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Kepler Spots "Perfectly Aligned" Alien Worlds
astroengine writes "When NASA's Kepler space telescope started finding planets at odd angles to their parent stars, scientists wondered if our solar system's tidy geometry, with the planets neatly orbiting around the sun's equator, was an exception to the rule. That idea can be laid to rest thanks to an innovative use of the Kepler data which aligned three planets circling the sun-like star Kepler-30 with a giant spot on the star's surface. 'The planets themselves are not all that remarkable — two giant Jupiters and one super-Earth — but what is remarkable is that they aligned so perfectly,' astronomer Drake Deming, with the University of Maryland, told Discovery News."
I'm a software engineer so my knowledge is rather limited, but I'd have assumed that the orbits of planets would tend to be in the same plane as the spinning of the galaxy, so if you look at a mostly flat galaxy, you'll find mostly aligned orbits, and if a galaxy was more... "chaotic", the orbits would be likewise less aligned in respect with each other.
I agree. Light speed is too slow. We must go straight to Ludicrous Speed!
Tic-Tac-Toe, Global Thermonuclear War, and relationships all have the same winning move.
It makes perfect sense in the realm of popular statistics... thousands of reports come out saying smoking/chocolate/coffee/alcohol/etc is bad for you. Then one comes out saying that there are some positive aspects of <product>, and the world thinks "Ah. So <product> is not so bad for you after all!".
Still... in the scale of the galaxy, spotting another such system in the galaxy proves that earth isn't the _only_ one, and the chance that we've seen the only other well-aligned solar system in the galaxy is pretty small so it's fair to say there are others, probably millions of others. So it doesn't prove it's common, but at least it's probably not uncommon.
Universe is 2D.
The 3D stuff is just to milk more money!
HOWEVER, and here's the paradox: if not all stars have orbiting planets, then the number of stars with orbiting planets is less than infinite, ie, finite.
Bzzzt! Fail - thanks for playing.
Once you start playing with infinite numbers you have to be very careful with concepts like "less than" or "more than". Just because you can demonstrate that one set is in some way smaller than another infinite set does *not* demonstrate that the smaller one is finite.
Consider the set of natural numbers - 1,2,3,4 etc. This is infinite. Then consider the set of even natural numbers - 2,4,6,8 etc. Clearly there are members of the first set which are not members of the second set, and so one might be tempted to conclude that the second set is in some way smaller, and therefore by your argument, finite.
In fact one can set up a one-to-one mapping between the two sets:
12
24
36
etc. and thus both sets have precisely the same (infinite) number of members.
If I get all this "limitless/infinity" stuff correct, then, in theory, in a limitless/infinite universe there would be an infinite number of "flat" solar systems.
But we can't set up one-to-one mapping between the allegedly infinite set of all stars, and the set of all stars without planets. We don't even know whether it would be a two-to-one mapping, or any x-to-one mapping. Some stars might have been divested of their planets by passing near other stars. There's no mathematical rule.
Once you start playing with infinite numbers you have to be very careful with concepts like "less than" or "more than".
Numberphile has a nice video about different types of infinity: http://www.numberphile.com/videos/countable_infinity.html
The planets are merely aligned in the same plane - and not perfectly.
When I first read the headline, I was expecting to read about a ring of planets sharing the same orbit - what would be equivalent to the first stage of maneuver for the development of a niven ring or even a dyson sphere. Now that would have been exciting news.
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if the universe is infinite, then there are an infinite number of stars. It follows that orbiting those infinite stars is an infinite number of planets.
"Would you like a cheese and ham Breville?"
"Wait. Something's happening. It's opening up! My God, it's full of apricots!"
No, but we can set up a fraction. Let's say that 1/1000 stars have orbiting planets. That would be infinity/1000, which equals infinity. Still not finite. As another commenter noted, there is a one-to-one mapping of rational numbers (3/4, 1/72, 399/12, etc.) to integers.
Or, as my sig used to say, "Space is big - really big. Better pack a lunch."
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Actually you don't. At least not if you are starting from the assumption that there are infinite stars in the first place. No matter what the process is that results in flat star systems SOMETHING caused it, that something has a probability of occurring, all probabilities can be represented as a fraction of the sample set since in this case your sample set is infinity stars and any fraction of infinity is also infinity you don't have to actually know the probability of occurrence.
I found that the easiest way for them to grasp the difference between countable and uncountable infinities is the difference between whole numbers and real numbers. A countable infinity will always have a finite number of elements between any two elements (whole numbers) where as an uncountable infinity will have an infinite number of elements between any to elements in the set (real numbers).
This is severely misleading, as there are an infinite number of elements between any two rational numbers, yet the rational numbers are still countably infinite.
If you really want to explain it correctly, then the best way is talk about one-to-one correspondence. Having a one-to-one correspondence with the natural numbers is what it means to be countably infinite, and has a direct analogy to people counting with their fingers. Cantor's diagonalization argument shows why you can't count the reals, or more technically, construct a one-to-one correspondence between the reals and the natural numbers. His argument is actually quite understandable and illuminating.