Why is NON DISCRETE logarithm problem not hard as the DISCRETE logarithm problem (so computationally hard)? I've already read this question about the difference between discrete and non discrete logarithms.
But I still have problems to clarify my mind about why the Discrete Logarithm Problem is computationally hard while the NON Discrete Logarithm Problem is not, as I read in my Cryptography and Security book.

What are the computation differences? Why can I, for example, easily break a non discrete logarithm cipher but not a discrete one?
The main point is that the entire apparatus of calculus applies to exponentiation over the real numbers. For instance, if $a$ and $b$ are close, then $g^a$ and $g^b$ are close as well. The exponential function and its inverse are nice, so you can use infinite series for your computation, and some partial sum will be close enough to the correct answer. Or since exponentiation is monotonic, you can use binary search.

The groups we use for cryptography are usually discrete, and the apparatus of calculus no longer applies. For example, there is no sensible distance measure that relates the distance between $a$ and $b$ and the distance between $g^a$ and $g^b$. And this means things end up being more difficult.