EPT
"You only think that because you cannot comprehend the thought of the infinite algorithms."
Malice. My adversary.
"There is nothing infinite about algorithms, " said I. "They all have a step 1, a step 2, a step 3, and so on until at one point the algorithm terminates."
Malice chuckled at my foolishness - "And how long is your algorithm? Does it have a trillion steps? Well then I give you an algorithm with one more step than that!"
Silence. I cannot set any finite limit on length - and have no time, for Malice has thrown me off the lighted path onto a dimly lit road. It is one tile wide, and stretches forward as far I can see, and as far back - and then some, no matter how far I walk in either direction. Curiously, some tiles are adorned with cotton candy and others with kittens.
I suddenly realize - I am walking on the infinite tape of a Turing Machine. The kittens and cotton candy are binary - I walk upon the continuum, and I am the decimal point. Stretching behind me to infinity are the fractional places, and before me the integral section.
"Malice, I have you!" I shouted, having had inspiration which overcomes infinity.
"So you noticed, your tape holds a place for every real number".
"Of course, more so in fact that any number of steps your fancy algorithm contains - no matter how high it may be! You'll never generate a successor this time."
Brightness. A light appears at the end of infinity in either direction. Malice smiles at me tauntingly. "Oh there is a successor. It awaits you at the end of infinity, if you can reach both of them at once."
How can I go forward both ways at once? I cannot look left and right at the same time - what a contradiction. Collapse. The tape is cut and lined up at myself, the decimal point.
Of course - I cannot look left and right at the same time but I can switch between them faster than any speed. I zigzag, going forward inexorably, touch home on both top and bottom, then to one on top, one on bottom, two on top, two on bottom, accelerating endlessly, doubling my speed in half the time over and over.
And then - it is done. I've reached the end of infinity. They're not all robots. They can't be.
+ Show Spoiler +
I swear I was not on drugs for this.
