Teletransportation paradox explained (again)

 I've written a previous article explaining how teleportation and/or mind uploading will actually be "the real you". But I realized it was hard to read, so I'm going for a simpler, condensed explanation in this article (with pictures). 

The essence of this "proof" is a very simple proof by induction common to mathematics. 

Imagine there are two brains, A and B. Brain A is your original brain. Brain B is a perfectly physically identical copy of your brain that was created/materialized in a new location. 

1. Swapping a 1-atom chunk from each brain, won't result in your consciousness "jumping over" from brain A to brain B. 
2. If swapping an X-atom chunk from each brain won't result in your consciousness "jumping over" and changing locations, then neither would swapping an X+1 atom chunk. For example, if in one case the swapped chunks were 1 trillion atoms big, and you hypothesize there is no "jumping over" in this case, it would be irrational to claim that there would have been a jumping over if the chunks had been just 1 atom bigger.  
3. #1 establishes the base case, and #2 establishes the proof-by-induction ladder all the way to swapping the whole brain. Therefore, swapping your whole brain must be the same as not swapping anything at all. 

So copying yourself then doing nothing, is exactly the same as copying yourself and then swapping your bodies. Even from "your" point of view. This sounds like crazy talk, but if you disagree you'd have to poke a hole in the proof by induction outlined above, in which, as far as I know, there isn't any. 

One common theme for rebuttal would be to bring up the Sorites Paradox (aka, "when does a grain of sand become a heap of sand"). However, you'd then be claiming that as you gradually move more and more atoms over, your consciousness is gradually going more and more into the new brain. For example, you'd be saying that at 50% swap, your consciousness is half in the old brain, and half in the new brain. This doesn't make any scientific sense as there is no physical way for a consciousness to be magically telepathic and feel things from both brains at the same time. Remember both brains are physically identical in every single scenario. Therefore, if you agree a mind is caused by nothing more than its physical materials, there's no way for any of the minds in those brains to feel "partially dead" or "partially moved over". 

To understand why this is not a paradox, requires abandoning some very deeply rooted intuitions about consciousness: 

• You are your physical brain: False. You are the information which is produced by the physical brain. Your consciousness is the information itself, not whatever substrate the information happens to be running on. 
• There is a continuous self, aka "I think therefore I was": False. There's only "I think therefore I am". You can consider your present self to be a new consciousness that beliefs they're the old one from yesterday. There's no physical evidence for an extra thread of continuity to your past self any more than what your brain's memories are telling you to believe. 

Once you abandon the incorrect assumptions about consciousness, everything starts to make way more sense, and the paradoxes resolve themselves. I understand that my claims are extraordinary which require extraordinary evidence, but I believe the proof by induction is more than enough to satisfy this requirement. As the saying goes, “once you eliminate the impossible, whatever remains, no matter how improbable, must be the truth.”

P.S. the most common response to this argument I have found over the years, is people say "it doesn't make sense to see from two pairs of eyes at once". I am honestly baffled by this and do not understand why people believe this is implied by my argument. If this was your reaction, please re-read and understand the post. The fact that magical telepathy cannot exist is precisely why we can conclude there is nothing that needs to "jump over" in the first place (it's an illusion).