Depends upon how information is defined.
Now a string of 20 0's can mean almost anything that we want it to mean depending upon how we encode a message
So how can 20 0's
not contain information?
Well in information theory we are not concerned with the
meaning of a message (that is the concern of the two people communicating)
In Information theory we define the information content of a message by the number of changes required to send the message
If there are many changes to send in order to convey a message then we say it has a large informatiion content
If there are no changes ro send to convey a messsage, then we say the message has zero information content.
BUT, a message that has no information content can be as significant as a message that contains a lot of information
Thus in the 8-bit messages
10101010 has many changes and contains a lot of information
00000000 has no changes and contains no information
However both message can have
meaning and both messages can have exactly the same significance.
But only to the end users, not to us getting ready to send the messages.
Your 20 0's could mean red, or blue, or 1.04 million, or 2, or 0 - almost anything that you wish it to be.
But to us preparing to convey the message there is no information content. There may be meaning or significance but we are not concerned wuth that
This means we simply have to indicate to the far end that the next string to be considered is the set empty of informatio 00000000.....
To do that we do
not have to send the full string of 0's
The number of
changes necessary to send the message defines the information content, not any meaning that the message may have.
For example the total absence of information can have as much significance (or meaning ) as a lot of information being transferred
.
For example if you imagine informatiion being transferred by a flashing light 1 = ON, 0 = OFF then if we were to transfer a string of 20 digits of alternate 0's and 1's you would see a flashing light and you would say information is being transferred (in fact the flashes
are the information)
If we were to transfer a string of 20 0's you would see nothing - no information is being transferred. however th eabsence of information has meaning.
Similarly if you were to transfer a string of 20 1's you would simply see a steady light - no information is being transferred.
This is not academic.
If a communication system has a string of 20 0's to send, in order to get the maximum efficiency out of the communication channel, the 20 0's are simply not sent for example the sending link might just send a single control bit indicating that the next 20 bits are 0
Similarly if a string of 20 1's is to be sent, the sending end can simply send one digit indicating that the next 20 digits are 1.
That is really one of the prime functions of the design of a communication link - looking for strings of unchanging digits - if a string of digits is unchanging we can simply not send them and send a couple of digits telling that far end that the next string of length N is either 1 or zero.
We can in fact go further than that and look for repeated patterns, if a pattern of digits repeats itsel then we are sending redundant onformation and can arrange that only the forst set of th erepeating pattern is sent. That is the basis of compression.
Basically, unless we are sending
changes we are not sending new information - we are sending a repeated 'state' that has meaning but not information and once that 'state' is communicated to the far end there is no need to transmit the repeated pattern.