Would you like to play a game?

Would you like to play a game?

This game only has one rule. It’s based on the premise that you had two parents, and you agree that–so far as we know–every human being who has ever lived had two parents.  Agreed?  If you think I’m trying to trick you, take a minute to think about it, and make sure that you agree before we continue.

OK, so you agree that you had two parents. So, you will also agree that your two parents each had two parents, these are your four grandparents. So, you have 6 very recent ancestors. Now, you will also agree that each of your 4 grandparents each had 2 parents, so that’s 8 great-grandparents for a total of 14 recent ancestors.  Of course, each of your great-grandparents had two parents which gives you 16 great-great-grandparents, and a total of 30 recent ancestors.

Allowing for about 25 years per generation,   going back 4 generations, those 30 ancestors lived about 100 years ago. 

1
2
4
8
16

If you have been avoiding recreational drugs, you can probably see where this is going. It is similar to the “Chess Problem” thought experiment believed to have originated in ancient India, and since restated many times throughout history by various mathematicians and philosophers. If you are unfamiliar with this old chestnut, it goes like this:

If you were to place one grain of rice on the first square of a chessboard and then double the number of grains of rice on each subsequent square, you would end up with a very large number of grains of rice by the time you reached the 64th square. In fact, the final number of grains of rice would be:

 

18,446,744,073,709,551,615

 

That’s over 18 quintillion grains of rice! To put this number into perspective, it’s estimated that the total amount of rice produced globally in 2021 was around 500 million metric tons, which is equivalent to around 5 trillion grains of rice. So, the number of grains of rice you would end up with on the 64th square of the chessboard is truly mind-boggling.

Similarly, you are probably familiar with Zeno of Elea, a Greek philosopher who lived in the 5th century BC. He is famous for his paradoxes, which are thought experiments that challenge our common sense understanding of the world. One of Zeno’s famous paradoxes involves an archer shooting an arrow at a target. According to Zeno, the arrow can never actually reach the target!

A Demon Haunted World by Carl Sagan
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Zeno’s argument is based on the idea that motion is an illusion. He argues that in any given moment, the arrow is only occupying one place in space, and is therefore at rest. It is only through a sequence of such moments that motion appears to occur.

 

So, when the archer shoots the arrow, it is first at rest. When it moves, it must move from the place it is currently occupying to another place. But in order to do so, it must first travel half the distance between these two places. It must then travel half the remaining distance, and then half the distance again, and so on, infinitely many times. Since there are infinitely many such distances to travel, the arrow can never actually reach the target.

 

 

You figure it out.  Zeno has blown people’s minds for millennia.

Back to our ancestors.  So far we have:

# of People	Who?
1	You		Years ago	Cumulative Total
2	Your parents		25	2
4	Your grand parents		50	6
8	Your great-grandparents		75	14
16	Your great-great-grandparents		100	30
32	Your great-ancestors		125	62
64	Your great-ancestors		150	126
126	Your great-ancestors		175	254
252	Your great-ancestors		200	506

 200 years ago, a date very recent in history, less than 10 generations upstream, 506 people were responsible for you being here today. If only one of them had broken the chain, no you!  Poof!

Assuming our average generation length of 25 years, then we can estimate the number of generations between the year 1 BC and the present year of 2023 as follows:

 

2023 to 1 BC = 2024 years

2,024 years / 25 years per generation = 80.96 generations

So, if we assume an average generation length of 25 years, then the year 1 BC would be approximately 81 generations ago, rather few in number, relatively speaking.

Continuing this simple pattern of doubling every generation, taking it back to the year 1 BC, we can estimate that in that year, you have approximately 2^41 (2 to the 41^st power) personal ancestors, approximately 2.2 trillion human beings.  For those not on drugs, there are two obvious problems. 

1. According to United Nations estimates, the world population reached a population of around 300 million in the year 1 BC. Note that these numbers can vary a lot, but not enough to affect our point, and incest couldn’t possibly account for the extrapolations here. There would have to have been so much incest going on, we would all have webbed feet today!

2. Although it is a very broad “guesstimate,” the total, cumulative number of human being who have ever lived on the planet could be no more that 108 billion. Whatever the actual number, there is no way it syncs with the number of 2.2 trillion ancestors responsible for you sitting there reading this article. And remember, we have only gone back as far as the year 1 BC. There were thousands of years of human history and human breeding prior to that.

So, what is the explanation?  Sorry, I don’t have one. You will have to come up with your own theory, but you will have a lot of company and competition from brilliant mathematicians and philosophers throughout history. It is probably OK to just play around with the thought experiment and allow yourself to be mystified and enjoy the ride.

So, what’s my point?  Do I even have one? 

Yes, indeed, and I am going to put this as delicately as I possibly can. Resist the effort of people to blow smoke up your ass in order to manipulate, “gaslight” and brainwash you, especially if they are trying to get you to give them money.  Try to identify and resist your own very human tendency to be native, gullible, credulous and superstitious. In other words, resist your own tendency to blow smoke up your own ass, and then doing it to your friends until it goes viral. Be wary of the power that mathematical sleight of hand has to mesmerize and manipulate without yielding anything true and useful.

I’ll just close by sharing my speculation that people like Elon Musk and others who are peddling the idea that our world is actually just a simulation are using a similar mathematical sleight of hand to prove a hunch or an intuition. It is a hunch that may or may not be true, but at this stage in our evolution, we have no way of knowing.  Maybe the proponents innocently believe it or maybe they are just blowing smoke up their own ass and passing it along to us.  We love you Elon, you are a hero, a national treasure, but we are not in a simulation.  Get over it and get us to Mars!

Fondly,

Khon Kaen, Thailand
11 May 2023

Originally posted 2023-05-11 21:45:44.