We present a Brouwerian example showing that the classical statement 'Every Lipschitz mapping f : [0; 1] -> [0; 1] has rectifiable graph' is essentially nonconstructive. We turn this Brouwerian example into an explicit recursive example of a Lipschitz function on [0; 1] that is not rectifiable. Then we deal with the connections, if any, between the properties of rectifiability and having a variation. We show that the former property implies the latter, but the statement 'Every continuous, real-valued function on [0; 1] that has a variation is rectifiable' is essentially nonconstructive.