There are arguments for the existence of god that rely on the notion that the only source of ((brand) new) information is a mind. There are, of course, problems with these arguments, foremost of which is equivocation. Information means different things to different people and in different contexts. Pretending that the term means one thing only and gliding from one meaning to another permits all sorts of self-deception on the part of the apologist.
I want to try to explain (and dismiss) one example of this apologetic trickery, but to do that I have to make it quite clear what information is and isn't.
When an apologist, like Max Andrews, provides this equation:
or one like it, it is clear that he is talking about a different sort of information than he is when using a variation of this equation:
and he talks about the evidence B in terms of "background information". (He actually splits the "evidence" into two parts, one that he calls "evidence" (call it E) and the other that he calls "background information" (call that B). This is something we've come across before. The effect is, as I have argued, to make P(A|(B&E)=P(A). In other words, you get nothing from the faffing about with impressive-looking probability equations other than some mild confusion.)
The Shannon entropy equation refers to the information content of m, which could be a message, and is basically a measure of how unlikely m is - which means you need to know what values m may take.
I'll try to make this concept a little more concrete.
Say that a father is away on a business trip and sends a message back to his teenage son: "send socks". Even before we try to quantify the amount of information in this message, we could be safe in saying that it isn't enough. How to send them (post, express mail, courier pigeon?) isn't detailed. When to send them isn't detailed. Quantity is not detailed. And the teenager might be quite justified in asking "Which socks?" - unless of course the father only owns one type and colour of sock, all of which are of equal quality (either all with holes in them or none with holes in them).
There's a subtle linkage between how much information is in the message and how much information is required. For example, this message could contain one single bit of information for the son, a request to transition to the "send state" after having previously been in a "no-send state". There could have been an existing agreement as to how, when and what to send based on the receipt or non-receipt of this short message. So the knowledge state of the recipient has an impact on the amount of information being conveyed.
If the father had written "Send one new, unused pair of ankle-high blue socks with yellow stripes, located to the left in the top-drawer of dresser, via express post, immediately" and this course of action had already been agreed, then no more information would have been conveyed than in the message "send socks".
But imagine that everything had been agreed apart from precisely which socks had to be sent. Imagine further that the father had two types of socks, black sock and brown socks. Adding the word "brown" to the message adds one bit of information to the message because there is a range of two possible valid messages "send black socks" and "send brown socks". The more possible valid messages that could be sent, the more information is contained in the message "send brown socks". We can think of that in this way, the message "send brown socks" also contains the information "don't send black socks". If the father has a wide range of socks, then the message "send brown socks" also contains the information "don't send black socks", "don't send pink socks", "don't send orange socks", etc, etc.
And it's here that information can be thought about outside the context of sending a message. Say we were in the father's bedroom standing in front of his dresser with the top drawer open. We reach in and take out a pair of socks, we identify them as black. Given that we know that he has only black and brown socks (and that we have assumed, due to the principle of indifference, that he has equal numbers of black and brown socks), then we know that the probability of having selected a pair of black socks was P(Black)=0.5 and so the information associated with that selection was I(Black)=-log2(p(Black))=1bit. If there were 20 different types of socks in the drawer, the probability of having selected a pair of black socks would have been P(Black)=0.05 and we'd have I(Black)=-log2(p(Black))=4.3bits of information.
A standard CD can hold 847MB of data, with 110MB of that being set aside for error correction. This is close to about 6.8 billion bits which means that the information on a CD is equivalent to uniquely identifying one pair of socks out of 102000000000 pairs (847MB is equivalent to about 2GBan). Or one star out of 102000000000 stars (although there are only about 1021 stars in the observable universe). Or one grain of sand out of 102000000000 grains of sand (but there are only about 7.5x1018 grains of sand on Earth, meaning that if every star had two temperate rocky planets as sandy as the Earth (I'm saying that Mars is sandy and ignoring that it's smaller than the Earth, so probably has less sand), then there'd be about 1.5x1040 grains of sand in the universe).
(This is probably why Max Tegmark feels confident enough to suggest that the initial data in the universe could have been so simple as to be contained on a single CD-ROM. Although he immediately suggests that even the CD-ROM might not be necessary - in accordance with his suggestion that the universe (or multiverse) overall may contain hardly any information at all.)
A complicating factor here is the one that probably trips up overly excited apologists such as Max Andrews. Selecting one specific grain of sand from the universe, using the assumptions above, represents a rather unimpressive 16.558 bytes of data (and I'm overselling it slightly since 25616.558=7.509955x1039, meaning that I am being cavalier and suggesting that it doesn't matter if I add about 1037 additional grains of sand to universe … about half the number of grains of sand that would exist on as many Earths as there are grains of sand on Earth). But if we didn't care about the specific grain of sand and just wanted a grain of sand, the information in that grain of sand would be much, much less. The less specified the selection is, the less information there is in that selection. There's still some information in the selection of "grain of sand" from the range of things that could be subject to this process, but the game "20 questions" demonstrates just how many different things can be uniquely identified with a sequence of 20 carefully framed "slice questions" - a little over a million. Double the number of questions and you can uniquely identify 1012 different items … with precisely 5 bytes of information.
Going back to the sock drawer, if the father just wanted any old pair of socks, then the probability of drawing them from the sock drawer would be Pr(socks)=1. (Note that I am assuming here that there are socks in the sock drawer, which may not always be the case, but the point at the moment is about the probability of selecting a pair of socks from a set of existent socks, not about the probability of the socks being existent.) The information in this is precisely zero because logx(1)=0, irrespective of the value of x.
In other words, the more you don't care about the result, the less information there is in that result. This, hopefully, makes intuitive sense - think about the difference between the news that Khloe Kardashian has been on a new diet and the news that Prince has died (Purpleness Be Upon Him), both reported in April 2016. One event led to widespread dismay and spontaneous demonstrations of grief on the streets of Minneapolis and the other one I only noticed because I was momentarily delayed in a supermarket checkout aisle and it was easy 2 see (it) on the cover of a magazine. Reports of Prince (PBUH) dying contained information. Reports of Khloe getting marginally less fat is so lacking in information that I lack the care factor necessary to
And this is where the argument of people like Max Andrews becomes circular.
We, as part of the universe, do care about the fact that we exist. Therefore, for us, this is interesting information. We are also part of a selection event, in so much as the universe does appear to be fine-tuned, in that were certain constants and laws slightly different then life like ours would not be possible. We can imagine situations, or alternate universes, in which we would not exist (counterfactuals), and from this glean "information". For example, if the strong nuclear force were stronger by more than one part in 50 (and all other constants were held at existing values), then diprotons would be stable leading to the failure of stars to form (due to the rapid consumption of all hydrogen in the first minutes after the Big Bang). So we can posit a universe in which the strong nuclear force was stronger by one part in 20, or twice as strong, of four times as strong, or seven times as strong. And we could keep going, infinitely, providing different multiples and then claim that just this one single fact contains infinite information.
(A problem here, of course, is that we don't know that all of these values are valid, let alone equally valid. And there was a caveat, "all other constants were held at existing values". There are solutions in which the strong nuclear force may be higher and other constants being at different values still allows for unstable diprotons. The bottom line is that we don't really know how unlikely it is that the strong nuclear force lies in the convenient range that it does, and "we don't know" is equivalent to "no information".)
But when it comes to the existence of the universe, it doesn't really matter how interested the constituent elements are in it. It's a question of how interested the universe is and, unless that is a mind, it's not a huge leap to suggest that the universe isn't interested at all. In which case, there is no information in the universe as a whole.
What appears to be a novel argument on the part of Max Andrews is that because there is so much information in the universe, and minds are the only originators of "brand new information" (this part is a standard creationist claim, usually centred on genetic speciation), then there must have been an antecedent mind to have initiated the universe (or multiverse). But this is circular, the universe as a whole only has information if the universe itself is a mind or there is a mind external to the universe that cares about what is inside it. (The universe (or multiverse) would also have to be contingent, meaning only the universe/multiverse could have been different. There's no information in a necessary thing being as it necessarily must be.)
So, unless he is suggesting that the universe itself is a mind, Andrews is presupposing that there must be a god of some sort, that therefore the universe contains a huge amount of information (presumably due to extreme contingency of it) and therefore that there must be a god as the source of that huge amount of information.
This is completely circular and therefore totally useless as an argument for what he so desperately wants to argue. It's amazing that this got accepted as a thesis, but I guess that when both of your supervisors are dedicated god-botherers then so long as your answer is "god did it", you can get away with any old nonsense.