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A Turing Machine Built With Lego, And a Place To Put It

timothy posted more than 2 years ago | from the try-that-with-lincoln-logs dept.

Programming 74

New submitter Otis_INF writes "To honor Alan Turing, two researchers at the CWI built a simple LEGO Turing Machine, to show everyone how simple a computer actually is. Primary goals were to make every operation as visible as possible and to make it using just a single LEGO MINDSTORMS NXT set." And if a simple Turing machine gets old, Reader miller60 adds a link to this Lego data center "that recreates all the major features of an IT facility, assembled from 5,772 pieces, 28 figures, and 1 meter of fiber optic cable. The builder, Tanaka, has uploaded details to the Lego Digital Designer Gallery so others can build and adapt their own."

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Melted (0)

srussia (884021) | more than 2 years ago | (#40372169)

It's a Turing machine dammit, not a web server!

Distinctions adding up (2)

Tablizer (95088) | more than 2 years ago | (#40372477)

The very first Lego device to be slashdotted

Re:Distinctions adding up (2)

ackthpt (218170) | more than 2 years ago | (#40372523)

The very first Lego device to be slashdotted

Waiting for the first Lego Botnet...

Re:Distinctions adding up (5, Funny)

Tablizer (95088) | more than 2 years ago | (#40372601)

Waiting for the first Lego Botnet...

Gives a new meaning to "my smartphone's been bricked!"
     

Re:Distinctions adding up (0)

Anonymous Coward | more than 2 years ago | (#40377245)

Does it run Minecraft? A computer running on Minecraft blocks running on Lego would be cool.

Re:Distinctions adding up (0)

Anonymous Coward | more than 2 years ago | (#40377767)

Divide by Zero.

Re:Melted (2)

beelsebob (529313) | more than 2 years ago | (#40373499)

It's not... there's no infinite tape!

Hmm... (2)

Antony T Curtis (89990) | more than 2 years ago | (#40372207)

My personal opinion: I don't like their implementation.

I would prefer to see a version which uses a long "tape" which is covered in a thin film and the data recorded using different coloured dots from whiteboard markers.

Just my 2.

Re:Hmm... (1)

vlm (69642) | more than 2 years ago | (#40372355)

whiteboard markers will dry out too quickly. Been there, thought of that.

Re:Hmm... (1)

Bob the Super Hamste (1152367) | more than 2 years ago | (#40374991)

Well what about those round one post Lego dots. That might be doable.

Re:Hmm... (1)

vlm (69642) | more than 2 years ago | (#40375585)

Might work, might be a bit fumbly. The closest "solution" I could come up with involved something that looks like a magnetic chess piece with a little neo-magnet on the bottom and a gripper on top. Given a decent gripper/mover I could implement something like that on my milling machine table right now. This brings up my really weird idea of a robot arm making QR codes using black square magnets on a steel sheet. But this is getting pretty far off from the original "mostly-electromechanical" design.

Re:Hmm... (0)

Anonymous Coward | more than 2 years ago | (#40375039)

The lego "ideas" booklet had a couple of models like that.

The first was a programmable crane which used those 8x24 tiles and those 8 tooth gears and racks
  to do the programming. One channel was alway filled to drive the instructions through the reading mechanism.
Reading the instructions simply involved linking the small gears to a turntable for left and right.
Another channel was used to lower and raise the arm of the crane. The last two were used to lower and raise the cable.

There was also a lego plotter which used pens attached to a twin rack system. Though it was the motors that were connected directly.

Re:Hmm... (0)

Anonymous Coward | more than 2 years ago | (#40381615)

Different coloured dots and a camera. This has already been done.
It would have need electronics, unless someone find a way to read the colors with pure mechanics systems...

It's an LBA, not a TM (5, Insightful)

Prune (557140) | more than 2 years ago | (#40372261)

At Turing machine has infinite tape (memory). You cannot build one in the real world**. This is a deterministic LBA (linearly bounded automaton). **for two reasons preventing infinite storage: 1. a real world automaton is limited in extent by its light cone, and you cannot rely on this growing forever since accelerating expansion of the universe eventually will prevent outer parts of the device from communicating back with lightspeed signals 2. the Bekenstein bound limits information density: you can only store a finite information in a finite space--so no arbitrary precision real numbers

Re:It's an LBA, not a TM (2)

Prune (557140) | more than 2 years ago | (#40372667)

Why did I get moderated down? Here are references backing up my post: http://en.wikipedia.org/wiki/Linear_bounded_automaton [wikipedia.org] http://en.wikipedia.org/wiki/Bekenstein_bound [wikipedia.org]

Re:It's an LBA, not a TM (0, Troll)

Anonymous Coward | more than 2 years ago | (#40372927)

Why did I get moderated down?

You were modded down because you are an annoying Aspie. I know that people with an ASD often get confused by social cues, so allow me to explain: this is a cool project and it upsets people if you pedantically suggest it's not what the consensus definition claims.

Essentially, no one cares that a Turing Machine is impossible to realize. At most, this fact was worthy of a side comment at the end of a long post about how cool Lego robots are.

Hope that helps.

Re:It's an LBA, not a TM (1)

Prune (557140) | more than 2 years ago | (#40373023)

Nowhere did I diss the Lego project. I just added a minor informative correction. The true Aspies are the ones getting their panties in a knot and overreacting over something small. Nice trolling attempt, though.

Re:It's an LBA, not a TM (0, Troll)

Anonymous Coward | more than 2 years ago | (#40373297)

The fact that you don't even realise that you dissed this cool Lego project is a symptom of your Aspiness.

Your are factually correct. But noone cares because it isn't about obscure minutae but about a cool project. With Lego's, no less!

Re:It's an LBA, not a TM (2)

Prune (557140) | more than 2 years ago | (#40373437)

>But noone cares

Except for those that modded me up.

Re:It's an LBA, not a TM (0)

Anonymous Coward | more than 2 years ago | (#40381457)

>But noone cares

Except for those that modded me up.

So your fellow spergs got mod points? Color me impressed.

Re:It's an LBA, not a TM (0, Troll)

Anonymous Coward | more than 2 years ago | (#40373333)

Nowhere did I diss the Lego project. I just added a minor informative correction.

You're correct; however, social cues are often implicit. In this case, the negative emotional reaction caused by your post was due to the fact that it was tacitly perceived as detracting from the accomplishment of the project creators.

You see, your correction (and the "tone" of the post) were perceived as implicitly confrontational against the project creators. *They* called it a Turing Machine, and you are claiming they are wrong even though this is a very decent simulacrum.

Basically, had you praised the project first and mentioned the actual Turing Machine definition "in passing", people would have reacted to your post more positively.

Re:It's an LBA, not a TM (0, Flamebait)

Prune (557140) | more than 2 years ago | (#40373517)

It's not effective trolling if you have to put so much effort into it. See, you're the one that spent a bunch of effort making multiple AC posts here, whereas I got more karma boost. Kid, I was trolling on IRC while your grandfather was in diapers. Go back to 9fag

Re:It's an LBA, not a TM (0)

Anonymous Coward | more than 2 years ago | (#40373365)

He's right. Your social skills are somewhat lacking. However it's clear you lacking social skills are preventing you from seeing your lacking social skills. So please continue with your ASD since no one can help you.

Re:It's an LBA, not a TM (0)

Prune (557140) | more than 2 years ago | (#40373471)

Re:It's an LBA, not a TM (3, Informative)

gl4ss (559668) | more than 2 years ago | (#40373259)

Look, I may be an annoying aspie too here, but the project isn't cool because it uses a fucking computer to simulate a computer.

"Therefore, to avoid limiting the instruction size and to protect the running program, we chose to write the instructions to a file on the NXT brick and uses the simplest interpreter to run these instructions."

so the point is just to be a pointless cool looking device. it's not implemented in lego.

Re:It's an LBA, not a TM (0)

Anonymous Coward | more than 2 years ago | (#40375361)

Ignore that ape tit. This whole "asperger" thing is so out of hand in regard to over-diagnosis. Like some random dipshit troll has the medical knowledge to accurately tell who has what. Oh right because he checked its definition on wikipedia and is now a medical expert.

From your post I learned what the bekenstein bound is and I find it to be very interesting shit. So good on you, fuck that guy. Good day sir.

Re:It's an LBA, not a TM (0)

Anonymous Coward | more than 2 years ago | (#40377857)

Careful, Prune is a bit paranoid. He thinks there is only one AC responding to him. Of course, had each individual AC bothered to sign in, he would have just accused us of being sockpuppets.

In fact, he probably thinks this is an elaborate attempt to reverse troll him.

Re:It's an LBA, not a TM (0)

Anonymous Coward | more than 2 years ago | (#40373445)

More like a finite automaton. Everything this machine does can be simulated by DFA so it's about as powerful as a regular expression (not the Perl or grep or sed etc. kind but the real thing). Nothing to see here, move along ... Oh, and do grab one of those complimentary theory of computation books on your way out, you might actually learn a thing or two.

Re:It's an LBA, not a TM (1)

Prune (557140) | more than 2 years ago | (#40373775)

Nope. This can handle context-sensitive grammars. Nice trolling attempt.

Re:It's an LBA, not a TM (0)

Anonymous Coward | more than 2 years ago | (#40374143)

Dude... once you limit yourself to finite memory, you essentially have a (veeeery big) finite automaton.

Strictly speaking, _every_ computer on earth is a finite automaton - because once you limit the availabe memory, you have a _finite_ set of states that your computer can be in - and that set of states can be modeled by a DFA.

Re:It's an LBA, not a TM (0)

Anonymous Coward | more than 2 years ago | (#40378019)

This reminds of once upon a time when I helped a couple of math students with the programming assignment (this was first year at college). They chose the assignment to build a matrix library in SML which we had to use, and couldn't figure out how to model it with lists in SML. When I suggested a simple model and they had the aha moment, one of the said, smugly, but how can you then represent a matrix of infinite size?

Well, what matters is whether you can make it arbitrarily large, not infinite. The LEGO model is not supposed to be used for proofs, you know.

Re:It's an LBA, not a TM (1)

neonsignal (890658) | more than 2 years ago | (#40378661)

Obviously they hadn't heard of Georg Cantor. He would have had no trouble representing an infinite matrix using an infinite list.

Lego data center is the future! (2)

LeoDeSol (1323269) | more than 2 years ago | (#40372299)

Modular design is certainly the way most new data centers are going!! And who is more modular than Lego????????

Gay (-1)

Anonymous Coward | more than 2 years ago | (#40372315)

Turing machine is old shit. Build an i7 and then I'd be impressed. LOL

Re:Gay (-1)

Anonymous Coward | more than 2 years ago | (#40373051)

It is good that you have reached the point where you are ready to admit that you are gay. Now you just need to reach the point where you dare to do it without being anonymous.

Turing machine emulation using physical memory (5, Informative)

vlm (69642) | more than 2 years ago | (#40372333)

As has been (kinda harshly) hashed out on hackernews, this is really a turing machine emulated on a NXT using lego as a physical memory display. This is still cool, but its not "turing machine built out of lego" except by the extreme interpretation that a NXT computer is sold by the lego corporation.

There have been some genuine mechanical turing machines built with varying level of success.

Its pretty easy to make an electromechanical relay based turing machine if for no reason other than price (well, price compared to when I was a kid, its still gonna be a chunk of change)

When I was a teenage kid a simple DPDT 12 volt relay at radio shack cost me something like two HOURS of labor income, and now as a "highly" paid jack(-ass) of all computational trades I can buy a simple DPDT from Mouser for something like two MINUTES of labor income. I've got a bitslice ALU design (admittedly not a turing machine) down to about 22 relays per bit. Latching relays are about 50% more money than non-latching. Also QPDT relays are "cheap" and commercially available.

large PCBs are expensive. Yet sockets and hand wiring is not cheap either (although it looks cool)

I'm stuck on (electro-)mechanical memory storage devices. There was a single bit core memory design from a 1970s electronics magazine that used simple steel washers as cores, terrible magnetic properties but cheaply and widely available. However I don't want an electronic design. Latching relays are cheap enough for registers and ... surprisingly enough ... latches ... but they're a bit expensive for main memory. For example an Altair size of memory made of latching relays would cost me about 256 bytes * 8 bits * 3 bucks per latching relay equals $6.1K just for storage not to mention decode logic. Until I can figure out a way to get below $1/bit purely electromechanically I think I'm stuck.

The history of computation, since the 1940s (before even my time) has always been "computation is cheap, memory is expensive"

Re:Turing machine emulation using physical memory (-1)

Anonymous Coward | more than 2 years ago | (#40372545)

You allude to an important point: Lego is a corporation.
It is NOT a mass noun for the the bricks they sell.
Those are Legos.

it's like a fairtale come true! (2)

Thud457 (234763) | more than 2 years ago | (#40372687)

Lego is a corporation.

In America, that makes him a REAL boy!


Careful, that's totally different than a Real Doll.

Re:Turing machine emulation using physical memory (0)

Anonymous Coward | more than 2 years ago | (#40373603)

Wrong, according to the company that makes them they are "Lego bricks". There is no such word as "Legos".

Re:Turing machine emulation using physical memory (0)

Anonymous Coward | more than 2 years ago | (#40374079)

Fortunately, companies don't get to dictate our language.
I get that they're afraid of trademark dilution. So what?
They're still Legos.

Re:Turing machine emulation using physical memory (2)

Dogtanian (588974) | more than 2 years ago | (#40375573)

You allude to an important point: Lego is a corporation. It is NOT a mass noun for the the bricks they sell. Those are Legos.

Wrong, according to the company that makes them they are "Lego bricks". There is no such word as "Legos".

Fortunately, companies don't get to dictate our language.
I get that they're afraid of trademark dilution. So what?
They're still Legos.

You can call them that if you like. Many other people (particularly in Britain and outside the US) *do* use the mass noun "Lego" and "Legos" just sounds stupid to us.

The point being since neither term is officially endorsed, they're both equally valid or invalid despite your protestations. BTW, I like how you pompously declare imply that "Legos" is the *correct* term, then- when it's pointed out that this has no official status- change things round and say that "companies don't get to dictate our language [..] they're still Legos." Well, no, and their lawyers weren't asking us to call them "Lego" either, so your point was? :-)

I've noticed that the "Lego / Legos" dispute is a matter that seems to get people annoyed out of proportion to its importance. I suspect that this is because Lego (or *cough*... "Legos") is something we grew up with and have a strong personal connection with, even if we don't play with it any more.

In my case, I call it "Lego" and always have done. However, I don't have any strong feelings about the matter- aside from my belief that those who refer to them as "Legos" should be rounded up and executed, that is. ;-)

Re:Turing machine emulation using physical memory (1)

kasperd (592156) | more than 2 years ago | (#40373269)

this is really a turing machine emulated on a NXT using lego as a physical memory display. This is still cool, but its not "turing machine built out of lego" except by the extreme interpretation that a NXT computer is sold by the lego corporation.

According to the video (which is now working) it reads the state of those lego pieces using an optic sensor. So they are not just used for display, they are used as actual memory. There is no requirement as to how you implement the state machine of a turing machine, except that it has to be final state. And the NXT is final state. So it is a turing machine.

Are you implying that you cannot include an NXT in something and say that it is built out of lego? Surely the NXT is overkill for the task, but I don't think lego is selling components that are less overkill while remaining a suitable replacement in the specific machine.

Re:Turing machine emulation using physical memory (0)

Anonymous Coward | more than 2 years ago | (#40374529)

Right now the EE in me is going through the numbers for the components and size you're describing and wondering if you have a 200A breaker to power your design from XD

Re:Turing machine emulation using physical memory (1)

vlm (69642) | more than 2 years ago | (#40375753)

If you're talking about my 22 relay bitslice ALU assuming I could magically energize all 22 relays simultaneously (unlikely) on a 8 bit CPU design the entire ALU could only draw 22 * 8 * .1 = about 20 * .1 * 8 = 2 * 8 = 16 or so amps. Compared to ham radio gear that's nothing. I have a HF transceiver that draws something like 25 amps at 100 watts out on ssb voice peaks and that is not unusual at all in the hobby.

If you're talking about my insane $6000 relay based memory unit yeah the current draw is why I'm going latching relays, no current draw except when you switch states. This also makes them static instead of dynamic, I could power down the works and come back in a month and the memory would still be loaded. The decode logic only burned a couple amps worst case, as I recall. The only problem is 2048 latching relays are kind of expensive at a couple bucks a piece yet 256 bytes is kind of memory constrained.

I've put quite a bit of thought into it, and really the only thing stopping me is bulk memory storage. Yes I could use a microcontroller, a large memory chip, some optoisolators, and some SSRs but its way more fun to do it all electromechanically... if its possible.

Re:Turing machine emulation using physical memory (0)

Anonymous Coward | more than 2 years ago | (#40374619)

Nowadays, we simply use Minecraft, and be done with it.

Re:Turing machine emulation using physical memory (1)

JoeMerchant (803320) | more than 2 years ago | (#40376333)

The history of computation, since the 1940s (before even my time) has always been "computation is cheap, memory is expensive"

That may have changed now with 2TB for $99....

I/O bandwidth on the memory is still a little more expensive than the CPUs it connects to, but 2TB is a pretty infinite storage pool if you've got the patience to wait for it.

Hell, even 2GB of DRAM, or 256MB of cache feels infinite in terms of pre-1980s computers.

That has been done before (4, Informative)

kasperd (592156) | more than 2 years ago | (#40372337)

Re:That has been done before (0)

Anonymous Coward | more than 2 years ago | (#40373207)

+1. I immediately thought of this video too.

Re:That has been done before (1)

Jorl17 (1716772) | more than 2 years ago | (#40374605)

Yes, at university, a great professor showed us this video.

Re:That has been done before (0)

Anonymous Coward | more than 2 years ago | (#40392517)

-1 They didn't say the answer to any of the questions they asked in the beginning.

The Turing Machine (0)

Anonymous Coward | more than 2 years ago | (#40372447)

I am not quite sure, but I think that they built a Turing machine, while I think these people [1] built a universal Turing machine.
[1] http://graal.ens-lyon.fr/rubens/

Before you ask: (1)

Tablizer (95088) | more than 2 years ago | (#40372503)

In theory it actually can run Linux (if you are really really patient)

Re:Before you ask: (1)

Belial6 (794905) | more than 2 years ago | (#40372991)

I think it would be funnier to run LOGO on it.

Re:Before you ask: (2)

Bob the Super Hamste (1152367) | more than 2 years ago | (#40375139)

For a truly perverse experience it needs to be a Lego Turing machine to emulate an Apple ][ running LOGO to control the Lego Turing machine. I some how feel I have now stumbled upon some weird edge case of the halting problem related to my childhood and that I need to go dig out my computational theory book.

Re:Before you ask: (1)

Belial6 (794905) | more than 2 years ago | (#40376599)

Specifically Turtle LOGO running on a Lego Turing machine.

I'll bet this isn't a real Turing Machine (1)

dkleinsc (563838) | more than 2 years ago | (#40372505)

Otherwise, how the heck did they come up with an infinitely long tape?

Re:I'll bet this isn't a real Turing Machine (1)

rossdee (243626) | more than 2 years ago | (#40372693)

For an infinitely long tape you need an infinite number of LEGOs.
I guess LEGO will be glad to sell them to you (subject to their maximium production rate) and they could probably keep up to the needs of the machine.

Any billionaires want to fund such a project?

Re:I'll bet this isn't a real Turing Machine (2)

onemorechip (816444) | more than 2 years ago | (#40377317)

Wouldn't they have to be aleph-nullaires? I.e., the infinitesimal percent?

Re:I'll bet this isn't a real Turing Machine (4, Funny)

Sarten-X (1102295) | more than 2 years ago | (#40372701)

That's the newsworthy part. They created a mechanism that takes snide comments from the Internet, and converts them to mechanical storage!

Turing's Revenge (1)

Tablizer (95088) | more than 2 years ago | (#40372571)

If Professor Turing patented a TM these days, he could sue for royalties on every computer, big and small. I almost wish he had as revenge for the crappy way the British gov't treated him.

informa7iv3 SHITSHIT (-1)

Anonymous Coward | more than 2 years ago | (#40372635)

Great stuff... (2)

CaptainHayashi (2590981) | more than 2 years ago | (#40372763)

...but I'd like to see how they'd implement the lambda calculus in Lego.

Maybe this is how one finally proves, after decades of bickering and argument, which model of computation is better- by seeing which one looks prettier when you make a visualiser for it out of brightly coloured snappable bricks.

An another one in Lego without electronics (0)

Anonymous Coward | more than 2 years ago | (#40372795)

http://videotheque.cnrs.fr/video.php?urlaction=visualisation&method=QT&action=visu&id=3001&type=grandPublic

Unfortunately, the video is in french. The machine works with Lego pneumatic cylinders so it's entirely mechanical.

Re:An another one in Lego without electronics (0)

Anonymous Coward | more than 2 years ago | (#40427707)

And unlike the one in TFA, where the program itself seems to be stored on a chip, this one looks like it has it "encoded" in the bricks themselves...

Not really a Turing machine, but no surprise (1)

Theovon (109752) | more than 2 years ago | (#40374859)

A Turing machine is defined by a tape and a manipulator, and a state machine defining how those tape symbols are manipulated. The former is visible in the video. The latter is not. It appears they're using a mindstorm (itself a microcomputer) to perform the function of the state machine. I think this is cheating.

In fact, the whole state machine part of the Turing machine has always been rather nebulous to me. Yes, I understand the state transitions, but no physical mechanism is described (in CS theory texts) to implement it. The only physical parts of the TM are the tape and manipulator, while the state machine is left as an exercise for the imagination of the reader. In a way, I think that's cheating too.

Re:Not really a Turing machine, but no surprise (0)

Anonymous Coward | more than 2 years ago | (#40376797)

The state can be implemented by a rotating drum. Based on the symbol a button is pushed on the currently selected segment of the drum that sets the current symbol to write, the next drum position and the direction. On the next movement the machine springs in motion, writing the symbol, rotating the drum and then moving to the next symbol. This could be implemented completely mechanically.

Re:Not really a Turing machine, but no surprise (1)

neonsignal (890658) | more than 2 years ago | (#40378907)

The implementation of the state machine is of less interest because it is finite. The aim of the exercise is to reduce the the notion of computability to a machine-like process. The most simple conception is that only one part of the machine is infinite and variable. That is why Turing needed to show how to implement a Universal Machine as a single Turing Machine, so that the transition table could be made fixed in size (and after that point, uninteresting in implementation). It would have been sufficient to posit a human reading a pencil and paper transition table and methodically applying the transitions to the tape; the important part is that the process is "mechanical" meaning without the involvement of creativity, not "mechanical" meaning that it can be realized in a mechanical form.

Of course, if you want to build a model of a Turing Machine, then the implementation does become more interesting, so I agree with you that this Lego model is only half of the puzzle.

Re:Not really a Turing machine, but no surprise (1)

anyanka (1953414) | more than 2 years ago | (#40382557)

Besides, you don't need a fully mechanical state machine and an infinite tape to show the interested public some of Turing's highly important computer science work (as opposed to impressing the Slashdot crowd, or showcasing the Engima code breaking work, which seems to be what most 'normal' people associate with him these days).

With that goal in mind, I think the project has been highly successful – it has been reported in major Dutch newspapers and generated a lot of interest in the Netherlands.

Re:Not really a Turing machine, but no surprise (1)

Arancaytar (966377) | more than 2 years ago | (#40378943)

The mindscrew is that every physical machine, including the microcomputer (as well as this "Turing machine" itself, with its finite tape), is technically a finite state machine. The theoretical model of a true Turing machine requires the availability of infinite memory.

You could say that the deterministic finite state machine can be any (deterministic) physical device conceivable, while the infinite tape is the one part that cannot be built in reality.

The only reason it's "simple" (1)

Oscaro (153645) | more than 2 years ago | (#40375765)

The only reason it's "simple" is that one of its parts is a full computing device.

I'd have preferred a "hardware" implementation...

Ruting would have been 100 on Saturday (1)

peter303 (12292) | more than 2 years ago | (#40376205)

Born June 23, 1912

Cheating! (0)

Anonymous Coward | more than 2 years ago | (#40379527)

Mindstorms has a computer in it. That's cheating.

It's not very impressive to build the simplest possible computer out of... a vastly more powerful computer!

Just what is _that_ supposed to demonstrate?

slowest computer ever. (1)

issicus (2031176) | more than 2 years ago | (#40395875)

I do love legos though..
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