Principia Discordia

Principia Discordia => Apple Talk => Topic started by: P3nT4gR4m on September 19, 2010, 03:37:58 PM

Title: Attn: Math nerds
Post by: P3nT4gR4m on September 19, 2010, 03:37:58 PM
If one were inclined to do so I believe it would be possible, using this newfangled mathematics I've heard so much about, to calculate the surface area of a sphere with the same radius as the average distance from the earth to the sun (149 million kilometers) and express that as a factor of the surface area of the earth itself (5.1 × 108 km2)

Unfortunately I don't math or I'd know how to work it out myself. Maybe someone here can help? I'd like a serious answer to help with a project I'm currently working on but, in lieu of that, piss-take answers will suffice.

Come on math boffins - impress me!
Title: Re: Attn: Math nerds
Post by: Rumckle on September 19, 2010, 03:52:51 PM
5.47 x 10^8 S

Where S is the surface area of the earth. Assuming your numbers are kosher, I didn't check them.
Title: Re: Attn: Math nerds
Post by: P3nT4gR4m on September 19, 2010, 04:27:11 PM
I don't know what in the fuck you just wrote, you lost me at "^"

Just tell me a number of times, damnit  :argh!: eg. 10 times, 100, times, a million times or whatever
Title: Re: Attn: Math nerds
Post by: Rumckle on September 19, 2010, 04:32:56 PM
10^8 means 10 to the power of 8

in other words, it will be

547 million times the surface area of the earth
Title: Re: Attn: Math nerds
Post by: P3nT4gR4m on September 19, 2010, 04:36:09 PM
Awesome! Thanks for that  :D
Title: Re: Attn: Math nerds
Post by: Rumckle on September 19, 2010, 04:38:11 PM
no probs, may I ask what's it for?
Title: Re: Attn: Math nerds
Post by: P3nT4gR4m on September 19, 2010, 05:09:41 PM
http://i75.photobucket.com/albums/i312/P3nT4gR4m/SolarSystemMk2.jpg (http://i75.photobucket.com/albums/i312/P3nT4gR4m/SolarSystemMk2.jpg)

I've only just started this. It'll get better, honest :oops: The idea is a dyson sphere with another sphere under construction around it. The second sphere has the same radius as the distance from earth to sun and I'll be writing a bit of blurb to go along with it which is why I wanted the numbers.

It also means my scale is off on the inner sphere surface - each hexagon would be about a couple of million times the surface of earth so there's no way you'd see that kind of detail but I think I'll leave it like that cos it makes it look cosier.

X will be where I'm sticking a factory plant collecting the carbon pellets that the planet harvester is firing at it and building a new hexagonal section. Y will be a hex section being fitted into place. I got another 10 or 11 days to finish this, I'll post the finished pic if you're interested.
Title: Re: Attn: Math nerds
Post by: Prince Glittersnatch III on September 19, 2010, 08:41:42 PM
NEEEEERRRRDDDDSSSS  :argh!:
Title: Re: Attn: Math nerds
Post by: Don Coyote on September 19, 2010, 09:03:08 PM
Quote from: Lord Glittersnatch on September 19, 2010, 08:41:42 PM
NEEEEERRRRDDDDSSSS  :argh!:

Geometry be very hard and complex.

BURN THE WITCH!!!!!!!!!!!
Title: Re: Attn: Math nerds
Post by: Rumckle on September 20, 2010, 01:03:46 AM
Quote from: Doktor Vitriol on September 19, 2010, 05:09:41 PM
http://i75.photobucket.com/albums/i312/P3nT4gR4m/SolarSystemMk2.jpg (http://i75.photobucket.com/albums/i312/P3nT4gR4m/SolarSystemMk2.jpg)

I've only just started this. It'll get better, honest :oops: The idea is a dyson sphere with another sphere under construction around it. The second sphere has the same radius as the distance from earth to sun and I'll be writing a bit of blurb to go along with it which is why I wanted the numbers.

It also means my scale is off on the inner sphere surface - each hexagon would be about a couple of million times the surface of earth so there's no way you'd see that kind of detail but I think I'll leave it like that cos it makes it look cosier.

X will be where I'm sticking a factory plant collecting the carbon pellets that the planet harvester is firing at it and building a new hexagonal section. Y will be a hex section being fitted into place. I got another 10 or 11 days to finish this, I'll post the finished pic if you're interested.

Sweet, that's awesome!
Title: Re: Attn: Math nerds
Post by: Requia ☣ on September 20, 2010, 03:00:46 AM
Why would you build a Dyson sphere around a Dyson sphere?   :?
Title: Re: Attn: Math nerds
Post by: P3nT4gR4m on September 20, 2010, 07:23:06 AM
For SCIENCE!  :argh!:
Title: Re: Attn: Math nerds
Post by: Jasper on September 20, 2010, 08:45:34 AM
Quote from: Requia ☣ on September 20, 2010, 03:00:46 AM
Why would you build a Dyson sphere around a Dyson sphere?   :?

I think you mean, why would xzibit write sci-fi?
Title: Re: Attn: Math nerds
Post by: P3nT4gR4m on September 20, 2010, 09:54:24 AM
If you must know it's so they can spin it round and provide day/night cycles.  :sad:
Title: Re: Attn: Math nerds
Post by: Rumckle on September 20, 2010, 10:02:41 AM
Quote from: Doktor Vitriol on September 20, 2010, 09:54:24 AM
If you must know it's so they can spin it round and provide day/night cycles.  :sad:

I think I get it, the outside one isn't actually a Dyson sphere, right? It's just a planet formed to be a sphere. Hence, wanting to know the surface area. That's pretty neat. Though, the energy needed to create gravity would be enormous I'd think.

Is the inside based on images from Google Earth? Or is it just me?
Title: Re: Attn: Math nerds
Post by: P3nT4gR4m on September 20, 2010, 10:16:07 AM
I grabbed the planet surface from nasa but, now I know the actual scale I'm going to have to redo it with satellite views of earth or something. You're right - the secondary sphere isn't a dyson, it's haditation, the exact right distance from the sun for human life to flourish. Gravity I've taken a bit of  liberty with - the hex sections would have to made of some kind of super dense something or other, cos if I had it spinning for centrifugal purposes the habitable are would only be a thin strip along one axis of the sphere. Fuck it - it's thousands of years in the future - they can do things like that then :P
Title: Re: Attn: Math nerds
Post by: Rumckle on September 20, 2010, 10:24:18 AM
Quote from: Doktor Vitriol on September 20, 2010, 10:16:07 AM
Gravity I've taken a bit of  liberty with - the hex sections would have to made of some kind of super dense something or other, cos if I had it spinning for centrifugal purposes the habitable are would only be a thin strip along one axis of the sphere. Fuck it - it's thousands of years in the future - they can do things like that then :P

Actually, no matter how dense the material is, there will be no gravity inside the sphere. But, I'm sure thousands of years in the future they can figure something out.

Also, do you plan on placing the original Earth in the picture?
Title: Re: Attn: Math nerds
Post by: P3nT4gR4m on September 20, 2010, 10:33:47 AM
Quote from: Rumckle on September 20, 2010, 10:24:18 AM
Quote from: Doktor Vitriol on September 20, 2010, 10:16:07 AM
Gravity I've taken a bit of  liberty with - the hex sections would have to made of some kind of super dense something or other, cos if I had it spinning for centrifugal purposes the habitable are would only be a thin strip along one axis of the sphere. Fuck it - it's thousands of years in the future - they can do things like that then :P

Actually, no matter how dense the material is, there will be no gravity inside the sphere. But, I'm sure thousands of years in the future they can figure something out.


Surely if the segments had enough mass? Each segment will weigh a million earths - wouldn't that help?

Quote from: Rumckle on September 20, 2010, 10:24:18 AM
Also, do you plan on placing the original Earth in the picture?

Hadn't really thought about it - I assumed this would be galaxies away.
Title: Re: Attn: Math nerds
Post by: P3nT4gR4m on September 20, 2010, 10:38:48 AM
http://i75.photobucket.com/albums/i312/P3nT4gR4m/57/57.jpg (http://i75.photobucket.com/albums/i312/P3nT4gR4m/57/57.jpg)

blurb mk1 (lemme know if i've fucked up any of these numbers)

QuoteEverything begins with the Dyson Sphere. It takes just a little over two years to cap the star. Once this phase is completed the energy it generates is used to power the whole construction process. Next we begin harvesting planets. Thermonuclear "mole" charges are sent deep into the core of the planet, each one taking up a specific position, to form a cone shaped array of charges which are then detonated in unison. Our carbon factory collects the debris and converts it into pellets of pure carbon, each one with a mass in excess of two hundred and fifty thousand metric tons. These pellets are then fired directly into the Dyson's gravity well and collected there by the habisphere construction plant which turns them into hexagonal habisphere segments, each of which has an inhabitable surface area approximately three point six million times that of the earth.

Once the hex segment is completed it's moved out of orbit and fitted into place in the habisphere where terraforming begins. Our original solar sysem was capable of sustaining around ten billion souls, with energy resources stretched to beaking point. Most of our solar energy was just pouring out into space. A Habisphere can sustain more than five hundred million times that number with an energy supply that is never more than fifteen percent utilised, even at full population. This, ladies and gentlemen, is why we like to refer to our Habispheres as "Solar System 2.0"


We'll be arriving at Habisphere 57 in a few hours. Welcome to your new home!
Title: Re: Attn: Math nerds
Post by: Rumckle on September 20, 2010, 10:41:13 AM
Quote from: Doktor Vitriol on September 20, 2010, 10:33:47 AM
Surely if the segments had enough mass? Each segment will weigh a million earths - wouldn't that help?


No, the gravity from the closest segment would be cancelled out by the gravity of all the other segments. To stop everything on the inside of the shell from floating toward the sun artificial gravity would need to be generated.

(you can read more here, but there is a lot of maths http://en.wikipedia.org/wiki/Shell_theorem )

Quote from: Doktor Vitriol on September 20, 2010, 10:33:47 AM
Hadn't really thought about it - I assumed this would be galaxies away.


Oh right, my bad, I thought that this was our solar system.
Title: Re: Attn: Math nerds
Post by: Rumckle on September 20, 2010, 10:51:11 AM
Quote from: Doktor Vitriol on September 20, 2010, 10:38:48 AM
http://i75.photobucket.com/albums/i312/P3nT4gR4m/57/57.jpg (http://i75.photobucket.com/albums/i312/P3nT4gR4m/57/57.jpg)

blurb mk1 (lemme know if i've fucked up any of these numbers)

QuoteEverything begins with the Dyson Sphere. It takes just a little over two years to cap the star. Once this phase is completed the energy it generates is used to power the whole construction process. Next we begin harvesting planets. Thermonuclear "mole" charges are sent deep into the core of the planet, each one taking up a specific position, to form a cone shaped array of charges which are then detonated in unison. Our carbon factory collects the debris and converts it into pellets of pure carbon, each one with a mass in excess of two hundred and fifty thousand metric tons. These pellets are then fired directly into the Dyson's gravity well and collected there by the habisphere construction plant which turns them into hexagonal habisphere segments, each of which has an inhabitable surface area approximately three point six million times that of the earth.


TBH, this mass seems a bit low, if those are the pellets you can see forming a line into the factory. (Maybe 250 million would be better, that would give the pellet an approx volume of 1km cubed)

Edit:
Other numbers seem good though.
Title: Re: Attn: Math nerds
Post by: P3nT4gR4m on September 20, 2010, 12:59:09 PM
Quote from: Rumckle on September 20, 2010, 10:51:11 AM

TBH, this mass seems a bit low, if those are the pellets you can see forming a line into the factory. (Maybe 250 million would be better, that would give the pellet an approx volume of 1km cubed)

Edit:
Other numbers seem good though.

Cheers! Thas exactly the kind of thing I was after. I guess, gravity wise, I either go with a spinning ring (which I don't like the idea of) or I take artificial gravity as a given.

Title: Re: Attn: Math nerds
Post by: Payne on September 20, 2010, 01:20:02 PM
Quote from: Doktor Vitriol on September 20, 2010, 12:59:09 PM
Quote from: Rumckle on September 20, 2010, 10:51:11 AM

TBH, this mass seems a bit low, if those are the pellets you can see forming a line into the factory. (Maybe 250 million would be better, that would give the pellet an approx volume of 1km cubed)

Edit:
Other numbers seem good though.

Cheers! Thas exactly the kind of thing I was after. I guess, gravity wise, I either go with a spinning ring (which I don't like the idea of) or I take artificial gravity as a given.



Iain M. Banks' (his Sci-Fi moniker) ways of getting around such things in a similarly advanced culture is to allow Mega Computers that have small presence in the "real" world (through ingenious jiggery pokery and fields and such) control things like gravity through similar use of fields. Just an idea, but you can assume if this is galaxies away then certain givens in Physics such as relativity and the seperation of forces (especially gravity) have been resolved or modified in such a way that a computer could manage that for you.

In any case, regardless of your need for a certain level of integrity in the image, the image itself looks purdy even in its unfinished state.
Title: Re: Attn: Math nerds
Post by: Triple Zero on September 20, 2010, 03:39:05 PM
Quote from: Doktor Vitriol on September 20, 2010, 09:54:24 AM
If you must know it's so they can spin it round and provide day/night cycles.  :sad:

You did base this on Larry Niven's Discworld, didn't you? If you didn't you should read it, because they do that exact sort of thing, except with a doube strip (like a belt, and one sort of dotted belt) instead of a sphere. It also contains the exact sort of scifi-wank that you're asking about, in the sense that Larry Niven actually thought out all this shit and made sure the numbers sort worked out (so you could steal them :-P). Plus the book itself aint bad either, I believe it has a zillion sequels, too, but I never read those.
Title: Re: Attn: Math nerds
Post by: Rumckle on September 21, 2010, 09:45:11 AM
Huh, my physics lecturer mentioned Niven in today's lecture (we were discussing Neutron Stars).
Title: Re: Attn: Math nerds
Post by: Don Coyote on September 21, 2010, 03:37:22 PM
Trip you mean Ringworld. Discworld is Terry Pratchett.
Title: Re: Attn: Math nerds
Post by: Triple Zero on September 26, 2010, 03:09:44 PM
yes.
Title: Re: Attn: Math nerds
Post by: P3nT4gR4m on September 26, 2010, 05:40:34 PM
Near enough finished (http://i75.photobucket.com/albums/i312/P3nT4gR4m/57/57-f.jpg)

Some details...

1 (http://i75.photobucket.com/albums/i312/P3nT4gR4m/57/detail1.jpg) 2 (http://i75.photobucket.com/albums/i312/P3nT4gR4m/57/detail2.jpg) 3 (http://i75.photobucket.com/albums/i312/P3nT4gR4m/57/detail3.jpg)
Title: Re: Attn: Math nerds
Post by: Fredfredly ⊂(◉‿◉)つ on September 26, 2010, 07:02:16 PM
i keep reading this thread as Meth Nerds  :sad:
Title: Re: Attn: Math nerds
Post by: Triple Zero on September 26, 2010, 11:53:55 PM
Quote from: Doktor Vitriol on September 26, 2010, 05:40:34 PM
Near enough finished (http://i75.photobucket.com/albums/i312/P3nT4gR4m/57/57-f.jpg)

Some details...

1 (http://i75.photobucket.com/albums/i312/P3nT4gR4m/57/detail1.jpg) 2 (http://i75.photobucket.com/albums/i312/P3nT4gR4m/57/detail2.jpg) 3 (http://i75.photobucket.com/albums/i312/P3nT4gR4m/57/detail3.jpg)

AWESOME SHIT P3NT!! :mittens:

tiny bit of criticism: I think the woman's head in the main picture might be slightly too bright, still?
Title: Re: Attn: Math nerds
Post by: Rumckle on September 27, 2010, 01:55:48 AM
Sweet!

:mittens:
Title: Re: Attn: Math nerds
Post by: Telarus on September 27, 2010, 08:11:27 AM
Sweet.

I agree with Trip that the woman's face is a bit bright.

Tips if you're using photoshop:

Create a "Levels adjustment layer", drag to one layer above the woman. Hold CTRL and click on the line between the two layers (in the layer palette). This "attaches" the adjustment layer to the one below it (so it only affects that layer). Use the middle slider (Gamma) to adjust the brightness of the woman only. (Nudging it to the right will darken the layer, nudging it left will brighten it).

Looking forward to the finished pic.
Title: Re: Attn: Math nerds
Post by: P3nT4gR4m on September 27, 2010, 10:11:03 AM
Quote from: Telarus on September 27, 2010, 08:11:27 AM
Sweet.

I agree with Trip that the woman's face is a bit bright.

Tips if you're using photoshop:

Create a "Levels adjustment layer", drag to one layer above the woman. Hold CTRL and click on the line between the two layers (in the layer palette). This "attaches" the adjustment layer to the one below it (so it only affects that layer). Use the middle slider (Gamma) to adjust the brightness of the woman only. (Nudging it to the right will darken the layer, nudging it left will brighten it).

Looking forward to the finished pic.

I used a similar approach to darken her down so I can tweak the slider if you think she needs it. Something else you might be interested in is how I got the blue and orange backlighting. Using a levels adjustment for each I first messed about with the individual RGB levels until I had a colour I liked then click on the adjustment layer mask and hit CTRL+I to turn it completely black. Then, with the layer mask still selected, spray white on the places you want to light - if you go too far swap brush colour for black and spray over the bit you want taken away.
Title: Re: Attn: Math nerds
Post by: Telarus on September 27, 2010, 11:03:24 AM
Nice. Masks are fun!

Edit: Oh, I think I know what's making me think she's too bright. The [rocket/exhaust] from the factory in the lower left are dim blue-ish compared to her face, a couple of the stars in the background, and the bright yellow in the upper left. If you brighten those [rocket/exhaust] up that should even the image out.
Title: Re: Attn: Math nerds
Post by: P3nT4gR4m on September 27, 2010, 11:50:17 AM
You've nailed it - the engine glow! I knew there was something wrong down there but I was pretty sure it wasn't the girl. That engine glow will totally balance it. Cheers man, you're a lifesaver!

And yeah - masks rule! For unbelievable control over contrast try this trick - make two levels adjustment layers - one for highlight and one for shadow take a copy of your main image and convert it to black and white. now copy and paste the black and white copy into the adjustment layer masks (ctrl + click on the mask to paste directly in there) and invert the one that's for shadows.

Now tweak the highlight and shadow adjustments to your hearts content and rejoice in how much control you have over the end result!

Title: Re: Attn: Math nerds
Post by: Telarus on September 28, 2010, 02:07:12 AM
Quote from: Doktor Vitriol on September 27, 2010, 11:50:17 AM
You've nailed it - the engine glow! I knew there was something wrong down there but I was pretty sure it wasn't the girl. That engine glow will totally balance it. Cheers man, you're a lifesaver!

And yeah - masks rule! For unbelievable control over contrast try this trick - make two levels adjustment layers - one for highlight and one for shadow take a copy of your main image and convert it to black and white. now copy and paste the black and white copy into the adjustment layer masks (ctrl + click on the mask to paste directly in there) and invert the one that's for shadows.

Now tweak the highlight and shadow adjustments to your hearts content and rejoice in how much control you have over the end result!

That is fucking sweet.