But MechanicalTulpa is good for far more than economizing on cost. The key lies in T-Wave's proprietary recursive tulpa technology, whereby our tulpas themselves create tulpas, and so forth, potentially ad infinitum.

One day you talk with a bright young mathematician about a mathematical problem that's been bothering you, and she suggests that it's an easy consequence of a theorem in cohistonomical tomolopy. You haven't heard of this theorem before, and find it rather surprising, so you ask for the proof.

"Well," she says, "I've heard it from my tulpa."

"Oh," you say, "fair enough. Um--"

"Yes?"

"You're sure that your tulpa checked it carefully, right?"

"Ah! Yeah, I made quite sure of that. In fact, I established very carefully that my tulpa uses exactly the same system of mathematical reasoning that I use myself, and only states theorems after she has checked the proof beyond any doubt, so as a rational agent I am compelled to accept anything as true that she's convinced herself of."

"Oh, I see! Well, fair enough. I'd still like to understand why this theorem is true, though. You wouldn't happen to know your tulpa's proof, would you?"

"Ah, as a matter of fact, I do! She's heard it from her tulpa."

"..."

"Something the matter?"

"Er, have you considered..."

"Oh! I'm glad you asked! In fact, I've been curious myself, and yes, it does happen to be the case that there's an infinitely descending chain of tulpas all of which have established the truth of this theorem solely by having heard it from the previous tulpa in the chain." (This parable takes place in a world without a big bang -- tulpa history stretches infinitely far into the past.) "But never to worry -- they've all checked very carefully that the previous tulpa in the chain used the same formal system as themselves. Of course, that was obvious by induction -- my tulpa wouldn't have accepted it from her tulpa without checking his reasoning first, and he would have accepted it from his tulpa without checking, etc."

"Uh, doesn't it bother you that nobody has ever, like, actually proven the theorem?"

"Whatever in the world are you talking about? I've proven it myself! In fact, I just told you that infinitely many tulpas have each proved it in slightly different ways -- for example my own proof made use of the fact that my tulpa had proven the theorem, whereas her proof used her tulpa instead..."