@tomr,
tomr wrote:For anyone still interested in Ughaibu's construction I think I figured it out:
Ughaibu also claims that a human being through willed actions can construct such a number by selecting its digits.
No, you haven't figured it out.
Take some suitable willed action, for example, this post. I am writing what I want to write, thus voluntarily fulfilling my intentions. So, if there are realisable alternatives, then I have free will and the world is not determined. From this it is already quite obvious that there is no conflict between nondeterminism and free will. Nevertheless, by constructing the
prefix of a real number, from this willed action, that there is no incompatibility can be made clear. For each word in the post, choose 1 if the word has an odd number of letters and a 0 if it has an even number. Preserve the order, concatenate and append to "0."
0.0101010000011001010100101000001100010001110100000111010001010000010010000000100110011000101101010100111100100001111001 is the prefix I've extracted from the beginning of this post. Notice that this number is not entailed by the post, I could equally have reversed the parity, or selected the numbers according to a different feature, used a different base, etc. As this is the prefix of a real number, the probability of it's continued expansion being computable, is zero, but, of course, I can continue it. It's now: 0.01010100000110010101001010000011000100011101000001110100010100000100100000001001100110001011010101001111001000011110010101101100000000100101110010001110111011010001001001101111000100110011 and as there is no logical reason that I can't continue to add to this number indefinitely, there is no logical conflict between my willed action and mathematical randomness. In short, the blindingly obvious fact that willed actions are not impossible in a nondetermined world is clearly established.