# The Carter Catastrophe

Hari Seldon, the mathematical genius who invented Psychohistory, has a math question for me:

The Carter Catastrophe argument is that if everyone who ever lived or ever will live were to assume “I’m in neither the first 1% or the last 1% of humans to be born”, 98% of them would ultimately be correct, and the smaller the margin (“I’m not in the first or last 0.1% of humans to be born”), the greater the fraction of humanity for which the statement is true.

An Asimovian galaxy, in which millions of planets are inhabited for tens of thousands of years, would have quintillions of human beings living in it over the aeons, and therefore, we pre-spaceflight humans would be in the first 0.00001% of humans to ever be born.

The argument says that we can safely assume that we are not in that special 0.00001% (or more specifically, that there’s a 99.99999% chance that we’re not), and that therefore, humanity won’t expand out into the galaxy and remain there for tens of thousands of years.

I never liked the argument, or its implication that the grander the sci-fi future, the less likely it is to happen, but have never come up with an actual response to it.

My comment: the argument is not an argument at all, merely a series of three disconnected statements.

The number of errors is almost too great to count.

To see this, let us use the same type of reasoning in another case.

Disconnected Statement 1: Suppose every man who ever lived or ever will live were to utter the sentence, “I am either the first man or the last man to be born.”

We can take it on the authority of books written by Moses or Mary Shelly that there are exactly two men who utter the sentence truthfully: Adam, and Lionel Verney. (Other sources list the First Man as Ask or Izanagi, and Last Man as Robert Neville or Reginald Powell, but let us credit Moses and Shelly for now).

Let us assume the total number of mankind through all time is two hundred billion and two. This means that two hundred billion men speak the sentence falsely, and only two speak true. Therefore the percent chance of a man existing who can speak the sentence truly is a one hundred billion to one.

Disconnected Statement 2: We can safely assume no one person we are likely to meet is in that special “one hundred billion to one” speck of unlikelihood where the two truthful speakers reside. It is statistically indistinguishable from zero.

Disconnected Statement 3: Therefore neither Adam nor Verney ever existed, therefore the human race never existed, because there is no first man. And, by the same logic, therefore also the human race will never pass away, because there is no last man.

Do you see the error in the reasoning?

A second example may be clearer:

Disconnected Statement One: We also have it on good authority that at one time Noah, and his three sons, and their wives, along with Deucalion and his wife Pyrrha, were the only people alive on a drowned world: Ten people. We have it on good authority that the world population by AD 2025 will be eight billion. This is roughly eight percent of all humans who ever lived, from the Paleolithic to the present, which is estimated at one hundred billion.

Suppose every human who ever lived were to utter the sentence “I was aboard the Ark.” The percent chance of a man existing who can speak the sentence truly is a ten billion to one.

One of the descendants of Japheth was Christopher Columbus. Had he never been born the New World would never have been discovered, and the amount of arable land available for human population growth never reach the acreage needed to sustain eight billion by 2025.

Disconnected Statement Two: We can safely assume no one person we are likely to meet is in that special “ten billion to one” speck of unlikelihood where the truthful speakers reside. It is statistically indistinguishable from zero.

Disconnected Statement Three: Therefore Noah and his family never existed; therefore Christopher Columbus never existed; therefore the New World was never discovered.

There are many errors in this argument. Let me see if I can list them.

- One of the errors is ambiguity: the word ‘percent’ is being used in two different meanings.
- A second error, is argument from ignorance: the argument switches between the future perfect tense and the present tense, and thus switches deceptively between what is known and what is unknown.
- A third error is mere irrelevance: after an unlikely event has happened, there is no “percent chance” of it happening. The thing is done. It is certain.
- A fourth error is that the argument is circular.
- A fifth error is the unwarranted and outrageous assumption that describing the past predicts the future. This fallacy is so widespread it has its own name: the Gambler’s Fallacy.

Let us look at each in turn.

The first and main error that is going on in this so-called argument is the first one. Carter (the man making the argument) is merely using the word “percent” as a vague metaphor to mean “hard to believe.”

If I walk up to Lionel Verney in his youth, before the plague destined to wipe out mankind even begins, I would find it hard to believe indeed that I am speaking to the Last Man. In the common, that is, metaphorical, sense of the word, the event of meeting the Last Man on Earth would be unlikely.

Likewise, if I walk up to Neil Armstrong, I might find it hard to believe I am indeed speaking to the First Man on the Moon: starstruck, I might continue in my disbelief even after meeting him. This is a report of a psychological condition. It has nothing to do with mathematics.

On the other hand, if I walk up to Mrs. L .Jagi Wright, my wife, a quick calculation on your mental abacus will tell you that the number of people able to be the one woman in the whole world who married John C Wright the science fiction author is (eureka!) exactly the same as the number of people able to be the First Man on the Moon. In both cases, it is the whole population of all men who ever lived minus one.

The current world population of seven billion is roughly seven percent of all men since the paleolithic ever born: so call this number one hundred billion.

Now, then: what is the percent chance of one person out of all men ever born, being the First Man on the Moon? Likewise, what is the percent chance of one person out of all men ever born, of being the one woman to whom I am wed?

At first glance, it would seem as if the chance of the happy meeting in either case can be expressed in terms of a ratio of one hundred billion to one. There are one hundred billion humans; I am one human; ergo my chance of being me is one hundred billion to one. What an unlikely miracle!

But wait. My chance of being me does not involve any ‘chance’ at all. It am certain that I am me.

Likewise, when I go home this evening, my ‘chance’ of meeting my wife is much higher than my chance of meeting Neil Armstrong, for she lives at my house and he does not.

The word ‘chance’ refers to situations where the factors feeding into a chain of cause and effect leading from one in a series of repeated and repeatable events are unknown, but the number of outcomes is known.

By ‘repeated and repeatable’ is meant events like coin tosses or rolling dice or any other group of events where we ignore the differences between one event in the series and another. For example, tossing a coin in South Carolina in 1890, and tossing a coin in West Virginia in 1980 are, for the purposes of a coin toss, an identical event.

Only if the coin is not balanced, or it is a two-headed coin, will a causal factor be present that influences the outcome sufficiently for us to regard the event as a cheat, that is, tossing a two headed coin is not considered a member of the set “a coin toss.” You would not have an umpire toss a two-headed coin at the beginning of a football game to see which team starts with the ball. No analysis of the percent chance of a coin toss landing heads or tails includes two-headed coins.

By “the number of outcomes is known” in this case we mean two: the coin always lands heads or tails. The number of times coins have landed on edge, or were carried off in mid-toss by mischievous jackdaws, is so unlikely as to be considered an Act of God.

In the case of a balanced die, we mean six outcomes are known , we just do not know which of the six it shall be.

In the more interesting case of two dice, we mean eleven outcomes are known.

In the case of one die, the probability of each outcome is even: rolling a one is no more nor less likely than rolling a six.

In the case of two dice, we ignore which die the pips appear on, and six-and-one combination is regarded, for our purposes, as the same as five-and-two or four-and-three. Hence, in the case of two dice, the probability of each outcome is not even: snake-eyes and boxcars is thirty-six to one odds, whereas rolling a seven is six to one odds.

Now, from the point of view of an all-knowing demiurge, which way the coin lands is as determined by the mechanical laws of the universe as the orbits of planets or the timing of a total eclipse of the sun. We predict eclipses because we know all the factors of the causes, such as position, mass and momentum of the heavenly bodies, which lead to the outcome. We do not predict coin tosses because the very slight differences in pressure and force of the umpire’s thumb each time he flips the coin are too difficult to measure and calculate. But it is easy to imagine that a skilled juggler could flip a saucer or a discus so that it always made the same number of turns in midair, and landed where and as he wished.

The reason why we use coin tosses rather than solar eclipses to decide which team starts with the ball is precisely because both teams beforehand are equally ignorant of the outcome of the toss, as are the umpires and spectators, whereas humans for years have been able accurately to predict solar eclipses. From the point of view of an all-knowing demiurge, however, all the factors leading to the outcome of a coin toss equally are known. From his point of view, the outcome is certain; hence there is no chance involved. We might as well have used a two-headed coin.

So the word chance does not refer to a cause of any event, nor can it refer to single or unique events, nor to events in the past, nor any other event where the outcome is known hence certain.

The word ‘chance’ can only refer to events that are, like coin tosses, held to be identical to all other events of the same category, where the number of outcomes is known beforehand (heads or tails) but the some particular factors causing the outcome are not known beforehand (the acceleration of gravity and the weight of the coin can be known, but the exact placement and pressure of the umpire’s thumb cannot be known).

The word ‘percent’ means ‘out of a hundred’ and is used to express the ratio between one outcomes and trials of events regarded in a series or sequence.

Like the word ‘chance,’ the word ‘percent’ refers to the exact degree of human ignorance concerning causal factors, and only applies to cases where the events are held to be identical (all coin tosses are the same mathematically, even if the coins differ), where the outcomes are known, and the factors are not.

Like the word ‘chance,’ the word ‘percent’ does not refer to unique events, does not refer to events whose outcome is known, does not refer to events whose number of possible outcomes is not known.

From time to time, we speak of a past event, even though the result is now known hence certain, as if it were still uncertain, on the grounds that we can so easily imagine things having had gone another way, if only things had been different. A narrow escape, a near-miss, an unexpected mishap, even after the event is done, can be spoken of as likely or unlikely.

All such talk is metaphorical. It expresses our sensation, emotion, judgment, or estimation about might-have-beens given our ignorance before the outcome was known. In each case, however, our hypothetical all-knowing demiurge could have predicted all outcomes far in advance.

Upon repeated viewings of STAR WARS, for example, I am in the position of the all-knowing demiurge. Since I have seen the film before, and I know full well that Luke Skywalker, space farmboy, will turn off his targeting computer and make a skillful but unexpected shot putting a torpedo into the thermal exhaust port of the Death Star. Han Solo, lovable space rogue, will declare it to be a million to one shot.

But I and others have seen the film a million times, and all million of us see him make the shot each time, not just once. This is because it is a film: the outcome does not change between viewings. (Unlike whether Han shot first, which does change, or tries to).

The shot is a million to one but only from Han’s point of view, only given Han’s ignorance of the factors leading into the outcome. He is expressing astonishment, because he judges that the unknown factors leading to the successful shot should have much more easily lead to the unsuccessful outcome.

He is literally saying that if a million more shots were taken again under the same conditions, known and unknown, all would miss; but this again is a metaphor.

Obviously if conditions were exactly the same down to the last nuance, we would be merely running the film again. He means that if the known conditions where the same and the unknown conditions were in each of the other possible cases to be different, those unknowns would lead to unsuccessful outcomes.

Luke and (one presumes) the ghost of Ben know full well that the mystical Force is guiding the shot, but this is not known to Han. Ergo even as a metaphor, the use of such an expression as ‘million to one’ is limited. It differs by the degree of knowledge of each observer.

In reality, Han is offering Luke a compliment: he is saying the boy’s marksmanship is better than that of a million other fighter-pilots. The unknown factors being discussed are not matters of random mechanical failure in the firing system, or the good luck of not being shot down by the enemy, but, rather, are the eagle-eye, firm hand, and steely nerves of the pilot.

So, let us look back at our hypothetical: What are the percent chances of any one person out of all men who ever lived being selected as the First Man in the Moon or being selected as my wife?

Now, this is not a statement of mathematics, even if it is dressed in mathematical garb, because it says nothing about reality. It is a statement about a hypothetical universe where some mechanism (let us imagine a time machine from Gallifrey shaped like a roulette wheel) can guarantee (1) the wheel will select a human being (2) it will be a human either now living or once alive (3) the factors determining which person selected are the same for each person, and (4) all the factors are unknown.

Under these conditions, we hold a billion sets of one hundred trials. The number of times Mr. Armstrong or Mrs. Wright is selected per trial can also be expressed in a ratio of percent, that is, per one hundred.

But there is not now nor ever will there be a roulette wheel shaped time machine.

There is no selection process, not even a hypothetical one, which ignores all the factors leading to the outcome of me finding my wife at my home at night, or in any other particular time or place or condition, rather than Neil Armstrong strangely returned from beyond the grave. Our all-knowing demiurge knows exactly where both these people are at all times.

So, unlike Han Solo complimenting Luke Skywalker’s marksmanship, in this metaphor where we express our astonishment about causes unknown, we are talking about the causes that make each man who he is rather than someone else. Unless you believe in reincarnation or in a multiverse of infinite parallel continua, there is in fact no chance of anyone being anyone other than who he is.

The words expressing your percent chance of you being someone else contain no literal meaning.

At beast, we are discussing might-have-beens, and confessing that, due to our limited knowledge, that had we guessed how my life, or yours, or Neil Armstrong’s might have otherwise turned out, we are astonished that things turned out as they are rather than some other way which we would have found beforehand to be easier to believe.

So, this first objection renders Carter’s argument nonsense. Consider his first disconnected statement.

His hypothetical is that all men will spontaneously utter a statement about their position in the history of mankind, early or late, and he observes that if all men are claiming to be in the first or last generation, that only a small percent out of the whole population, past and future, will speak truthfully.

But, applying the above analysis, all this means is that if all men express metaphorical astonishment at the unexpected event of each man being himself of his generation, rather than being some other man of some other generation, only those in the first generation are expressing astonishment at being in the first generation truthfully. Everyone from later generations is lying. Again, Carter says only those in the last generation expressing astonishment at being in the last generation do so truthfully. Everyone from earlier generations is lying.

It does not mean that our all-knowing demiurge, having a list from a history book of all generations from Adam to Verney laid out open on his lap before him, flips a coin or tosses a dart or uses some other mechanism to generate an outcome controlled by unknown factors, in order to decide arbitrarily which generation shall hereafter be the last: and each generation on the list is in equal danger of being the one on which the random dart lands.

This is the unspoken assertion Carter is attempting to get the gullible listener to heed and believe. But when spoken, its absurdity is obvious.

The last generation is the last. There is no chance involved, any more than there is any chance involved in the question of whether Neil Armstrong is the First Man in the Moon. The moon landing is done; the outcome is certain.

Likewise, from the point of view of Han Solo, who knows nothing about the force, the chance of making a torpedo shot without a targeting computer seems like a million to one. From the point of view of Luke, he may have been more certain. Both I and the all seeing demiurge have seen the movie before: to us, the thing is certain and admits of no reasonable doubt (unless Rian Johnson maliciously edits the recording, that is).

In a hypothetical situation, we can pretend we know as much or as little about the situation as the hypothetical demands. We can pretend to be all-knowing demiurges, in which case the chance of any outcome other than what our omniscience foresees is zero. We can pretend to be ignorant babies, in which case every fact, including whether I am I when I might have been someone else, is a source of infinite astonishment, and everything is a million-to-one miracle.

Carter’s second error is introduced with his second disconnected statement. “We can safely assume that we are not in that special 0.00001%” of men who correctly say that they are in the first one percent of all the generations to come.

By some leap of logic, from the statement that it is a safe assumption that we are not in the first one percent of all generations, we are asked to leap to the conclusion that it is certain that we are not in the first one percent of all generations. I do not comprehend what is even supposed to justify that leap. The two sentences are disconnected. They have no necessary nor logical relation to each other.

Adam, alone in Eden, is not making a safe assumption about his position in the timeline of generations. Likewise Varney, having buried the penultimate human, and seeing all the earth void of human life beneath his feet, has no doubts and need make no assumption.

So why are we making any sort of assumption?

Carter is playing a sleight of hand on his listener. In the first disconnected sentence, see above, he supposes that there is a fixed and definite number of all the men ever born or ever to be born summed up from generations of man throughout time, let us say, one hundred billion and one.

This statement is in the future perfect tense: we are seated on the throne of the all-seeing demiurge, looking at all history, past, present and to come, in one glance, and counting the people and assigning them to the table of generations in chronological order.

From this Carter generates some ratio expressing the metaphorical astonishment we suffer when contemplating the difference between the number of people who are you (one) and the number of people who are all the rest of mankind (one hundred billion). Or, rather, Carter expresses metaphorical astonishment concerning the difference in the number of generations compared to the first and last.

In the second disconnected sentence, he invites the reader only to contemplate what he himself knows for sure about his position inside time about whether he is or is not in the first generation, and therefore father to countless quintillion of men to come. We know the number quintillion, the size of the galaxy filled with men, because we were omniscient just a moment ago, and we counted them.

This statement is in the present tense: we are suddenly no longer omniscient. We are being asked to estimate our position in the table of generations based on one and only one bit of information: what are the odds, if we select each generation totally at random, that we will be in the first generation out of quintillion generations, rather than some generation other than the first?

But why, praytell, are we being asked to estimate our position based on nothing but the odds of selecting one generation totally at random? By a very cursory examination of the world around me, I can detect that we humans currently, out of the quarter billion stars in the Milky Way, notice that only, two bodies, Earth and Moon, in this one star system, Sol, have ever felt the footprint of man.

If the omniscient demiurge gives us certain knowledge that quintillions of people will some day populate the stars of Milky Way, then the conclusion that we are in the first one percent of the generations of man is inevitable. So there is no probability involved, no guesswork.

But if the omniscient demiurge tells us that the total numbers of man for all history is one hundred billion, and if we count all prior generations and realize that the sum of the dead generations is ninety-three billions, then the conclusion that this generation of seven billion is the last generation is also inevitable.

But if the omniscient demiurge is silent, and we do not know whether or not man will rule the stars in eons yet to be, and do not know between quintillion or one hundred billion, what shall be the sum total of the numbers of man through all time, then, logically, we cannot deduce, even by remotest guesswork, just from knowing the numbers of men present and men past, what our position might be in the table of generations.

If quintillion men are fated, we are in the first one percent. If one hundred billion men are fated, we are the last one percent.

So, by switching from future perfect, where we know the total number of man, to present tense, where was know only the past, we are in effect switching topics, or, rather, switching universes. Instead of talking about a universe holding an Asimov galaxy of quintillion men, we are suddenly in a universe were the future is unknown, hence the numbers of men is unknown, hence the ratio of men alive to men yet to be born is unknown.

Even if it were logical to deduce from the ratio generated by spinning the hypothetical time travelling roulette wheel of Gallifrey that a lower ratio of living to unborn means we occupy an earlier percentile of the first generation, or that a higher ratio of living to unborn pushes us farther away from the first generation (and it is not logical so to deduce) Carter’s argument would still not follow:

Because he asks us to hypothetically pretend we know from the demiurge the total number of unborn men fated to be, and because that number is dizzyingly high, deduces we are born early in the history of man. But then he asks us to rely only on our human knowledge, and to us the future is a blank. Carter calls it safe to assume that we are not born early in the history of man, since the total number of those born after us is so dizzyingly high, therefore the total number of unborn men fated to be is low.

Imagine a gypsy tell you that you will have a wife and ten kids. You then realize that, if selected totally at random, you have only one chance in twelve of being the father in such a family, rather than the bride or offspring. One in twelve is not good odds: it is mathematically indistinguishable from zero. Therefore you do not exist and never spoke with a gypsy. But if the nonexistent gypsy tells the nonexistent man he is having only two kids, his odds are one in four. If you have a wife an no kids, the ratio is two to one. Those are reasonable odds, so you exist again.

The only way to be certain of existing is never to marry, have no wife, and then the ratio of family members to fathers is one to one, or unity, in which case your existence is certain. If your existence is certain, therefore you are bulletproof and immune to disease and can never die.

But if the gypsy cannot see the future and tells you no number at all, it is not safe to assume that the number is high. It is not safe to assume that the number is low. It is not safe to assume anything at all, since by hypothesis you are dealing with an unknown value. The ratio between x and one hundred is X%, which is to say, unknown. If the event happens in x number of outcomes out of one hundred trials, then, by definition, that number is finite, therefore not indistinguishable from zero.

The third error is irrelevance. The conclusion simply does not follow from the premise.

From the premise that “we have but one percent chance of being in the first one percentile of all humans fated ever to live” and from the middle premise that “one percent is but one chance out of a hundred!!” what follows is “we have but one one chance out of a hundred chance of being in the first one percentile of all humans fated ever to live.”

Should in fact it turn out that we are in the first one percentile, once this fact is known, there is no more chance, which is another word for human uncertainty about cause and effect, involved at all.

The conclusion, “It is safe to assume one in one hundred is not good odds, therefore is it certain that we are not in the first one percentile; therefore the numbers of generations coming after us certainly must be low. That is the duty they owe us, to keep their numbers low, in order to prevent us from ending up in the first one percentile.” Is simply an arbitrary statement. There is no word in logic for this type of error, since it is merely irrelevant.

The argument that it is safe to assume we are not in the early history of mankind, therefore this proves we are not in the early history of mankind is also circular.

If I assume this is the last generation of man, I can conclude we will not conquer the stars. If I assume that we will conquer the stars, I can conclude this is not the last generation of man. Dressing up this tautology in mathematical talk does not save it from begging the question.

Also, substitute any unique historical event for conquest of the stars, and apply the exact same argument, and you will see its absurdity. What are the odds that I was born in the generation that landed on the moon? One in ten billion. That is mathematically indistinguishable from zero, is it not? Therefore I was never born and man was never on the moon!

Finally, let us talk about the Gambler’s Fallacy, which this argument has in spades.

I confess this is a particular pet peeve of mine, and a source of endless cold and aloof exasperation, or would be, if my dispassionate Vulcan brain were able to conceive emotions.

I blame Pascal. That brilliant polymath, so wise and clever in so many fields, opened a floodgate of ambiguity when he attempted a mathematical analysis of gambling.

A friend of his, the professional gambler Antoine Gombaud, the self-styled Chevalier de Méré, turned to Blaise Pascal and asked him to analyze his betting strategies mathematically, in order to divide up fairly the money in the kitty of an interrupted dice game Gombaud had been playing with a knight. Gombaud and the knight had agreed to divide the kitty based on each man’s chance of winning.

The game had been one where the diceplayer who wins a certain number of rounds wins the whole kitty, and the two players in this case each had won a different number of rounds. Pascal used his famous triangle to calculate out, not how many rounds each man had won heretofore, but what each player’s expectations of winning were for each round hereafter.

Obviously if they had agreed the whole kitty should go to whoever won best two out of three of a coin toss, and both had won one round so far, they would have declared their odds of winning even, and split the kitty in half.

But if the game was best of three out of five, and the knight had won two rounds but Gombaud none, the knight must win only one more round of the remaining three, whereas Gombaud must win all three.

In the simple case of winning three out of five when the knight is up by two, the knight’s chance of winning is fifty percent each coming round, since he need win only once. Gombaud needs to win all three yet-unplayed rounds.

There are only four possible outcomes: 1. the knight wins round three, or 2. the knight loses round three but wins round four, 3. knight loses twice more but wins the tie-breaking last round 4. Gombaud sweeps the remaining three rounds.

Of the four outcomes, all of which are equally likely, Gombaud loses three times out of four. Hence a fair division of the kitty of this interrupted game is one quarter to Gombaud ; the knight gets three quarters.

So far, so good. The difficulty came when Gombaud asked Pascal how to bet on ongoing games, using the math to calculate and play the odds.

What Pascal should have told him is that neither coins nor dice have any memory, and that the chance of a coin landing heads is one-in-two, no matter how many times the coin has landed heads before; the chance of rolling boxcars is one-in-thirty-six, no matter how many times the dice have rolled before, and no matter the previous rolls.

Now, when using probability in hindsight, so say that the one time I tossed ten coins in a row and they all landed heads, the chances of that are 1/1024 or about 0.000967% — but from this it does not follow that if you walk up to a man who has just thrown nine heads in a row, his chance of tossing yet another heads is low. It is not. His chance is still fifty-fifty.

It is just that the aggregate chance of something happening which is fifty-fifty having the same outcome ten times in an uninterrupted row is one in one thousand twenty four.

Which means that if you toss ten coins one thousand twenty four times, the chance of having them all land heads at least once is average odds, or fifty-fifty. And the first trial out of the one thousand twenty four times might be the one time all ten coins land face up. Or it might be the last trial. Or any one in between. Or it might happen twice or not at all. All these things can be described in terms of ratios between expected outcomes and real outcomes.

What cannot be done is predicting the future.

Probability does not work that way. The Gambler’s Fallacy says that something unlikely in the aggregate is therefore unlikely in the particular.

Suppose you just drew the Ace of Hearts and the Ace of Diamonds from a freshly shuffled deck of 52 cards. The chance of you drawing the Ace of Spades and having three aces is still exactly the same as the chance of you drawing the Trey of Clubs: one in fifty.

The aggregate chance of drawing three aces in a row on your first three draws, is, of course, lower than that: a shade over one in a thousand (0.00018172, if my rusty math skills are correct). But that does not change the particular chance.

Likwise in the Carter argument. The aggregate percent chance of our generation being the first to invent hyperdrive, therefore being absurdly few in number compared to all the stars our children might colonize, is as small as any number mathematics can name.

And , by the simple trick of increasing the number of our utterly imaginary posterity, we can make that ratio as small suits our rhetorical purpose.

But the actual percent chance… if you insist on a misleading metaphor… of our generation inventing hyperdrive is one hundred percent if we can and do, or zero percent if we can’t or don’t.

Carter’s argument relies on conflating particular percent chance with aggregate. It is the Gambler’s Fallacy writ large.

To speak of the likelihoods of events determined by human action, is even more of an error. Whether we are the last generation to use the Earth before destroying it, or the first generation to invent hyperdrive the conquer the stars does not depend on dice or coin tosses, but on what we do with our lives.

And the chance of each man to be himself, as we noticed above, is a certainty.