Interesting Stuff Thread

Chuck Stone

Sulla Felix wrote: »

Berlin ban on circumcision except on cases of medical necessity. Jews and Muslims not happy.

"I'm here to stand for the freedom of religious rights," protester Fereshta Ludin told the BBC

It's absolutely disgusting that people describe mutilating the genitals of children a 'religious freedom'.

Chuck Stone

Chuck Stone wrote: »

It's absolutely disgusting that people describe mutilating the genitals of children a 'religious freedom'.

Apparently it's fine when it's willies.

Delirium

Hubble has spotted an ancient galaxy that shouldn’t exist

This galaxy is so large, so fully-formed, astronomers say it shouldn't exist at all. It's called a "grand-design" spiral galaxy, and unlike most galaxies of its kind, this one is old. Like, really, really old. According to a new study conducted by researchers using NASA's Hubble Telescope, it dates back roughly 10.7-billion years — and that makes it the most ancient spiral galaxy we've ever discovered.

"The vast majority of old galaxies look like train wrecks," said UCLA astrophysicist Alice Shapley in a press release. "Our first thought was, why is this one so different, and so beautiful?"

robindch

Deleted User wrote: »

German government has already said they'll legislate to specifically make it legal again, pathetic.

At least hacking off bits of young girls is outlawed. Progress of a kind, I suppose.

BTW, it makes interesting, if sobering, reading to read the UK's Home Office's "facts about female genital mutilation" and see how many apply to male genital mutilation:

http://www.homeoffice.gov.uk/crime/violence-against-women-girls/female-genital-mutilation/

joseph brand

South Korea rejects creationist interference in school textbooks.

pressure group Society for Textbook Revise had managed to persuade textbook publishers to drop sections from their books that discussed the evolution of horses and the Jurassic-era early avian-like dinosaur Archaeopteryx. Now, however, a special panel convened by the South Korean government has recommended that the publishers ignore the creationists' arguments -- which should mean that textbooks reintroduce the old segments before the start of the next school year.

A small victory. Can I get an Amen?

Sulla Felix

koth wrote: »

Hubble has spotted an ancient galaxy that shouldn’t exist

God, the comments are depressing.

How do they know it's old? Has any human lived enough to know that? Have they ever set foot somewhere there? How did they measure their age? how do they know when it was formed?
Those are less than 0.0000001 % of the questions I can formulate to prove that science is bull****

Anyway, I'm not sure I see why it's a surprising find. Surely we should be expecting to find a certain proportion of "pristine" galaxies?

mikhail

Sulla Felix wrote: »

God, the comments are depressing.

There are two things which are infinite, according to Einstein: the universe and human stupidity. And he wasn't sure about the universe.

Anyway, I'm not sure I see why it's a surprising find. Surely we should be expecting to find a certain proportion of "pristine" galaxies?

It's all about the age - it's only a three billion years after the big bang. Basically, if you take the current mathematical models of how things worked initially, and spin them forward that long, they haven't settled down to looking like modern galaxies. I don't know what they mean precisely, but I would expect there to be a lot more free material (gas) and a smaller number of big, bright stars, possibly in more erratic orbits. So either they measured the age wrong, or something's funny with their maths, or it's a staggeringly unlikely fluke. Interesting no matter what the eventual conclusion. I'm surprised no one's claimed it proof of divine intervention yet. Or maybe they have - I'm not going near the comments on io9.

Sulla Felix

mikhail wrote: »

There are two things which are infinite, according to Einstein: the universe and human stupidity. And he wasn't sure about the universe.


It's all about the age - it's only a three billion years after the big bang. Basically, if you take the current mathematical models of how things worked initially, and spin them forward that long, they haven't settled down to looking like modern galaxies. I don't know what they mean precisely, but I would expect there to be a lot more free material (gas) and a smaller number of big, bright stars, possibly in more erratic orbits. So either they measured the age wrong, or something's funny with their maths, or it's a staggeringly unlikely fluke. Interesting no matter what the eventual conclusion. I'm surprised no one's claimed it proof of divine intervention yet. Or maybe they have - I'm not going near the comments on io9.

Ahh, so it's almost too old looking to be that young or something? Interesting.

decimatio

robindch wrote: »

At least hacking off bits of young girls is outlawed. Progress of a kind, I suppose.

I couldn't help but read that in Hitchens' voice.

Kivaro

joseph brand wrote: »

South Korea rejects creationist interference in school textbooks.



A small victory. Can I get an Amen?

Amen, brotha.

Kivaro

Apparently 6,000.

Higgs Boson Confirmed; CERN Discovery Passes Test.
According to this anyway.

Put it another way, there is a one-in-300-million chance that the Higgs does not exist.
I'm cool, so I can call it the "Higgs" now.

That's scientists for you.

pauldla

Mathematician Claims Proof of Connection between Prime Numbers

A Japanese mathematician claims to have the proof for the ABC conjecture, a statement about the relationship between prime numbers that has been called the most important unsolved problem in number theory.


If Shinichi Mochizuki's 500-page proof stands up to scrutiny, mathematicians say it will represent one of the most astounding achievements of mathematics of the twenty-first century. The proof will also have ramifications all over mathematics, and even in the real-world field of data encryption.

http://news.yahoo.com/mathematician-claims-proof-connection-between-prime-numbers-131737044.html?_esi=1


I've said it before: we live in exciting days, ladies and gents!

Genghiz Cohen

That gave me shivers!


... oh god! IM A NERD!

Dades

Kivaro wrote: »

Put it another way, there is a one-in-300-million chance that the Higgs does not exist.

Unconvinced! It either exists or it doesn't - so that's an equal chance either way in my book. :pac:

shizz

pauldla wrote: »

Mathematician Claims Proof of Connection between Prime Numbers



http://news.yahoo.com/mathematician-claims-proof-connection-between-prime-numbers-131737044.html?_esi=1


I've said it before: we live in exciting days, ladies and gents!

Never before has an article made me feel like such an idiot.

mikhail

shizz wrote: »

Never before has an article made me feel like such an idiot.

Don't worry about it; that wasn't the friendliest article for someone with no background in maths.

The key thing to get is that any number can be written as a product of prime numbers, and there's only one way to do that for each number. For example,

84 = 2 x 2 x 3 x 7

or to write that another way

84 = (2^2) x 3 x 7

The square free part of a number is just the number left if you take out the squared numbers. In the example above, it's 3 x 7 = 21.

These numbers seem to be useful if you're trying to prove things about equations like a^2 + b^2 = c^2. Like a lot of number theory, this stuff seems kind of pointless, but if you can prove certain relationships, it's actually really powerful stuff because it's so fundamental.

Bannasidhe

mikhail wrote: »

Don't worry about it; that wasn't the friendliest article for someone with no background in maths.

The key thing to get is that any number can be written as a product of prime numbers, and there's only one way to do that for each number. For example,

84 = 2 x 2 x 3 x 7

or to write that another way

84 = (2^2) x 3 x 7

The square free part of a number is just the number left if you take out the squared numbers. In the example above, it's 3 x 7 = 21.

These numbers seem to be useful if you're trying to prove things about equations like a^2 + b^2 = c^2. Like a lot of number theory, this stuff seems kind of pointless, but if you can prove certain relationships, it's actually really powerful stuff because it's so fundamental.

I have no idea what all of that means but it's very sexy.

Sarky

We invented numbers to make sure we were getting the number of goats we bartered for. Turns out numbers are bloody amazing.

seamus

Sometimes it sounds like mathematicians invent concepts just to make themselves look useful. "Square-free"? Never heard of it in my life.

I haven't had nearly enough coffee to try and read the wiki article (another) 3 times and understand what's going on there. But it sounds important, so yay.

pauldla

shizz wrote: »

Never before has an article made me feel like such an idiot.

Actually, me too. I'm not a maths head at all, but I get do the significance of it (I think).

Thanks to mikhail for making it easier to understand!

robindch

http://en.wikipedia.org/wiki/Abc_conjecture

My head hurts.

magicbastarder

robindch wrote: »

http://en.wikipedia.org/wiki/Abc_conjecture

My head hurts.

why? it's easy as 1-2-3.

Turtwig

shizz wrote: »

Never before has an article made me feel like such an idiot.

Starting with a 1000, add:
40;
1000;
30;
1000;
20;
1000;
and 10.

Answer please?

Not 5,000. Do it again.

Name all fourteen punctuations marks in the English Language.

Now, you're an idiot.:D

shizz

mikhail wrote: »

Don't worry about it; that wasn't the friendliest article for someone with no background in maths.

The key thing to get is that any number can be written as a product of prime numbers, and there's only one way to do that for each number. For example,

84 = 2 x 2 x 3 x 7

or to write that another way

84 = (2^2) x 3 x 7

The square free part of a number is just the number left if you take out the squared numbers. In the example above, it's 3 x 7 = 21.

These numbers seem to be useful if you're trying to prove things about equations like a^2 + b^2 = c^2. Like a lot of number theory, this stuff seems kind of pointless, but if you can prove certain relationships, it's actually really powerful stuff because it's so fundamental.

Well I've a background in engineering maths haha. I still don't really see the significance. What exactly is being proven?

sponsoredwalk

Here's a different formulation of the abc conjecture, slightly modified to make it easier to understand:

If I pick some random number e > 0 then there will always exist another number D such that if a + b = c then max(a,b,c) ≤ D(abc)¹⁺ᵉ

Before explaining this I'll rewrite it with actual numbers:

If I pick some random number, say 2, which is greater than zero then there will always exist another number D, say 1 in this case, such that if 3 + 4 = 7 then max(3,4,7) ≤ C(3·4·7)¹⁺², i.e. max(3,4,7) ≤ 1·(84)³, i.e. 7 ≤ (84)³, i.e. 7 ≤ 592,704

Here max(a,b,c) means the maximum of a, b or c, so max(3,7,4) = 7.

To understand (abc)¹⁺ᵉ:
First, more or less we can say that 2¹ means 2 multiplied by itself once.
Second we can say that 2² = 4 can be written like 4 = 2·2 = 2² = 2¹⁺¹.
Third we look at 4² = 16. Since 4 = 2·2 we can rewrite 16 = 4² =(2·2)².

So max(a,b,c) ≤ D(abc)¹⁺ᵉ just means that the biggest of your 3 numbers will always be smaller than some multiple D of the product of the 3 numbers, abc, as long as you raise the product abc of your 3 numbers to some power. This multiple will depend upon the number you originally chose raise abc to.

Pick 1, 8 & 9 as our a, b & c & we get:
max(1,8,9) ≤ D·(1·8·9)¹⁺ᵉ ---> 9 ≤ D·(72)¹⁺ᵉ
If I choose e = 1 then 9 ≤ D·(72)¹⁺¹ ---> 9 ≤ D·(72)².
So here we see that given e = 1 > 0 there exists another number D, say D = 1, such that max(1,8,9) ≤ D·(1·8·9)¹⁺ᵉ because 9 ≤ 1·(72)². See here that D is hypothesized to exist after we've picked our e value.

This theorem only holds if a, b & c have no common factor other than 1 (i.e. 4 & 6 have a common factor of 2 because 4 = 4·1 = 2·2 & 6 = 6·1 = 2·3 - so 4 & 6 won't feature in this theorem together, while 5 & 6 have no common factor other than 1 because 5 = 5·1 & 6 = 6·1 = 2·3, so we could use these).

What the theorem says is that most of the prime factors of certain numbers must occur to the first power, so in mikhail's example of 84 = 2²·3·7 we see most of the prime factors have no exponent like 2 has. Further it says that if you have small numbers, like 2 in 84 = 2²·3·7, that are raised to higher powers than 1 than there should be a big prime factor, e.g. 7, only to the first power so as to offset the balance & compensate. So if we had 2ⁿ + 1 = k then k would have a large prime factor as long as n is large. Picking n = 6 gives 2⁶ + 1 = 65 = 65·1 i.e. a large prime factor of 65... This is what the article means more or less when talking about the "square-free" part.

Also, note that max(a,b,c) ≤ D(abc)¹⁺ᵉ implies a ≤ D(abc)¹⁺ᵉ, b ≤ D(abc)¹⁺ᵉ & c ≤ D(abc)¹⁺ᵉ, so instead of a, b & c we choose aⁿ, bⁿ & cⁿ we can use the fact that a + b = c is part of our hypothesis to work on aⁿ + bⁿ= cⁿ, i.e. Fermat's last theorem for relatively prime integers...

That's all I know about it, the way the article talks about it all makes little sense to me quite frankly, it seems like they're discussing the above with different algebra chosen specifically to make it awkward...

Turtwig

sponsoredwalk wrote: »

Here's a different formulation of the abc conjecture, slightly modified to make it easier to understand:

If I pick some random number e > 0 then there will always exist another number D such that if a + b = c then max(a,b,c) ≤ D(abc)¹⁺ᵉ

Before explaining this I'll rewrite it with actual numbers:

If I pick some random number, say 2, which is greater than zero then there will always exist another number D, say 1 in this case, such that if 3 + 4 = 7 then max(3,4,7) ≤ C(3·4·7)¹⁺², i.e. max(3,4,7) ≤ 1·(84)³, i.e. 7 ≤ (84)³, i.e. 7 ≤ 592,704

Here max(a,b,c) means the maximum of a, b or c, so max(3,7,4) = 7.

To understand (abc)¹⁺ᵉ:
First, more or less we can say that 2¹ means 2 multiplied by itself once.
Second we can say that 2² = 4 can be written like 4 = 2·2 = 2² = 2¹⁺¹.
Third we look at 4² = 16. Since 4 = 2·2 we can rewrite 16 = 4² =(2·2)².

So max(a,b,c) ≤ D(abc)¹⁺ᵉ just means that the biggest of your 3 numbers will always be smaller than some multiple D of the product of the 3 numbers, abc, as long as you raise the product abc of your 3 numbers to some power. This multiple will depend upon the number you originally chose raise abc to.

Pick 1, 8 & 9 as our a, b & c & we get:
max(1,8,9) ≤ D·(1·8·9)¹⁺ᵉ ---> 9 ≤ D·(72)¹⁺ᵉ
If I choose e = 1 then 9 ≤ D·(72)¹⁺¹ ---> 9 ≤ D·(72)².
So here we see that given e = 1 > 0 there exists another number D, say D = 1, such that max(1,8,9) ≤ D·(1·8·9)¹⁺ᵉ because 9 ≤ 1·(72)². See here that D is hypothesized to exist after we've picked our e value.

This theorem only holds if a, b & c have no common factor other than 1 (i.e. 4 & 6 have a common factor of 2 because 4 = 4·1 = 2·2 & 6 = 6·1 = 2·3 - so 4 & 6 won't feature in this theorem together, while 5 & 6 have no common factor other than 1 because 5 = 5·1 & 6 = 6·1 = 2·3, so we could use these).

What the theorem says is that most of the prime factors of certain numbers must occur to the first power, so in mikhail's example of 84 = 2²·3·7 we see most of the prime factors have no exponent like 2 has. Further it says that if you have small numbers, like 2 in 84 = 2²·3·7, that are raised to higher powers than 1 than there should be a big prime factor, e.g. 7, only to the first power so as to offset the balance & compensate. So if we had 2ⁿ + 1 = k then k would have a large prime factor as long as n is large. Picking n = 6 gives 2⁶ + 1 = 65 = 65·1 i.e. a large prime factor of 65... This is what the article means more or less when talking about the "square-free" part.

Also, note that max(a,b,c) ≤ D(abc)¹⁺ᵉ implies a ≤ D(abc)¹⁺ᵉ, b ≤ D(abc)¹⁺ᵉ & c ≤ D(abc)¹⁺ᵉ, so instead of a, b & c we choose aⁿ, bⁿ & cⁿ we can use the fact that a + b = c is part of our hypothesis to work on aⁿ + bⁿ= cⁿ, i.e. Fermat's last theorem for relatively prime integers...

That's all I know about it, the way the article talks about it all makes little sense to me quite frankly, it seems like they're discussing the above with different algebra chosen specifically to make it awkward...

Mother f**k sponsored all that math and no LaTeX. You are a disgrace to your profession.

robindch

boards supports [latex]\TeX[/latex]:

eg:

[[SIZE="2"]l[/SIZE]atex]
P = \frac{\displaystyle{
\sum_{i=1}^n (x_i- x)
(y_i- y)}}
{\displaystyle{\left[
\sum_{i=1}^n(x_i-x)^2
\sum_{i=1}^n(y_i- y)^2
\right]^{1/2}}}
[/latex]

...produces...:

[latex]P = \frac{\displaystyle{
\sum_{i=1}^n (x_i- x)
(y_i- y)}}
{\displaystyle{\left[
\sum_{i=1}^n(x_i-x)^2
\sum_{i=1}^n(y_i- y)^2
\right]^{1/2}}}[/latex]

decimatio

sponsoredwalk wrote: »

Here's a different formulation of the abc conjecture, slightly modified to make it easier to understand:

If I pick some random number e > 0 then there will always exist another number D such that if a + b = c then max(a,b,c) ≤ D(abc)¹⁺ᵉ

Before explaining this I'll rewrite it with actual numbers:

If I pick some random number, say 2, which is greater than zero then there will always exist another number D, say 1 in this case, such that if 3 + 4 = 7 then max(3,4,7) ≤ C(3·4·7)¹⁺², i.e. max(3,4,7) ≤ 1·(84)³, i.e. 7 ≤ (84)³, i.e. 7 ≤ 592,704

Here max(a,b,c) means the maximum of a, b or c, so max(3,7,4) = 7.

To understand (abc)¹⁺ᵉ:
First, more or less we can say that 2¹ means 2 multiplied by itself once.
Second we can say that 2² = 4 can be written like 4 = 2·2 = 2² = 2¹⁺¹.
Third we look at 4² = 16. Since 4 = 2·2 we can rewrite 16 = 4² =(2·2)².

So max(a,b,c) ≤ D(abc)¹⁺ᵉ just means that the biggest of your 3 numbers will always be smaller than some multiple D of the product of the 3 numbers, abc, as long as you raise the product abc of your 3 numbers to some power. This multiple will depend upon the number you originally chose raise abc to.

Pick 1, 8 & 9 as our a, b & c & we get:
max(1,8,9) ≤ D·(1·8·9)¹⁺ᵉ ---> 9 ≤ D·(72)¹⁺ᵉ
If I choose e = 1 then 9 ≤ D·(72)¹⁺¹ ---> 9 ≤ D·(72)².
So here we see that given e = 1 > 0 there exists another number D, say D = 1, such that max(1,8,9) ≤ D·(1·8·9)¹⁺ᵉ because 9 ≤ 1·(72)². See here that D is hypothesized to exist after we've picked our e value.

This theorem only holds if a, b & c have no common factor other than 1 (i.e. 4 & 6 have a common factor of 2 because 4 = 4·1 = 2·2 & 6 = 6·1 = 2·3 - so 4 & 6 won't feature in this theorem together, while 5 & 6 have no common factor other than 1 because 5 = 5·1 & 6 = 6·1 = 2·3, so we could use these).

What the theorem says is that most of the prime factors of certain numbers must occur to the first power, so in mikhail's example of 84 = 2²·3·7 we see most of the prime factors have no exponent like 2 has. Further it says that if you have small numbers, like 2 in 84 = 2²·3·7, that are raised to higher powers than 1 than there should be a big prime factor, e.g. 7, only to the first power so as to offset the balance & compensate. So if we had 2ⁿ + 1 = k then k would have a large prime factor as long as n is large. Picking n = 6 gives 2⁶ + 1 = 65 = 65·1 i.e. a large prime factor of 65... This is what the article means more or less when talking about the "square-free" part.

Also, note that max(a,b,c) ≤ D(abc)¹⁺ᵉ implies a ≤ D(abc)¹⁺ᵉ, b ≤ D(abc)¹⁺ᵉ & c ≤ D(abc)¹⁺ᵉ, so instead of a, b & c we choose aⁿ, bⁿ & cⁿ we can use the fact that a + b = c is part of our hypothesis to work on aⁿ + bⁿ= cⁿ, i.e. Fermat's last theorem for relatively prime integers...

That's all I know about it, the way the article talks about it all makes little sense to me quite frankly, it seems like they're discussing the above with different algebra chosen specifically to make it awkward...

Me fail english? That's unpossible!

Turtwig

Apologies if there's typos it was a rushed job of an excellent but ugly post, might do a re-edit later.

sponsoredwalk

I can't believe you guys don't appreciate the beauty of these little html symbols, I mean look at them!
Δ ∇ ∀ ∃ ∋ ∈ ∉ ℒ{f(t)} = ♥ ◊ ♠ ♣ ♦ ∴ ∅ ℕ ℤ ℙ ℚ ℝ ℂ ℵ ℘ ℑ ℜ ∫ℯˣ ∮ ∂ ±÷ × • · ≡ ≠ ≅ ≈ ≤ ≥ √ ∑ᵢ ← ↑↔ ↓ → ↦ ⇒ ⇔ θ ∀ ☺ ⊕ ⊗ ⊥ ∞ ∝ ¯ ⋀ ⋁ ಠ _ಠ

All I'm missing is a superscript m & n

Cheers for the latex :cool: