# What is the intuition behind slack variables, penalty and minimization of support vector machines? [duplicate]

I would like to understand more deeply what the purpose and intuition of slack variables is in support vector machines.

I know that slack variables are used to minimize

$$\frac{1}{2} ||w||^2 + C \sum_{n=1}^{N} \xi_n$$ and is the distance to the support vectors, but it seems really strange.

I noticed that using a small Penatly constant $$C$$ allows more error, but why is this? I think it would still be more minimal having less errors as well.