How would you do that?
Cognitive load is a fairly general phenomenon, not limited to memorizing long numbers. You can experience cognitive load simply by living a busy life where you are constantly thinking about other things, and not able to be "present".
My anecdotal evidence seems to show the opposite. It is easier to e.g. dedicate the time to work out when I have a fairly busy job than when I am sitting at home collecting unemployment. The reason is that in the first case I am proud of myself, invigorated, uplifted, the opposite of depressed (hedonic?) and feel like "You go man! You were awesome today, now go and totally crush that workout too!" and in the second case I hate myself, feel depressed, feel like "You are just a useless bum, nobody will ever employ you, you cannot do anything r...
I was recently reading a blog here, that referenced a paper done in 1999 by Baba Shiv and Alex Fedorikhin (Heart and Mind in Conflict: The Interplay of Affect and Cognition in Consumer Decision Making). In it, volunteers are asked to memorise short or long numbers and then asked to chose a snack as a reward. The snack is either fruit or cake. The actual paper seems to go into a lot of details that are irrelevent to the blog post, but doesn't actually seem to contradict anything the blog post says. The result seems to be that those with a higher cognitive load were far more likely to chose the cake than those who weren't.
I was wondering if anyone has read any further on this line of research? The actual experiment seems to imply that the connection between cognitive load and willpower may be an acute effect - possibly not lasting very long. The choice of snack is made seconds after memorising a number and while actively trying to keep the number in memory for short term recall a few minutes later. There doesn't seem to be anything about the effect on willpower minutes or hours later.
Does anyone know if the effect lasts longer than a few seconds? If so, I would be interested in whether this affect has been incorporated into any dieting strategies.