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_Pax._
http://www.washingtonpost.com/business/tec...ry.html?hpid=z1

Yeah. Widescale, publicly-accessible WiFi networking. Welcome to, uh, 2065-ish ...?
Lionhearted
*Smirk*
Technology, it's moving faster then people are willing to admit. I tell people that in 5 to 10 years you'll have fully integrated AR displays in your contacts or glasses, in 10 you're going to have tactile feedback AR control over these devices and I'll be sitting in a park playing AR chess with some guy on the other side of the planet.
For some reason that always blows peoples mind, make them think Im crazy or they simply don't believe it...
_Pax._
Personally, I would double those timeframes, as far as "significant market penetration" goes. But for early adopters? Hell, yes.
Draco18s
QUOTE (Lionhearted @ Feb 4 2013, 12:43 PM) *
For some reason that always blows peoples mind, make them think Im crazy or they simply don't believe it...


And I tell people that our odds (as a species) colonizing a planet outside our solar system is 0, they look at me funny.

We'd need to violate the laws of physics to get a ship from here to there in anything measuring a reasonable time frame (i.e. faster than light).* Hell, the "wait calculation" on how soon we could get a ship out Barnard's Star (a mere 6 light years away) is 1104 years. And that doesn't account for things like nuking ourselves back to the stone age and assumes that we not only solve the problem of "speed" but also "how to survive interstellar radiation" or "how to survive/avoid collisions with interstellar material at high speed."

*Protip: habitable planets haven't been located in our galactic neighbors. The nearest one is 12 light years away...if you don't mind living in 158 degree weather. Or -40. The nearest mesoplanet (that is, one with a surface temperature near earth's) is 22 light years away.
Lionhearted
Europa (the moon!) ain't that bad if you look for prospect colonisation...
Draco18s
QUOTE (Lionhearted @ Feb 4 2013, 02:32 PM) *
Europa (the moon!) ain't that bad if you look for prospect colonisation...


Europa's not extrasolar. wink.gif
Lionhearted
No, but there's "habitable" worlds within our galactic neighbourhood... Well, she's gonna need a lot of work, eventually habitable.
_Pax._
Really, extrasolar colonisation will only be possible if we can either:

A) sidestep the laws of physics (the "Warp Speed" solution)
B) figure out workable cryogenics (the "Sleeper Ship" solution
C) figure out how to create and manage a self-sustaining environment that will last on the order of six to eight thousand years, and also how to create and sustain a self-balancing cultural order, in order to send out "generation ships"

I think C is more likely to be attempted, but I can't say whether it's more likely to succeed. I expect a trip on the order of 20 to 30 lighty-years will take as long as the whole of recorded human history ... at which point, presuming the "crew" haven't self-destructed themselves somehow ... I have no fucking clue what kind of people will arrive at their new world, nor if they'll even be interested in debarkign their perfect, sustainable world at all, anymore.
Lionhearted
d) Become immortal and go on one hell of a field trip.
e) Send the robots in our stead (currently a popular idea)
Draco18s
QUOTE (_Pax._ @ Feb 4 2013, 03:11 PM) *
Really, extrasolar colonisation will only be possible if we can:
(a) sidestep the laws of physics


Unlikely. The closest is the Alcubierre Drive, which may or may not cause utter annihilation of the destination with super-high energy gamma radiation when it decelerates.

QUOTE
(b) figure out workable cryogenics


Unlikely. There is an issue of "heating something back up again" ("flash heating") without outright searing the outside.
Not to mention all those electrochemical processes that aren't suspended when meat freezes. You'd have to find a way to jumpstart the brain and hope that permanent damage hasn't happened.

QUOTE
figure out how to create and manage a self-sustaining environment that will last on the order of six to eight thousand years, and also how to create and sustain a self-balancing cultural order, in order to send out "generation ships"


Technologically feasible, but unlikely. Someone will be a dick and throw the entire balance out of whack. And it wouldn't even necessarily be intentional or even noticed for several hundred years ("Your great-times-twenty grandfather borrowed a flashlight to read in bed after Lights Out when he was 8, and the extra drain on our resources was multiplied over the last 500 years and now there isn't enough power to adequately illuminate hydroponics. And that's why we are on strict reduced rations.").

QUOTE
I think C is more likely to be attempted, but I can't say whether it's more likely to succeed. I expect a trip on the order of 20 to 30 lighty-years will take as long as the whole of recorded human history ... at which point, presuming the "crew" haven't self-destructed themselves somehow ... I have no fucking clue what kind of people will arrive at their new world, nor if they'll even be interested in debarkign their perfect, sustainable world at all, anymore.


Getting to Bernard's Star (only 6 light years) assuming we could build a ship that is tied for "the fastest man made thing"* would take 19,000 years (over 6 times the duration of recorded history) to get there. Getting to the nearest "almost habitable planet" would take twice that.

*70,220 km/s, the Helios 2 star probe.
_Pax._
QUOTE (Lionhearted @ Feb 4 2013, 03:14 PM) *
d) Become immortal and go on one hell of a field trip.
e) Send the robots in our stead (currently a popular idea)


F) just like E, but with artificial wombs and stored genetic material for a few thousand species. Robots spend a few thousand years terraforming, then start popping out vat-grown babies ...
G) figure out how to upload/download human identities/personalities/memories, including into cloned bodies. Send a ship with clone-growing banks and a lot of memory storage ...



... though G is more like a variant of B, just with cloning and pseudo-AI mind storage, instead of cryogenics.
Draco18s
QUOTE (Lionhearted @ Feb 4 2013, 03:14 PM) *
d) Become immortal and go on one hell of a field trip.


Unlikely due to various constraints. Immunity to aging isn't a biological problem, but you're still left with the other issues: surviving in the vacuum of space for thousands of years.

QUOTE
e) Send the robots in our stead (currently a popular idea)


Possible, but not really the same thing as "colonizing."

QUOTE (_Pax._ @ Feb 4 2013, 03:20 PM) *
F) just like E, but with artificial wombs and stored genetic material for a few thousand species. Robots spend a few thousand years terraforming, then start popping out vat-grown babies ...


Technically viable. But there are issues with that, e.g. protecting that DNA from radiation. Not to mention hardware and software failures of all kinds (how do you even go about debugging a terraforming program?)

QUOTE
G) figure out how to upload/download human identities/personalities/memories, including into cloned bodies. Send a ship with clone-growing banks and a lot of memory storage ...


Unlikely, due to the computational complexity of the brain. Our brains are parallel processors, doing all calculations simultaneously. Computers are...less so.
Lionhearted
Draco, the alcubierre also require you to attain negative mass... Whatever the hell that means...
and exotic material containing more energy then the known universe to the power of ludicrous.
Worm holes seem plausible in comparison
_Pax._
QUOTE (Draco18s @ Feb 4 2013, 03:19 PM) *
Getting to Bernard's Star (only 6 light years) assuming we could build a ship that is tied for "the fastest man made thing"* would take 19,000 years (over 6 times the duration of recorded history) to get there. Getting to the nearest "almost habitable planet" would take twice that.


Except it wouldn't be tied. It would be much much faster.

See, what you need is a propulsion system that doesn't rely on chucking gigantic quantities of reaction-mass out the back end, in order to accelerate. Something like, say ... a really big, efficient laser. Sure, sure, maybe it only accelerates you at .01G. But it does that for four thousand years straight - before flipping the ship end-over-end, and spendign the second half of the journey decelerating at the same speed.

Truly the biggest hurdles for a generation ship are:
  • crafting an indefinitely self-sustaining ecosystem that provides food, air, and clean(able) water for the human population (at least 1 thousand to begin with, and growing the whole time);
  • devising an energy source whose fuel can last AT LEAST 150% as long as you expect the trip to take, without the need to refuel en route;
  • devising a system to provide absolute protection from radiation, at LEAST as well as the Earth itself does;
  • devising a system to provide protection from collisions, including with micrometeorite scale objects, while travelling at absolutely immense speeds;
  • devising a cultural/social model that is sustanable and scalable, across a journey at least 50% longer than the projected trip duration;
  • figuring out how to build something that will probably be at least a quarter the size of the frelling moon, AND move the whole thing without structural failures
  • Solving the problem of having the same structure and machines continue functioning for six or eight or ten thousand years, without being able to pull into a garage for a tuneup ... and without any spare parts beyond those you brought with you!


...

...

As for the (A) option, one option that combines somewhat with a generation-ship model is: if we can find a way to artificially generate gravity. Then you can make something like Alan Dean Foster's "KK drive": you generate a gravity well ahead of your ship, possibly an intense one ... either in a position locked relative to the generator(s), or, in a "flicker" pattern, constantly creating a new gravity well ahead of you, as the old one fades out of existance. Being able to steadily, forever, without expelling reaction mass, accelerate at just 5G or 10G, in a way that doesn't create torsional stress on your spaceframe ... well, let me tell you, that can achieve some INSANE velocities.

You'd still need all of the things Ilisted above - but your journey could be much, MUCH shorter. Which means, less need for spar parts, spare consumables, redundancies, and so on. And fewer generations of cultural drift, too!
_Pax._
QUOTE (Draco18s @ Feb 4 2013, 03:33 PM) *
(how do you even go about debugging a terraforming program?)

Test it out in intrasolar space. Because, hey look, MARS.

If the robots can do that without intervention, I think we can trust it to work elsewhere, with reasonable chances of success.
Lionhearted
I think I heard something about creating microgravities by having sectional rotating components...
Also Mars, lol
Draco18s
QUOTE (_Pax._ @ Feb 4 2013, 03:37 PM) *
See, what you need is a propulsion system that doesn't rely on chucking gigantic quantities of reaction-mass out the back end, in order to accelerate. Something like, say ... a really big, efficient laser. Sure, sure, maybe it only accelerates you at .01G. But it does that for four thousand years straight - before flipping the ship end-over-end, and spendign the second half of the journey decelerating at the same speed.


4000 years at 0.01G is too far. 82,400 light years too far (that's before decelerating).
(Note: this acceleration gets us up to 0.04c in 4,000 years, the below link performs the math on a solar sail ship, which has a maximum speed of 0.04c after infinite time)

However, I doubt one could sustain an acceleration of 0.01G for that long. Much less carry all of the fuel necessary to power said laser.

Feel free to work out the math for yourself
_Pax._
Fuel/power WOULD be the issue. But a M/AM power source might be able to pull it off. Or if interstellar hydrogen is plentiful enough, a bussard-like scoop to sustain a fusion plant (one capable of fusing more than merely hydrogen - perhaps going all the way up to things like thorium and such, that can then be used in old-fashioned fission reactors ...)



As for being too far - that all depends on how far you have to go, right?
Draco18s
QUOTE (_Pax._ @ Feb 4 2013, 04:04 PM) *
Fuel/power WOULD be the issue. But a M/AM power source might be able to pull it off. Or if interstellar hydrogen is plentiful enough, a bussard-like scoop to sustain a fusion plant (one capable of fusing more than merely hydrogen - perhaps going all the way up to things like thorium and such, that can then be used in old-fashioned fission reactors ...)


M/AM: possibly.

Bussard-Ram wouldn't work in reverse (to decelerate).
_Pax._
QUOTE
Bussard-Ram wouldn't work in reverse (to decelerate).


That depends on how the ram works in the first place. Also, on how the propulsion system can be aimed. If you have the ability to flip the propulsive component of your ram-and-laser setup around, then the ram still faces forward. Heck, at that point, the act of scooping up more interstellar gas, would itself help decelerate you (since that effect on your own inertia would no longer be working against your efforts, but instead, be owrking with it).

Let's say the laser puts out ... oh, a more sane number: 0.00000125G of "push", and the rams produce 0.00000025G of "push". While accelerating, your net thrust is 0.0001G: subtract the Ram force from the Laser force. But your deceleration instead adds the two, for 0.0000015G of force. You accelerate for 2/3 of the trip, then decelerate for 1/3 of it.

I'm not up to doing the math myself (honestly, it makes my head swim just to try and figure those equations out - it's been a quarter century since I was in highschool, even!!), to know how long it would take to travel, say, 20, 40, 100, or 200 lightyears, with those numbers: 2/3 time-to-target at 0.0000010 gravities acceleration, then 1/3 time-to-target at -0.0000015 gravities deceleration.

But ... 0.000001 gravities is 0.0000098m/sec. Close enough to call it 0.00001m/sec ... so slow, you could out-WALK the thing for months, if not years, of it being in operation. Nonetheless, one year is ... well, 365.25x24x60x60 = 31,557,600 seconds, so, our velocity should be ... 3,155.76 meters per second, about 0.015c; even allowing for dilation effects, you should be able to hit 0.05c within ten or twenty years.

Now, sure, sure. At that speed, even instantly accelerating from a dead stop (HA!), it would take 300 years of ship-time to go ~15 light years to reach that mesoplanet. But, you know? That's still a damned sight better than two to three thousand years.
Draco18s
QUOTE (_Pax._ @ Feb 4 2013, 04:28 PM) *
Nonetheless, one year is ... well, 365.25x24x60x60 = 31,557,600 seconds, so, our velocity should be ... 3,155.76 meters per second, about 0.015c; even allowing for dilation effects, you should be able to hit 0.05c within ten or twenty years.


1) I already did the math that 0.01G of acceleration gets up to 0.04c in 4 thousand years, there's no way in hell 0.0001G hits that in 10 or 20 years.

2) 3,155.76 meters per second is not "about 0.015c." You forgot about 3 extra zeros. The number you're looking for is 0.0000105c

3) Your total distance after 1 year is 6.4 * 10^-7 light years. After 100 years, you've gone 0.006 ly. Even a full 1000 years you've only gone 0.64 ly.*

*This math is easy: distance in meters = 1/2(acceleration in m/s)(time in seconds, squared). Tip: a light year is 9,460,730,472,580,800 meters (exactly) using a year of 365.25 days.
_Pax._
QUOTE (Draco18s @ Feb 4 2013, 04:33 PM) *
1) I already did the math that 0.01G of acceleration gets up to 0.04c in 4 thousand years, there's no way in hell 0.0001G hits that in 10 or 20 years.

I did say "back of napkin" math.

QUOTE
2) 3,155.76 meters per second is not "about 0.015c." You forgot about 3 extra zeros. The number you're looking for is 0.0000105c

Yes, I made an order-of-magnitude error when I cut my postulated acceleration by those exact orders of magnitude. Oops.

So, yes, it will take a lot longer to "get up to speed". Again, "oops".
Draco18s
QUOTE (_Pax._ @ Feb 4 2013, 04:47 PM) *
I did say "back of napkin" math.

Yes, I made an order-of-magnitude error when I cut my postulated acceleration by those exact orders of magnitude. Oops.

So, yes, it will take a lot longer to "get up to speed". Again, "oops".


Should have been a clue that you were off. wink.gif

Also: math is fun biggrin.gif
Anything solvable with math is fun to calculate, which is why I found out that a roleplaying character of mine (not Shadowrun) is the direct ancestor of the entirety of the world's population of his species (because hooray time travel and genetic intermingling).
Lionhearted
Funny how this came from a supposed matrix thread...
Suffice to say space is huge, like ridiculously huge, like gigantically unfathomably ridiculously huge...
Draco18s
QUOTE (Lionhearted @ Feb 4 2013, 05:58 PM) *
Funny how this came from a supposed matrix thread...
Suffice to say space is huge, like ridiculously huge, like gigantically unfathomably ridiculously huge...


Yup.

(Fun activity: find a number larger than the observable universe* by orders of magnitude)

*Or its number of sub-atomic particles.
Sengir
QUOTE (Draco18s @ Feb 4 2013, 09:19 PM) *
Unlikely. There is an issue of "heating something back up again" ("flash heating") without outright searing the outside.
Not to mention all those electrochemical processes that aren't suspended when meat freezes. You'd have to find a way to jumpstart the brain and hope that permanent damage hasn't happened.

First of all, you'd have to find a way for freezing a body without destroying the cells, to say nothing of sub-celluar structures like dendrites. The best current science can do is preserving small samples of single tissue types. Really, cryonics is nothing more than Ancient Egypt mummification.

Anyway, BTT: How exactly is that idea different from current technologies like HSPDA? Free access would be something new, sure, but that has nothing to do with the technology...
nezumi
QUOTE (Draco18s @ Feb 4 2013, 03:33 PM) *
Unlikely, due to the computational complexity of the brain. Our brains are parallel processors, doing all calculations simultaneously. Computers are...less so.


I don't think even YOU believe this is a serious hurdle. Sure, we can't do it in 2013, probably not even in 2020, but 2060?

We know it's possible to build a computer that can run a human mind because we have physical samples. They're called brains.

The issue is not 'can it be done', but rather, 'can we make one which accepts our choice of power, that can be reinforced against new environmental conditions, and can enable more efficient data transfer'.

We also don't need to reach the full speed of the human brain. It's a 7,000 year journey. What's the rush? A computer that hosts a human mind, but runs one hundredth of the speed will be quite sufficient, if augmented with AIs and other tools.
Draco18s
QUOTE (nezumi @ Feb 5 2013, 10:00 AM) *
We also don't need to reach the full speed of the human brain. It's a 7,000 year journey. What's the rush? A computer that hosts a human mind, but runs one hundredth of the speed will be quite sufficient, if augmented with AIs and other tools.


Can we do it eventually? Yes.

Technically we can do it today if you don't mind the 2.5 hour wait time per millisecond of actual brain-time.

But that's just the brain. It's not dealing with things like personality, emotions, creativity, etc. etc.
Halinn
QUOTE (Draco18s @ Feb 5 2013, 04:56 AM) *
(Fun activity: find a number larger than the observable universe* by orders of magnitude)

*Or its number of sub-atomic particles.


Graham's Number. Easy.
Draco18s
QUOTE (Halinn @ Feb 5 2013, 02:53 PM) *
Graham's Number. Easy.


Now name a bigger number using fewer characters.
(That is, fewer characters than it takes to represent what Graham's Number is without typing "g-r-a-h-a-m-'-s-n-u-m-b-e-r," because merely writing Graham's Number in Knuth up-arrow notation takes more characters than particles in the universe.)

Do that, and I'll name a number so large that it cannot be computed.
(Graham's Number is large, but computable, that is, a computer with infinite time and infinite memory could eventually arrive at the exact value)
_Pax._
QUOTE (Draco18s @ Feb 5 2013, 03:16 PM) *
Now name a bigger number using fewer characters.
(That is, fewer characters than it takes to represent what Graham's Number is without typing "g-r-a-h-a-m-'-s-n-u-m-b-e-r," because merely writing Graham's Number in Knuth up-arrow notation takes more characters than particles in the universe.)


(∞^∞)^∞

What do I win?
Draco18s
QUOTE (_Pax._ @ Feb 5 2013, 03:21 PM) *
(∞^∞)^∞

What do I win?


An F, because infinity isn't a number.

However, here's my impossibly large number:

BB(BB(100))

Where BB(n) is a function that returns the maximum number of steps a Turing machine can take and still halt (i.e. not run infinitely) given that the machine has n rules.

Protip: BB(12) is greater than Graham's Number.
Lionhearted
Draco... Isn't that probable infinity, just like pi?
Draco18s
QUOTE (Lionhearted @ Feb 5 2013, 03:41 PM) *
Draco... Isn't that probable infinity, just like pi?


Pi is not infinite. It just has an infinite number of digits. The value of pi, itself, is quite finite.

Graham's Number on the other hand, has a finite number of digits and finite value.

Busy Beaver numbers are like Graham's Number, but cannot be computed, because it would take a function capable of solving the halting problem. Which, by definition, can't exist.*

While non-computable, they are still finite (if unknown).

Funfact: if such a computer could be built to solve the halting problem it could not solve its own halting problem. Thus we can give that machine a Busy Beaver function, BB2(n). And so on, for even more complex and powerful machines.

Leading to a new, largest number formats, such as:

BBBB(100)(BB(100))

And similar.

*Assume some function f(n) which takes a program as input. If n runs forever, return false, else return true.

Do this:

function loop() {
if(f(loop)) {
loop()
}
else {
return;
}
}

If "loop" runs forever, quit. Else run forever.
Lionhearted
So... Can this be solved or not, or can it be solved in theory but not computed?
If so can you estimate the value?
Were good at estimates... Yes we are.

*nods and smiles* This is the part where I try to look pretty and attentive when I really understand bugger all...
Me and numbers... Don't mesh very well.
Draco18s
QUOTE (Lionhearted @ Feb 5 2013, 03:54 PM) *
So... Can this be solved or not, or can it be solved in theory but not computed?
If so can you estimate the value?


Given that the (estimated) value of BB(12) exceeds Graham's Number* I cannot provide an estimate for BB(100) much less passing the value of that back into the BB() function itself.

Suffice to say, that if every plank-volume of the known universe were used to store a decimal value, and that this memory space was used to hold the number of digits of the estimated value, there wouldn't be enough room. In fact, I'm not even sure that'd be enough space to hold the number of digits of that value.**

* http://en.wikipedia.org/wiki/Busy_beaver#Known_values

** Knuth-Plank-Volume-Notation?
Halinn
QUOTE (Draco18s @ Feb 5 2013, 09:22 PM) *
BB(BB(100))

BB(BB(xkcd number))
Sengir
QUOTE (Lionhearted @ Feb 5 2013, 09:54 PM) *
So... Can this be solved or not, or can it be solved in theory but not computed?

The halting problem is proven to be undecidable. In layman's terms, the halting program is about creating a program which takes an arbitrary program as input and outputs whether the program runs into an endless loop or not, and it can be proven that such a program cannot exist.
Mystweaver
You guys are are so easily side tracked!

This topic started as a reference to "the wireless matrix" where over in the states, the FCC is considering opening up a wavelength for communal access of wi-fi enabled devices (whether this is your PC, tablet, TV, microwave, dishwasher, CCTV system or whatever).

Somehow this got immediately changed to the colonization of planets outside our solar system (couldn't see the like for this jump).

Now you are chatting about semantics of which ma thematic numbers are actually infinite or not and whether it is feasible to record and remap the human brain into a clone.

All very interesting I have to admit, but never-the-less rather off topic.

By all means continue. I am finding it all quite fascinating smile.gif
Draco18s
QUOTE (Halinn @ Feb 5 2013, 05:46 PM) *
BB(BB(xkcd number))


As the Busy Beaver numbers grows faster than any computational equation, BB(BB(BB(100))) will be larger still (probably).

BBBB(100)(BB(100)) is definitely larger.
Eisen
QUOTE (Draco18s @ Feb 4 2013, 05:33 PM) *
1) I already did the math that 0.01G of acceleration gets up to 0.04c in 4 thousand years, there's no way in hell 0.0001G hits that in 10 or 20 years.

2) 3,155.76 meters per second is not "about 0.015c." You forgot about 3 extra zeros. The number you're looking for is 0.0000105c

3) Your total distance after 1 year is 6.4 * 10^-7 light years. After 100 years, you've gone 0.006 ly. Even a full 1000 years you've only gone 0.64 ly.*

*This math is easy: distance in meters = 1/2(acceleration in m/s)(time in seconds, squared). Tip: a light year is 9,460,730,472,580,800 meters (exactly) using a year of 365.25 days.


His first idea was right. The math was a bit off.

9.8 m/s * .01 * (60 *60 * 24 * 365 = 31,104,000 s) = 3,048,192 m/s at 1 year. That is .010168 % LS. Somehow you're dividing by an extra 1000.
Accelerate at 1/10 m/s^2 for 31 million seconds, and you will be going a tad over 3 million m/s, not 3000 m/s.
Draco18s
QUOTE (Eisen @ Feb 5 2013, 09:49 PM) *
His first idea was right. The math was a bit off.

9.8 m/s * .01 * (math)


That's for 0.01G, which was my post.

His was 0.0001G
Halinn
QUOTE (Draco18s @ Feb 6 2013, 02:02 AM) *
As the Busy Beaver numbers grows faster than any computational equation, BB(BB(BB(100))) will be larger still (probably).

BBBB(100)(BB(100)) is definitely larger.

I'm not about to get into a full-on big number game, but you might enjoy this thread from the xkcd forums. It's only supposed to deal with computable numbers, but I can tell you that I stopped being able to follow it after a couple of pages.
Draco18s
QUOTE (Halinn @ Feb 6 2013, 08:02 AM) *
I'm not about to get into a full-on big number game, but you might enjoy this thread from the xkcd forums. It's only supposed to deal with computable numbers, but I can tell you that I stopped being able to follow it after a couple of pages.


The Busy Beaver sequence is non-computable and grows faster than any computable sequence. It's even been proven to be non-computable.

But yes. Large number functions in that thread boggle my mind. I can only categorize them into Ackerman Sequences of large size (and the ones where people failed to realize just how big some of the previous numbers were).
Halinn
QUOTE (Draco18s @ Feb 6 2013, 02:25 PM) *
The Busy Beaver sequence is non-computable and grows faster than any computable sequence. It's even been proven to be non-computable.

I know. It was just a disclaimer for the thread. I'd wager that some of the insane functions they defined in that thread are quite a lot larger than BBBB(100)(BB(100)), but I'm not well enough into mathematics to be sure.
Draco18s
QUOTE (Halinn @ Feb 6 2013, 09:11 AM) *
I know. It was just a disclaimer for the thread. I'd wager that some of the insane functions they defined in that thread are quite a lot larger than BBBB(100)(BB(100)), but I'm not well enough into mathematics to be sure.


Given that there is no estimate for BB2(2), there's no real way to be sure. Remember, that's the maximum number of steps a computer capable of solving the halting problem (for a standard Turing machine*) can take, if it has 2 rules.

*That is, it is a Turing machine capable of computing BB(n)
Lionhearted
Can't... resist... any... longer!
NERDS!
Draco18s
QUOTE (Lionhearted @ Feb 6 2013, 09:36 AM) *
Can't... resist... any... longer!
NERDS!


Yes. And?

Edit:

Blew a hole in one of the reigning champion numbers from page 4. Not sure if it had been pointed out in a later post (between 5 and 31, inclusive) as there are a lot of pages.
http://forums.xkcd.com/viewtopic.php?f=14&...268418#p3268418
Lionhearted
Embrace it? nyahnyah.gif
Draco18s
QUOTE (Lionhearted @ Feb 6 2013, 09:47 AM) *
Embrace it? nyahnyah.gif


I cast magic spells program computers for a living. wink.gif
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