Changes

<math>  -\log(0.0625)  > -\log(0.125).  </math>

<math>  -\log(0.0625)  > -\log(0.125).  </math>

And an event occurring with probability = 1 is a certain event, which will carry no information. Consequently -log(1) = 0.   

And an event occurring with probability = 1 is a certain event, which will carry no information. Consequently, -log(1) = 0.   

If all these properties should be maintained for all possible divisions of messages written in different alphabets, then the negative logarithm of the probability is a very good candidate for being a measure of information.  

If all these properties should be maintained for all possible divisions of messages written in different alphabets, then the negative logarithm of the probability is a very good candidate for being a measure of information.  

== The continuous case ==

== The continuous case ==

In the continuous case the discrete frequency function is replaced by a continuous probability density function, (p. d. f.) , f(x), and H may be written

In the continuous case the discrete frequency function is replaced by a continuous probability density function, (p. d. f.), f(x), and H may be written

<math>  H = - \int f(x) \log f(x) dx  .</math>

<math>  H = - \int f(x) \log f(x) dx  .</math>

http://web.telia.com/~u91131915/mountain_crest.GIF

http://web.telia.com/~u91131915/mountain_crest.GIF

After a sufficiently large number of generations, the increase in [[average information]] may result in the green cluster. Actually, the mean fitness is the same for both red and green cluster (about 65%). The effect of this adaptation is not very salient in a 2-dimensional case, but in a high-dimensional case, the efficiency of the search process may be increased by many orders of magnitude. Besides, a Gaussian distribution has the highest [[average information]] as compared to other distributions having the same second order moment matrix, Middleton, 1960.

After a sufficiently large number of generations, the increase in average information may result in the green cluster. Actually, the mean fitness is the same for both red and green cluster (about 65%). The effect of this adaptation is not very salient in a 2-dimensional case, but in a high-dimensional case, the efficiency of the search process may be increased by many orders of magnitude. Besides, a Gaussian distribution has the highest average information as compared to other distributions having the same second order moment matrix, Middleton, 1960.

== History of applications ==

== History of applications ==