SPACE

[Absolute_Zero]

I heard of that. Still cant get my head around how thats possible in some bases but not others.

A year after the initial announcement, Plouffe published a method that works with any base. Slower than the base 2/16 method, complexity O(n^3log(n)^3)

Later, Bellard improved the complexity to O(n^2)

'C' decimal implementation:
https://ideone.com/J4Nqs1

/maths

[gumboot]

Only base 2 is special, there. Any other power of two base can be calculated by finding n consecutive binary digits.

[Darkflame]

I heard of that. Still cant get my head around how thats possible in some bases but not others.

A year after the initial announcement, Plouffe published a method that works with any base. Slower than the base 2/16 method, complexity O(n^3log(n)^3)

Later, Bellard improved the complexity to O(n^2)

'C' decimal implementation:
https://ideone.com/J4Nqs1

/maths

Thanks for that. Gone into a glourious black hole of this stuff.
I honestly thought it was proved impossible to get the nth digit in other bases - no idea how that was in my head, but glade to be wrong.

I love this;

Code: Select all

#define _ F-->00||-F-OO--;
int F=00,OO=00;main(){F_OO();printf("%1.3f\n",4.*-F/OO/OO);}F_OO()
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}
To make it more accurate, change the circle to be bigger.

(http://www.ioccc.org/winners.html 1988 )

[Absolute_Zero]

http://www.bbc.co.uk/iplayer/episode/b0 ... ty-control

A bit meh, but a couple of elements were interesting to me...

38:00 - an elegant hypothesis of dark energy as an anti-grav force produced by matter/anti-matter particle-pair creation in vacuum quantum fluctuations. The fate of this notion depends on CERN's confirmation that anti-matter falls "up"... ongoing.

55:20 - a condensed matter [super]-sensor that can detect the gravitational field of a human at ~1 metre.

[zip accident]

an elegant hypothesis of dark energy as an anti-grav force produced by matter/anti-matter particle-pair creation in vacuum quantum fluctuations. The fate of this notion depends on CERN's confirmation that anti-matter falls "up"... ongoing.

While anti-matter falling up is an elegant hypothesis, it wouldn't explain dark energy, because that involves the creation of new (empty?) space-time in between the old space-time.

[Absolute_Zero]

Wot? Did you watch the link where indicated? And, umm, no it doesn't.

[zip accident]

Wot? Did you watch the link where indicated?

Nope, I'm pretty cautious about random clips and this seemed to be a very long one. Which probably means long adverts to wait through, even if you can then skip to the relevant minute.

And, umm, no it doesn't.

Are you sure? if the inflating balloon analogy is that inaccurate why use it at all?

[pogo]

You misunderstand the metric expansion of space. It does not require the creation of new empty space time. The expansion is happening because of the Big Bang. Things are still flying apart because of it. They are getting further apart accordingly so the distance between them is growing, but the space between them is empty, nothing needs to be created to fill it.

Where Dark Energy comes in is, although we know why space is expanding, the expansion should be slowing down due to the gravitational attraction of everything we can see. It isn’t, it’s speeding up. Dark Energy is the postulated cause of this, although like Dark Matter we so far have been unable to detect it or fit it into our existing models for the fundamental building blocks of physics. I.e. we have no idea what form it takes.

[Absolute_Zero]

Zip, it's the BBC iPlayer - no adverts beyond the self-promotional kind.

It is unclear what relation, if any, exists between dark energy and inflation. Even after inflationary models became accepted, the cosmological constant was thought to be irrelevant to the current universe.

https://en.wikipedia.org/wiki/Dark_energy

[gumboot]

You misunderstand the metric expansion of space. It does not require the creation of new empty space time. The expansion is happening because of the Big Bang. Things are still flying apart because of it. They are getting further apart accordingly so the distance between them is growing, but the space between them is empty, nothing needs to be created to fill it.

If the expansion of space were just momentum and not the insertion of extra space, then wouldn't that circle right back to leaving "how can the observable universe be larger than the radius of the wavefront of the big bang?" unanswered?

[zip accident]

You misunderstand the metric expansion of space. It does not require the creation of new empty space time. The expansion is happening because of the Big Bang. Things are still flying apart because of it. They are getting further apart accordingly so the distance between them is growing, but the space between them is empty, nothing needs to be created to fill it.

If the expansion of space were just momentum and not the insertion of extra space, then wouldn't that circle right back to leaving "how can the observable universe be larger than the (diameter?) of the wavefront of the big bang?" unanswered?

That's my problem expressed nicely.

[Darkflame]

My understanding of current theory is certainly the big bang caused a expansion in space itself, not merely in matter.
We are all on a 3d surface of a metaphorical 4d balloon which is expanding. We can tell this partly because it looks like everything is moving away from everything else - it isn't all moving away from one central point.

Certainly it would be much easier and nicer to comprehend if it was just matter in space moving. Much like it would be nicer if time dilation was just about the observed time of clocks, rather then the real duration experienced changing. Doesn't match measurements though. The universe is weird.

[pogo]

You misunderstand the metric expansion of space. It does not require the creation of new empty space time. The expansion is happening because of the Big Bang. Things are still flying apart because of it. They are getting further apart accordingly so the distance between them is growing, but the space between them is empty, nothing needs to be created to fill it.

If the expansion of space were just momentum and not the insertion of extra space, then wouldn't that circle right back to leaving "how can the observable universe be larger than the radius of the wavefront of the big bang?" unanswered?

One reason is the metric expansion of space is not limited by the speed of light. Another is there is no such thing as “the wavefront of the big bang” out there. The observable universe keeps growing but not because of any physical change in the universe. It’s just that over time more and more light reaches us from further and further away.

[gumboot]

You misunderstand the metric expansion of space. It does not require the creation of new empty space time. The expansion is happening because of the Big Bang. Things are still flying apart because of it. They are getting further apart accordingly so the distance between them is growing, but the space between them is empty, nothing needs to be created to fill it.

If the expansion of space were just momentum and not the insertion of extra space, then wouldn't that circle right back to leaving "how can the observable universe be larger than the radius of the wavefront of the big bang?" unanswered?

One reason is the metric expansion of space is not limited by the speed of light.

You just said that things are "still flying apart", and that this does not involve the insertion of extra spacetime, and now you say they way in which they're doing this is not limited by the speed of light. So now we have things moving relative to each other at greater than the speed of light and we no longer have the insertion of extra spacetime to reconcile this...

So you're saying that the speed of light is not a fundamental limit, then?

[pogo]

It’s a [local] limit on how fast things can move in space, not a limit on the universe itself. The observable universe is by definition the things we can see. And as the universe is only 13.8 Bn years old, it means the observable universe is no more than 13.8 Bn light years round. But the universe is thought to be much bigger than this.