# What is the intuition behind the entropy formula used in the ID3 algorithm?

What is the intuition behind the following entropy formula used in the ID3 algorithm?

$$\text{info}(D) = -\sum_{i=1}^m p_i \log_2(p_i)$$

The answer for the minus sign is in section 6. The probability logs are less than or equal to $$0$$, so the minus sign guarantees that information (entropy) is always greater than or equal to $$0$$.