Nine candidates are running for president of the country Tierra de Los Mentirosos. The key issue is taxes. One of the nine candidates will lower taxes, and each of the others will either raise taxes or leave taxes unchanged. The candidate who will lower taxes always tells the truth. Any candidate who will raise taxes always lies. Any candidate who will leave taxes unchanged sometimes lies and sometimes tells the truth. The candidates are numbered 1 through 9, and here is a statement made by each:
- Either 3, 5, 7, 9 or I will lower taxes.
- I will leave taxes unchanged.
- Either 5 is telling the truth or 7 is lying.
- 1 is lying.
- Either 2 or 4 is telling the truth.
- 3 is lying.
- 1 is not going to lower taxes.
- I will raise taxes, and 9 will leave taxes unchanged.
- I will raise taxes, and 6 is lying.
You are given confidential information that lets you know whether candidate 8 will leave taxes unchanged. With this information, you are also able to determine which candidate will lower taxes. Which candidate will lower taxes?
People Power
Hans said that the total physical power output level, in watts, for the population of humans on Earth as biological machines, exceeds the total wattage of all of the nuclear power plants on Earth. Ivana did a slightly different calculation and found that the nuclear plants had about the same or higher total wattage. How might Hans and Ivana, respectively, have done their estimates and who is right?
There are about 7.4 billion people on Earth today. Humans get effectively all of their energy from food, and on average the rate of food energy intake is equal to the total rate of expenditure of energy. You can find various estimates of world average daily caloric intake per person, but a reasonable, somewhat high estimate would be around 3,000 calories/day, which is about the intake of China, and about 800 lower than the highest countries like the United States. Food calories are approximately equal to 4,200 joules of energy. So, the total daily gross energy output of humans is about 7.4 billion humans x 3,000 food calories/day x 4,200 joules/food calorie = 9.324 x 1016 joules/day. A watt is a joule/second and there 24 hours/day x 60 minutes/hour x 60 seconds = 86,400 seconds/day. So for humans, we get (9.324 x 1016 joules/day)/(86,400 seconds/day) = 1.08 trillion watts. It could be argued that some of this energy is wasted heat and should not be counted, e.g., humans are about 20 percent to 40 percent efficient at producing mechanical energy. This could lead to an estimate ranging from 216 billion to 432 billion watts. On the other hand, maintaining body temperature is important to life, and it could also make sense to count all of this thermal energy.
There are about 440 commercial nuclear power reactors in the world, accounting for virtually all of the production of nuclear energy. Commercial nuclear reactors typically produce about 1 billion watts each when operating and operate most of the time. One source places total annual nuclear electric energy production at about 2.5 x 1015 watt-hours/year. There are 365 days/year x 24 hours/day = 8,760 hours/year. So, these numbers give (2.5 x 1015 watt-hours/year)/(8,760 hours/year) = 285 billion watts. Note that nuclear reactors only convert about 30 percent of heat energy into electricity. So, the total thermal power is closer to 285 billion electrical watts/ (0.3 electrical watts/thermal watt) = 950 billion thermal watts.
The most likely difference between Hans and Ivana is how much human thermal power is counted as useful or meaningful power: Hans might have estimated 432 billion watts for humans, Ivana might have estimated 216 billion watts, and both might have used the 285 billion watts of nuclear electric power. It would not make much sense, but another possibility is that Ivana might have compared total nuclear thermal power to total human mechanical power. Alternatively, they might have both used total thermal power, but Ivana might have used a somewhat lower average daily caloric intake, like 2,500 food calories/person-day. In any case, the truly remarkable thing is that, however things are accounted for, the total biological power of humans on Earth is roughly equal to the total production of nuclear power on Earth.
