No it will not. There is not enough space in the universe to contain the number 1 google, let alone 1 googleplex. No computer in this universe will EVER be able to answer that question.
Thus, there is a limit to the amount of irrational numbers we are able to hold. We can only create rationals - the true irrationality of numbers like pi and e are not representable in this universe, only rational approximations of them are. So his argument is completely invalid: There already is such a limit!
Sir Isaac Newton was said to be one of the most brilliant scientists ever to have existed. His findings said that if we ran fast enough, we, material objects, could catch up to and even outrun light beams. He was later proved wrong by James Clerk Maxwell, as he found that light behaved like a wave rather than like particles, and theorized that light was a complicated and peculiar wave, later called an electromagnetic wave. He also stated that you could never catch up to a light wave. Eventually, they were both proven wrong and right at the same time by Albert Einstein, IQ 160, who found that light behaved as a wave, but consisted of a stream of particles called "photons".
Einstein believed we lived in a relatively clock-like universe, where everything was predictable. This man, who unified the opposing theories of Newton and Maxwell, was proven entirely wrong in this statement of a clock-like world by quantum physicists, who discovered that the electron behaves in an entirely unpredictable pattern. Einstein couldn't leave his classical sense of logic, and refused to accept the idea of randomness in the universe, but when in the quantum levels it is too wrong to use our own intuition for the guidelines of the universe.
Einstein was proven wrong about his view of the universe that used the classical intuition that has guided us far in the universe. Maybe you are using classical intuition in giving the universe, and our technology, a limit, and saying that there would be no way to calculate the google plexth digit of pi, but why does this make much sense? And more importantly, why is the computer calculating something exact rather than randomness? Is there some concreteness in the existence of irrationality presented by this?
Let's look at a few facts.
http://www.numberworld.org/misc_runs/pi-5t/details.html
5 trillion digits of pi calculated by a computer in 90 days. That's honestly a lot of digits to calculate in 2160 hours.
https://en.wikipedia.org/wiki/Quantum_computing
This type of computer can calculate EXTREMELY fast, as it has more states than 0 and 1. While development is in its infancy, it can quickly become something much more extraordinary than it already is. With our current model of the quantum computer, let's make a comparison (though an unlikely scenario will be compared to it; I haven't actually calculated anything).
Let's say that an ordinary man was calculating 9999999^10. It would take him hours to complete this by hand, especially since he has to keep track of every digit of every number while doing his calculations. The quantum man, however, does this in less than a minute. The ordinary man takes a very long time learning how to talk, but the quantum man says his first words the morning after birth and speaks proper english by the end of the day. The ordinary man takes years developing a precise calculation of the law of gravitation, while the quantum man takes just under a week to perform the same task.
With this in mind, how sure are you that you cannot calculate the google plexth digit of pi? You seem to be incredibly sure of pi being incalculable.
And, by the laws of physics, the quarks, electrons, and neutrinos that exist within an atom existed since the beginning of time - even before we discovered them. The Earth went around the Sun because of Einstein's law of gravitation ever since the Earth was formed. And, like the existence of subatomic particles and the law of gravity, the google plexth digit of pi, whatever it is, exists as we speak, despite the lack of it being calculated by us.
One final point to make. Is our universe itself even close to rational? Nothing within it is remotely logical or rational by the very definitions of the word. We calculate complex numbers like pi and the square root of two, and they are
irrational. The laws of quantum physics themselves state that an electron can "borrow" energy and go through a solid object without damaging itself or the object it ghastly goes through. Does the universe itself even make enough sense to allow us to say that pi and e cannot be calculated to such a precise degree as the google plexth digit past the decimal?
A small thing to finish with, but I have a 1 in 10 chance of correctly telling you what the google plexth digit of pi is, and there is nothing you can do to stop me :^)
