Comments on The Odds Are One: Odds Holding Steady At One

OK, here goes my stab at the Doomsday Argument.
2006-04-16T10:29:00.000-07:00
OK, here goes my stab at the Doomsday Argument.

There are only two possible hypotheses:

ED: Early doom: doom happens after 100 million humans
LD: Late doom: doom happens after 800 million humans

Finding myself as human number 60 million, according to the Doomsday Argumen I should believe ED is true. Actually, what the argument says is that I should follow the following rule:

R-ED: IF my birth rank <= 100 million THEN I believe ED

Let's see the performance of this rule. If ED is true. 100 million people will be able to use this rule (because their birth rank is <= 100 million). And all of them will be correct (because the rule predicts ED, which is true). That is, assuming ED true, the rule has a 100% accuracy (everytime it is applied, it is correct).

If ED is false (LD is true), the first 100 million people will also apply the rule (because the left hand side is true), but all of them will be wrong because now LD is true and the rule predicts ED. That is, assuming LD is true, the rule has 0% accuracy. Everybody who can apply this rule will be wrong (under LD).

Summarizing, the performance of rule R-ED is:

100%, if ED is true
0% , if LD is true

Let's now see what happens with the opposite rule:

R-LD: IF my birth rank <= 100 million THEN I believe LD

Using R-LD, if ED is true, the first 100 million persons will be wrong (0%). But if LD is true, the first 100 million will be right (100% accuracy).

Thus, the performance of rule R-LD will be:

0%, if ED is true
100%, if LD is true

These results are equivalent to R-ED, and it shows that, if my birth rank is <= 100 million, it does not really matter whether a person believes ED or LD, contrary to the Doomsday Argument. It all depends on whether ED is more likely a-priori than LD. Which is as it should be.

The odds are one of me being me :)

Cheers,

Ricardo Aler
16 April 2006
http://www.uc3m.es/uc3m/dpto/INF/aler

I guess everytime the argument is wrong, it should...

2006-04-16T09:22:00.000-07:00

I guess everytime the argument is wrong, it should count as evidence against itself :)

It's true that any one human in history could have...

2006-01-20T13:29:00.000-08:00

It's true that any one human in history could have made the argument, as could any human who will ever live. Of course, only 5% of all humans who will ever live would be wrong about their 95% confidence interval. All we can do is hope that we are 'special' in some way that makes us, coincidentally, fall in the first 5% of all humans. For example, one could argue that being in the reference classes 'humans before space exploration' or 'humans before counter-measures for doomsday were implemented' confers us with 'early adopter' characteristics. On the other hand, the reference classes 'WMD-era humans' and 'global-warming-era humans' suggest we have 'late adopter' characteristics. In the end we can probably say that there are unknown quantities which add uncertainty to the doomsday argument. Incidentally, from the doomsday argument and the antrophic principle we can also infer that there might not be additional technological civilizations in this planet after ours.

Yeah, I think that's right. If humanity ended tomo...

2005-11-16T21:43:00.000-08:00

Yeah, I think that's right. If humanity ended tomorrow due to nuclear holocaust or we were all Oryx-and-Crake'd, I think we'd agree that the Doomsday Argument didn't predict it (well, we wouldn't agree on much, because we'd all be gone). Nor, if humanity goes on to exist for another billion years after this argument has been made, would it actually prove that it was wrong. Which goes a long way towards illustrating that this argument doesn't prove at all what it seems to on the surface.

I stumbled across this blog while clicking the lit...

2005-11-16T19:54:00.000-08:00

I stumbled across this blog while clicking the little randomizer up top (something I do when I want to remind myself how many languages I don’t speak). I was instantly intrigued by the idea of the Doomsday problem. When I read the bit about the Damned Lies of Language (which I prefer to call the Damned Lies of Perception), I was reminded of seeing the Monty Hall problem for the first time. I still can’t shake the feeling that the problem is a trick…the probability of your first choice being correct also goes up. That the math supports switching you choice seems like a problem of our conception of the situation. As soon as you are asked if you would like to change your guess, you are actually faced with a new, 50/50 choice: door number 1 or door number 2? Whether you stick with the original choice (by which I mean CHOOSE to stick with your original choice) or switch, your chances of winning are fifty percent. That keeping your original guess is not a new choice is merely an illusion. I’m probably wrong, I don’t really know much about this stuff.

Anyway, the Doomsday problem seems to make a similar presumption that messes with our conceptions (besides the presumption that the human population WILL end, or that it continues its path of exponential growth, etc.). The objection seems inherent in the “Yeah, but the Doomsday Argument has been true for everyone who has ever lived or is currently alive…” Again, presuming the constant geometric growth of humanity, the Doomsday model never predicts any change in the imminence of Doomsday, so it isn’t useful. Our observations neither tend to prove or disprove the argument, right?