I spent quite a lot of time many years ago doing my own independent checks on astronomy.

I started down this line after an argument with a friend who believed in astrology. It became apparent that they were talking about planets being in different constellations to the ones I'd seen them in. I forget the details of their particular brand of astrology, but they had an algorithm for calculating a sort-of 'logical' position of the planets in the 12 zodiacal signs, and this algorithm did not match observation, even given that the zodiacal signs do not line up neatly with modern constellations. They were scornful that I was unable to tell them where, say, Venus would be in 12 years time, or where it was when I was born.

So challenged, I set to.

The scientific algorithms for doing this are not entirely trivial. I got hold of a copy of Jean Meeus' Astronomical Algorithms, and it took me quite a lot of work to understand them, and then even longer to implement them so I could answer that sort of question. They are hopelessly and messily empirical (which I take as a good sign) - there is a daunting number of coefficients. Eventually I got it working, and could match observation to prediction of planetary positions to my satisfaction - when I looked at them, the planets were where my calculations said they should be, more or less.

It's hard with amateur equipment to measure accurate locations in the sky (e.g. how high and in which direction is a particular star at a particular time), but relative ones are much easier (e.g. how close is Venus to a particular star at a particular time). The gold standard for this sort of stuff is occultations - where you predict that a planet will occult (pass in front of) a star. There weren't any of those happening around the time I was doing it, but I was able to verify the calculations for other occultations that people had observed (and photographed) at the date and times I had calculated.

These days, software to calculate this stuff - and to visualise it, which I never managed - is widely available. There are many smartphone apps that will show you these calculations overlaid on to the sky when you hold your phone up to it. (Although IME their absolute accuracy isn't brilliant, which I think is due to the orientation sensors being not that good.) This makes checking these sorts of predictions very, very easy. Although of course you can't check that there isn't, say, a team of astronomers making observations and regularly adjusting the data that gets to your phone.

I was also able to independently replicate enough of Fred Espenak's NASA eclipse calculations to completely convince me he was right. (After I found several bugs in my own code.) Perhaps the most spectacular verification was replicating the calculations for the solar eclipse of 11 August 1999. I was also able to travel to the path of totality in France, and it turned up slap on time and in place. This was amazing, and I strongly urge anyone reading this to make the effort to travel to the path of totality of any eclipse they can.

Until I'd played around with these calculations, I hadn't appreciated just how spectacularly accurate they have to be. You only need a teeny-tiny error in the locations of the Sun/Moon/Earth system for the shadow cast by the moon on the Earth to be in a very different place.

I also replicated the calculations for the transit of Venus in 2004. I was able to observe it, and it took place exactly as predicted so far as I was able to measure - to within, say, 10 seconds or so. (I didn't replicate the calculations for the transit in 2012 - no time and I'd forgotten about how my ghastly mess of code worked - and I wasn't able to observe it either, since it was cloudy where I was at the time.)

More recently, you can calculate Iridium flares and ISS transits. Again, you have to be extremely accurate in calculations to be able to predict where they will occur, and they turn up as promised (except when it's cloudy). And again, there are plenty of websites and apps that will do the calculations for you. With a pair of high-magnification binoculars you can even see that the ISS isn't round.

All this isn't complete and perfect verification. But it's pretty good Bayesian evidence in the direction that all that stuff about orbits and satellites is true.

Do you think that human beings will allow a single corporation to control a significant fraction of the world's resources? How will the company avoid anti-monopoly laws? Does a an AI CEO actually have control over a corporation, or does it only have the freedom to act within the defined social roles of what a "CEO" is allowed to do? I.e. it can negotiate a merger but can't hire a bunch of scientists and tell them to start mass producing nerve gas.

The U.S. government spends more money in a single year than the combined market capitalization of the 10 largest companies in the world.

In what sense does google "control a very large proportion of the world's computing resources"? Google maybe has the compute power equivalent to a handful of supercomputers, but even that isn't organized in a particularly useful way for an AI looking to do something dramatically different from performing millions of internet searches. For the vast majority of problems, I'd rather use ORNL's Titan than literally every computer google owns.

Do you think that human beings will allow a single corporation to control a significant fraction of the world's resources? How will the company avoid anti-monopoly laws? Does a an AI CEO actually have control over a corporation, or does it only have the freedom to act within the defined social roles of what a "CEO" is allowed to do? I.e. it can negotiate a merger but can't hire a bunch of scientists and tell them to start mass producing nerve gas.

The U.S. government spends more money in a single year than the combined market capitalization of the 10 largest companies in the world.

In what sense does google "control a very large proportion of the world's computing resources"? Google maybe has the compute power equivalent to a handful of supercomputers, but even that isn't organized in a particularly useful way for an AI looking to do something dramatically different from performing millions of internet searches. For the vast majority of problems, I'd rather use ORNL's Titan than literally every computer google owns.

It is odd that you highlight the Bedford Level Experiment, rather than other methods that have been used for thousands of years. The new experiment has the advantage that it can be performed by a single person in a single afternoon. It has the disadvantage that it shows that the Earth is flat.

Eratosthenes measured the north-south curvature of the Earth by making observations separated by hundreds of miles. It could be applied east-west with good clocks, or, as you suggest, with the simultaneity of telephones. Since I'd have to travel hundreds of miles anyway to reach the straight canal in Bedford, it has little advantage over Eratosthenes's method. I suppose you could make a similar observation by climbing a mast on a ship the right distance from shore, but the ocean waves add noise not present on the canal. It does have the advantage of requiring less geometry. Since the Bedford experiment used 1/100 the distance, it required 100x the accuracy of angular measurement. This is easy to overlook, since the measurement is not phrased that way, but I think this is why it encounters new sources of error.

Older experiments are generally easier. While everything is easier to measure today, the main advance is in measuring time.

I spent quite a lot of time many years ago doing my own independent checks on astronomy.

I started down this line after an argument with a friend who believed in astrology. It became apparent that they were talking about planets being in different constellations to the ones I'd seen them in. I forget the details of their particular brand of astrology, but they had an algorithm for calculating a sort-of 'logical' position of the planets in the 12 zodiacal signs, and this algorithm did not match observation, even given that the zodiacal signs do not line up neatly with modern constellations. They were scornful that I was unable to tell them where, say, Venus would be in 12 years time, or where it was when I was born.

So challenged, I set to.

The scientific algorithms for doing this are not entirely trivial. I got hold of a copy of Jean Meeus' Astronomical Algorithms, and it took me quite a lot of work to understand them, and then even longer to implement them so I could answer that sort of question. They are hopelessly and messily empirical (which I take as a good sign) - there is a daunting number of coefficients. Eventually I got it working, and could match observation to prediction of planetary positions to my satisfaction - when I looked at them, the planets were where my calculations said they should be, more or less.

It's hard with amateur equipment to measure accurate locations in the sky (e.g. how high and in which direction is a particular star at a particular time), but relative ones are much easier (e.g. how close is Venus to a particular star at a particular time). The gold standard for this sort of stuff is occultations - where you predict that a planet will occult (pass in front of) a star. There weren't any of those happening around the time I was doing it, but I was able to verify the calculations for other occultations that people had observed (and photographed) at the date and times I had calculated.

These days, software to calculate this stuff - and to visualise it, which I never managed - is widely available. There are many smartphone apps that will show you these calculations overlaid on to the sky when you hold your phone up to it. (Although IME their absolute accuracy isn't brilliant, which I think is due to the orientation sensors being not that good.) This makes checking these sorts of predictions very, very easy. Although of course you can't check that there isn't, say, a team of astronomers making observations and regularly adjusting the data that gets to your phone.

I was also able to independently replicate enough of Fred Espenak's NASA eclipse calculations to completely convince me he was right. (After I found several bugs in my own code.) Perhaps the most spectacular verification was replicating the calculations for the solar eclipse of 11 August 1999. I was also able to travel to the path of totality in France, and it turned up slap on time and in place. This was amazing, and I strongly urge anyone reading this to make the effort to travel to the path of totality of any eclipse they can.

Until I'd played around with these calculations, I hadn't appreciated just how spectacularly accurate they have to be. You only need a teeny-tiny error in the locations of the Sun/Moon/Earth system for the shadow cast by the moon on the Earth to be in a very different place.

I also replicated the calculations for the transit of Venus in 2004. I was able to observe it, and it took place exactly as predicted so far as I was able to measure - to within, say, 10 seconds or so. (I didn't replicate the calculations for the transit in 2012 - no time and I'd forgotten about how my ghastly mess of code worked - and I wasn't able to observe it either, since it was cloudy where I was at the time.)

More recently, you can calculate Iridium flares and ISS transits. Again, you have to be extremely accurate in calculations to be able to predict where they will occur, and they turn up as promised (except when it's cloudy). And again, there are plenty of websites and apps that will do the calculations for you. With a pair of high-magnification binoculars you can even see that the ISS isn't round.

All this isn't complete and perfect verification. But it's pretty good Bayesian evidence in the direction that all that stuff about orbits and satellites is true.

Is there an easily visible consequence of special relativity that you can see without specialized equipment?

A working GPS receiver.

I only believe that depends on special relativity because I was told so; if I'm so skeptical I suspect that scientist lied to me about special relativity, then I should be equally suspectful of engineers telling me GPSes have to take special relativity into account to work right.

This is a very interesting game. At a meta-level though, my belief in a lot of science is grounded in its usefulness. If people who believe in Newtonian physics can make me float in the air in a gigantic metal tube hurtling at 500 miles/hr while I sip my Coke, I suspect their belief is well-justified.

Yes, and many a medieval could have reasoned thusly:

If these people can contruct such a magnificent thing as Amiens Cathedral, I suspect their beliefs are well-justified.

Could the NSA, the security agency of the most powerful country on Earth, implement any of these schemes?

Er, yes, very easily.

Do you believe that if Obama were to ask the NSA to take over Russia, that the NSA could easily do so? If so, I am speechless.

Let's look at one of the most realistic schemes, creating a bioweapon. Yes, an organization like the NSA could probably design such a bioweapon. But how exactly could they take over the world that way?

They could either use the bioweapon to kill a huge number of people, or use it to blackmail the world into submission. I believe that the former would cause our technological civilization, on which the NSA depends, to collapse. So that would be stupid. The latter would maybe work for some time, until the rest of the world got together, in order to make a believable threat of mutual destruction.

I just don't see this to be a viable way to take over the world. At least not in such a way that you would gain actual control.

Now I can of course imagine a different world, in which it would be possible to gain control. Such as a world in which everyone important was using advanced brain implants. If these brain implants could be hacked, even the NSA could take over the world. That's a no-brainer.

I can also imagine a long-term plan. But those are very risky. The longer it takes, the higher the chance that your plan is revealed. Also, other AI's, with different, opposing utility-functions, will be employed. Some will be used to detect such plans.

Anyway, the assumption that an AI could understand human motivation, and become a skilled manipulator, is already too far-fetched for me to take seriously. People around here too often confound theory with practice. That all this might be physically possible does not prove that it is at all likely.

For a fully-capable sophisticated AGI, the question is surely trivial and admits of many, many possible answers.

Could the NSA, the security agency of the most powerful country on Earth, implement any of these schemes?

The NSA not only has thousands of very smart drones (people), all of which are already equipped with manipulative abilities, but it also has huge computational resources and knows about backdoors to subvert a lot of systems. Does this enable the NSA to implement your plan without destroying or decisively crippling itself?

If not, then the following features are very likely insufficient in order to implement your plan: (1) being in control of thousands of human-level drones, straw men, and undercover agents in important positions (2) having the law on your side (3) access to massive computational resources (4) knowledge of heaps of loopholes to bypass security.

If your plan cannot be implemented by an entity like the NSA, which already features most of the prerequisites that your hypothetical artificial general intelligence first needs to acquire by some magical means, then what is it that makes your plan so foolproof when executed by an AI?

Another class of routes is for the AI to obtain the resources entirely legitimately, through e.g. running a very successful business where extra intelligence adds significant value. For instance, it's fun to imagine that Larry Page and Sergey Brin's first success was not a better search algorithm, but building and/or stumbling on an AI that invented it (and a successful business model) for them; Google now controls a very large proportion of the world's computing resources. Similarly, if a bit more prosaically, Walmart in the US and Tesco in the UK have grown extremely large, successful businesses based on the smart use of computing resources. For a more directly terrifying scenario, imagine it happening at, say, Lockheed Martin, BAE Systems or Raytheon.

These are not quick, instant takeovers, but I think it is a mistake to imagine that it must happen instantly. An AI that thinks it will be destroyed (or permanently thwarted) if it is discovered would take care to avoid discovery. Scenarios where it can be careful to minimise the risk of discovery until its position is unassailable will look much more appealing than high-risk short-term scenarios with high variance in outcomes. Indeed, it might sensibly seek to build its position in the minds of people-in-general as an invaluable resource for humanity well before its full nature is revealed.