I've developed an algorithm that predicts the future of mankind...and it doesn't look good

Great Debates
81

Humans definitely come with a number. As you said, it’s not stamped on your head, but it’s definitely mathematically describable. There’s sound reasoning to describe what it is, give or take a few billion. The linked Vox article uses 100 billion, so let’s go with that.

In post #72 above, I described how to understand why, whatever our current number is, we’re most likely closest to 50% of that number. The farther you stray from 50%, the more work needed to explain why you think our cohort is closer than every other cohort to the beginning or end. You can demonstrate it in extremis - assume we’re at the 1% or 99% point, consider the implications - either things will stay the same forever, or they’re about to get really bad.

So least-effort and highest-probability assumption is that we’re close to the midpoint. Rephrased as a probability, the likelihood of current population doubling is 50%. Not the certainty - the probability.

From that it’s a straightforward matter of looking at current population rates, and estimating how long it will take to get there. If we use a credible demographic estimate of 100 billion, and we’ve demonstrated there’s a 50% chance that we add another 100 billion, and we put the current birthrate at 134 million: there is a 50% chance that the average birthrate drops to zero in 746 years.

If you don’t like 100 billion, fine. Some estimates say 60 billion. It’s not going to be 1 billion or 1 trillion though. The method of calculation remains the same.

That doesn’t mean the giant meteor ends exactly everyone in exactly 746 years. That’s just how long it will take to double if the current birthrate holds for 746 years. It is not certain that we are at 50% of cumulative births. That’s not a certainty, it’s just the peak probability.

If you think we’re at less than 50%, the more you need to explain why average birthrate should remain >= 134 million for 746 years. If you don’t have better information, then the best guess is 746 years. If you think it’s more, then you need to explain why population is going to decline.

Otherwise, we assume it’s going to remain exactly the same. Is that crazy? If you looked at growth trends in 1970, you’d have said yes, the population rate has increased at a frighteningly fast rate in the past couple of centuries. But if you’d used a probability forecast based on the mediocrity principle, it would have told you, this is unlikely to continue on forever. Lo and behold, the current forecast is that the population growth rate will stabilize relatively soon, around 2100 by some estimates.

So it seems likely that the population rate will stay stable or decline. That means a 50% chance that the average reproduction rate falls to 0 in around 746 years, depending on how many people you think have already been born. It’s not absolute, there’s a lower but real chance it will turn out to be 646 years or 846 years. But the highest probabilty given an assumption fo 100 billion is 746 years.

82

You said 100 was the endpoint in the example I’m talking about

83

You guys are still working on this? I can’t go to the Emperor of the Universe with these numbers!

84

The emperor can listen to that weird little guy with the visisonor while he waits; I’m sure he’ll be fine with the delay

85

When I say 50 is the endpoint in any count it occurs, it is the endpoint at the time it is counted. The count may or may not continue at that point.

The formula being shilled here says that whatever you have counted to 50, there is a 50% chance that the count will end between 67 and 200. The formula is wrong because of infinity issues; probability should never be calculated with an unknown denominator. Anyway, we’ll run through the case where the count does end at 100 and 50 is a midpoint.

Now use a time machine to drop yourself at a random point in the count. Clearly you are as likely to be dropped at position 3 or position 98 as position 50. And remember that you have utterly no information about what you are actually counting, you can’t use observations to determine anything about when the count will end. If you are dropped in position 3, ask the person who is doing the count at 3, do you think they are going to say “yeah, despite me knowing nothing about this object, this really feels like a count of 100. I’ll defer to the person counting at 50, they really know more about it than I do.” Despite the person at position 3 knowing that there are an infinite number of counts that end between 4 and 12, which is what the same formula is telling the person at 3 at the time that the count of 3 occurs. No, they “somehow know” that this is a 100 count and the person at 50 is really the one to listen to. Same with the person at 98, despite knowing nothing about what they are counting and knowing that many counts go on past 100, they “somehow know” that this is a 100 count and the person at 50 has made the correct determination. This is not going to happen in any blind count, and the person at 50 is using an anchoring fallacy to believe they are in the middle of any count.

As I said, probability should not be used with undefined denominators. Suppose you are counting an unknown object and you have reached the count of 3. This formula says there will be between 1 and 9 more objects 50% of the time. In any random count that has reached 3, is this really true? The question is unanswerable. Because there are an infinite number of counts that are between 4 and 12, and an infinite number that are not. There are infinite ways to count even a finite set of objects. Count all of the water molecules in the world. Continue your count by counting all of the half water molecules. Continue that count by counting quarter water molecules and so on. This is a count of a finite object that will extend into infinity. But the answer of 50% between 4 and 12 is clearly false and should not be given out by any reputable mathematician.

86

You wrote:

87

What’s “unknown denominator” here, specifically? Do you mean the total number of outcomes, that it’s a problem if this is infinity? Just trying to make sure I understand.

88

The first statement is referring to the process of counting. Any number is the (temporary) endpoint of a sequence at the time it is counted.

Infinite counts are taking place. You ask for a pause in all counts that reach 50. At that point, 50 will be the endpoint in all of the counts that reach 50. You release the pause and the counts continue. 50 will be the endpoint in the infinite number of counts that reach 50. It won’t be the endpoint in the infinite number of counts that move past 50. It will be the midpoint in the infinite number of counts that end at 100.

The second point is that the midpoint has no particular significance. It is not any more important to the count than 3 or 98 or any other number. In completely blind counts with no information about the object being counted, there is not going to be any way to tell whether the third instance of an object is the third of three or the third of a trillion. The two counts are indistinguishable. There’s not even a distribution, since there are an infinite number of counts that end at any number on into infinity.

So I’ve counted to 50, it’s a ridiculous assertion that there’s a 50% chance that my count ends between 67 and 200. You can’t calculate 50% of infinity. The universe of even numbers is infinite, just as the universe of all numbers is infinite. 50% doesn’t exist there. You have absolutely no information when a completely blind count will end. None at all. This rule should not be used by anyone. Find out some information about what you are counting, then you have a clue.

89

Before i go onto anything else, can you acknowledge or deny the value of guessing 50 for the original finite example you suggested.

90

The example where I said 100 units existed in all? Yes, there is nothing special about 50 and its place in counting to 100. Random number generator, 50 gets chosen 1 time in 100, same as any other number in the sequence.

50 will be the midpoint in counts that finish at 100. But there is no way to distinguish that in any particular blind count. There is no way to know that your 50 will be a midpoint.

Due to infinity issues, there’s also not a 50% chance that all counts that reach 50 fall within the 67-200 range. Since there are an infinite number of counts that reach any number up to infinity. No calculation of probability is possible in blind counts with no fixed end point.

91

You have two items. All you know about them is that one has existed for a thousand years and one was just created last week. Now you are asked to wager some amount of money on a bet: which one of these items will still exist ten years from now?

You are crazy if you pick the newer item. The fact that something has lasted a thousand years is information. And if that’s all the information you have, you should use it.

It’s not dispositive - a piece of shipwreck could last a thousand years but deteriorate rapidly once it’s out of the water. A piece of gold jewelry that was made an hour ago is likely to still exist after ten years. Stone Buddha statues that have lasted for thousands of years can be blasted into rubble in seconds by religious fanatics. But all of that is information you do not have for the purposes of the discussion.

Given no information about the nature of two objects other than their age, the odds are that the one that has existed the longest can be expected to survive longer. The formula we are talking about just quantifies this effect.

92

Do you agree that for the finite case of a random number generator selecting between 0 and 100 that

You are going to be within 25 of the right number 50% of the time. That may be valuable information to you or it may not be - depending in circumstances.

93

You keep saying “infinity issue”, but using a verbal description I’m not clear what you mean.

If it’s so obvious, there must be a very basic equation to represent what you’re talking about. This will help clarify why it’s impossible. What’s that equation?

94

In practice Hari Seldon can only provide error bounds and checklist procedures. If the math is really that impenetrable, then you are left with his expertise and track record. That’s problematic.

In fiction, Seldon should lead an Impossible Mission Force, choosing a team of skilled experts each week to stabilize the galaxy. If the Mule appears smoke should pour out of the back side of the computer while error messages say, “Does not compute.”

95

No, assuming any sort of bell distribution in data is a mistake.

Take the introduction of states to the Union. 13 in the first decade, counting by ratification date of the Constitution. If you’re assuming a bell distribution, it should go up from there, no? No, that was the most we ever had in one decade.

The 25th and 26th states were Michigan and Arkansas. A bit of a slow period for state introduction actually, it was 15 years between Missouri and Arkansas. Then another bigger push until the 1910s, a semi hard stop and seemingly an actual hard stop after Alaska and Hawaii. This is all knowable… if you know something about the data. If you don’t, it’s certainly not a bell distribution, and the states that wind up being in the middle aren’t particularly indicative.

Or you’ve got infinite sets like prime numbers where there is no middle, the process just continues forever.

I don’t think something winding up in the middle is necessarily significant.

96

So I think I hear the problem as:

  • Probability is represented as a fraction of 1/N, where N is the number of possible outcomes.
  • The calculation is therefore dividing 1 by N.
  • It’s impossible to divide 1 by infinity (or by zero, just to be thorough).
  • If we don’t know anything at all how many outcomes there are, then there could be infinite outcomes or 0 outcomes.
  • If there could be infinite outcomes, then calculating probability on that outcome set is entirely and utterly impossible, because the denominator is a moving target and it might be infinity or 0.

Have I got your reasoning right, have I missed anything?

97

Still talking about your example of a random number generator constrained to produce a number between 0 and 100., not a sequence of events or an infinite set.

98

So let’s take the numbers from the article. Homo sapiens has been around for 200,000 years. Total number of humans that have ever lived is about 100 billion. Number of humans alive now is substantially greater than much of history.

Ok, calculation 1 says there have been air about 100 billion lives so far, and I must assume as a random person I am in the middle. Ergo, the total number of human lives will reach around 200 billion. Given birth rates, etc., calculation says it will take about 760 years to reach that number. Ergo, we have 760 years left.

Calculation 2 says humans have been in existence for 200,000 years. As a random human, I assume I am in the middle. So therefore, humanity should last another 200,000 years.

Same methodology, vastly different answer. Only difference is what we assume we are the middle of.

Tell me why one assumption makes more sense.

99

Because the first assumption isn’t an assumption. It’s an intermediate conclusion derived from Bayesian probability, which is well-understood and not at all controversial. That theorem is applicable because growth in human population can be represented in several valid ways, and a useful way is as a continuous random sequence. Continuous because it increases one at a time, random because the intervals are basically random, sequence because humans are born one after the other. That’s not because they come out of a baby factory with numbers stamped on their heads, it’s because most things in the universe don’t happen at exactly the same time. Another important factor is that we’re talking about the observer’s place in sequence, which will return to.

Let’s restate that again: those aren’t assumptions. They are logical conclusions that tell us that Bayesian probability is the best tool. Bayesian probability isn’t some weird new woo-woo theory. The basics have been known for centuries, it was used in WW2 to adjust artillery fire, it’s now being used to build AI and it’s now being used for machine learning. The only new thing here is the choice to apply it to humanity, and it fits for the reasons I described above.

So those aren’t assumptions, those are conclusions. To be clear they’re not conclusions of _certainty, they are conclusions of probability. Probability doesn’t stop being true because if it misses reality here and there. Flip a 10-side dice 10 times. You ought to hit 8 one time, but you might not. That doesn’t mean your 10% forecast was wrong, or that you should change it. It’s still the best tool for the job, if you understand what the job is.

When we talk about the principle of mediocrity, that is not a basis for any of the conclusion. It explains the above conclusion. You might ask: “how does it make sense that we’re 50% mark in the sequence of born humans? That sounds very specific. I think you made it up, and I don’t have time to check the math.”

The answer: most people aren’t special, so you aren’t special, and the least special place is exactly in the middle. You’re probably not special enough to be exactly at the midpoint even, but you’re probably around there. That’s why the Bayes theorem makes sense, and that’s how you can understand what’s going on if you haven’t gotten round to looking at the math.

There is a very faulty assumption here: you assumed could take the 50% conclusion the above, which describes the probability of an observer’s place as part of a continuous random sequence, and apply it to years. But years are not a continuous random sequence, and they’re not observers. Humans are. That’s why you can’t take the 50% from above and slap it on there.

Now - you actually could ask the question, if a spaceman visited earth and noticed humans had been around for 200,000 years, nothing about their population, he could ask: if I’m an unspecial spaceman, what’s the chance that these guys will disappear between the next 66,666 to 600,000 years? That answer is 50%. 25% chance that it’s sooner than that, 25% chance that it’s later.

If all you know is how old the thing is, that’s the best you can do. It’s all we have for things like for walls and pyramids if we know nothing else about their durability. But we can do better for humans, since we know a little about them. We know we can safely describe them as a sequence, we know how many there are, we know how fast the sequence is currently going up. That means Bayesian analysis is an appropriate tool here, and the results are already discussed.

One final thing I’ll mention is that, again, that’s a probabilistic forecast of average birthrate. It says there’s a 50% chance the annual birthrate drops to zero 760 years from now. 50% is the best we can do for a specific year. If you want 95% then it’s a range of 66,666 years to 7.4 billion years I think. Not specific enough to be useful (not that 50% at 760 is super useful). If you want 100% then the range is “the future.”

Hope that helps. I’ve enjoyed going over this in detail and I’ve learned a lot fact-checking this article.

100

You can just wait five years and the numbers will be different. Regardless of how many future people will actually be born.

Everyone’s in the middle. The first person ever born was in the middle. The last person ever to be born will be in the middle. Someone in 500 AD when there had been 50 million people in history, the estimate would be that there would be 50 million more. Because everyone is in the middle.

I’m not sure why anyone would use this for an actual forecast. Since the formula is at its absolute worst at the actual beginning and end, when it’s likely most important to be accurate.