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The article, from a "creationist" web site, is commenting on Hawking's book, The Grand Design, in which Hawking postulates; "that invoking God is not necessary to explain the origins of the universe, and that the Big Bang is a consequence of the laws of physics alone. In response to criticism, Hawking has said; "One can't prove that God doesn't exist, but science makes God unnecessary."
Those who take the bible literally, will object to that of course. They have no use for such things as science anyways. As creationists are all "faith based", argumentation in regards to science is totally lost on them. Hawking does not state an absolute in his book but offers instead, a mathematical and scientifically sound explanation of a "possible" alternative to the creationist concept.
It's only plausible, if you have faith. In this case, not a faith in G-d, but a faith in chance.
First we have to assume that string theory... is correct. Which as the name implies, it is theory, not fact. It is a possible answer, that somewhat fits what we know, and we know very little.
If we take that as truth, then we can use a mathematical basis for saying that the total net energy, based on the calculations we have, is zero. If you take the positive energy, and negative energy, and add them up together, the answer is zero.
This implies that no external source of energy is needed, because the pluses and minuses balances out.
Is that true? We don't even know. But if we assume that is true, just like we assume string theory is true, then possibly it is true that the universe could create itself, because there is no need for some external energy to create it.
When you go threw every single basis, and label each unproven claim to be a faith based assumption, which is what it really is... you see it's nice... it's a neat concept... but honestly not much substance.