norway's cannot randomly bump a signaling invent from one type to another clearly now we can step back and begin to define the capacity of a communication system using these two very simple ideas first how many symbol transfers per second which we called symbol rate and today it's known simply as a baaaad for a nearby doe and we can define this as and words and symbol transfers per second number two how many differences personable which we can think of as the symbol space how many symbols can we select from at each point and we can call this ass and as we've seen before these parameters can be thought i love as a decision tree of possibilities because each symbol can be thought of as a decision where the number of branches depend on the number of differences and after and symbols we have a tree with ass to the power of an leaps and since each path through this tree can represent a message we can think i have the number i've leaves as the sizeof the message space and this is easy to visualize the message space is simply the whip have the basic one of the streets and it defines the total number of possible messages one could send given a sequence event symbols for example let's see alice and bob a message which consists of two clocks and they're using a hard verses soft flock as their communication system this mean she has the ability to find one up for possible messages to bop and if instead they were using a system of hard versus medium versus of blocks then with two pox she has the ability to find one ove 32 the power two equals nine messages and with reply ox this jumped 21 up 27 messages now if instead alice and bob were exchanging written notes in class which contain only two letters on a piece of paper been a single note would contain 10 of 26 to the power to or 676 possible messages it it's important to realize now that we no longer care boat the meaning applied to these chains have different since merely how many different messages are possible and the resulting sequences could represent numbers names feelings music or perhaps even some alien alphabet we could never understand when we look at a communication system now we can begin to think about its capacity that's how many different things you could say we could then use the message space to define exactly how many differences are possible in any situation and this simple yet elegant idea forms the basis for how information will be later to find and this is the final step that brings us to modern information theory and it emerges and early 20th century for the