Turing machine, and so be capable of universal computation. Such systems possess a type of unpredictability qualitatively stronger than that which has been previously discussed in the study of low-dimensional chaos: Even if the initial conditions are known exactly, virtually any question about their long-term dynamics is undecidable."
If you cut a body by a plane through its center of gravity you _do not_ necessarily have equal volumes on either side of the plane.
He didn't say you have equal volumes. He said you have equal masses.
Cutting a body through it's center of mass doesn't still doesn't necessarily leave equal masses on either side of the (hyper-)plane. The center of mass lets you ignore the distribution of mass as a function of position (density) for certain types of problems. This is not one of them. What you are saying is still trivial, still wrong, and still not the ham sandwich theorem.
What you call the Ham Sandwich Theorem is true, trivial, and most definitely _not_ the Ham Sandwich Theorem.
The theorem states that there is a plane that has equal portions of ham and of each slice of bread on either side. If you cut a body by a plane through its center of gravity you _do not_ necessarily have equal volumes on either side of the plane.
Can you explain how this relates to the very long bit of legalese at the beginning of all the Project Gutenberg ebooks then? I've always been confused as to why one isn't allowed to remove it. (I found one in the wild once, published and bound, at B&N, without the statement. It shared some typos, so I assume it came from PG.)
Slashdot Mirror
Ok, say it shorter, wise guy.
Lightning Bolt!
Reminds me of the weed eater joke. (Moderately offensive.)
given this:
Unpredictability and undecidability in dynamical systems
Abstract: "We show that motion with as few as three degrees of freedom (for instance, a particle moving in a three-dimensional potential) can be equivalent to a Turing machine, and so be capable of universal computation. Such systems possess a type of unpredictability qualitatively stronger than that which has been previously discussed in the study of low-dimensional chaos: Even if the initial conditions are known exactly, virtually any question about their long-term dynamics is undecidable."
I remember the Moties in The Mote in God's Eye building a "toilet" that never needed cleaning.
If you cut a body by a plane through its center of gravity you _do not_ necessarily have equal volumes on either side of the plane.
He didn't say you have equal volumes. He said you have equal masses.
Cutting a body through it's center of mass doesn't still doesn't necessarily leave equal masses on either side of the (hyper-)plane. The center of mass lets you ignore the distribution of mass as a function of position (density) for certain types of problems. This is not one of them. What you are saying is still trivial, still wrong, and still not the ham sandwich theorem.
What you call the Ham Sandwich Theorem is true, trivial, and most definitely _not_ the Ham Sandwich Theorem. The theorem states that there is a plane that has equal portions of ham and of each slice of bread on either side. If you cut a body by a plane through its center of gravity you _do not_ necessarily have equal volumes on either side of the plane.
Not any more.
nautilus-actions + wipe or shred or whatever...
I'm sure Boomer is pretty good at it.
So that's why you wrap bacon around it!
Can you explain how this relates to the very long bit of legalese at the beginning of all the Project Gutenberg ebooks then? I've always been confused as to why one isn't allowed to remove it. (I found one in the wild once, published and bound, at B&N, without the statement. It shared some typos, so I assume it came from PG.)