## 5. Doomsday Argument

The Doomsday argument ( DA ) is a probabilistic argument that claims to predict the number of future members of the human species given only an estimate of the total number of humans born so far. Simply put, it says that supposing the humans alive today are in a random place in the whole human history timeline, chances are we are about halfway through it. Denoting by *N* the total number of humans who were ever or will ever be born, the Copernican principle suggests that humans are equally likely (along with the other *N* − 1 humans) to find themselves at any position *n*, so humans assume that our fractional position *f* = *n*/*N* is uniformly distributed on the interval (0, 1] prior to learning our absolute position. If we take that 60 billion humans have been born so far (Leslie’s figure), then we can estimate that there is a 95% chance that the total number of humans *N* will be less than 20 × 60 billion = 1.2 trillion. Assuming that the world population stabilizes at 10 billion and a life expectancy of 80 years, it can be estimated that the remaining 1140 billion humans will be born in 9120 years. Depending on the projection of world population in the forthcoming centuries, estimates may vary, but the main point of the argument is that it is unlikely that more than 1.2 trillion humans will ever live.

## 4. Brain in a Vat

There has been no more influential thought experiment than the so-called “ brain in a vat ” hypothesis, which has permeated everything from cognitive science and philosophy to popular culture. The experiment asks you to imagine a mad scientist has taken your brain from your body and placed it in a vat of some kind of life sustaining fluid. Electrodes have been connected to your brain, and these are connected to a computer that generates images and sensations. Since all your information about the world is filtered through the brain, this computer would have the ability to simulate your everyday experience. If this were indeed possible, how could you ever truly prove that the world around you was real, and not just a simulation generated by a computer? If you’re thinking this all sounds a bit like *The Matrix*, you’re right. That film, along with several other sci-fi stories and movies, was heavily influenced by the brain in a vat thought experiment. At its heart, the exercise asks you to question the nature of experience, and to consider what it really means to be human.

## 3. Balls and Vase Problem

The Ross–Littlewood paradox (also known as the balls and vase problem or the ping pong ball problem ) is a hypothetical problem in abstract mathematics and logic designed to illustrate the seemingly paradoxical, or at least non-intuitive, nature of infinity. More specifically, the Ross–Littlewood paradox tries to illustrate the conceptual difficulties with the notion of a supertask, in which one is trying to complete an infinite number of tasks sequentially. The problem starts with an empty vase and an infinite supply of balls. One then performs an infinite number of steps, where at each step balls are added as well as removed from the vase. The question is then posed: *How many balls are in the vase when one is done?*

To complete an infinite number of steps, let us assume that the vase is empty at two minutes before noon, and that one performs the steps as follows:

- The first step is performed at one minute before noon.
- The second step is performed at 30 seconds before noon.
- The third step is performed at 15 seconds before noon.
- Each subsequent step
*n*is performed at 2^{1−n}minutes before noon.

This guarantees that a countably infinite number of steps is performed by noon. At each step, 10 balls are added to the vase, and one ball is removed from the vase. The question now is: *How many balls are in the vase at noon? *Answers to the puzzle fall into 4l categories. 1) The most intuitive answer seems to be that the vase contains an infinite number of balls by noon. 2) However, suppose that the balls of the infinite supply of balls were numbered, and that at step 1 one inserts balls 1 through 10 into the vase, and removes ball number 1. At step 2, one inserts balls 11 through 20, and removes ball 2. This means that by noon, every ball *n* that is inserted into the vase is eventually removed in a subsequent step (namely, step *n*). Hence, the vase is empty at noon. 3) Although the state of the balls and the vase is well-defined at every moment in time *prior* to noon, no conclusion can be made about any moment in time *at* or *after* noon. Thus, for all we know, at noon, the vase just magically disappears. 4) The problem is ill-posed. To be precise, according to the problem statement, an infinite number of operations will be performed before noon, and then asks us about the state of affairs at noon. But, if infinitely many operations have to take place (sequentially) before noon, then noon is a point in time that can never be reached.

## 2. Schrödinger’s Cat

Schrödinger’s cat is a thought experiment, often described as a paradox, devised by Austrian physicist Erwin Schrödinger in 1935. It illustrates what he saw as the problem of the Copenhagen interpretation of quantum mechanics applied to everyday objects. The thought experiment presents a cat that might be alive or dead, depending on an earlier random event. A cat is trapped in a box with radioactive material, a Geiger counter, and a mechanism rigged to release poison if particle decay is detected. According to Erwin Schrödinger, the cat exists in two probable states. But that doesn’t track with reality (cats are not both alive and dead). Proposed in 1935, the postulate illustrates that some quantum concepts just don’t work at nonquantum scales. Also that Schrödinger was a dog person.

## 1. Maxwell’s Demon

Maxwell’s demon is a thought experiment created by the Scottish physicist James Clerk Maxwell, in which a supernatural being is instructed to attempt to violate the second law of thermodynamics. The second law of thermodynamics ensures (through statistical probability) that two bodies of different temperature, when brought into contact with each other and isolated from the rest of the Universe, will evolve to a thermodynamic equilibrium in which both bodies have approximately the same temperature. The thought experiment demonstrates Maxwell’s point by describing how to violate the 2nd Law to “show that the 2nd Law of Thermodynamics has only a statistical certainty.” In the experiment an imaginary container is divided into two parts by an insulated wall, with a door that can be opened and closed by what came to be called ” Maxwell’s Demon“. The hypothetical demon is able to let only the “hot” molecules of gas flow through to a favored side of the chamber, causing that side to appear to spontaneously heat up while the other side cools down.

Excellent article:

Similar to Galileo’s thought experiment, one great thought experiment in history to settle a scientific controversy was by Alhazen (Ibn-al-Haytham in arabic, circa 1000 AD), who settled a 1000-year old controversy of which direction light traveled in. It was not understood whether light came from object to the eye, or whether eye shot out some rays which interacted with the objects. Alhazen argued that it couldn’t be the latter, since we are able to see distant stars the moment we open our eyes, and also since eye suffers from looking at a very bright light. See the section of ‘Vision’ on this page: http://en.wikipedia.org/wiki/Alhazen