After failing in 100 attempts, they decide to rest until the next day. While setting up their beds, Leez notices that Yuta has left. She asks Ran about magic without calculations again. Ran uses hoti brahma to create two large loops—one normal, one with a single twist—and asks her to imagine gluing the edges of the loops. For the first loop, Leez guesses that it would form a tube shape, then correctly guesses that doing the same is impossible for the second loop because of the twist. Ran compliments her for guessing correctly right away, but Asha dismisses the accomplishment. Ran recalls that even Rana had trouble figuring it out at the academy, and scolds Asha for judging Leez at the standards of magicians. When Asha glares at him though, he stops, worried that he's giving off the impression of being interested in Leez, whom he still thinks is Asha's girlfriend.
Leez asks him to continue, and Ran explains that in the case of the second loop, it is still possible to guess a theoretical shape, though most people can only imagine an incomplete answer. Leez points out that indeed, it wouldn't be possible to draw it unless one makes the shape intersect itself, but that doesn't correspond to the image in her head. Asha is surprised by her answer. Ran is really surprised as well, as it reveals that like him, Leez can learn magic without calculations. However, Asha dismisses the whole concept, noting that using magic by guesswork makes one dangerous to those around them. Ran is annoyed at Asha's inability to give praise to 'his girlfriend', then suggests teaching Leez a spell that doesn't cause much damage even if it fails: hoti kubera.
Spoilers and TriviaEdit
- From Currygom's blog entry for this episode:
- (Asha): (Note: The Korean version of this episode was released 11-20-2011.) For Asha's birthday(11-21), I drew her lots and lots! Even in the scenes where Ran is talking, the focus was on Asha... lol
- (Leez looking defeated): There isn't much for Leez to eat here... for obvious reasons. She must be on the strictest diet she's ever done. But a certain attribute of hers just won't go away.
- (loops): I tried to put together an explanation, but skipped most of headache-inducing stuff. Because we exist on a dimension lower than where the solution to this problem exists, it is literally impossible to understand, just like how a 1-D being would be unable to understand "circle" and a 2-D being wouldn't understand "sphere."
- Ran and Leez "know" the answer, but they cannot express it.
- (Rana getting frustrated): I used to do stupid things like this, too...
- (Asha and Ran): ★ Pop Quiz! ★
What is this probability Asha was trying to explain? The fastest to tell me the answer to the closest 0.01% gets free music. (For areas 52 to 100, the probability is same.)
Wow, the answer is already out. Super fast!
Answer: (48/49)^100 = roughly 12.72%
- Mizura's explanation: There are 49 possible areas to reach. Assuming equal probability for each, the probability of not reaching area 100 in any one attempt is 48/49, or 97.959%, and the probability of not reaching it in 100 attempts is (48/49)^100 = 0.12721, or about 12.72%.
- For the test, Ran is referring to the Klein bottle, which can only be visualized in four dimensions. Some people are actually capable of such visualizations.