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Are Some Things About the Universe Fundamentally Unknowable? (forbes.com)
StartsWithABang writes: As we peel back the layers of information deeper and deeper into the Universe's history, we uncover progressively more knowledge about how everything we know today came to be. The discovery of distant galaxies and their redshifts led to expanding Universe, which led to the Big Bang and the discovery of very early phases like the cosmic microwave background and big bang nucleosynthesis. But before that, there was a period of cosmic inflation that left its mark on the Universe. What came before inflation, then? Did it always exist? Did it have a beginning? Or did it mark the rebirth of a cosmic cycle? Maddeningly, this information may forever be inaccessible to us, as the nature of inflation wipes all this information clean from our visible Universe.
Forbes's insistence that I drop adblockers, when their ads have been empirically detected dispensing malware, is one of them.
So is StartsWithAWhimper's insistence of posting his blogspam here.
Yes, Ethan, there is. How can you possibly be making enough money writing your crummy blog with malware ads on it? It is unpossible that you can be making money with it.
Let's use your example of quantum computers. We have strong theorems about what a quantum computer can do compared to a classical computer. In particular, BQP, the class of problems that a quantum computer can do in polynomial time https://en.wikipedia.org/wiki/BQP0 is in PSPACE https://en.wikipedia.org/wiki/PSPACE, the class of problems that a classical computer can do in polynomial space (where polynomial in both cases means polynomial in the length of the input). This means that a quantum computer *cannot* massively extend what one can do much beyond speeding up some calculations, and other theorems show that this is a general pattern. Holevo's theorem and a few other similar theorems say more or less that you cannot use n qubits to simulate n+1 bits https://en.wikipedia.org/wiki/Holevo's_theorem. And in fact, the conjecture strongly is that BQP is *much smaller* than PSPACE.
Now, you might say that you just meant quantum computing as an example. But people have actually thought about what possible computing analogs would make sense that would be even more powerful than quantum computers. So for example, Scott Aaronson has looked at models involving access to a hidden variable http://www.scottaaronson.com/papers/qchvpra.pdf and it turns out that while they are naturally more powerful than quantum computers, again their are pretty strong limits on what they can do.
Moreover, we have pretty good ideas at this point of upper bounds on what physically can be computed and stored in an area. One example of this is the holographic principle https://en.wikipedia.org/wiki/Holographic_principle which puts pretty severe limits on how much information can be stored or presented. And even if the holographic principle is *wrong* (not implausible), and let's say that somehow it isn't just wrong in the obvious way (where the amount of information increases directly proportional to the volume) but in fact does so according to say a 20th power of the volume with a constant out front that in the relevant units is a hundred times as large as that in the holographic bound, one would *still* have nowhere near enough bits to plausibly do this sort of thing.
Frankly, when I give the sort of problem I mentioned earlier, instead of using a small stack of exponentials, I normally use the Ackermann function https://en.wikipedia.org/wiki/Ackermann_function and say something like A(100) +1, which is insanely bigger than the number I used. So even if you don't buy the arguments above, just use a number like that which is easy to specify mathematically and is mindboggingly larger.