DSimon comments on The Up-Goer Five Game: Explaining hard ideas with simple words - Less Wrong

29 Post author: RobbBB 05 September 2013 05:54AM

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Comment author: DSimon 06 September 2013 02:27:21PM *  8 points [-]

Mr. Turing's Computer

Computers in the past could only do one kind of thing at a time. One computer could add some numbers together, but nothing else. Another could find the smallest of some numbers, but nothing else. You could give them different numbers to work with, but the computer would always do the same kind of thing with them.

To make the computer do something else, you had to open it up and put all its pieces back in a different way. This was very hard and slow!

So a man named Mr. Babbage thought: what if some of the numbers you gave the computer were what told it what to do? That way you could have just one computer, and you could quickly make it be a number-adding computer, or a smallest-number-finding computer, or any kind of computer you wanted, just by giving it different numbers. But although Mr. Babbage and his friend Ms. Lovelace tried very hard to make a computer like that, they could not do it.

But later a man named Mr. Turing thought up a way to make that computer. He imagined a long piece of paper with numbers written on it, and imagined a computer moving left and right that paper and reading the numbers on it, and sometimes changing the numbers. This computer could only see one number on the paper at a time, and also only remember one thing at a time, but that was enough for the computer to know what to do next. Everyone was amazed that such a simple computer could do anything that any other computer then could do; all you had to do was put the right numbers on the paper first, and then the computer could do something different! Mr. Turing's idea was enough to let people build computers that finally acted like Mr. Babbage's and Ms. Lovelace's dream computer.

Even though Mr. Turing's computer sounds way too simple when you think about our computers today, our computers can't do anything that Mr. Turing's imagined computer can't. Our computers can look at many many numbers and remember many many things at the same time, but this only makes them faster than Mr. Turing's computer, not actually different in any important way. (Though of course being fast is very important if you want to have any fun or do any real work on a computer!)

Comment author: DSimon 10 September 2013 02:51:00PM *  0 points [-]

So what is Mr. Turing's computer like? It has these parts:

  1. The long piece of paper. The paper has lines on it like the kind of paper you use in numbers class at school; the lines mark the paper up into small parts, and each part has only enough room for one number. Usually the paper starts out with some numbers already on it for the computer to work with.
  2. The head, which reads from and writes numbers onto the paper. It can only use the space on the paper that is exactly under it; if it wants to read from or write on a different place on the paper, the whole head has to move up or down to that new place first. Also, it can only move one space at a time.
  3. The memory. Our computers today have lots of memory, but Mr. Turing's computer has only enough memory for one thing at a time. The thing being remembered is the "state" of the computer, like a "state of mind".
  4. The table, which is a plan that tells the computer what to do when it is each state. There are only so many different states that the computer might be in, and we have to put them all in the table before we run the computer, along with the next steps the computer should take when it reads different numbers in each state.

Looking closer, each line in the table has five parts, which are:

  • If Our State Is this
  • And The Number Under Head Is this
  • Then Our Next State Will Be this (or maybe the computer just stops here)
  • And The Head Should write this
  • And Then The Head Should move this way

Here's a simple table:

Happy 1 Happy 1 Right
Happy 2 Happy 1 Right
Happy 3 Sad 3 Right
Sad 1 Sad 2 Right
Sad 2 Sad 2 Right
Sad 3 Stop

Okay, so let's say that we have one of Mr. Turing's computers built with that table. It starts out in the Happy state, and its head is on the first number of a paper like this:

1 2 1 1 2 1 3 1 2 1 2 2 1 1 2 3

What will the paper look like after the computer is done? Try pretending you are the computer and see what you do! The answer is at the end.

So you can see now that the table is the plan for what the computer should do. But we still have not fixed Mr. Babbage's problem! To make the computer do different things, we have to open it up and change the table. Since the "table" in any real computer will be made of very many parts put together very carefully, this is not a good way to do it!

So here is the amazing part that surprised everyone: you can make a great table that can act like any other table if you give it the right numbers on the paper. Some of the numbers on the paper tell the computer about a table for adding, and the rest of the numbers are to be added. The person who made the great table did not even have to know anything about adding, as long as the person who wrote the first half of the paper does.

Our computers today have tables like this great table, and so almost everything fun or important that they do is given to them long after they are built, and it is easy to change what they do.

By the way, here is how the paper from before will look after a computer with our simple table is done with it:

1 1 1 1 1 1 3 2 2 2 2 2 2 2 2 3
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