How Much Does Information Weigh?
How much does Information Weigh?
(or — Help! I Can’t Stop Plagiarizing from The Impossible Library)
By Robert Joyce — Edited by Brian Joyce
A powerful institution has baptized us in a dogma. I’m not talking about the church. This time academia rather than religion has created a nearly inescapable assumption about the universe, an assumption that powerfully colors our view of reality. The materialist academy believes that there is no God, no miracles — that there is nothing in this universe other than material. They maintain this position, despite the fact that the evidence of a miraculous portion of the universe engulfs our everyday lives. The existence of information itself denies the materialist mantra. As you read this little essay, you are decoding the information contained in the characters on your computer or phone screen. I hope that by the end of this article, you are as completely astounded as I am that the information you are reading — the information itself — is literally a miracle.
First, let’s just agree on what we mean by a miracle. In the hyper-materialistic climate that we find ourselves, the modern materialist scoffs when presented with the miracles of Jesus as proof of his divine nature. ‘These accounts cannot be trusted’, the materialist asserts. ‘These miracles could not have happened because they have no place in a material universe.’ He doubts the veracity of the biblical miracles, because of two things: their improbability and their dependence on a non-material cause. It seems clear that these two criteria encompass what most people mean by a miracle.
The Impossible Library
To see how these two criteria apply directly to the phenomenon of information, consider the Holy Bible. The King James Version contains 3,116,480 alphabetic characters. When we add the bare minimum punctuation and spaces, we end up with 3,961,821 typographical places necessary to produce a legible copy of the Bible.
Now suppose we produce a book for each possible iteration of those typographical places. In other words, suppose we make every possible book substituting the 26 characters of the English alphabet, plus just the basic punctuation marks (period, comma, and question mark) and blank spaces, for 30 possible typographic elements, in each possible position. We find that we would need 30^3,961,821 (i.e. 30 raised to the 3,961,821st power) books to have every possible combination.
We have just described a phantasmagorical library. If we were privy to such a library, imagine the awe-inspiring features it would provide. The library would contain one and only one copy of the King James Authorized Version in all its proper typography. There would also be copies of the Bible with the chapters in every possible order. There would be a copy of the Bible with every character in reverse order. There would be Bibles with all the spaces at one end, Bibles with the punctuation only at the beginning, or no punctuation at all. But now the really strange features of the library begin to emerge.
This library would also contain nearly every book ever written, except for those few, which are longer than the Bible. Think of it! It would contain a copy of Treasure Island with the excess space all at one end. It would include the Chronicles of Narnia, side by side, all in one volume. Homer, Augustine, Marx and Hemingway would be represented exhaustively. It would have everything ever written by Shakespeare, including the lost plays, and every poem Paul Simon meant to write. It would have an English translation of every book lost in the fire of the great library in Alexandria.
When discussing this idea with my son, he pointed out an even stranger and more astounding feature of this library — it would even contain every book that will ever be written! It would have books of science revealing all the secrets of the universe yet to be discovered. The most perplexing puzzles still eluding the minds of our greatest scientists would be solved within the books of this library, in easily understandable English! If only! And yet it cannot be. This library is nothing but a pipe dream — a true impossibility.
Can You Say ‘Big?’
This collection of books is so large, that words like “large”, “massive”, “gargantuan”, simply don’t have any way of wrapping themselves around it. The best estimate of the total number of particles in the known universe currently stands at around 10^86 (i.e. 10 raised to the 86th power). And yet, our library contains 30^3,961,821 (i.e. 30 raised to the 3,961,821st power) books, each the size of the Bible. If our library was made of atoms like the kind we have in our everyday bibles, we would not be able to make any significant fraction of this library using every atom in our universe. This library would not fit in our universe — would not fit in a billion universes! It is an impossible library.
Even the shortest verse in the Bible — Jesus wept — is an impossible project. Leaving out punctuation and capital letters, we would need 27^10 (i.e. 27 raised to the 10th power) note cards to write every iteration of spaces in ‘jesus wept’ if we wrote one on each card. That’s a whopping 5,559 trillion note cards. Within that stack would be every English word with ten letters or less, and every phrase whose characters and spaces add up to ten places. The Oxford English Dictionary contains 171,476 words in current use. But even if there were 500,000 cards that had some kind of discernible meaning on them, the vastness of the number of nonsense cards would make the meaningful ones un-findable. If you were to look at each card for 1 second, it would take you 176 million years to get through them all, just to find the meaningful cards.
From the standpoint of probability, as you can now clearly see, any piece of information, coded in a moderately complex system of symbols, is unlikely in the extreme. It is just as impossible as any miracle that Jesus ever performed. That is the nature of symbolic systems. Those meaningful pieces of information are the winning tickets in an astronomical lottery that dwarfs the imagination.
The Ghost in the Machine
A completely different facet of information confounds the materialist just as easily. Information is non-material. Picture this:
You are sitting in your living room with an extremely accurate scale sitting on the coffee table between you and your materialist friend. On the scale is a small pile of 45 matchsticks. Each match weighs 0.2 grams, for a total of 9 grams.
Your scale is so exact that it is currently measuring the change of weight as the matches absorb and evaporate atmospheric H2O as they approach the average humidity in the room. We are talking about changes in the range of 0.001 grams, that’s thousandths of a gram. You wait until the humidity of the matches has reached an equilibrium, then wearing latex gloves, which have been relieved of any particles or moisture, you carefully rearrange the matches into the following shape.
The matches now contain information. But when you take the measurement again waiting long enough for the scale to reach an equilibrium, you see that the weight has not changed even by 0.001 of a gram. If you could measure the weight to down to the individual atoms, there still wouldn’t be any change. The matches remain unchanged but the information is there. The information in ‘jesus wept’ doesn’t weigh anything, because it is not material. The message is independent from the medium, and therefore has a non-material existence. You can reproduce the precise same information in any medium you choose — matches, rocks, pencil on paper, Morse code, or finger paint. You could use land mounds as seen from the sky, or xenon atoms arranged on a crystalline nickel substrate like IBM once used to demonstrate their nano-scale techno capabilities.
The materialist may point out that information is dependent on material — that information does not exist independently from a medium. And to this I reply, ‘of course there is a necessary intersection of material and information.’ But that does not disqualify information from its “miracle” status. Just as with anything we call miraculous, there is a necessary intersection with this world. Miracles don’t happen in heaven, they happen here in this physical world. Moreover, just like the appearance of the Holy Bible in physical form, miracles are impossible and non-material in their cause and essence.
Mind Over Matter
Up to this point, I have been purposely ignoring the elephant in the room — or should I say, the human in the room? Something even more miraculous than information itself lies behind information — the human mind. Don’t worry — that does not negate the miraculous nature of information itself in the slightest. But it does suggest some more fascinating ideas that need to be discussed before we are done.
Where do all these miracles known as books (and remember just how miraculous they truly are) come from? There is a device? — object? — entity? — known as the human mind, which creates? — produces? — these miracles in perfect form. These miraculous, meaningful, impossible winning lottery tickets, these books, come right out of the human mind one after another. It’s as if we have an object that can pick a winner from the impossible lottery every single time. But no, we intuitively understand that the mind creates them by force of will.
It stands to reason that the object/entity which creates these impossible things called books, is even more improbable than the books themselves. And if the information which it creates is immaterial, how can we suggest that the entity producing the information is purely material? Can material produce something immaterial?
But then where do these miraculous human beings come from? Easily the most stunning moment in my intellectual life, my greatest revelation about the nature of reality, has to be that moment when I realized that humans are made out of words.
Human beings are unfolded from an information system uncannily like the English alphabet. In our DNA we find letters, words, sentences and punctuation, and if you add up all the information in a single example of the human genome, it turns out to be the size of a long novel. We don’t have to go over the random library idea again to see that the chances of randomly generating a human being are indistinguishable from zero, but here is one small example.
The protein hemoglobin colors our blood red and carries the oxygen our bodies need for life. Hemoglobin was plentiful in the blood that ran down the arms, back and side of Jesus, staining the wood of the cross. This crucial protein is made out of 141 amino acids. I am greatly simplifying this, but the word for hemoglobin written in our DNA is made up of 141 spaces, each of which contains the letter for one of 20 possible amino acids. So the chances of hemoglobin coming into existence randomly, assuming that the information system is already in place, is 1 in 20^141 (i.e. one in twenty raised to the 141st power).
If life began at the Big Bang, 13 billion years ago (which of course it did not), and if a billion generations of cells were randomized by mutation and reproduced every second (which of course is a ridiculous idea in itself) there would have only been 10^27 (i.e. 10 raised to the 27th power) generations of possibilities since the inception of our universe, just to encode a single protein, a single word in the novel of our lives.
But of course that is not the situation. Life did not begin at the earliest until about three billion years ago, and each generation since then has taken far longer than one nano-second to mutate and reproduce. There has not been enough time in this universe to randomly generate the King James Bible, the human genome, or even the protein hemoglobin. We are surrounded by miracles.
Now I turn to our materialist friends and ask the simple question: Where then did that information in our cells come from? The science of evolution offers no answer to that question. Yes, human minds are the force behind the miracle of typographical information, but what is the correlate of mind behind the information system that codes us into existence? From what mind came the words that make me? Christian, you know. It was written in that miraculous object called the Holy Bible, “In the beginning was the Word.”
(c) Copyright Robert Joyce
Robert Joyce lives in Spokane Washington with his wife Anne and two children still at home, Joshua and Noah. Another son, Brian lives nearby. The younger of two daughters, Mackenzie was recently married to Isaiah and lives in the same town. He counts the closeness of his adult children one of his greatest blessings. His oldest child, Hillary, who is married to Luke also lives in town, and is the mother of his two grandchildren, Glorianna and Joyce. He’s gone nuts over his grandchildren and hopes to have many more.
When he’s not occupied with his expanding family, he works as a computer desktop support specialist at Gonzaga University, and carves out a little time each week to work on his writing. In 2017, he self-published his first book, Sinner Son Bride – A Coherent Theology of God’s Intent.
Check out Robert's blog here.