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Are Calculators Smart?

Date: 06/02/2001 at 20:12:02
From: nicole
Subject: Calculators

How come calculators are so smart?
Do calculators have artificial intelligence?

Date: 06/03/2001 at 13:46:40
From: Doctor Ian
Subject: Re: Calculators

Hi Nicole,

Calculators are not really smart. If a calculator is sitting in a 
burning house, does it know that it needs to get out of the house? 
Does it know that it needs new batteries periodically, and how to get 
them? Can it recognize a face, or tell a cat from a dog?  

Calculators are very good at one particular thing, but as a rule of 
thumb, being very good at one kind of thing often means that you'll be 
very bad at other kinds of things.

People are very, very good at some kinds of things, and very, very bad 
at others. The things people tend to be good at are messy, creative 
tasks, with lots of noisy data - for example, being able to recognize 
a friend even though it's dark out, and she's wearing something she's 
never worn before; or being able to understand a waitress in a 
restaurant even though she has a very strong accent; or knowing who is 
on the other end of the phone even though he's only said 'hello'; and 
so on. 

The things people tend to be bad at are things that require the same 
things to be done over and over and over and over, without any 
variation. In other words, people are bad at boring things.  

Which works out nicely, because calculators are very good at boring 
things, but awful at anything that requires any kind of creativity!

Here's one way to think about this. If you tell a calculator to divide 
324 by 56.59, it can only come up with one possible answer. That's not 
very smart at all. A person, on the other hand, might be able to come 
up with dozens of different answers, or even help you see that the 
computation you're trying to do is the wrong one. 

For example, suppose I ask you to compute 110! divided by 106!, where 
'!' means 'factorial', which is defined this way:

  1! = 1

  2! = 2 * 1 = 2

  3! = 3 * 2 * 1 = 6

  4! = 4 * 3 * 2 * 1 = 24

and so on. This gets very large very quickly - so large that most
calculators can't compute a number like 110!.  

So with most calculators, you're just stuck trying to solve a problem 
like this, because as soon as you enter '110' and hit the '!' button, 
the calculator will say the equivalent of 'Too big!'.  

But here's what a person would do:

  110!    110 * 109 * 108 * 107 * 106 * 105 * 104 * ... * 2 * 1
  ---- = -------------------------------------------------------
  106!                            106 * 105 * 104 * ... * 2 * 1

       = 110 * 109 * 108 * 107

And then he would use the calculator to multiply the four numbers 

So which is smarter, the person or the calculator? 

Here is a more extreme example of the point I'm trying to make:

  Humour: Building Height - Josh Parris   

>Do calculators have artificial intelligence?

I suppose it depends on what you consider to be a 'calculator', and 
where you draw the line between programming and 'intelligence', but 
using the normal meanings of those words, the answer is: no, 
calculators do not have intelligence, artificial or otherwise. 

Does this help?  Write back if you'd like to talk about this some 
more, or if you have any other questions. 

- Doctor Ian, The Math Forum   
Associated Topics:
Middle School About Math

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