Exponential Assembly Top Down Nano

NanotechNews.com writes: "The article describes a new milestone in the Top Down nanotechnology process: "Exponential assembly is a manufacturing architecture starting with a single tiny robotic arm on a surface. This first robotic arm makes a second robotic arm on a facing surface by picking up miniature parts ? carefully laid out in advance in exactly the right locations so the tiny robotic arm can find them ? and assembling them. This is an exponential growth rate, hence the name exponential assembly." Standard MEMS, the largest independent high-volume manufacturer of Micro Electro Mechanical Systems and Zyvex created a partnership, the second article available here. This partnership could lead to a better assembling technology in MEMS and the Top-Down Nanotechnology and Nanolithography."

Comments

finally

[vkt-tje]

finally nanothech for real!!

dns style?

[zencode]

what i want to know is, ...does each arm have the knowledge - independant of each other or something else - of how to complete it's job.

My .02,

Re:dns style?

[fantom_winter]

what i want to know is, ...does each arm have the knowledge - independant of each other or something else - of how to complete it's job. I imagine so. Knowledge can be represented in numerous ways. certainly mechanical knowledge is a good example of this. like a can opener may have the "knowledge" of how to open a can, mechanically at least.

Re:dns style?

[caffeinated_bunsen]

Nope. From the article:

Externally provided power and computer control would make all the robotic arms on a surface operate synchronously and in parallel.

Reading the article usually helps.

MEMS - to - Nano

[Schwarzchild]

Pretty cool. Up until now I thought these were two totally separate fields. Looks like they are using MEMS technology to reach the nanoscale.

Hitchhiker's Guide was there first

[devphil]

Anybody else remember that scene in Mostly Harmless where Ford Prefect breaks down the door to the head editor's office?

There are little nanotech bots in the doorframe whose sole purpose in life is to wait until this happens. Then they crawl out of the frame, assemble each other into larger bots, rebuild the door, disassemble each other, crawl back into frame, and wait...

Anyhow, I know some people working with MEMS. Very cool stuff.

Re:Hitchhiker's Guide was there first

[grammar nazi]

Hitchhiker's Guide takes place in the future. Thus, it can't be first. It may even be last, since, by then the earth is long since demolished (before being put back together).

Please take note of this and correct it in all future nanotech related comments.

What I've always heard about nanotech is that the main idea is that the robots are self-replicating. The example that frequently comes up is one where you put a few robots into a vat of liquid raw materials (a.k.a. molten metal) and they start creating more robots. Eventually when there are enough nano-bots, all of them manufacture an automobile.

Re:Hitchhiker's Guide was there first

[cyberdonny]

> ...before being put back together...

Actually, the earth was never re-assembled. What actually happened was that the last few books of the "trilogy" took place in a different "parallel universe", where a couple of key decisions were made differently than in the first books: earth not demolished, and Trillian didn't go with Zaphod. No reconstruction, just different choices.

Re:Hitchhiker's Guide was there first

[CiaranMc]

"Hitchhiker's Guide takes place in the future"

Umm... nope.

It starts in the mid-80's and continues from there.

It takes place off-planet, which is why the tech is so advanced.

-Ciaran

Re:Hitchhiker's Guide was there first

[Uberminky]

Actually Feynman probably started the whole thing off with his famous talk given in 1959. And of course there was Von Neumann in the 40s. Anyhoo. It's cool reading all this stuff from way before I was even born, about crazy stuff we've barely even tried to grapple with yet... :)

so what?

[AndyChrist]

What's the use of a robotic arm if all it can do is make more robotic arms? (Well, I suppose if it can make robotic arms that can do something besides replicate...)

huh?

[zencode]

i'm looking at the video - the second in particular - and ...this doesn't look interesting, let alone revolutionary.

what you have is a top plate interacting with a bottom plate with exponential surface area! first the top plate touches 1, then 2, then 4. yay! dear sweet god, please, someone enlighten me!

My .02,

Re:huh?

[tono]

uhh, well you see.. it's like, this thing.. where the arms create arms which create arms, which create arms.. recursion I think it's called.. and it makes my brain hurt, but it's not really revolutionary because computer folk have been doing this sort of thing on a much smaller scale for awhile.. but in manufacturing it's frankly ingenius.. unless I missed the entire point of the article in question in which case disregard the above as it's 4:06 in the am for fuck sake

Re:huh?

[BradleyUffner]

I had to think about it for a little while before I came up with a way that it could work. Instead of each arm creating exact copies of it's self, it creates a smaller version of it's self. Each recuresions ends up with a smaller arm then before, until eventually you end up with a tryly nano arm, or something like that. Ohh well, its early and I havnt had any coke yet, so it minght not work that way... sigh....

Re:huh?

[Blade]

Simple.

The manual process can make one arm per time-slice (however long that takes) using what looks to be a single, large, expensive device.

However, by building a single arm manually, and then moving the surface to another location you can breed more arms, at 2 per time-slice, then 4 per time-slice, etc.

Once you have 1024 [for example], you chop them up using another device, and place them on another surface in any arrangement you desire and get them to build things.

1024 manually takes 1024 time-slices, 1024 exponentially takes 11 time-slices.

Re:huh?

[villy]

Think in terms of manufacturing costs. IC fabrication center costs rise almost exponentially with the size and complexity of the dies they are making. With MEMS, the cost to build one arm is fixed, and if arms can help "make" themselves, the cost to build a larger component goes down significantly. That's the thinking, anyway.

Alrighty!

[Rhinobird]

Cool! How soon before I can turn the planet into a ball of grey goo? BWAHAHAHAHAHAHAHAHA!

Re:Alrighty!

[BMazurek]

Yeah, that's the scary part of this IMHO. Get some machine with self-replicate orders, release it into the wild, and viola. In very short order, exponential growth causes the entire planet to get wiped out.

This whole concept frightens me.

Re:Alrighty!

[tim_maroney]

That would indeed be a concern, if not for the fact that machines require energy. Gray goo would not only need to replicate itself; it would need to extract energy from the environment. No one knows how it could do that on a large scale, or if. Photosynthesis is a slow way to conquer the world.

Consider that it takes an entire multinational industrial system to provide the power to a single tank and then ask yourself how much we need to worry about gray goo. In the la-la land of nanotechnology, little concerns like power source and heat dissipation are not interesting enough to consider, compared with fanciful speculations about Fantastic Voyage cell repair robots and smart mists.

Re:They're gonna take over the world

[Omnifarious]

We've got lots of those already. :-)/p>

Then what?

[Deanasc]

This is pretty cool but what use is there for a surface covered with tiny lever arms? All movement syncronized and identical to it's neighbor. I mean aside from selling them as "The Worlds Greatest Micro Back Scratcher" in Hammacher Schlemmer catalogs.

Re:Then what?

[Blade]

Once the arms are complete, you chop them off the surface they are on, re-arrange them, and place them on another surface. You can then use them to build other things, by putting together a little miniature assembly line.

Building them is the first stage, building millions of them is necessary, so building them quickly is essential.

Richard 'God' Feynman

[rde]

Elsewhere on Xyzzy's site you can find the original nanotech (and, indeed, MEMS to nano) talk; "There's Plenty of Room at the Bottom". If you've read anything about Feynman, you're already a fan. If you haven't, this is a good place to start.

Programmable?

[Arkleseizure]

Can these robotic arms perform other actions, or are they designed in advance only to construct replicas of themselves?
Perhaps you could grow them onto the underside of your boss's shoes and watch him slide around on a million tiny scuttling legs. A worthy use of the millions this must have cost.

How does this work?

[fantom_winter]

Okay, picture a 2-D surface upon which these parts are laid. Now there is one arm in the middle of this. Let's say that each arm produces another arm in t=1. Now there are 2 arms, then 4, etc... Hence the O(2^n) sorta growth rate.

Here is my question. Assuming the arms are stationary, it is reasonable to assume that they can only build an arm adjacent to itself (and if they move, moving would be a O(n) process).... This means that for any grid area n^2, there are(n+2)^2 adjacent squares.

Because of this fact, I don't see how these things can achieve any more than a O(n^2) growth rate, because the adjacent resources available to these bots would be O(n^2).

Anyone know how these buggers get around this limitation?

Re:How does this work?

[Helge Hafting]

They have a potential for O(n^2) growth - if you can move them away fast enough. Bots building replicas inside a blender might achieve that for a while. Bots on a surface is limited to (n^2), or possibly (n^2.x) if the surface is fractal. Bots turning a planet into goo will be limited to (n^3)...

Re:How does this work?

[grammar nazi]

"picture a 2-D surface..."

"...Because of this fact, I don't see how these things can achieve any more than a O(n^2) growth rate..."

You assume that they use a 2-D surface. To remedy this problem, all they need to do is not use a 2-D surface or use a 2-D surface and when the arm is built, it get's transfered to a new location away from where it was built. An assembly line has always been an efficient way to manufacture products. Perhaps the robots would create assembly lines as they were created. Then in a 2-D space they would be able to obtain an exponential growth rate.

Re:How does this work?

[fantom_winter]

You assume that they use a 2-D surface. To remedy this problem, all they need to do is not use a 2-D surface or use a 2-D surface and when the arm is built, it get's transfered to a new location away from where it was built. An assembly line has always been an efficient way to manufacture products. Perhaps the robots would create assembly lines as they were created. Then in a 2-D space they would be able to obtain an exponential growth rate.

Well, all that would do is make it a O(n^3) limitation, which would still be polynomial and not exponential growth....

Also, the act of transfering the arm is going to be at least a O(n) process which would also limit production. since there are three dimensions in which to move, this limitation would also be o(n^3) in nature. picture things moving away from each other at a constant rate but getting bigger at a rate of S=n^3. They would eventually overlap and consume each other.

Re:How does this work?

[fantom_winter]

They have a potential for O(n^2) growth - if you can move them away fast enough. Bots building replicas inside a blender might achieve that for a while. Bots on a surface is limited to (n^2), or possibly (n^2.x) if the surface is fractal. Bots turning a planet into goo will be limited to (n^3)...

Okay, I can see arguing the blender idea, beacuse one could say that it would be a limitation of the size of the blender that limted production, given enough random motion, but it seems that even this is sorta deceptive because of the lmiitations of 3-space.

The blender, as it mixes is after all going to increase in nanobot density which means there will be a amount of stuff around it, and mixing of an infinite blender doesn't really make much sense, because how would a particle get from one edge of an infinite blender to the other?

Re:How does this work?

[boldra]

The most likely answer would seem to me to be that the mfg process *is* the movement. ie an arm starts building at the functional end, then finishes building at the attached end (which is where the power supply is?). This would mean that when the construction is complete the arm is already an armlength away.

I'm not so hot on the math here, but could it still be exponential if the movement were taken into account as part of the mfg process (simultaneous or not)?

2nd motor: (Tmfg + Tmovement)
3 + 4th motor: (Tmfg + Tmovement)
5 - 8th motor: (Tmfg + Tmovement)

Re:How does this work?

[RobertFisher]

First, I think you are correct in pointing out that exponential growth cannot strictly apply for very long before the system becomes "starved" for resources. This is true in natural populations, and we expect the same should apply here.

However, your order estimates are incorrect.

This means that for any grid area n^2, there are(n+2)^2 adjacent squares.

Yes, and the rate of growth is determined by the difference between these two, which is O (n), not O(n^2).

Because of this fact, I don't see how these things can achieve any more than a O(n^2) growth rate, because the adjacent resources available to these bots would be O(n^2).

In fact, it is O (n). To easily visualize this, imagine the system in 1D for a moment. After the first unit assembles its nearest neighbors, each additional unit builds the next unit at the end of the line of units. This leads to a constant rate of growth. In 2D, the rate of growth is determined by the rate of change of the area, not length, which leads to O (n). In 3D, the rate of growth is determined by the rate of change of the volume, which leads to O (n^2). The result in each case is easy to visualize : it is limited by the boundary of the N-D volume the units have already filled.

All this said, I think this whole discussion doesn't emphasize that even an O (n) growth rate can be vastly enormous for large enough n. The main problem is that it appears much slower to start up than a truly exponential process, which could be realized for a longer duration if the newly built units were "mixed" randomly into the grid. This could be the case if each unit could be assigned to move some random distance under its own power, after each building cycle. Eventually, however, the exponential rate of growth will turn over when the system's capacity is reached.

Re:How does this work?

[fantom_winter]

In fact, it is O (n). To easily visualize this, imagine the system in 1D for a moment. After the first unit assembles its nearest neighbors, each additional unit builds the next unit at the end of the line of units. This leads to a constant rate of growth. In 2D, the rate of growth is determined by the rate of change of the area, not length, which leads to O (n). In 3D, the rate of growth is determined by the rate of change of the volume, which leads to O (n^2). The result in each case is easy to visualize : it is limited by the boundary of the N-D volume the units have already filled.

Yes! You are right! However I would like to save face and say that something that is O(n) is also O(n^2)... heh, technically. The boundary of a square is 1-D and a surface of a region in 3-space is 2-D... I see your point.. It's worse than I expected.

newly built units were "mixed" randomly into the grid. This could be the case if each unit could be assigned to move some random distance under its own power, after each building cycle. Eventually, however, the exponential rate of growth will turn over when the system's capacity is reached.

Wouldn't the fact that the systems had to move limit the process? After all, moving takes time, and the amount that they would have to move would be going up on the at least the same order as the size of the region.

Re:How does this work?

[Arkleseizure]

Not wanting to be a smartarse, but this is all true only if each arm builds its replica on its own plate -see reply to parent.

Re:How does this work?

[dlkf]

Your O(n^2)(which should be O(n) as pointed out in another reply) limitation is only on space as you state. However, the O(2^n) growth rate is a limitation on time. Thus, if you double the area of the plate, you can make roughly twice as many arms but with only one more time step, not twice as many time steps.

These nanobots are really tiny (hence the name) and you will need to make lots of them to do anything useful. If you are trying to make 10^15 of them, you dont want to have to make them one at a time, a thousand at a time or even a million at a time (all have a o(n) growth rate), that would take all too long. By having an exponential growth rate, they can focus on making larger plates to grow the nanobots on rather than making more nanobot producing factories.

Re:How does this work?

[fantom_winter]

nobody seems to be reading this article, but just in case, I have some comments on this...

Your O(n^2)(which should be O(n) as pointed out in another reply) limitation is only on space as you state. However, the O(2^n) growth rate is a limitation on time. Thus, if you double the area of the plate, you can make roughly twice as many arms but with only one more time step, not twice as many time steps.

An interesting point, although I still don't exactly see how the things could grow exponentially at all without some kind of motion to move the "center" nanobots.

In a sense, its like having localized depletion of resources. The oldest bots would be surrounded by younger bots, and I don't see how this is avoidable, even given the complex geometry of these plates.

My contention remains that localized "starvation" of these bots would limit their growth rate to polynomial time. (Which aint bad)

Re:How does this work?

[Joe 'Nova']

I think it's like diamond shaped crystal growth along a surface, adding bits along the edges, rather than an exponential growth. I've added growth charts to show what I mean.
A '1' can only build 2's(for efficiency sake), 2->3, so on, and a 'b' unit(second gen) can build a 'c', 'd', and 'e', with all resources used up. In other words, max useful assembly life of these things is t+3, because the one that built them is on one side.
Growth pattern
---4
--434
-43234
4321234
-43234
--434
---4

Lattice timing chart
_______|5F|__|3E|__
_______|4E|__|2D|__|4F|__
_|5E|4D|3C|2B|1A|2C|3D|4E|5F|_
____|5F|__|3D|__|3E|__|5G|
__________|4E|__

You get the idea, I hope. It isn't quite a Von Neumon(sp) machine, but getting there! The idea is to make two, then go out and explore, colonise and whatever. I think the nanos are on the right track, but How they do it is another thing! Why, at 100 microns, they could assemble circuitry! Imagine the non-lithography, no chemical advantage! neat!
I just can't wait for them to check microstructures for flaws, improving quality, etc.

Re:How does this work?

[dlkf]

I still don't exactly see how the things could grow exponentially at all without some kind of motion to move the "center" nanobots.

I dont see why you need to move the bots if you can move the plane. As it says in the article:

While each robotic arm would have only two degrees of freedom, the surface itself could be moved in X, Y and Z.

I know im assuming alot about the process here and I could be completely wrong on this, but if you move the planes in an organized way, it is plausible that you wont have to move the bots and that they wont crowd each other too much either. This is because each bot doesnt make a new bot on its own plane, it makes it on the opposite plane. Thus, bot1 on plane1 makes bot2 on plane2. Currently bot1 is still close to bot2 since the plates havent moved much. Next, big machine moves plate2 1 meter parallel to plate1. Now, bot1 is 1 meter away from bot2. Bot1 and bot2 have plenty of room to reproduce. Repeat till bots are too dense to reproduce. Clean up mess and start over.

Now if your plates are large enough, you wont have to worry about crowding for quite a while. The only problem would be in coming up with the scheme to move the plates and in making big enough plates. I guess you could call this "moving the center nanobots" even though you arent really touching them in any way, just moving the plates they are on.

Re:How does this work?

[grammar nazi]

Very interesting, and correct fantom_winter.

I think that you could achieve exponential growth on a 2D surface however. Here's how...

1. Each existing robot builds an additional robot.
2. Each existing robot then relocates such that there is enough room to build an additional robot.

Technically, that is exponential growth (w.r.t generation or iteration). One can argue that the relocation step takes longer and longer each time, but it's still exponential growth.

It all comes down to whether your 'n' is an iterative or a temporal element.

I'm not trying to talk you down or say that your are wrong.

What about an assembly line that the robots moved down as they got built. The 'just-completed' robot at the end of the assembly line would then contribute to building the next robot. Since more and more robots were joining the assembly line, each robot could do less work. Since each robot was doing less work, the assembly line could move faster and faster, thus attaining an exponential growth rate.

I know, I know that assembly line would only approach the speed of light or some asymptote which was representitave of the robots' speed. But it's a cool idea.

Re:How does this work?

[Winged Cat]

How about creating the robots in motion to each other? That is, at the end of each manufacturing step, the newly created robot and the creator robot push off from each other. Possible problem: for robots A,B,C,D, where D created B, then D made C and B made A, C and B might collide since they'd be pushed towards each other. Workaround: for each generation, pick a new direction so you something that robot X creates doesn't run into something that robot Y creates. This would be limited in the number of generations by how much of an angle difference you would need, but by making the push-off velocities fast enough and the robots small enough, you could scale this up to whatever finite limit you wanted to.

Intriguing concept. . .

[Salgak1]

And, oddly enough, an old one. This is an extension of the technique first suggested by Richard Feynman in 1959. Additionally, this looks to be MUCH faster than previous suggestions, using Atomic Force Microscopes or Scanning Tunneling Microscopes for positioning and/or assembly, as was done by IBM

However, it does seem limited to assembly of pre-fabricated parts. Still, it's another step on the road to genuine nanotechnology.

What would be nifty, would be to merge this technology with chemical assembly: i.e. the smallest manufacturable arm, with a range of active tips, which use enzymatic techniques or positional assembly to build even smaller. . .

Nice concept, but how do you ..

[RedLaggedTeut]

Nice concept, but how do you proceed after you have completed 8 nanomachines ? having re-order the created machines so they get a new surface to build other robots on takes time and thinking.

x....

xx...
xx...

xxx..
xxx..
xx...

And now where is the exponential growth ? Rather better to push them apart every step, but can you really do this if you want to use silicon/hard material based nanontech ?

x.......

xx......

x.x.....

xxxx....

x.x.x.x.

Re:Nice concept, but how do you ..

[seanellis]

You do it like this - remember you can move the two facing plates as far as you like. On a 1-d surface, with space for 8 arms, you might get this (forgive awful ascii-art):

Step 1: Start just overlapping, and build:

_______1.......
........

_______1.......
.......2

Step 2: Slide half-way back, and build

___1.......
.......2

___1...4...
...3...2

Step 3: Slide half the remaining distance back, and build

_1...4...
...3...2

_1.7.4.6.
.5.3.8.2

Step 4: Slide the one remaining slot back, and build

1.7.4.6.
.5.3.8.2

1D7B406A
95F3C8E2

Presto! 2^n robots in n steps, with no relocation required. Once you've made a line of robots like this, repeat by translating in the other dimension after each step, and voila!

In order to allow the final plane to do non-trivial stuff after its finished, you give each machine a unique address etched into the control electronics layer rather than the MEMS layer. But in order to allow the things to operate in lockstep, you can also have a "multicast" address (255.255.255.255?) which will address all devices on the chip. This would be useful even after manufacture as a master reset or as a way of shuffling finished components off the chip at the end.

Sean Ellis

Why just scratch BACKS

[AndyChrist]

Lube it up and the possibilities are greatly expanded.

This reminds me of an old short story

[kmcardle]

Many moons ago in Omni magazine, I remember reading a fictional story about nanotech.

A guy built a robot that was supposed to build a single copy of itself at one tenth the size. He made an error in the program, and each robot built ten copies of itself at one tenth the size. The robots eventually got so small the would duplicate at a very high rate. The guys house was eventually destroyed, and the only thing that saved the day was a rainstorm that rusted the robots to death.

Anybody remember this one? Anybody got a link to it?

Re:This reminds me of an old short story

[kmcardle]

Oddly enough, the story took place in the UK.

Please read the article

[gnalle]

This means that for any grid area n^2, there are(n+2)^2 adjacent squares.

Reading the article you get the answer: The arms are put the surface of a plates. In front of this plate you put a plate without arms. Now the one plate puts arms on the surface of the other other plate. Afterwards you put each plate in front of a plate without arms. Repeating this proces will generate exponential growth. You would also get exponential growth if you had somehow put the arms in water and added new unnassembled arms, to maintain the same concentration of assembled arms.

It would be exponential

[Arkleseizure]

In each step of the process, each robotic arm builds a replica of itself on the _opposite_ plate. That means that at each step the number of arms is multiplied by two - ie. exponential growth.
Since the arm is not building the replica on the plate it occupies itself, all that is required at the next growth step is for the plates to be moved relative to each other in such a way that each arm is facing an empty area of the opposite plate.

Simplified, or what?

[Simon Hibbs]

Sorry, we're supposed to be impressed?

I'd like to see a macro-scale implementation of
this. Where are the servos that move the arms?
What about power distribution and controll
signaling? How are these attached to the arms,
and how do you make sure the power, signaling
and servo attachments don't get in the way?

If you've already manufactured all the parts and
laid them out in a perfect pattern on the two
surfaces, why not do all the assembly at that
stage? Surely this level of assembly is the
simples step in the manufacture process? So
simple that it's completely unnecessery.

Simon Hibbs

This was proposed by Robert Heinlein in Waldo-1950

[macemoneta]

The idea of using robotic arms (which Heinlein called "Waldos" to create progressively smaller robotic arms was described by SCI-FI author Robert Heinlein in his 1950(!) book, Waldo. It's about time someone actually did it :-)

Hey stupid moderator!

[91degrees]

Ever seen Lexx? Season two had an alien that had lots of floating arms that escaped and started replicating themselves.

Therefore this is not offtopic.

Re:Hey stupid moderator!

[cheetham]

yup... I've seen it ;-) It was Mantrid who started it, and IIRC he was part human, part insect, part mechanical himself. (He minds was trasnfered to a machine using an insect organ I think.) The robot arms eventually turned most of the universe into robot arms... How do you stop these tiny tiny robot arms? with a giant bug? ;)

Demoronize /.

[SEWilco]

I see question marks in odd places in the /. posting. Either the syntax and grammar are worse than usual, or those are non-displayable characters. I guess it's time to build the demoronizer into the slashsubmissions scripts.

Re:Demoronize /.

[BeanThere]

Strangely, I also see the ?'s, and I'm browsing with IE 5 at the moment. The ?'s should be showing up under non-MS browsers, as I understand it.

Re:They're gonna take over the world

[91degrees]

And they're the last thing that anyone wants. :P

How do you "feed" a robotic arm?

[renoX]

Let's suppose that you build a robotic arm.

You have to build also the "control" part in order to pilot the move of the arm, it can be as difficult to make as building the arm itself.

The next problem: how does the arm catch the needed molecules?
This may be easy if there is only one type of molecules: put the robot inside a solution of these molecules.
But if you need more than one type of molecules??

I can see an easy solution for the first arm, but for the second? How do you connect it to the energy source, to the molecules tank?

What I find strange is that nobody has designed a complete working auto-replication system with nano-bot.
Sure to a degree, the firt nano-bot design will be dependant of the way it has been built, but I think that trying to simulate as completely as how it COULD work would be an interesting baby step..

Grey goo takes over the world, film at 11

[ConceptJunkie]

I can't think of anything to say, I just liked the subject...

Sorry.

bootstrap problem ahead!

[Lumberjock]

This first robotic arm makes a second robotic arm on a facing surface by picking up miniature parts carefully laid out in advance in exactly the right locations so the tiny robotic arm can find them. I see. And who made those exponential many miniature parts and laid them out carefully in advance? An army of even tinier, exponentially self-replicating Waldos, perhaps? Looks like the good old chicken-and-egg to me..

Nanobots!, a poem

[Orifice]

Nanobots! Nanobots! Nano-nano-nano bots! Can't get enough of them nano-bots!

I love you, Xev/Zev!

[Aciel]

Brings to mind a really awful show on Scifi entitled Lexx...

Aciel
aciel@speakeasy.net

Re:I love you, Xev/Zev!

[cheetham]

If you're gonna say Lexx awful, at least say why you think it's awful. I enjoyed it, it's not for everyone though....

gingerbread men

[alan2001]

If you've already manufactured all the parts and laid them out in a perfect pattern on the two surfaces, why not do all the assembly at that stage?

As I understand it, you can mass-produce the components using micro- (and perhaps nano-)lithography like a cookie cutter, but what you end up with looks like a bunch of cookies on a cookie sheet. You need the robot arms to put the, er, cookies together.

It's not exponential

[The NT Christ]

You highlight a cell in a 2D or 3D space. Then you run the algorithm: for each highlighted cell, highlight its neighbours. The algorithm takes 1 unit of time. How many cells are highlighted after time T?

The answer, of course, is polynomial in T, and *not* exponential at all. For exponential growth the cells must move apart; in this algorithm, the early cells are quickly surrounded by other cells and can do no more work.

Re:It's not exponential

[Orifice]

Please, for the love of nanobots, take your valid quantitative reasoning elsewhere. We're never gonna make it to nano-utopia by listening to skeptics like you.

It's quadratic or linear growth, isn't it

[jeti]

Picture this system growing. It's either an expanding sphere or an expanding circle on a surface. So you get quadratic or linear growth, dont't you?

exponential till you build something practicle

[bug1]

The moment you build something other that a robot that builds other robots the proccess stops being exponential.

Sounds like pipe dream, why stop at nano machine robots, why not make a big robot that builds other robots... who hasnt thought of that before.

Heinlein already did this in "Waldo"

[John Constantine]

Not to diminish the coolness of the idea, but he described this a couple of decades ago.