My statement is not based on observational evidence alone. Several countries have done the experiment. See the various things Bangladesh has done, for example. There's even a great TED talk on it.

Educating women is by far the most effective means of reducing population growth, and various agencies from national governments to the UN have discovered that it's extremely difficult to do that until people have enough to eat. Otherwise the kids go to work growing food instead of going to school. That's also a contributing factor to poor families having lots of kids - cheap labour to help out growing food or running the business. "Who's going to take care of me when I'm old" seems to be less than a primary concern when you don't have enough to eat.

Since the OP is referring to a population problem.

There aren't. From outside the event horizon, a singularity of a particular mass is indistinguishable from an object with that matter distributed evenly throughout the volume within the event horizon, or a shell of matter right at the event horizon. Never mind from ten thousand light years away.

The other part, about stars never being able to form an object with an event horizon, is, at least in principle, observationally testable. But I don't think we've examined any stellar black hole candidates closely enough.

The slowest population growth (it's negative) is in the first world, among populations that have plenty of food. Your assertion simply isn't supported by reality.

An abundance of food creates leisure time, which allows people, especially women, to do things like go to school. Educated people, especially women, have fewer babies. As has been shown over and over and over, the solution to population growth problems is secure basic needs followed by education. The only problem is that it works too well.

Fucking makes problems better. Fucking without contraceptives makes things worse.

Don't worry, that will change in a hurry when the boomers start going into nursing homes. There are lots of bedpans that are going to need emptying.

From the summary:

"Emanuel says that Americans seem to be obsessed with exercising, doing mental puzzles, consuming various juice and protein concoctions, sticking to strict diets, and popping vitamins and supplements, all in a valiant effort to cheat death and prolong life as long as possible."

Omitting the fad stuff, exercise and eating well improve the length of time you will remain healthy. The quote makes it sound like taking care of yourself will just let you hang on by your fingernails for a little bit longer. The opposite is actually true. Exercise, diet and mental engagement in particular improve health and mental function in old age, not necessarily overall longevity.

If you want to be a healthy octogenarian, take care of yourself now. If you want to be frail and going in for your third bypass operation, don't.

There's actually some decent research on that point. A surprising number of people die very close to the age they expect to, more than can be explained by genetics. The placebo effect is a powerful thing.

I'm convinced I'm immortal, so things might be interesting in forty or fifty years.

Enjoy your life, don't wait for your retirement. I don't see an especially good chance of ever being able to retire. Plus there are a lot of things I want to do while I can comfortably walk for eight hours a day, see, hear and smell well, and take a hit or two.

Because exercising, eating well and being mentally engaged don't help keep you healthy to an older age.

They had observational data from 381 people. The seven are a preliminary study to find the causal direction of the correlation observed in the bigger group. Seven isn't a lot, but it's decent for a preliminary look supporting something seen in a larger group.

Except that it's quite difficult to measure either side of that equation.

Both.

To study the effect of NAS in humans, we examined the relationship between long-term NAS consumption (based on a validated food frequency questionnaire, see Methods) and various clinical parameters in data collected from 381 non-diabetic individuals (44% males and 56% females; age 43.3 ± 13.2) in an ongoing clinical nutritional study. We found significant positive correlations between NAS consumption and several metabolic-syndrome-related clinical parameters

Finally, as an initial assessment of whether the relationship between human NAS consumption and blood glucose control is causative, we followed seven healthy volunteers (5 males and 2 females, aged 28–36) who do not normally consume NAS or NAS-containing foods for 1 week. During this week, participants consumed on days 2–7 the FDA’s maximal acceptable daily intake (ADI) of commercial saccharin

An observational study that people who consume artificial sweeteners tend to be heavier, have lower waist to hip ratios, higher blood glucose, etc. doesn't tell you whether eating artificial sweeteners does that or vice versa. An experiment where you take people and put them on artificial sweeteners does. So they took their observational correlation and did a (preliminary) experiment to find out what direction the causation is.

Sand.

Saccharin, sucralose, aspartame, sucrose and glucose were the primary groups tested. Decreases in glucose tolerance were observed between the artificial sweetener groups and the sugar groups.

As a secondary experiment, they used the saccharin group to investigate the mechanisms because it showed the strongest effect. It's possible that saccharin works by a different mechanism than the others, and I suspect they'll investigate that possibility in the future, but the primary finding applies to all the sweeteners tested.