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

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?

[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.

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.

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?

[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?

[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?

[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.

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?

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.