Hi BAUT first post! This isn't meant to be a claim about anything, rather a little thought experiment.

If you imagine a graph of the “Total Population of Humanity Over Time” (something like this) since it's inception until its eventual demise, the graph would look largely exponential at first with perhaps a plateau at some point and a decline sometime eventually in the future. Now split the graph into two: the first part measuring from time=0 where there was "1 human" up until now, and the second part measuring from now until the end of humanity, whenever that may be. If you take the area under the first half of this graph, which represents the total sum of all humans that have existed up to this point, and compare it to the area under the second half of this graph, which represents the total sum of all humans that will exist until the end of our species at some point in our future, what is the likelihood (probability) that we are currently living in the early growth phase, the plateau phase, or humanity's end phase? In other words, what is the probability that the line separating the past and the future totals of the human population is near the beginning, middle, or end of this graph?

To answer this question we must ask ourselves:
Where on this graph is the line at its most statistically probable point then?
And the answer:
A line at or near the middle of this curve.

The simple fact that we are alive right now is either…

1) Becoming more and more improbable as the length of time of humanity’s existence and therefore total population increases into the future. A statistical improbability.

2) With our current time falling right in or near the middle of humanity’s existence which assumes an equal number of humans living before and after us. A statistical probability.

If our existence is improbable our population hasn’t reached its plateau yet, and will still have more to grow. However, if we assume our very existence is more probable than less probable, then more than likely our population will hit a peak soon and fall drastically in a very short period of time.

In case it's useful..

The Origin of Life: Descent of Electrons

I've heard of this type of reasoning before, but I'm not overly impressed by it simply because you can prove just about anything with statistics.

Let me relate an old joke. A mathematician goes hunting with a friend. He sees a quail and shoots, but misses to the left. He shoots again and misses to the right. Then he puts away his gun. His friend asks why he's putting his gun away when he had missed his target. The mathematician replies, on average, the bird is dead.

The fact is, we don't know what the curve of human existence will be like. In fact, I seriously doubt it will be a normal bell distribution as we're likely to meet a precipitous demise. Or just as likely, if we colonize space/other planets/moons, the curve might take on an exponential quality. And if we spread ourselves far and wide enough, we will likely evolve into different species over time (or may change ourselves directly), so the whole question of our existence becomes moot.

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Conscious reasoning is an attempt to justify the choice after it has been made.

See: The Carter Catastrophe - A Statistical Doomsday Argument

I'd say more but my browser is crashing faster than I can type.

Search BAUT forum for "Carter Catastophe" for a bit more.

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Welcome, Blyxa.

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Yes, as DrWho says, you've laid a wide swath. I think you may need to state the assumptions of your model, Blyxa, and not claim that it reflects reality without more evidence. You make assumptions without stating them or where they come from. Respeciation is a possibility; in that case, would humanity die out if homo sapiens did? Also, if humans stuck around in the galaxy for another billion years, would your question even be relevant to us in the present? And, if so, would the human experience in the future be similar to that now? It all seems very nebulous.

If you wish to show a correlation of reality with your model, you may want to talk at least a little about land usage, the availability of clean food and water, industry and pollution, the unlikelihood of extraterrestrial settlement. Chances are, these are topics too big for this thread, so you may want to find evidence out there that can be quickly referenced.

BTW, welcome to BAUT!

Yes, this argument came first from the Australian physicist Brandon Carter, in the 1980s, so has ended up being referred to as the Carter Catastrophe. 01101001 has already linked, above, to a thread in which it was discussed at length.

Grant Hutchison