Dr Arroway meets an extraterrestrial ?“Caretaker?”, page 366.
?“I want to know about your myths, your religions. What fills you with awe? Or, are those who make the numinous unable to feel it?
----- You make the numinous also. No, I know what you?’re asking. Certainly, we feel it. You recognize that some of this is hard for me to communicate to you. But, I?’ll give you an example of what you?’re asking for. I don?’t say this is it exactly, but it?’ll give you a flavor of our numinous.
----- It concerns pi, the ratio of the circumference to the diameter. You know it well, of course, and you know that you can never come to the end of pi. There?’s no creature in the universe, no matter how smart, who could calculate pi to the last digit --- because there is no last digit, only an infinite number of digits. Your mathematicians have made an effort to calculate it out to (none of them seem to know); let?’s say the ten-billionth place.
----- You won?’t be surprised to know that other mathematicians have gone further. Well eventually (let?’s say it?’s the ten-to-the-twentieth power place) something happens. The randomly varying digits disappear, and for an unbelievably long time there?’s nothing but ones and zeros.
And the zeroes and ones finally stop? You get back to a random sequence of digits? -- Seeing a faint sign of encouragement from him she raced on.
And the zeroes and ones? Is it product of prime numbers?
----- Yes, eleven of them.
You?’re telling me there?’s a message in eleven dimensions hidden deep inside the number pi? Someone in the universe communicates with us by mathematics? But, help me. I?’m really having trouble understanding you. Mathematics isn?’t arbitrary. I mean pi has the same value everywhere. How can you hide a message in pi? It?’s built into the fabric of the universe.
----- Exactly.
She stared at him.
----- It?’s even better than that, he continued. Let?’s assume that only in base-ten arithmetic does the sequence of zeroes and ones show up, although, you?’d recognize that something funny?’s going on in any other arithmetic. Let?’s also assume that the being who first made this discovery had ten fingers.
----- You see how it looks? It?’s as if pi has been waiting for billions of years for ten-fingered mathematicians with fast computers to come along. You see, the message was kind of addressed to us.?”
Inspired by the Numinous, Page 427.
?“At the Station, she had learned a kind of humility, a reminder of how little the inhabitants of Earth really knew. There might, she thought, be as many categories of beings more advanced than humans as there are between us and the ants, or maybe between us and the viruses. But it had not depressed her. Rather than a daunting resignation, it had aroused in her a swelling sense of wonder. There was so much more to aspire to now.?”
Messages in the Fabric of the Universe, page 430.
?“Hiding in the alternating patterns of digits, deep inside the transcendental number, was a perfect circle, its form traced out by unities in a field of noughts.
The universe was made on purpose, the circle said. In whatever galaxy you happen to find yourself, you take the circumference of a circle, divide it by its diameter, measure closely enough, and uncover a miracle; another circle, drawn kilometers downstream of the decimal point. There would be richer messages farther in.
It doesn?’t matter what you look like, or what you?’re made of, or where you came from. As long as you live in this universe, and have a modest talent for mathematics, sooner or later you?’ll find it. It?’s already here. It?’s inside everything.
You don?’t have to leave your planet to find it. In the fabric of space and in the nature of matter, as in a great work of art, there is, written small, the artist?’s signature. Standing over humans, gods, demons, subsuming Caretakers and Tunnel Builders, there is an intelligence that antedates the universe.
The circle had closed. She found what she had been searching for.?”
Sagan?’s Lectures on Natural Theology
It seems to us that Carl Sagan?’s collected speeches to the Gifford Lectures on Natural Theology in 1986, and published in 2006 as ?“The Varieties of Scientific Experience: A Personal View of the Search for God?”, was an extensive discussion of his thoughts on the ?“numinous.?”
Throughout he appears to be searching for the sacred and the holy in the uniqueness of our isolated place in the universe, indications of living matter on nearby planets and some of their moons, the possibilities of extra-terrestrial life, the universality of the laws of physics, the complexity of nature, and other natural phenomena.
In the Introduction, Ann Druyan mentions that Sagan had planned to write a book entitled "Ethos" about the spiritural perspectives he drew from the "revelations of science."
These speeches were delivered at about the same time as the publication of ?“Contact.?”