“I know (or could readily rediscover) how to build a binary adder from logic gates. If I can figure out how to make individual logic gates from Legos or ant trails or rolling ping-pong balls, then I can add two 32-bit unsigned integers using Legos or ant trails or ping-pong balls.”
To me this sounds pretty much like a domain error. Your ‘theoretical’ binary adder, is a function of Binary x Binary → Binary x Binary. Your Lego adder has a different domain, it’s function is: Lego x Universe\Lego → Lego x Universe\Lego
Now you need a tranformation from Lego x Universe\Lego → Binary x Binary, so you can check whether they are doing the same operation, addition that is.
Now, if you’re saying they are doing the same kind of addition, then I can show you a counter-example by just destroying the Lego adder before it mechanically ends its ‘addition’ (remember I am part of Universe\Lego!). You’ve got two choices: Either the Lego adder is not doing ‘addition’, or your assumption what ‘addition’ is, is wrong.
“Here’s a question from a layman: if untold trillions of new universes are being created all the time, where is all that energy coming from to create them?”
Well, you’ve got the same problem with a single world: Where did the energy for our ‘single’ Universe when ‘it was created’ came from?
The problem here is that you assume that universes are created which did not exist before; in this case you indeed need to take the energy from somewhere. But as I understand, they never did not exist (beware of double negation!). They already existed before the split took place in your personal memory.
But somehow I still can’t buy into this thing; where is the symmetry? Why do splits happen into the future, but not into the past?
Of course, we evaluate the past according to the information we retrieve over time (that’s the whole point of Bayes/Markov, isn’t it?). In this way you can say, that with every bit of information/evidence, our memory makes a split into the past. In this way ‘fresher’ memory gets mixed up with ‘decaying’ memory and thus we get a different/more diffuse image of the past.
But it doesn’t sound the same like the ‘future’ splits. We don’t have a fresh memory of the future; taking the example of lotteries. We don’t remember their outcome seconds before.