The problem is you have it backwards, the bumps are what is real. Your distribution is a reflection (an image, a photograph) of what is i.e. think of the order of operations, photon bounces/is ejected from object (carrying information) hits your eye, eye translates the signal. The signal reaches your mind, mind derives a thought from the information your eye has received, therefore when you 'self generate' ideas, you got those ideas from the outside world first. Therefore in our minds we're really just manipulating 'holographic' reflections of what is on the outside. If you actually had to make your bumps in a distribution out of real stuff in the real world, you would find out things. This is why I always transport mathematical reasoning back into the 'real world' I think terms of "What would it be made of?".. if this is 'infinite' in terms of our thoughts (i.e. if we had infinite strings of data), but if we actually had to make say pi out of stuff in the real world. We would run out of stuff to make distinct numbers from, therefore. Pi is "infinite" only in imaginary space, in the real world, pi ends (i.e. when you make pi with stuff).
In a computer pi would have to be stored somewhere, pi would fill up any amount of memory, hard disk space, and processing power you could throw at it, therefore, pi in the real world is truncated, it eventually ends somewhere when you consider the real world is made of stuff.