Any scientists around?
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So, oil is created by animal remains that are subjected to sedimentary processes, and then brought to a simmer by metamorphic processes, correct -- or close enough?
How exactly does this fit into modern science? How was the arctic so livable millions of years ago?
Is evolution wrong? Is global warming wrong? Is Earth crust displacement true?
Or is the arctic just a massive sea animal graveyard where everything goes to die? Even so, wouldn't the crustaceans just eat everything eventually? The bones would simply be eroded into sediments before they could be subjected to such heat and pressure as to form oil.
Unless the idea is that they melt out of the sediments and pool, but, if that were the case, then why wouldn't the liquified bones, etc, simply continue heating until they were broken down entirely and their molecules scattered?
How does oil in the arctic make any sense?
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If scientists ever found a way of manipulating chromosomes, could this lead to a possible cure for down's syndrome, autism, and aspergers?
Hell, could this lead to humans finally having the ability to modify themselves to how they desire by changing their race, gender, and possibly even their sexuality?
Heine Borel and nutty intervals
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Yo /sci/ so whilst learning about topology I got up to the section on the general definition of compactness. For a bit of context I thought I'd have a look at Hardy's proof of Heine-Borel. One of the examples Hardy gives us is the set of all closed balls centre p/q rational in [0,1], radius ?/q^3. Obviously for some values of ? this is a closed cover of [0,1].
Then he tells us to consider the maximum length of a finite subcover: Turns out this is 2?*(1+1/2^3+2/3^3+3/4^3+...).
Obviously the series converges to a finite value, so for sufficiently small ? this is less than one. Thus we can't find a finite subcover so we can pick a ?>0 such that the set of intervals doesn't cover [0,1].
I must say, I guess it's sinking in but feels highly counterintuitive - you'd think you could, given any r in [0,1] find an interval of that form for any ?.
So my question is, /sci/, what is the maximum possible value of ? for which we won't have a cover? And which values will be missed?