When it comes to seemingly improbable events, an important question we need to ask is: how many times in a row can serendipity be invoked, before our suspicions should be aroused that maybe something else is going on?
To illustrate, suppose you decide to enter the “One In A Million” lottery. The rules are simple. It is held once a week. It is one dollar a ticket, and there are a million tickets available. Each week there is one winner, who receives close to a million dollars.
If you choose to buy one ticket a week, the chance of you winning in any week is one in a million. But suppose you had a rich friend, whose name also happens to be Rich, for reasons I won’t go into here. Rich offers you the following wager: “Before you enter the next lottery, pay me a thousand dollars. If you win the next two lotteries in a row, I will pay you ten million dollars.”
Is this a good offer? To decide, you need to work out the probability of winning two of these lotteries in a row. If you buy one ticket each week, you have a one in a million chance of winning an individual lottery; but since you need to win two in a row for Rich to pay up, and each lottery is independent of the previous one, you have to multiply together the odds of winning each one separately. A million multiplied by a million is a trillion, so you would have a one in a trillion chance of winning both in a row.
For this reason, I think the offer from your so-called friend is bad, because it’s incredibly unlikely you’ll win two in a row. It’s certainly not impossible, but it’s unlikely to happen to you in your lifetime, if you only buy one ticket a week.
Notice that it’s not merely a little more, but vastly more improbable, to win two “One In A Million” lotteries in a row compared with winning just one. Even so, these things do occasionally happen, even in lotteries with much worse odds of winning. People do occasionally win twice in a row.
If you could afford to buy a thousand tickets a week, you would increase your odds of winning one of these lotteries to one in a thousand, and so your chance of winning two in a row would be one in a million.
The key question, that also relates to the story of our freezing codfish, is: how many times could you win the “One In A Million” lottery in a row, before you could safely rule out serendipity? In theory, any number of sequential lottery wins is possible, but the odds shrink dramatically with each one we add to the sequence. Assuming you buy one ticket a week, winning two of these lotteries in a row is a One In A Trillion event. Three in a row would be a One In A Million Trillion event; and the odds shrink by a factor of one million with each extra lottery added to the sequence.
If you won it twice in a row, you would probably be amazed, but you might conclude that it was just incredible luck. If you won it three times in a row, I think you might start to wonder if something else was going on. Certainly, if you didn’t, then other people would.
If you won it four times in a row, with a trillion trillion to one chance (a trillion trillion is 1 with 24 zeros after it), I suspect the authorities would be called. The odds of this happening by chance are so remote that fraud, foul play or some other form of intelligent design would be a much better explanation than extraordinary luck. At the very least, it would probably be investigated seriously. In other words, I think suspicions would be seriously aroused at either the third or fourth lottery win in a row.
Now, we need to be careful when making arguments from probability, because other factors have to be considered. For example, if you purchase one ticket a week, two sequential lottery wins might be a One In A Trillion event, but if you could somehow live long enough to enter it for a trillion weeks, then it becomes quite likely you’ll win two in a row at some point in time. In other words, the solution here is lots of time. What may be improbable in the short term can become likely over a long enough stretch of time.
Alternatively, maybe you have a second rich friend who doesn’t like Rich, your first rich friend, and who agrees to give you the money to buy up most of the available lottery tickets for the next two weeks, with the agreement that if you don’t win both lotteries you owe him nothing, but if you do, you pay him five million dollars in return.
By purchasing most of the available lottery tickets for two weeks, it’s highly likely you would win both lotteries, and your first friend Rich, who had assumed you wouldn’t buy so many tickets, would have to pay you ten million dollars, leaving you with five million dollars after paying your second rich friend, plus the winnings from both lotteries. Your second friend had risked up to two million dollars of his own money, by giving you the money to buy up most of the lottery tickets over two weeks, but he had a very good chance of making his money back, plus an extra three million dollars.
Now, if nothing else, this might make a good movie plot. But it’s also fair to say that serendipity no longer played a major role here. Your second friend helped to orchestrate a winning situation, so you didn’t just get lucky. Then again, having these two rich friends, maybe you did.
In other words, probabilities do matter, as long as we also pay attention to the context. At the very least, they can help to indicate the point at which we can reasonably start to question the role of serendipity.
The story of the evolving antifreeze protein from the previous chapter is similar, in that the freezing codfish supposedly won the lottery multiple times in a row. They won it when several waves of the “duplication” serendipity wand multiplied the 27 or so nucleotide sequence, and then again when more waves of the wand duplicated the core 9 nucleotide antifreeze sequence multiple times.
It’s difficult or perhaps even impossible to calculate the specific odds of each event, since we have to factor in all the other things that might have happened, as well as the chances of a mutation getting past the mechanisms that are supposed to minimize duplication errors.
The freezing codfish continued their streak of incredible luck when a tagging sequence just happened to be lying around in the right place, allowing the emerging protein to be secreted into the blood. What was it even doing there? The researchers say it didn’t come from anywhere else in the genome, but evolved from scratch and just happened to be there.
I would suggest the odds of it evolving from scratch in just the right place are ridiculously small. However, if the order of species lineage is somehow incorrect, then maybe the tagging sequence was the remnant of a previously functional antifreeze gene. In this case, the chance of it being there would be high, although it’s intriguing that this part remained intact while the functional part of the protein didn’t, perhaps suggesting that the genome somehow preserved the tagging sequence just in case it was needed.
Our freezing codfish also won another huge lottery in a row when a control sequence supposedly translocated its way over to the evolving gene, or the other way round, apparently emerging de novo, just like the export sequence. Again, what are the odds? Unfortunately, they are impossible to calculate, but it’s not sufficient to say “translocation can happen.” This is like saying, “parcel delivery can happen.” It doesn’t explain the box of gold bullion on your doorstep addressed to you.
The other important factor here is, all of these things needed to happen quickly, since the gene couldn’t be manufactured until it had all the necessary components – the antifreeze sequence, the control sequence to allow the protein to be made by a ribosome, and the tagging sequence to get it into the blood.
A protein needs to be produced in order to be tested in the real world, and for the functional gene to give the organism a survival or reproductive advantage, which could then help to preserve the sequence intact throughout succeeding generations. But if it took too long to become a useful protein, mutations would have degraded the sequence. Therefore it only had a small window of opportunity to become functional. A million years would perhaps be too long, but let’s be generous and say a million years. Unlike colonies of hypothetical bacteria, schools of real fish take up a lot more space.
How many fish would be available for evolution to play with? Let’s squeeze in a trillion freezing codfish together, each one living an average of a year and then replacing itself every year, doing this for a million years. That’s a total of a million trillion codfish, or 1 with 18 zeros after it. This is a quite lot of fish. The important question is, will this allow nature to run enough trials to evolve all the right antifreeze components, and translocate them to the right place, in the required length of time? To keep things simple, if we say one fish has one mutation, then nature can run a million trillion trials.
Multiple copies of the 27 nucleotide sequence first need to be made, and then several copies of the 9 nucleotide antifreeze sequence. An individual duplication event might not be entirely rare, but we are talking about several such events in sequence here, all with exactly the right amount of genetic information being copied and pasted. This is like winning the lottery at least six or seven times in a row. It is highly improbable. Furthermore, as the codfish researchers acknowledged, the evolving gene wasn’t subject to natural selection, which meant nature didn’t have any reason to preserve it during its development. It was therefore more likely to mutate away before arriving at its final form.
What about the presence of the control sequence, needed so that the protein could be manufactured by a ribosome? In a previous chapter I showed that bringing two microproteins together through the deletion of ten nucleotides is a One In A Trillion event, but the odds become orders of magnitudes worse as we space the two microproteins further apart. The genomes of codfish are typically over half a billion base pairs in length. The probability of an existing control sequence and the antifreeze sequence coming together in a genome of this size, at least through insertions, deletions and letter swaps, is so small as to be virtually impossible.
If there was a specific mechanism that could translocate a control sequence to just the right place, this would help immensely. But if the researchers knew of such a mechanism, they would have told us what it is. Translocation itself is not a mechanism. It’s just a word that sounds more scientific than saying it got moved, which would then beg the obvious question: how did it get moved?
This is why I call translocation a serendipity wand. In evolutionary stories, specific sequences are said to have moved, often with little or no actual consideration for how likely or unlikely this is. It simply must have happened.
Finally, what are the chances of the tagging sequence, needed to tag the protein for export from the cell and into the blood, being just one nucleotide away in a genome that contains hundreds of millions of nucleotides? I’m not even sure what kind of lottery win this could be compared with. I suppose it would be like having multiple winning tickets turn up on your doorstep one morning.
My point is, from a mathematical point of view, I doubt any number of codfish could run enough mutational trials to achieve these things in the right sequence, let alone a million trillion of them.
However, from an evolutionary storytelling point of view, the fact that all of these things occurring in sequence are wildly improbable doesn’t matter in the slightest. It must have happened because the antifreeze gene is here, and the lucky Arctic codfish are no longer freezing their scales off. I am suggesting that perhaps there are other explanations for why it is here.
What I have shown is that evolutionary stories usually contain many assumptions, and often rely on remarkable serendipity. Organisms seem to keep getting incredibly lucky multiple times in sequence, despite overwhelmingly unfavorable odds. This suggests it might not be serendipity after all.
In the case of the freezing codfish, I think the problem is that the researchers assumed evolution must have happened, and then lined up the species in a lineage based on their evolutionary assumptions. But the species with an almost functional antifreeze gene is evidence that this species is actually losing information, not gaining it. The sequence appears to have devolved into a pseudogene, rather than being on the cusp of evolving into a gene.
The three species without the gene could have lost most of it because they no longer needed it, or maybe it wasn’t there in the first place. But if the export tagging sequence really is present at the right location in these three species, and isn’t just part of the storytelling, this would be evidence that they actually lost the functional part of the gene. In other words, this is devolution rather than evolution. Each of the seven species might have had the antifreeze gene, but some of them may have lost it because they found themselves in warmer waters where they no longer needed it.
Incidentally, by curious serendipity or intelligent design, the sticks that Jacob placed in the troughs are surprisingly similar to our serendipity wands. If you recall, while Jacob was working for Laban, he “took for himself a fresh stick from the poplar and almond and plane trees, and he peeled white peelings in them, to expose the white that was on the sticks.” 1 In the first part of this letter, I showed that what Jacob was doing with the sticks served as an analogy for how amino acids are put into ribosomes to create a protein.
The Hebrew words used here also seem to allude to a deeper meaning. The initial word used here for “stick” (mql) is singular, so even though it becomes clear from the account that Jacob has taken three sticks (the plural is used afterwards), I think the initial word is singular to remind us that one codon is actually three nucleotides attached to one another in a sequence. The ribosome reads one codon at a time.
In other words, we think of a codon as singular, even though it’s really made of three building blocks. The same is true of a protein. We think of a protein as a single item, even though it’s made up of a chain of amino acids.
The Hebrew words used to describe the sticks are very interesting. The word here translated as “poplar” (lbne in Hebrew, pronounced “liv-neh”) is similar to the word for “Laban” (lbn), which means “white.” It is a “duplication” of his name, but with a letter added, which can also happen in biological mutations.
The word translated “almond” (luz) is the word “Luz” in Hebrew, pronounced “lose,” and is also the name of the place where Jacob had his dream of the ladder, which in the first part of this letter I suggested was an analogy for the double helix structure of DNA. If Jacob took a stick from Luz, we could say the stick had been “translocated” to where he was now. Jacob renamed Luz to Bethel, meaning “house of God,” but biologists have replaced God with luck, mutations and serendipity wands.
The “plane” (ormun, pronounced “arm-own”) is another interesting word. The Hebrew transliteration ormun would look and sound a lot like the word “amino” in amino acid if we could just shuffle the “o” to the end and switch the “u” for an “i.”
“You can’t do that,” say skeptics. “That would be cheating!” Yes it would. But evolutionary theorists are allowed to do precisely this. New proteins supposedly evolve by duplicating out of old ones, and then amino acids and nucleotides shuffle around and change letters until a new function magically turns up.
Whatever you think of these ideas, we can say that the Hebrew words used to describe Jacob’s three sticks serve as useful metaphors for the serendipity wands of “duplication,” “translocation” and “magical steps” used by evolutionary theorists.
The word translated “fresh” (lk) to describe the sticks is pronounced in Hebrew more like “luck” or “lack” (but with the “ck” sounding more like the end of the word “ich” in German).
In a sense then, we could say that these are Jacob’s Sticks of Luck, which would make them surprisingly similar to our Wands of Serendipity. The word (lk) also comes from an unused root word meaning to be new, which is similar to the term de novo (from the Latin, “of new”) biologists use when they mean something came out of nowhere or was made from scratch.
If we can accept the possibility that the stories of Jacob and Laban are also meant to be metaphors for molecular biological processes (and I will present even more evidence for this a little later), which suggests God encoded this information in the story right from the beginning, then I think the Hebrew words used to describe Jacob’s three sticks are meant to show that God knew in advance what many biologists would do with the discoveries they have made.
They would take away God’s glory, and give it to luck – which would involve incredibly fortuitous duplications, virtually impossible translocations of specific sequences across the genome, and untested and vague magical steps involving nucleotides and amino acids, to transform one genetic sequence into another.
I don’t wish to take away from the great research microbiologists have done in discovering how life works at such tiny scales. What they have achieved is nothing short of incredible. But just as Jacob peeled away the bark to expose the white on the sticks, we need to peel away the veneer of evolutionary storytelling by the men and women who work in their white lab coats, to expose their Wands of Serendipity – or as Jacob might have called them, the Sticks of Luck.
1 Genesis 30:37.