Reader, my comments refer to the 1995 edition, of which I understand this to be an "expansion." Barrow, and you, would have benefited from a contraction. This earlier work (which I must assume provides you with the basis for that of which you read this review) is a poorly-organized, and poorly-edited mish-mash of hypotheses that point at Barrow's conclusion without lending any particular force to his argument.
Which is? The world is so because it is. Extraterrestrials, if they exist, must exist as they do. The four forces of the universe cannot be any different than they are, if the moon was not where it lives in the sky, mathematics would be far different now than what it is. And by the way, we have the Minoans to blame for constellations (bright bit of conjecture there!) Why this teleological fever? I suppose because our author, a new Candide, wants to point out that our aesthetic preferences are based upon our physical/evolutionary constructs, themselves based upon what we currently conceive to be givens of physics and chemistry (and this is not a bad idea), but they couldn't be otherwise.
All presented in a prose style that is occasionally amusing (the best part of the book are the quotes) but far too often has one struggle with paragraphs that straggle over far too many pages. Did Barrow's agent just throw up her hands? To say nothing of the editor - after all, as ideas and connections pour forth in a feverish fashion from Barrow's pen, one would like to read of his sources. Some are listed in the bibliography, none are footnoted in the text.
One would also have liked a few other critical readers before the text made it to print. Barrow provides conclusions that benefits his anthropocentric principles as if they generally were fait accompli, but they are only one of many that might be considered. For example: "...it could be that our liking for music is merely a by-product of an advantageous adaptation for coordinated actions." Yes, I suppose it could be. Or maybe not. At other times we read sentences appalling in their banality. Here's one:
"In the absence of catastrophes, our own existence is made possible by the presence of our friendly neighbourhood star: the Sun."
Do you know something now that you didn't before? Here's another:
"The strength of rocks and metals is fixed by the strength of the electromagnetic forces of Nature, and by the masses of protons and electrons."
And here's another:
"Mankind's awareness of the stars, and of the periodic changes in the appearances of the Sun and the Moon, was already well developed at the dawn of recorded history."
These were all taken at random. There are plenty more. Barrow would reply that they are taken out of context, to which it would be fair to ask him exactly what context he has in mind. It seems that there is nothing that will not support his thesis. And then there's an over-long excursion in chapter 5 where music is compared to mathematics - for what end? You'll never really know.
I am sorry for Barrow that I give this a single star, but not for you, as his potential customer. Although there are a few interesting ideas here, as well as some workable summaries of celestial events (precession, etc.) there are far too many windy connections for the work to stand. Barrow may believe that the past shapes the present, and thus the future, but for the most part yours will be better if you avoid this book.