There is another theory that says Neo and Smith (opposites) cancelled each other out when Smith took over Neo, and this is the sole reason Smith was defeated. While this is "mathematically beautiful" to think about (and it is an additional layer the Wachowskis very likely thought of), it just doesn't make as much sense when thought of as the only plot device to explain Smith's defeat. I don't think there is some mysterious, inevitable disintegration that must happen when opposites join. We saw Neo's body being used as a channel through which Smith was destroyed. It seems this was action proactively taken by Deus Ex Machina.
I also think Smith would have been smart enough to know that such a thing would happen if cancellation alone could destroy him, being the ultimate computer virus that is able to think and make decisions to ensure its own survival (and also having taken over every other program in the Matrix, including the Prime Program, the Oracle!). Oracle-Smith definitely would have forseen such a predictable way to die. But not even Oracle-Smith could forsee his own death when it is caused by Neo's non-understood decision to give himself up (see Smith: Smith's Defeat). Not only that, but if the Oracle knew Smith is Neo's opposite, certainly Smith would know too since he copied over the Oracle.
I've seen the argument made that Smith had no choice when it came to taking over Neo at the end of M3: even though Smith didn't want to, he had no ability to deny his purpose of destroying the ultimate anomaly, the One. Under this argument, it seems feasible at first that "opposites cancelled". But this doesn't seem consistent at all with how Smith behaves.
For example, just before Neo and Smith engage in the Burly Brawl in M2, Smith can't wait to copy over Neo. He isn't exactly saying, "Oh no, if I copy over you, it will cause us to become mathematically null, but alas I cannot deny the impulse!" No, Smith has no clue that taking over Neo could destroy him. Smith is practically foaming at the mouth in anticipation of copying over Neo. "...we're here to take from you what you tried to take from us. Purpose."
One reader named Sean T. sent me the following e-mail:
Consider the oracle stating that no one can see past a choice they do not understand. This point must apply to all, even Smith. Knowing this, I believe it is possible that Smith encountered this problem in facing a choice he could not understand. He knew that destroying Neo was the only way he could ever claim ultimate power, but at the same time, he was aware that destroying Neo COULD lead to his demise. With that knowledge, how could he ever see past his own decision to destroy Neo and therefore himself? He has already made the choice to destory Neo, therefore destroying himself. He knew that destroying Neo was the only path, but at the same time could not understand how he could possibly make a choice that would destroy him.
Smith existed to bring balance, just as Neo did, to the Matrix. In M1, Neo took his first step toward the power of the One when he destroyed Smith. This was later referred to as an imprint of Neo being placed on the piece of code that controlled Smith, therefore creating the counter-balance to the system required by Neo's gain in power. In my mind, Neo is not the One, but a part of it. Like Yin/Yang theology, the One is comprised of two halves creating the whole. In this case, Neo and Smith together create the One. Similarly is Buddhism being One is only achieved by becoming whole with the universe. At the end of M3, Smith had joined with the entire Matrix except for Neo. It is possible that the joining of Smith and Neo creates the One.
Again, I like the beauty of it, but it just doesn't make as much sense to me. First, it seems to me that whether Oracle-Smith couldnít see past his own choice or not is a moot point when we know for sure that Smith couldnít see past Neoís choice, and it was Neoís choice that seemed to dominate the focus and drama of that scene.
Second, and most importantly, I would argue that the reason Neo's surrender didnít quite feel right to Oracle-Smith was because Oracle-Smith didnít actually know that the Oracle canít see past choices people make that they donít understand. That moment was the first time Smith experienced the Oracleís only limitation, so he didn't understand why this moment of temporary blindness was happening. Smith did understand his choice to copy over Neo (in fact the explanation is extremely simple: it was his purpose to) Ė itís just that something didnít feel quite right because he couldnít see past Neoís choice.
Also, Smith: Smithís Defeat doesnít make as much sense if the cancelling opposites explanation were accepted.
I would guess that the Wachowskis thought of cancelling opposites in more symbolic terms, as a kind of imagery running parallel to the actual plotline explanation.
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