# Life in Outer Space – A Mathematical Approach

## Is There Really Intelligent Life Out There?

One of our previous articles discussed the minerals of Star Trek, giving rise to the hope that there is extraterrestrial life out there, but the real discussion about ET’s existence is a loaded subject.

For this article, we are going to focus on what the mathematical formulas tell us. The ones developed by astrophysicists; in other words, what are the odds that there really is intelligent life on other planets?

As difficult as it is to wrap our heads around the sun’s fusion process, which is equivalent to 100 billion atomic bombs per second, we will go one step further and try to understand the immense size of our universe, and subsequently, come up with a formula that scientists have developed to determine ET’s existence.

## So What Are the Odds?

It is estimated that there is an average of 1 – 2 billion stars in any recorded galaxy and there are over 2 trillion galaxies in the universe. If 10% of each galaxy contains a solar system, that is, it contains a star with planets revolving around it, then we can estimate that each galaxy has between 100 – 200 million solar systems, with some that may be fairly similar to ours.

If 1% of the stars in each solar system have a planet just distant enough from their sun where life could evolve, called the habitable zone or as some scientists like to call it, the Goldilocks Zone, we could have 1 – 2 million possible planets that could contain life. Going further, if 1% of these planets have the right ‘ingredients’ to build intelligent life, then there is the possibility that there may exist 10,000 stars that could have planets with intelligent life in each galaxy.

Cutting the odds even further, just to be more realistic, let’s take 10% of this result, which would equate to the possibility of 1,000 stars with extraterrestrial life in each galaxy.

That would mean that there could possibly be 1,000 x 100 trillion galaxies = 1,000,000,000,000,000 (1 quadrillion) planets with intelligent life. How many is that? Let’s take a look at this numerical comparison.

If we use the estimate of 200 trillion galaxies in the universe, that would mean ET may live on over 2 quadrillion planets in our universe.

On a separate note, don’t even try to comprehend how many fusion total reactions occur here every second when you include all of these stars. Fuhgeddaboudit!

## What About the Scientific Formulas?

The above calculations were based on a general assumption, considering the amount of these types of objects that have been calculated or physically found in the sky, but have the experts given the possibility of extraterrestrial life serious thought?

American astronomer and astrophysicist Dr. Frank Drake developed a formula that he presented at a meeting in Virginia in 1961. It is called the Drake Equation, which calculates the possibilities of life on other worlds within our own Milky Way galaxy.

We won’t go into the calculations, but in a general sense, it is based on our assumptions above but uses trigonometry to formulate a much more explicit and precise determination of ET’s existence. For you science and math connoisseurs, feel free to give it a shot below!

The terms are as follows:

N : The number of planets in the galaxy where electromagnetic emissions are detectable
R: The rate of stars that have the ability to have exoplanets with habitable zones revolve around them
fp : The fraction of those stars that actually have solar systems
ne : The number of planets in each solar system within the Goldilocks Zone
f: The number of planets on where life may actually exist
fi : The number of planets where intelligent life may exist
fc : The number of planets that have civilizations with a technology where we can detect their signals
L : The length of time that these civilizations have produced these signals

If these calculations result in any number above zero, just maybe Men in Black had it right!

# What is Concrete?

## What is Concrete?

Ever notice that just about every building has a concrete foundation?  There is a very good reason for this and it is not about aesthetics. Concrete has enormous compressive strength, meaning that it is an excellent material for holding up the weight that is above it.

Concrete is not just used for foundations, but also for columns, beams. slabs and just about anything where there is a load-bearing issue. Load bearing meaning an element that supports the weight above it. The amount of weight that the load-bearing element would support would depend upon how many concrete columns (or other concrete supporting materials) are available to support the whole load.

For example, a 30-story building has 10 supporting columns on the ground. That would mean that the weight is evenly distributed across each of the 10 columns or mathematically speaking, each concrete column would support 0.333 (10/30) of the load (building).

Another probably more identifiable example is the load-bearing walls in a house. If you live in a house, you have probably come aware of where your load-bearing walls are. These are the walls that actually hold up the house; however, for frame houses, concrete is not the usual load-bearing material, but heavy wood or steel instead.

In short, concrete is an excellent source for withstanding the heavy forces that are above it or more specifically, as an excellent compression material.

Did you know that concrete also gains more strength as it ages? With that said, let’s take a look at just what this compressive material is actually made of.

## What is Concrete Made Out of?

Concrete is a mixture of air, water, sand and gravel and the percentages of these elements are usually 20% air and water, 30% sand called fine aggregates and 40% gravel, with 10% being the cement; that is, 10% being the ‘glue’ that keeps all those other materials together. Remember, from our article on cement, it is just the binding material for the assembly of concrete. When the cement is mixed with water, it is called paste

This proportion is called the 10-20-30-40 Rule; however, the exact percentages of the materials can vary depending on the combination of the concrete mixture, including the type of cement and other factors that we will explain in this article.

## How are the Proportion of Materials that Form Concrete Determined?

So we know that concrete is a mixture of paste and aggregates and sometimes rocks. The paste coats each of the aggregates and as it hardens (the process is called hydration), concrete is born until it becomes a rock-solid mass, capable of withstanding a load much heavier than itself, but if the proportion of water and paste is not correct, this rock-solid mass can deteriorate causing unwanted and potentially dangerous consequences.

The trick is to carefully proportion the mix of the ingredients and much of it depends on the ratio of water to cement and this ratio is calculated by the weight of the water divided by the weight of the cement. A low water-content ratio yields high-quality concrete, so it is best to lower the ratio as much as possible without sacrificing the integrity of the concrete.

If the ratio results where there is too much water in the mixture, the aggregates become thinned out, resulting in weakening the concrete and we can figure out what that would mean.

Conversely, If there is not enough water in the mix, the water will evaporate too fast, comprising the integrity of the concrete and resulting in it being weak as well.

### What is the Strongest Concrete Mixture Ratio?

1:3:5 which is cement and aggregates (in this case, the aggregate is broken into sand (3) and gravel (5) and this is considered the ratio that would create the strongest concrete.

## How Much Time is Allocated Before the Finished Concrete is Used at the Construction Site?

There is a limit to how long the concrete can be poured after it is mixed. In the US, the limit is 60 minutes from the time the water mixes with the cement to the time of delivery to the construction site.

A safe time frame is up to 90 minutes, then the integrity of the concrete will start to deteriorate. That is why we see concrete mixers right at the construction site as no time is lost between the mixture and the pouring.

As the name applies, when steel (usually using steel bars, called rebars) is placed inside the slab where the concrete is going to be poured, it reinforces the strength of the concrete.

### How Does it Reinforce the Concrete?

We have been discussing compression strength; that is, how strong the material is when a heavy load is placed on it, but we haven’t discussed tensile strengthwhich is the opposite of compression.

Tensile strength represents the strength a material can endure when a force tries to pull or stretch it out. The reason why compression is so important when using concrete is that that is its main purpose – to hold up heavy loads, but concrete does have a limit on how much pull can be leveled on it as well, and there are situations where the tensile strength of concrete is put to the test. The weather being one factor, but there are more.

### Enter Steel

By integrating the rebars inside the concrete, the concern about stretching the concrete is greatly minimized. The combination of concrete and its accompanying reinforcing steel bars successfully manages these situations, because of steel’s high tensile strength; hence, you have a perfect storm of compressive and tensile strength in reinforced concrete (RC).

### What Happens if the Reinforcing Steel is Not Inside the Concrete?

Cracking of the concrete surfaces can occur, subsequently causing aesthetic issues, but if the tensile yield is really great, (e.g. a strong pull on the concrete) the situation can become unsafe, so without the steel rods to compensate for this pull, you will find cracks in the concrete or worse.

## Conclusion

Concrete is a mixture of sand, water, aggregates and cement. The amount of any of these elements will determine the strength of the concrete. Timing also plays a role as the concrete must be readily mixed within 90 minutes max, but 60 minutes is the usual requirement before being poured into its foundation or another element such as a column or slab.

By placing steel bars which is a mesh of steel wires (rebar) inside the concrete, the tension issue is resolved by aiding the concrete under tension.

So the next time you are walking in a building, especially a large structure such as a skyscraper, give thanks to the materials that allow you to be there, as well being thankful to the engineers who allowed it to happen!

## What is Cement?

If you were to say “I tripped on a cement block”, would you be wrong?

The answer is yes because there is technically no such thing as a ‘cement’ block, but there are concrete blocks; that is to say, cement is nothing more than the ‘glue’ that binds the materials that make up the concrete block, which is usually sand and gravel. So if you were to say “I tripped on a concrete block”, you would then be correct.

According to Wikipedia, cement sets, hardens and adheres to other materials to bind them together.In simple terms, cement is the centerpiece of what keeps the concrete intact.

## What Materials are Cement Made of?

The sand and gravel are called aggregates, and it is these materials that are bound together but remember, cement is not the material, it is the glue. So what makes up the cement?

The ingredients are mainly limestone and clay, which are extracted from quarries from around the world. Of course, the process of making cement is not that simple. The limestone is heated with clay to 2,640 °F in a kiln (an insulated chamber). This process is called calcination, which liberates molecules of carbon dioxide from the calcium carbonate (the main ingredient of limestone) to form calcium oxide, commonly referred to as quicklime

It is here where the quicklime chemically combines with the other materials to make a hard substance, called ‘clinker‘. Gypsum is then added to make Portland cement, the most common type of cement used, which is referred to in the industry as OPC.

## How does the Limestone Mixture Process Work?

The limestone rock is crushed in a machine appropriately called a crusher which reduces the limestone to a size of about six inches maximum. It is then fed into the second crusher where it is further reduced to under three inches. The mix is conveyed and then sent to a raw mill bin to be ground down even further.

In these bins are two chambers. One that dries the limestone and clay mix and the other that grinds it via hot gasses. Then, once all dry, it is moved to the grinding chamber called a ball mill.  Here a cylinder contains steel balls and rotates which causes the balls to fall back into the cylinder and onto the limestone mix; hence, grinders. 4 to 20 revolutions per minute is the general rotation of the cylinder, which is dependent upon the diameter of the ball mill.

What’s left when the grinding process is done is a product of fine and coarse material. The coarse material is useless in that state and is called reject where it is returned back to the ball mill for additional grinding. A machine called a separator does this part.

Having the limestone and clay grounded down to a fine powder is still not enough to complete the cement process. The mixture must then enter a device called a cyclone which is used to separate the fine grounded material from existing gases that still exist in it.

Then, the hot gas and fine materials enter a multistage “cyclone”. This is to separate the fine ground materials from the gases.

The result – a clean, fine powdery material and is renamed kiln feed.

Next, the feed is heated via a process called sintering, which is when the chemical bonds of the material are broken down using heat, and once complete, a new substance is formed called clinker.

The clinker is initially very hot and contains small, dark gray nodules from 1mm to 25mm in size where it is placed into a grate cooler for cooling from approximately 2550 °F to approximately 240 °F via the use of cooling fans.

And voila! You have cement!

## Final Note

Other elements are added to the clinker depending upon what the cement is going to be used for. In the case of Portland cement, gypsum is the additive.

And you thought that making cement was just adding powder and water. We hope you gained some good knowledge as to how cement is actually created. And the next time you get angry after you trip over a block that’s made up of limestone and clay, you know that it is concrete you take your anger out on and not the cement that put it together.

# How Buildings are Constructed Along Earthquake Fault Lines

One of the first structures built to withstand an earthquake was the Transamerica Pyramid, also called the Transamerica Tower. In this seismically active region, no engineering was spared to keep the building safe from earthquake tremors.

Located on 600 Montgomery Street, it rises 853 feet and 48 floors and was the eighth tallest building in the world in 1972. On the highest floor, 48, there is a conference room that has unobstructed 360-degree views of the San Francisco Bay area.

The building has a wide base that narrows upwards, much like the churches and buildings of antiquity, which is designed to give the structures their stability. No doubt this is an optimum method for buildings that reside along earthquake fault lines. From an environmental perspective, the pyramid design (hence the name), allows natural light to filter down to the streets below.

Looking to limit the degree by which the structure would twist and shake during an earthquake, engineers used a unique truss system with built-in steel, reinforced concrete, precast quartz aggregate and glass. It has two angular setbacks working their way up to the top of the tower and a 212-foot spire. There are two angular concrete structures on the east and west sides that protrude from the 29th floor rising upwards called wings. The wings are part of the structural engineering that went in to keep the building sturdy during an earthquake, but they also have a function. The eastern wing serves as an elevator and the western wing includes a staircase.

To reinforce the building even more, there is a truss system on the ground and lower floors which are designed to support both vertical and horizontal stresses. Truss designs are cross beams engineered to perfectly distribute the weight of a structure in order to withstand tension (pulling) and compression (pulling) forces.

Under the truss, beams are X beams over the ground floor, designed to brace the building against any type of torque movement.

This torque and stress reinforcement was tested in 1989 during the .71 magnitude Loma Prieta earthquake. The building successfully withstood the quake with no damage and no injuries.

In addition to above-ground stress reinforcement, there is an additional basement from earthquake tremors, consisting of a 9-foot deep concrete mat foundation, which lies on top of a steel and concrete block that goes 52 feet underground. This foundation contains 16,000 cubic yards of reinforced concrete, including over 300 miles of steel reinforcing rods. This concrete assists with the additional support of Compressive stress and tensile stress.

The Pyramid is a self-contained structure, which has its own 1.1-megawatt power system. Construction began in the fall of 1969 with the first tenant moving in in 1972 and is still standing gracefully today as a monument to earthquake building construction.

# The 2 Methods to Building a Subway

For those who love big cities (and even smaller ones), there’s no doubt you have ridden on one of their mass transit lines. With that said, have you ever wondered about the amount of engineering that has gone into building one? Well, here we will give you some basic information as to how they are constructed.

There are two basic methods to subway construction: “cut and cover” and the other is called “deep bore.”  Cut and cover refers to the complete opening of the street, down to where the subway would be built and deep bore refers to the burrowing strategy previously discussed in our Tunnel Boring article.

To determine which method is going to be used, an engineering and environmental review is necessary, which includes logistics, underground water determination, earth material, demographics and of course, costs, not to mention the bureaucracy of working with the different city agencies to determine where all the utility lines, water pipes and potential other tunnels are located.

This bureaucracy alone could take months or even years, And if any of these factors become obstacles, then additional planning would be required. The bottom line is that this whole procedure is a great undertaking and can get very complex.

So with this introduction, let’s delve into describing the engineering process by which each of these methods would be used.

## Cut and Cover Method of Building a Subway

This method is found in the building of some of the older subway systems, such as the Paris Metro, London Underground and the NYC subway. With this method, the pavement of the street is completely removed and then a hole is dug down into the ground.

“Cut and cover” is considerably cheaper than the “deep bore” method; however, the dig must parallel the street, so there is no room for more sophisticated planning, like curved tracks that fork off to some desired locations, unless the street above does the same.

Another undesirable factor is that “cut and cover” results in large holes in the street significantly causing traffic nightmares, as well as major inconveniences for store owners along the route.

## Deep Bore Method

The boring machine is a sophisticated and expensive apparatus that cuts through the underground dit by using circular spinning blades. The advantage this has over “cut and cover” is that they do not have to follow the street grid above, allowing much greater flexibility in the design of the subway lines, as well as not have to dig big holes along the route. The boring method is slow, but efficient and cuts through the earth at a rate of about fifty feet per day

The disadvantages are that the costs are significantly higher than cut and cover, where \$150 million would be a medium price.

## How the Subway Construction Method Is Decided

As mentioned, there are so many factors to consider when building a subway line, but the number of subway lines and the cost factors involved would be the major considerations.

For example: After extensive analysis of which method would be better to construct the Second Ave Subway in Manhattan, it was decided that the TBM would be more efficient, based upon the fact that cut and cover would cause so much economical damage, the boring method would be more practical, even though it is more expensive.

Just lowering this giant machine into the tunnel is a major task, not to mention expense, but it is worth it in the case of big-city construction.

Another major consideration was the amount of interruption and financial damage the cut and cover method would have caused, especially on a congested and commercial road like Second Ave. where the upper east side and midtown Manhattan would be commercially interrupted.

Considering how often there would have been complaints, especially in this time period, where community demonstrations are the norm, more and more TBM usage is becoming the preferred method, so as not to disturb life above ground. However, cut and cover construction may still be considered if the soil conditions are not up to standard.

An example of how the political consequences of cut and cover road disruptions can escalate, take a look at Vancouver B.C.’s recently opened Canada Line. A lawsuit was taken against the city of Vancouver and the plaintiff, a retailer with a store along the subway route where won C\$600,000 after cut and cover caused major financial hardship. Following that lawsuit, an additional 41 plaintiffs have taken legal action to recover financial damages.

# What the Future Holds

We are now in the 21st Century and with technology streaming at a rocket pace (e.g. artificial intelligence, at home video conferencing, sending a man to Mars) it will only be time before new engineering technologies will lead to faster, lighter and much less expensive boring machines. Then if you think some cities have excellent transportation facilities now, wait till these new machines come along and open the door to even more elaborate and reduced financial expense.