# Super Intelligence: Rise of the Machines

This article will be the beggining of a new series in which we examine the effects that artificial intelligence (AI), robots, and automation will have on human civilization. In this article, we’ll primarily be focusing on the implications of artificial general intelligence (AGI).

# String Theory and Colonizing the Multiverse

In this article, we’ll talk in laymen terms about quantum theory and general relativity and, specifically, how the two are related. We shall begin by discussing the well-known fact that these two theories—which describe how the universe works on the scale of the very small (quantum theory) and the very large (general relativity)—oftentimes contradict one another and they usually contradict each other on the scale of the very small (which is where general relativity breaks down and quantum mechanics gives us the correct picture). Now, something that is a little less well-known is that quantum theory and general relativity seem to, in some strange sense, make similar predictions about how nature is on vast size scales. Both theories predict that there are other universes and extra spatial dimensions. We shall close our discussion in this article by answering a question that we posed at the end of the article, Orbital Rings and Planet Building.

# Star Lifting: Colonizing the Stars and the Galaxies

In this article, we’ll discuss star lifting and its applications to interstellar and intergalactic space travel.

# Spaceship Comets and Highways Through Space

In this article, we’ll look at various different ways we could travel to the stars. We’ll first discuss how very small, but very fast probes could be accelerated to relativistic speeds using lasers (or masers); such probes could reach the nearest stars within the span of a human lifetime. This discussion will also lead us to the notion of an “interstellar highway” which we’ll discuss in detail. We conclude by discussing how asteroids and comets could also be used as spaceships to reach the stars.

# Preliminary Interstellar Missions: Prelude to the Stars

In this article, we discuss preliminary interstellar missions which will serve as preludes to missions involving sending spacecraft to stars. We primarily discuss using the Sun as a gravitational lens - a kind of “cosmic telescope” - to search for exoplanets which likely harbor life as well as those which likely do not.

# Leaving the Solar System: Introduction to the Outward Bound Series

This article is essentially a “teaser” of what we have in store for upcoming articles. Basically, I summarize ideas that will be discussed in tremendous detail in subsequent articles. These ideas are, primarily, interplanetary travel, interstellar travel, and intergalactic travel and how megastructures like orbital rings and star lifters (and a few others) will enable such voyages. We also give a very brief “teaser” on the redesign of the social and economic systems which underlie all industrial and social protocol.

# Gravitational Force Exerted by a Sphere

To find the gravitational force exerted by a sphere of mass $$M$$ on a particle of mass $$m$$ outside of that sphere, we must first subdivide that sphere into many very skinny shells and find the gravitational force exerted by anyone of those shells on $$m$$. We'll see, however, that finding the gravitational force exerted by such a shell is in of itself a somewhat tedious exercise. In the end, we'll see that the gravitational force exerted by a sphere of mass $$M$$ on a particle of mass $$m$$ outside of the sphere (where $$D$$ is the center-to-center separation distance between the sphere and the particle) is completely identical to the gravitational force exerted by a particle of mass $$M$$ on the other particle of mass $$m$$ such that $$D$$ is there separation distance.

# Orbital Rings and Planet Building: Prelude to Colonizing the Solar System

An orbital ring connected to the Earth by space elevators would reduce the cost of going to space to an amount comparable to an airplane ticket. This would cause a boom in the space tourism industry and eventually millions and even billions of people and tons of cargo will be moving from the Earth’s surface to space annually, and vise versa. This would necessitate an expansion in our space-based infrastructure to include space-based solar panels, a lunar mass driver, the routine mining of asteroids, and especially enormous space habitats (for all those billions of people to live in) such as the Standford Torus, the Bernal Sphere, or the O’Neil Cylinder. Orbital rings also allow you to build artificial planets and Dyson spheres, which would allow us to completely colonize the solar system. They would also allow us to build a Birch planet, a single planet with a surface area which exceeds the total surface area of all the planets in the Milky Way galaxy.

# Inward Bound: How Should We Colonize the Earth?

A star such as the Sun provides stupendous quantities of power. We earthlings tap into only a tiny fraction of the power of the Sun’s light that reaches Earth because so much of that power is lost when the Sun’s light is transmitted through the atmosphere. But what if we extracted the Sun’s solar energy from space by building large arrays of space-based solar panels? Space-based solar energy has myriad applications such as powering infrastructure and cities on the Earth, the Moon, or other worlds in the solar system; it can also be used to sterilize “space junk” and to create a highway between the stars for solar-sail spacecraft.

# Drake's Equation and Searching for Life in the Milky Way

In this lesson, we’ll discuss the prospect of life in the Milky Way galaxy beyond the Earth. We'll begin by discussing the speculations made in a paper written by Carl Sagan about the possibility of life in Jupiter's atmosphere. From there, we shall derive a formula which describes the habitable zone of a star. Using this formula and data obtained by the Kepler Space Telescope, we can estimate the total number of "Earth-like" planets in the Milky Way. From there, we discuss the fraction of those planets on which simple and intelligent life evolve; then we'll discuss the fraction of those planets on which advanced communicating civilizations evolve and what fraction of those civilizations are communicating right now.

# The Diversity of Exoplanets in the Galaxy

In this lesson, we’ll attempt to give a brief catalog of the very different classes of planets in the universe. We'll discuss Pulsar planets, hot Jupiters, Super Earths, ice and water worlds, and many more.

# Proof of the Theorem: $$\lim_{ϴ→0}\frac{sinϴ}{ϴ}=1$$

In this lesson, we’ll use the squeeze theorem and elementary trigonometry to prove that $$\lim_{x→0}\frac{sinx}{x}=1$$.

In this video, we’ll discuss Shkadov thrusters: a method of moving stars, star systems, and even entire galaxies.

# Proof of Green's Theorem

For a vector field $$\vec{F}(x,y)$$ defined at each point $$(x,y))$$ within the region $$R$$ and along the continuous, smooth, closed, piece-wise curve $$c$$ such that $$R$$ is the region enclosed by $$c$$, we shall derive a formula (known as Green’s Theorem) which will allow us to calculate the line integral of $$\vec{F}(x,y)$$ over the curve $$c$$.

# Gravitational Force Exerted by a Rod

Using Newton's law of gravity and the concept of the definite integral, we can find the total gravitational force exerted by a rod on a particle a horizontal distance $$d$$ away from the rod.

# Gravitational Force Exerted by a Sphere

To find the gravitational force exerted by a sphere on a particle of mass $$M$$ outside of that sphere, we must first subdivide that sphere into many very skinny shells and find the gravitational force exerted by anyone of those shells on $$m$$. We'll see, however, that finding the gravitational force exerted by such a shell is in of itself a somewhat tedious exercise. In the end, we'll see that the gravitational force exerted by a sphere of mass $$M$$ on a particle of mass $$m$$ outside of the sphere (where $$D$$ is the center-to-center separation distance between the sphere and particle) is completely identical to the gravitional force exerted by a particle of mass $$M$$ on the mass $$m$$ such that $$D$$ is their separation distance.

# Introduction to Double Integrals

In previous lessons, we learned that by taking the integral of some function $$f(x)$$ we can find the area underneath that curve by summing the areas of infinitely many, infinitesimally skinny rectangles. In this lesson, we'll use the concept of a double integral to find the volume underneath any smooth and continuous surface $$f(x,y)$$ by summing the volumes of infinitely many, infinitesimally skinny columns.

# How to Produce Water and Oxygen on Mars

The lack of oxygen in Mars' atmosphere and running liquid water on its surface is very inconveniant for any humans living their since oxygen and liquid water are necessary for humans to survive. Fortunatelly, there is an abundance of frozen water on Mars' surface. In this lesson, we'll discuss various techniques which can be used to extract all of this water. Once the water is obtained, by performing electrolysis on the water we can distill all of the oxygen from that water we need.

# Colonizing and Terraforming Venus

The first serious proposal in scientific literature on terraforming other worlds in the universe was about terraforming Venus. The planetary scientist Carl Sagan imagined seeding the Venusian skies with photosynthetic microbes capable of converting Venus's $$C0_2$$-rich atmosphere into oxygen. Other proposals involve assembling a vast system of orbital mirrors capable of blocking the Sun's light and cooling Venus until this hot and hellish world became very frigid and rained $$C0_2$$ from its atmosphere. The solleta would also be capable of simulating an Earth day/night cycle. To create oceans and an active hydrosphere on Venus, we could hurl scores of icy asteroids from the Kuiper belt to Venus and, upon impacting the Venusian atmosphere, would rapidly disintegrate releasing enormous quantities of water vapor into the atmosphere which subsequently condense to form the first seas on Venus. Or perhaps Saturn's moon Enceladus—containing a colossal subsurface ocean dwarfing that of the Earth's—could be sacrificed towards the end of creating the first seas on Venus. But even if humans never terraform this hellish world, they could still live their—partially at least—by deploying thousands of blimps into the Venusian skies capable of supporting a long-term, human presence of perhaps over a million people. Venusian sky cities. But eventually, after many millennia of terraforming Venus, a rich ecosystem of life—including us—could live on Venus's surface.

# Optimization Problem

If $$(x,y)$$ represents any point on the circle, if $$P$$ is a point fixed at the coordinate point $$(4,0)$$, and if $$d$$ represents the distance between those two points then, by using only calculus, we can find the point $$(x,y)$$ on the circle associated with the minimum distance $$d$$.