

Things I know are true, but I don't really believe - andreyf
http://abstrusegoose.com/73

======
michael_dorfman
I was skeptical clicking on the link, but it actually lived up to the title.

~~~
Herring
It should probably have been "Stuff i've been told is true but I don't
entirely understand"

~~~
ivankirigin
Most physics professors I've spoken to don't actually understand things like
quantum entanglement. They just say "the math works. that is all."

There is no intuitive understanding of a subject like that because neither
100K years of evolution of our brain now decades of real world experience
expose us to it.

~~~
Herring
Seemed more than just lacking intuitive explanations. In entanglement for
example, the answer is because it can't transfer information & you learn that
just fine in any intro to quantum class.

~~~
timcederman
Thank you. This is also the reason why faster than light 'travel' can occur,
if it doesn't transmit information.

Entanglement is slightly mysterious though as what is the physical mechanism
behind it?

~~~
yummyfajitas
The physical mechanism is that quantum mechanics governs a probability
distribution (the "wave" in "wave-particle duality") on _configuration space_
, not "physical" space.

Imagine you have two particles in 1 space dimension. The first particle has a
position x (1 real number), the second particle has a position y (1 real
number). "Physical space" would be the set of real numbers (R^1), while
configuration space is the set of _pairs_ of real numbers (x,y) (this set is
R^2). The first number in the pair represents the position of particle 1, the
second the position of particle 2.

An entangled state is simply a probability distribution on R^2 which is not a
product state (i.e. P(x,y) != P_1(x) P_2(y)). This means that knowledge of the
position of particle 1 gives you (possibly incomplete) information about the
position of particle 2.

One example of this is "probability 1/2 that x=0, y=0, 1/2 that x=1, y=1". The
minute you know x, you know y.

That's what entanglement is. What makes it weird is the idea that "knowing x"
(measuring it) changes things. An explanation of this is trickier. Still
understandable in principle (not just 'follow the math'), but too long for
this post.

~~~
ericb
>> too long for this post.

How about another post, then? :-)

------
noonespecial
Yeah, I don't believe they give those people honey roasted peanuts while they
ride in those metal tubes either.

~~~
tdavis
Don't believe it. They're usually pretzels now. Too many people allergic to
peanuts.

------
hugh
A late entry: the Banach-Tarski theorem:

<http://en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox>

~~~
nickb
Ahhh... you just caused a major flashback in my memory. I remember reading
about Banach-Tarski paradox about 7 years ago or so and it gave me so many
headaches. I think I read the paper explaining it trice and it still made no
sense to me and on my second reading I was convinced there was an error in an
equation somewhere.. I asked a math prof who's a brilliant theoretician and he
explained it to me and it still made little sense. Then I read von Neumann's
explanation and it finally started making some sense. The key to understanding
it is, like with many other concepts, to ignore your intuition and trust the
math behind it.

~~~
yummyfajitas
I'd say trust your intuition more than the math, but I'm more physicist than
mathematician.

To prove Banach-Tarski, you need to assume Zermelo-Frankel set theory (just
ordinary set theory) plus the uncountable axiom of choice.

In my view, this means the uncountable axiom of choice is false. This actually
breaks far less than you would expect. For most practical purposes, you only
need the countable axiom of choice, which is the intuitively reasonable
version.

The main thing the loss of the uncountable version breaks is the Hahn-Banach
theorem on spaces of dimension higher than countable infinity. This in turn
breaks quantum field theory on free space (not in a box), but that's broken
anyway.

------
apmee
The Nonexistence one is what often gets me. If and when I ever give it more
than a passing moment's thought, I have to take care lest it put me into an
unsettling trance-like state of bewildered and bemused incomprehension and
planar disorientation. Saves money on jazzy cigarettes let me tells you.

~~~
paulgb
I can relate to that. I used to feel a bit of a high when I was a young kid
just trying to contemplate what would exist if nothing existed. Not nothing as
in no matter, but no dimensions or time either. Thinking about that still puts
my mind into a weird state.

~~~
apmee
Some people, including (I suspect) most theists, seem terrified by this,
whereas I find it exhilarating and immensely humbling.

Funnily enough, it was actually while I was sat in church with my family when
I was younger (I've since lapsed profoundly and comprehensively, of course)
that my mind first began to wander to and wrestle with such concepts.

------
tptacek
XKCD used to be this engaging, before it devolved into in-jokes and IRC memes.

~~~
unalone
XKCD still is engaging. It's just become less consistent.

~~~
tptacek
"Tron Paul".

------
marketer
Weird.. I submitted this link a day ago (with the same url) and the dupe
detection wasn't hit.

<http://news.ycombinator.com/item?id=351975>

------
tocomment
What's the well ordered one about?

~~~
andreyf
A better example is the well-ordering of the reals. From wikipedia:

From the [axioms of math] one can show that there is a well-order of the
reals; it is also possible to show that [those axioms] alone are not
sufficient to prove the existence of a definable (by a formula) well-order of
the reals.

<http://en.wikipedia.org/wiki/Well-order>

So you can prove that set of real numbers can be well-ordered, but you can
also prove that an order cannot be defined.

Kind of how God exists, but cannot be perceived or comprehended ;)

(or maybe not)

~~~
Dilpil
Absolutely nothing like the proposition that god exists, and I wag my finger
at you for associating the concrete facts of mathematics with superstitious
claims backed up by hearsay.

~~~
ars
This is not reddit.

------
bsaunder
Cellular Automata ( <http://en.wikipedia.org/wiki/Cellular_automata> )
Particularly rules 110 and 30

------
jmtame
Error: unavailable?

~~~
pchristensen
<http://abstrusegoose.com/64>

------
hsmyers
Elves, definitely elves.

