Yeah. As explained in my comments policy, although I’ve had a recent hardship keeping up lately due to travel.

But it has indeed been extremely effective at destroying trolls. Ratio of serious commentary to trolling is better than almost 20 to 1 now. Most of them no longer even bother. Because they know they will have wasted their time and no one will ever get to see anything they write. While if they get approved, they get pwned immediately (a fact one even once complained about: by always posting his comment immediately with my reply, he accused me of violating his free speech, which was the funniest thing a troll ever said to me).

Richard has always had the policy that every post goes into moderation and only comes out when he has personally cleared it. This means that if he’s traveling or whatever, he may not be able to clear your posts as quickly as you might like. It doesn’t mean that your post has been deleted. This is all explained in the Comments Policy, at the top of every page.

This policy is somewhat inhibiting of discussion, but on the other hand, it puts a stop to a lot of nonsense. It’s a trade-off.

When you say something that contradicts established science, your first hypothesis should be that you’ve gotten something wrong, and then endeavor to find out what that is. I can’t help you if you drop that procedure, and I’m left to do it for you.

And I don’t think you can blame me for being confused by the apparent reasoning of your August 25th reply (14.4 million women must replace the population of 60 million people and therefore must have 4.2 babies per woman), since 60 million was not only your hypothesized population number but also just happened to be, approximately, the entire population death rate over the 30-year child-bearing range for women–which is the much more relevant number that you neglected to mention / explain.

I’m not sure I understand the last paragraph in your recent reply. “…due to rounding up the digits in the rates table…” Which digits in which column? Why would the digits be consistently rounded up? Was there an explanation of this in the source? I would think rounding errors would average out unless there is some other bias in the way the values were collected / reported.

Either way, it’s not that big of a deal. Now that I understand the meaning of column 4, I agree with you–Marshall’s estimates in his Amazon review comments are way off. Your source predicts ~5 babies per woman–an entirely reasonable number. Thanks for taking the time to reply to my posts so that I could make sense of the table.

Look, I am basing my statements on actual demographic science, by actual demographic scientists. You seem to be denying science from the armchair, because you don’t understand their math. The table (last column) is not per-year, but per year-group. You’d notice this if you tried working out how the average life expectancy (column 2) is generated by the mortality rate (column 4) for the starting age (column 1). You also aren’t even remotely doing the right math.

Let’s start with an analogy.

America has a population of about 300 million. Approx. 113 million are between 18 and 44. So about 62 million women who can bear children, over a span of 26 years. The number of people in America who die each year is about 2.5 million. Therefore we need 2.5 million births per year. In a 26 year period that’s 65 million babies. Or approx. 1 baby per woman of childbearing age.

Let’s go backwards. The ancient Roman Empire had a population of about 60 million. For approx. 14.4 million women who can bear children, over a span of 30 years. I estimated the average replacement rate is 4.2 births per such woman. That works out to 60.48 million births per 30 years or about 2 million births per year. In a 30 year period that’s 65 million babies. More than the 60 million population to be replaced. That means the death numbers are about the same (2 million die per year), which means the death rate in ancient Rome was four times higher than in modern America (2.5/300 vs. 2/60 = 1/120 vs. 1/30).

So if you want to test this with the table, use the correct math:

For any five year period (because the death rates in column four are per year-group and the table is mostly in five-year groups):

Year 0-1 => 60 million x .04 = 2.4 million => 2.4 x .36 = 864,000 deaths => sum: 864,000 deaths
x 5 = 4.32 million deaths for five years

Group 1-5 => 60 x .1 = 6 => 6 x .24 = 1.44 million deaths => sum: 5.76 million deaths
Group 5-10 => 60 x .11 = 6.6 => 6.6 x .06 = 396,000 deaths => sum: 6.156
Group 10-15 => 60 x .11 = 6.6 => 6.6 x .05 = 330,000 deaths => sum: 6.486
Group 15-20 => 60 x .1 = 6 => 6 x .07 = 420,000 deaths => sum: 6.906
Group 20-25 => 60 x .09 = 5.4 => 5.4 x .08 = 432,000 deaths => sum: 7.338
Group 25-30 => 60 x .08 = 4.8 => 4.8 x .09 = 432,000 deaths => sum: 7.77
Group 30-35 => 60 x .08 = 4.8 => 4.8 x .11 = 528,000 deaths => sum: 8.298
Group 35-40 => 60 x .07 = 4.2 => 4.2 x .12 = 504,000 deaths => sum: 8.802
Group 40-45 => 60 x .06 = 3.6 => 3.6 x .14 = 504,000 deaths => sum: 9.306
Group 45-50 => 60 x .05 = 3 => 3 x .17 = 510,000 deaths => sum: 9.816
Group 50-55 => 60 x .04 = 2.4 => 2.4 x .21 = 504,000 deaths => sum: 10.32
Group 55-60 => 60 x .03 = 1.8 => 1.8 x .25 = 450,000 deaths => sum: 10.77
Group 60-65 => 60 x .02 = 1.2 => 1.2 x .33 = 396,000 deaths => sum: 11.166
Group 65-70 => 60 x .01 = 0.6 => 0.6 x .41 = 246,000 deaths => sum: 11.412
Group 70-75 => 60 x .008 = 0.48 => 0.48 x .53 = 254,400 deaths => sum: 11.6664
Group 75-80 => 60 x .003 = 0.18 => 0.18 x .68 = 122,400 deaths => sum: 11.7888

(the numbers after that become insignificant and dwindling additions)

So we have approx. 12 million deaths per five years.

That’s approx. 12 / 5 = 2.4 million deaths per year.

Just about what I said.

So back to the first analogy:

The A.R.E. had a population of about 60 million. Approx. 14.4 million are between 15 and 45. So about 14.4 million women who can bear children, over a span of 30 years. The number of people in the A.R.E. who die each year is about 2.4 million. Therefore we need 2.4 million births per year. In a 30 year period that’s 72 million babies. Or approx. 5 babies per woman of childbearing age. Again, roughly comparable to many comparable third world countries.

And 2.4 deaths per year is an overcount, because the total per-five-year death count of 12 million is actually an over-count by about 2 million, due to rounding up the digits in the rates on the table. That’s why the better method is to use the one I started with. Which notably gets pretty much the same result.

Unless I’m badly misinterpreting Frier’s table, which I don’t think I am, I stand by my math: by multiplying together the values in the right two columns of Frier’s table and then summing all those terms (e.g. 4%*36% + 10%*24% + 11%*6% + … 0.3%*68% + 0.1%*99.5% = 14%), I get the fraction of the total population that die each year and therefore the fraction that needs to be replaced to maintain a stable population. Clearly a 14% annual death rate is much higher than my idyllic 1% annual rate hypothesized above (not inconceivable, though, for ancient times), and that 14% must be replaced by, as you state, 24% of the population (fraction of population who are child-bearing-aged women). For a woman living through those entire 30 years, she must, on average, produce (14/24)*30 babies = ~17 babies. The only questionable number for me is the 14%–whether I am calculating that correctly. If you get a different number, state what you think it is and why, but then you need only plug it into the calculation: (x/24)*30 to get the expected number of babies per woman (who lives through the entire child-bearing age range).

I think you’ve done the math wrong. You need to use the middle column (the latter column is per year-group, not per year, for example). I also don’t know where you get your odds of a birth per year from that table. It says nothing about that.

Here is a proper approach: suppose there are 30 million women and 30 million men, for 60 million people. The middle column of Frier’s Life Table tells you 48% of that population (and thus 48% of the women) are of childbearing age (between 15 and 45). So we have 14.4 million women who have to replace 60 million people. That’s an average birth rate of 4.2 children per woman. That’s not unusual in third world nations most similar to ancient conditions.

(This means an average of 2.2 per mother, or more than half, of all children born do not have to survive to childbearing age for population stability. Which is as the table indicates. As the third column shows–when read correctly–43% of those born are dead before childbearing age, i.e. 15. That’s why life expectancy at birth is 21, but shoots up to 48 for anyone who survives childhood.)

Marshall is a bit of a loon. He constantly argues against established science with feigned incredulity. He used to deny that the law of large numbers entails the infinite monkey theorem. Even though that’s a well established fact. Now he is claiming to know better than actuarial tables for actual existing countries today (many third world nations show the same averages as ancient Roman grave studies), developed by actual professional demographers. I cite my sources. For him to pretend to know better than actual scientists using actual real data is just laughable. Why does anyone take him seriously anymore?