Most computer scientists and information technologists consider that data is 'raw facts' while information is 'data plus meaning'. We have discovered that bits stored in memory are 'data' with no meaning, it is the way we interpret the data that makes it information. With images the bits in memory become information when they appear on screen and we recognise the pattern they form.
We recognise a face when we see one because we have doing that since infancy but how many of us would recognise the path of a particle when we saw it? Look back at the images you made earlier. How much information does each one contain? Is it possible to measure the amount of information in the images? Do some images contain more information than others? Is it possible to create an image with no information in it? What is the most information that we can pack into our 20x20 grid? Difficult questions!
Computers deal with information: how can information be measured? What contains most information, a telephone directory or a novel or a text book? One feature of information is that it should tell you something that you don't know already. The more surprising a piece of information the more information that it conveys. Think of jokes and punch lines!
Try guessing numbers for which there is some information attached such as age.
Now try guessing numbers in certain ranges, say 1-10. One pupil writes down a number and the others try to guess what it is by asking a single question each. Work out a strategy for identifying the mystery numbers. Record the number of guesses taken to find the numbers. What is the effect of increasing the range of numbers, for example 1-100, 1-1,000, 1-10,000?
Illustrate the process of identifying a mystery number in a decision tree (try 0-7 and 0-15). Note that in these trees the location of a number can be represented by its binary string with 0 for 'no' and 1 for 'yes'. For example, 5 is Yes-No-Yes or 101.
According to Claude Shannon the amount of information in a coin toss is one 'bit', that is two possible outcomes, heads or tails. Shannon called the information content of a message its 'entropy'. Where there are 4 possible outcomes the number of bits is 2, for 8 outcomes 3 bits, for 16 outcomes 4 bits. What is the amount of information when drawing a card from a pack? This depends on the information you are seeking, the suit, the card value or the two combined. The information in a card drawn from a standard deck is either 2 for the suit (4 suits in a pack) or something between 3 and 4 for the value (13 values in a pack from 2 to ace).
Each member of a pair writes down a simple short sentence (5-6 words). One member of the pair tries to guess the sentence one letter at a time. The pair records the number of guesses taken for each letter and counts them up for each letter. Work out the average number of guesses for each letter and then compare findings across the class.
This gives some measure of the information stored in the letters of an English sentence. It is generally known that the meaning of a piece of text can still be understood even when some letters are removed. Languages contain some redundancy (extra information) to ensure a message is understood; removing the redundancy leads to compression while adding information to correct errors increases the size of the message. What common form of communication routinely uses compression? (Leaves out letters and words but is still intelligible.)
In general a message cannot be compressed beyond its entropy (information content) without losing some of its content. When you want to be really sure that a message will get through (e.g. from outer space) you add error checking.