Comments on: Universal Turing Machine in 100 punchcards

By: Buddha Buck

Buddha Buck — Tue, 26 Jun 2012 02:46:00 +0000

I think a couple of things should be kept in mind:

1) The definition of a Turing Machine (TM) works perfectly well with an unbounded tape, not an infinite tape.

2) The only TMs which need an infinite tape are non-halting TM. Every halting TM only uses a finite tape.

3) Nearly every (if not every) computational class (e.g., P, NP, PSPACE, EXP, etc) only uses a finite tape who’s length can be bounded before running; Even NP-Complete problems only take a tape proportional to a polynomial of the input size.

So if you give me a computable problem, plus it’s input, I can give you a TM with a finite tape than can solve it.

And the point of a TM was not to pass the Turing Test, it was to prove that the set of computable numbers is countable.

By: ryuthrowsstuff

ryuthrowsstuff — Mon, 25 Jun 2012 00:02:00 +0000

I actually looked it up.

By: Tynam

Tynam — Sun, 24 Jun 2012 22:47:00 +0000

All that is true, but I stand by my claim. The English language has evolved to contain (outside of mathematical contexts, where I agree with you totally) the idea of ‘Turing machine’ as a synonym for any such state-based automaton. And this isn’t a harmful development – it’s a useful, compact phrase. Even if it does make the logician part of me wince for a second.

Nor is this a problem for Turing’s original discussion point. At least one machine which we *know* would pass the Turing test – an exact simulation of a human brain – is a finite machine. We know that an infinite-capacity-tape Turing Machine is not actually necessary for the test. I concede that a finite automaton is ultimately nothing more than a nifty version of Eliza, but then… so are we. (Unless you’re claiming to possess an infinite number of neurons, in which case I will have little choice but to bow to your superior intellect.)

After all, an awful lot of maths is based on us pretending that there’s no meaningful difference between finite-but-arbitrarily-large and countably-infinite.

By: Antinous / Moderator

Antinous / Moderator — Sun, 24 Jun 2012 21:50:00 +0000

It’s like a heterosexual version of Moby Dick.

By: semiotix

semiotix — Sun, 24 Jun 2012 18:24:00 +0000

Yes, yes, welcome to Bletchley Park! Now strip down to your knickers. Oh yes, it's for the war effort, you see. Quite essential, really.

By: knappa

knappa — Sun, 24 Jun 2012 15:18:00 +0000

Er, it is a finite automata but a deterministic one, not a non-deterministic one.

By: Nathan Hornby

Nathan Hornby — Sun, 24 Jun 2012 14:02:00 +0000

What’s funny is that I know significantly more about Bletchley Park and Turing as an adult. I grew up and went to school in Bletchley.

By: Yehuda Jonathan Berlinger

Yehuda Jonathan Berlinger — Sun, 24 Jun 2012 12:57:00 +0000

…
Maybe it’s nitpicking. But the difference between a Turing Machine and a finite state automaton is like the difference between infinite and finite, or between the alphabet and the entire works of Shakespeare (times infinity) i.e. Really Big.

The whole point of a Turing Machine being infinite was that it could theoretically simulate the responses of a human being (i.e. ANY response to ANY input) and therefore pass the Turing Test. A finite automaton is little more than a version of Eliza; a finite series of responses to a finite series of inputs. It’s a nifty calculator.

Finite automata are cool in their own right. Ones with really big tapes are cooler. But seeing them presented as Turing Machines is just painful.

Yehuda

By: nixiebunny

nixiebunny — Sun, 24 Jun 2012 10:00:00 +0000

If the tape is longer than the machine is physically capable of indexing through in a lifetime, it’s for all practical purposes infinitely long.

By: theclockworkcomputer

theclockworkcomputer — Sun, 24 Jun 2012 09:51:00 +0000

The 100 punchcards merely define the rule table of a Turing Machine, it is software. The machine itself is a computer, not a Turing Machine. The program thinks the memory is the tape and uses that.

By: Tynam

Tynam — Sun, 24 Jun 2012 08:19:00 +0000

Now you’re just nitpicking. In non-formal conversation, finite state-based automata are frequently referred to as ‘Turing machines’, and for very good reasons. (For all programs not exceeding the available tape capacity, there’s no difference. While infinite tape is impossible, ‘large enough’ is a reasonable approximation for many purposes.)

By: Yehuda Jonathan Berlinger

Yehuda Jonathan Berlinger — Sun, 24 Jun 2012 06:58:00 +0000

Ok, guys, PLEASE. A Turing machine requires an INFINITE sized tape. A Turing machine is theoretical and CANNOT EXIST.

A finite machine – a machine with a finite tape or finite memory – is a non-deterministic finite automata. NOT a Turing machine.

Thank you and good day,
Yehuda

By: eviladrian

eviladrian — Sun, 24 Jun 2012 06:16:00 +0000

The hardest part for me was realising that there was a puzzle.

By: Joseph Francis

Joseph Francis — Sun, 24 Jun 2012 03:51:00 +0000

Reminds me of a great episode of James Burke’s ‘Connections’
Episode 4:Faith in Numbers.
http://www.youtube.com/watch?v=ORY-mXXgJg4

By: nixiebunny

nixiebunny — Sun, 24 Jun 2012 03:46:00 +0000

Now, imagine the fate of the free world resting on your ability to solve that puzzle. Welcome to Bletchley Park.

By: Mark Dow

Mark Dow — Sun, 24 Jun 2012 02:32:00 +0000

It appears to be a simple puzzle — program his machine to give a desired output, which is his encoded name (there is another layer of complexity I don’t grok, the relationship between input and output). 10 minutes of debugging gets you to “Alan Turing” search results. Thanks, Alan, for showing us how to search any term, automagically. Thank FSM for high level formal languages.

By: B E Pratt

B E Pratt — Sun, 24 Jun 2012 01:44:00 +0000

Interesting. I am sorta able to get the binary numbers to match (at least at first), but I really am not quite sure what I am doing…. Thanks for pointing this doodle out

By: ryuthrowsstuff

ryuthrowsstuff — Sun, 24 Jun 2012 01:20:00 +0000

Surprised you guys haven’t posted on the current Google Doodle. Its some sort of Turing machine based puzzle game. And I am entirely incapable of figuring it out.