Understanding the limits
tim.thelion
between Turings laws of computing and the new world of computerized
fabrication. This is a brain dump, and I was thinking only after
typing throughout most of it.
If you remember. A Turing machine is a theoretical machine which,
given infinite energy, time, and memory, can preform any computing
task possible. The clear simple definition for Turing complete
computer languages made it easy for us to build thousands of
infinitely powerfull artificial computer languages in just a few short
years.
I'd like to propose a new theoretical machine. The Turing 2. The
Turing 2 is a machine which given an infinite amount of time, space,
energy, and input material(Be it neutrons, or BPA), can form any
object which is physically capable of existing. It's like a reprap,
that could create anything. We'll call the set of objects the Turing
2 can create set A.
Now obviously unlike the origional Turing machine the Turing 2 cannot
be built. We don't even know what IS physically possible and
impossible yet, and we arn't quite to the point of pushing quarks
arround into precice shapes at any scale. So for us set A is so far
undefined. We do know, however, that set A is infinite and contains
everything in the universe. Once we create a Turing 2, we will be
gods!
Lets define another set. Set B. Set B is the set of objects that an
infinitly large reprap could create using an unlimited suply of BPA,
unlimited time, and unlimited energy. This set is also infinite. But
it doesn't even include most day to day objects. So far, I cannot
print a computer on my reprap.
The development of a better reprap will mean increasing set B, so that
it is an ever larger subset of set A.
With our hands and eyes, we have created a huge subset of set A. We
have created large hardon supercoliders, and space ships, and medical
devices. Sure, we used tools, but these tools, from Turing's stand
point, are no more than intermediate steps in the process. With no
more than our imprecice tremoring hands we HAVE turned bare rock to
silicone chips in cell phones. It just took us a few hundred years
and far less than infinite space.
I'll define the subset of set A that humans are capable of creating
and call it set H. This is smaller than set A, because we are limited
by the Heisenburg uncertainty principle. There are things that are
capable of existing, that we are incapable of seeing, even with the
most precise equipment. When we think of fabrication, our goal,
should be a fabricator that can create the things in set H.
One puzzle popular among computer scientists is the creating of
esoteric turing complete programing languages like brainfuck and
Thue. These are excedingly simple languages with very limited sets of
commands, which, despite that, can be used to preform any programing
task availible.
My challenge to you guys, is to devise a robot, which is Turing 2
complete for set H. The set of all objects that humans can create
with their hands(including objects that they can create with tools
which they made with their hands, and tools made with hand made tools,
ect). Does this robot need oposable thumbs? I don't think so. A
high resolution eye ball? Probably not. What are the lower limits?
If you had a VERY SIMPLE robot on Mars, but unlimited time. What
basic functionality would you need to create a civilization?
Now there is a problem with this little game. Unlike the origional
game of Turing completeness, the rules of practicallity get in our way
to a greater extent. Even the human being is not Turing 2 to the set
of H complete on Mars, because he/she/it cannot breath. Similarly a
robot on Mars, could do great so long as it didn't fall into a
hole... Furthermore, robots in reality, won't last for an infinite
amount of time. They'll wear out. So I'll propose a small change in
the rules. Your robot, can chose a starting position, and teleport
itself back there at any time, minus any wear or tear.
My proposal for the basis of Turing 2 to the H machines is that they
need some way of
A, moving arround,
B, manipulating their environment
and C, seeing
As you see already, this puzzle is a little bit different than the one
reprap tries to solve, in that with repraps, we assume hypothetical
omnicience at the start of our sequence. We assume that our space is
empty.
It's also a bit different than that of mankind trying to build
civilization on this earth, because of intermediate steps. Humans are
able to increase the set of objects they are able to build by use of
tools, and the natural earth is shock full of tools ready for action
with out much manufacturing needed. We have rocks that you can rub
back and forth to make fire, and sticks to be used as leverage, and
rocks that can be broken and turned into blades. Any other random
envioronment doesn't contain these tools. There aren't sticks lying
arround on the ground of Mars. A human, trapped in an infinitely
large jail cell, with an infinite amount of concrete to work with,
lying about on all sides. Is similarly helpless, despite having an
infinite amount of time, energy, space, and input material.
Any thoughts on this?
Alvaro F. Boirac
I'm not entirely sure if constraints are tight enough to make the challenge meaningful.
Let me illustrate with an example.
You want your Turing RepRap to make a little bracelet with a plastic fastener.
Great! Did I say plastic? Make seismographs, dynamite, fetch geological maps, travel thousands of miles for oil exploration. Build oil-rigs, dig dry holes for the most part, ... finally get some oil, ... build a refinery, refine it! Bingo, We have some precursor polymers! finally make the plastic fastener.
If it's going to be so general, the problem should have some constraints related to time, the finite quantity of matter available in the surroundings (region, country, planet?), the relative abundance of some raw materials, etc.
How will the machine chose between oil exploration, substituting the fastener for metal, nettle rope, or using polymers from old coca-cola pastic bottles?
I think to make progress, some practicalities have to be taken into account. Then, the problem can be formulated as an optimization: The Turing RepRap will build "x". To do so it will minimise "time", "distance traveled" and maximize "material abundance", "recyclability", etc
Otherwise, if time, matter and energy are unlimited, you might as well build a fusion reactor to manufacture the periodic table, attach an all encompassing chemistry lab, and a complex robotic manufacturing plant. But isn't it too far fetched to give us any insight into what can really be done?
Regards,
Alvaro F. Boirac
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Patrick Anderson
> If you had a VERY SIMPLE robot on Mars, but unlimited time.
> What basic functionality would you need to create a civilization?
>
We would need energy inputs for our own bodies (food) which comes
from solar-powered, self-replicating manufacturing plants such as
Avocado trees.
> We have rocks that you can rub back and forth to make fire,
> and sticks to be used as leverage, and rocks that can be broken
> and turned into blades.
> There aren't sticks lying arround on the ground of Mars.
Interesting, the differentiator here is 'sticks', and sticks come
from trees...
DoktorJ
theoretical thought experiment than anything that is currently
realistic or possible to build. I think the basic idea is for people
to come up with the best/most efficient way to produce the largest
possible subset of H or all of H (though this seems unlikely even for
a thought experiment). I can see how these theoretical devices, while
currently impractical could be very helpful in providing inspiration
for devices that are currently realistic/possible. OP, feel free to
correct me if I'm misunderstanding.
Atrus
Greg
Turing 2 is a machine which given an infinite amount of time, space,
energy, and input material(Be it neutrons, or BPA), can form any
object which is physically capable of existing. It's like a reprap,
that could create anything. We'll call the set of objects the Turing
2 can create set A."
For a single element this will generally restrict the T2 to structural products. Functional products with electromechanical capabilities will typically require a range of materials with a range of (e.g. conductive/insulating) physical properties. One exception to this may be carbon, as CNT are notoriously anisotropic
So, the simplest T2 would be able to produce any [real] structure from a given single material.
The next step up T2 would be able to produce any [real] structure from ANY single material.
.
:
The ultimate T2 would be able to produce anything given everything.
One set of M of particular interest is the set required to reproduce the T2.
From: "openmanufact...@googlegroups.com" <openmanufact...@googlegroups.com>
To: Digest Recipients <openmanufact...@googlegroups.com>
Sent: Sun, May 8, 2011 7:37:09 AM
Subject: [Open Manufacturing] Digest for openmanu...@googlegroups.com - 3 Messages in 2 Topics
-
"tim.thelion" <tim.t...@gmail.com> May 07 12:26PM -0700
^
I wonder if anyone out there has done a hard theoretical comparison
between Turings laws of computing and the new world of computerized
fabrication. This is a brain dump, and I was thinking only after
typing throughout most of it.
If you remember. A Turing machine is a theoretical machine which,
given infinite energy, time, and memory, can preform any computing
task possible. The clear simple definition for Turing complete
computer languages made it easy for us to build thousands of
infinitely powerfull artificial computer languages in just a few short
years.
-
"Alvaro F. Boirac" <alph...@gmail.com> May 08 11:33AM +0100
^
-
Eric Hunting <erich...@gmail.com> May 07 05:51PM -0600
^
Design for an adult-scale Technics-like building toy that produces working human-powered vehicles.
http://www.wouterscheublin.com/projects/construction-toy/
If this were realized it could be a great experimenters' tool. It uses an interesting fastener scheme based on grooved rods/tubes that could be made of FRP.
Eric Hunting
erich...@gmail.com
Eugen Leitl
> I could be misunderstanding, but I think he was going for more of a
> theoretical thought experiment than anything that is currently
> realistic or possible to build. I think the basic idea is for people
> to come up with the best/most efficient way to produce the largest
> possible subset of H or all of H (though this seems unlikely even for
> a thought experiment). I can see how these theoretical devices, while
> currently impractical could be very helpful in providing inspiration
> for devices that are currently realistic/possible. OP, feel free to
> correct me if I'm misunderstanding.
Everyone is aware of http://molecularassembler.com/
and especially http://www.molecularassembler.com/Nanofactory/AnnBibDMS.htm
?
--
Eugen* Leitl <a href="http://leitl.org">leitl</a> http://leitl.org
______________________________________________________________
ICBM: 48.07100, 11.36820 http://www.ativel.com http://postbiota.org
8B29F6BE: 099D 78BA 2FD3 B014 B08A 7779 75B0 2443 8B29 F6BE
DoktorJ
concept, but is that the only and/or most practical method of
producing everything in set H, somehow I doubt it. Do we really have
to assume that the only way to perform this task is to build anything
and everything atom by atom? To me that strikes me as extremely
inefficient. How much energy does it take to channel each atom to
it's eventual destination? I don't know physics well enough to answer
that question, but my guess is that it's a lot more energy than it
would take to move a much larger amount of material through an
extruder, or simply through mechanical movements by physically picking
up and placing a larger object. Also, atoms don't normally come by
themselves, so you have to consider all the energy it takes to break a
molecule down into it's constituent atoms before transporting it
without allowing it to react with any other atoms before it reaches
it's final destination. Are we all going to have our own E-Cat just
to run this device, and even if we do, how do you safely transport all
this power from your E-Cat to your nano-assembler. What is wrong with
considering other options? Personally, I love the idea of a universal
nano-assembler, but let's not just assume that something we may not
even have within our lifetimes is the only option to achieve a large
subset of the same results.
On May 9, 4:33 am, Eugen Leitl <eu...@leitl.org> wrote:
> On Sun, May 08, 2011 at 06:37:02AM -0700, DoktorJ wrote:
> > I could be misunderstanding, but I think he was going for more of a
> > theoretical thought experiment than anything that is currently
> > realistic or possible to build. I think the basic idea is for people
> > to come up with the best/most efficient way to produce the largest
> > possible subset of H or all of H (though this seems unlikely even for
> > a thought experiment). I can see how these theoretical devices, while
> > currently impractical could be very helpful in providing inspiration
> > for devices that are currently realistic/possible. OP, feel free to
> > correct me if I'm misunderstanding.
>
> Everyone is aware ofhttp://molecularassembler.com/
> --
> Eugen* Leitl <a href="http://leitl.org">leitl</a>http://leitl.org
> ______________________________________________________________
Eugen Leitl
> Yes, I suspect most people who visit this group are aware of that
You're top-posting and not trimming your replies (message unchanged
below).
> concept, but is that the only and/or most practical method of
> producing everything in set H, somehow I doubt it. Do we really have
If you want to produce something arbitrarily patterned and picked
from the space chemistry allows you do not have many options.
> to assume that the only way to perform this task is to build anything
> and everything atom by atom? To me that strikes me as extremely
You don't have to build everything atom by atom.
> inefficient. How much energy does it take to channel each atom to
> it's eventual destination? I don't know physics well enough to answer
You will find the energetic analysis in the bibliography. (The precursor
species transported are not atomic).
> that question, but my guess is that it's a lot more energy than it
> would take to move a much larger amount of material through an
> extruder, or simply through mechanical movements by physically picking
How do you extrude a Menger sponge? A fractal antenna?
> up and placing a larger object. Also, atoms don't normally come by
> themselves, so you have to consider all the energy it takes to break a
> molecule down into it's constituent atoms before transporting it
> without allowing it to react with any other atoms before it reaches
> it's final destination. Are we all going to have our own E-Cat just
You will find that in the bibliography, too.
> to run this device, and even if we do, how do you safely transport all
> this power from your E-Cat to your nano-assembler. What is wrong with
> considering other options? Personally, I love the idea of a universal
> nano-assembler, but let's not just assume that something we may not
> even have within our lifetimes is the only option to achieve a large
> subset of the same results.
You don't have to use machine-phase. However, iterated deposition by
numerical control scales to machine-phase chemistry fabrication.
You do not have to go there. You can arrive there, eventually.
>
> On May 9, 4:33�ｿｽam, Eugen Leitl <eu...@leitl.org> wrote:
> > On Sun, May 08, 2011 at 06:37:02AM -0700, DoktorJ wrote:
> > > I could be misunderstanding, but I think he was going for more of a
> > > theoretical thought experiment than anything that is currently
> > > realistic or possible to build. �ｿｽI think the basic idea is for people
> > > to come up with the best/most efficient way to produce the largest
> > > possible subset of H or all of H (though this seems unlikely even for
> > > a thought experiment). �ｿｽI can see how these theoretical devices, while
> > > currently impractical could be very helpful in providing inspiration
> > > for devices that are currently realistic/possible. �ｿｽOP, feel free to
> > 8B29F6BE: 099D 78BA 2FD3 B014 B08A �ｿｽ7779 75B0 2443 8B29 F6BE
>
> --
> You received this message because you are subscribed to the Google Groups "Open Manufacturing" group.
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Eugen* Leitl <a href="http://leitl.org">leitl</a> http://leitl.org
______________________________________________________________
ICBM: 48.07100, 11.36820 http://www.ativel.com http://postbiota.org
Tiberius Brastaviceanu
DoktorJ
I generally visit, so I'm not familiar with the etiquette, but all the
quoted text that Google groups adds in there is automatically is
hidden, when I view my previous post. I'll try to brush up on the
best way to reply, though since other users may not be viewing it the
same way that I am. I'll also try to read more thoroughly through
that document. I am certainly no chemist or scientist and my
knowledge in terms of open manufacturing is more technical and
ideological than theoretical, so I apologize if my understanding of
the low level operation of such a machine is limited. As far as a
Menger sponge or a fractal antenna, can we really consider those to be
a part of H? With current technology, can we actually produce a true
Menger sponge? Anyway, I'm not sure we are well served by arguing the
point here. I think we can both agree that a universal assembler
would be great and that there will certainly be a whole lot of
iterative steps to get to that point, so I guess at this point, I'll
go research that document more and if I have a better idea for this
thought experiment, I'll post it.
Thanks for the additional info.