people sitting at the table

Taylor Principles of Management and the Classroom

Frederick Taylor (1856-1915) developed his management principles in response to the problems he was seeing in the workplace. IN this post, we will look at these principles and the backdrop to their origins.

Industrial Revolutions and its Problems

The Industrial Revolution led to major changes in the production of goods. Items went from being produced at home to being produced in factories. The work went from families working as a team to individuals working away from home. Natural these changes had pros and also cons.


The main pro has already been mentioned and involves the boost in productivity. However, among the cons was a lack of motivation, issues with determining how much to produce with workers and managers manipulating each other, and a general lack of standardization. Lastly, workers were concerned with wages, working conditions, and justice.

Life of Fredrick Taylor

In this context, Fredrick Taylor (1856-1915) emerges. Unable to go to college due to an injury, Taylor went to work in a factory and saw workers destroy tools to prevent overproduction, which they believed could threaten their employment. Witnessing this, Taylor decided to take an empirical approach to this problem.

Taylor applied several different methodologies to examine production, such as time series, standardization, division of labor, time management, and incentives in such context as piecework production. He was also a huge proponent of finding the right person for the job and moving people as necessary to achieve this benefit to the person and the employer.

Four Principles of Management

Below are the four principles of management according to Taylor

  1. Managers should use science for each aspect of a job.
  2. Select and train workers scientifically.
  3. Workers and management should work together to make sure work is done according to principles of management
  4. Responsibility and work should be divided equally between workers and managers

Managers need to make sure science is the tool used for making decisions. Science relies on and observation and analysis of data. Using a scientific process is considered superior to making intuition or gut decisions. When science is used, employees may not agree, but they can see the thought process behind the decision. The principle of data-driven decision is a foundational concept in data science today.

Workers should also be trained and selected scientifically. Again this gives the impression of objectivity and fairness in the decision-making process. Using intuition or other means makes management decision-making questionable.

The third principle emphasizes that everyone should work together from a scientific perspective. Through a united worldview, the assumption is to improve cooperation. The enemy appears to be subjectivity, and both workers and management should avoid this.

The final principle speaks to how management and workers must have a joint interest in responsibilities. The motivation behind this idea is to reduce the hostility that can sometimes arise in the workplace. Suppose everyone is a part of the decision-making. In that case, everyone should have a vested interest in the endeavor’s success.

Taylor and the Classroom

It is hard to see how Taylor’s principles apply in the classroom at the surface level. However, two ideas that come out of Taylor’s principles for teachers are the idea of fairness and dialog. A teacher must demonstrate fairness through the decisions that they make. Students will not agree with a decision at times made by a teacher, but it is important to know that the decisions teachers make are not arbitrary and capricious.

Dialog is also important. Students need to raise concerns openly even if their commands are not implemented. When people are allowed to share, they are often invested in the achievement, which is the same for many students.


Taylor’s principles of management were groundbreaking for them. Even after almost a century, the ideas laid down here inspire managers and leaders in various fields.

man raising right hand

Brief Intro to the History of Management

A simple definition of management would be coordinating a task(s) to achieve a goal. This often involves people, and such management is about coordinating people. Managing people can be viewed negatively and as a form of manipulation or positively in a way that empowers people to accomplish things. In either case, management has a long history. People have been trying to achieve goals for all recorded human history.

Ancient Management

Early forms of management date all the way back to ancient Sumer. The Sumerians, people from Mesopotamia, developed writing to manage their training empire. Merchants needed a way to keep track of their records regarding what was bought and sold, among other things. Writing was developed for this purpose, perhaps because the trade volume was too high to track by memory.


In the ancient city of Babylon, Hammurabi developed his Code of Hammurabi to manage behavior and control his people. The significance of the Code of Hammaruabi is that it is one of the oldest examples of law ever found. One of the more famous examples from this code is quoted below.

If a man put out the eye of another man, his eye shall be put out. [ An eye for an eye ]

Code of Hammurabi Line 196

The example above is the law of retribution or lex talionis. The law of retribution is found in many other places. One example would be the Bible. A later King named Nebuchannezer developed the idea of incentives by providing more food to workers who produced more.

Ancient Egypt also had contributed to management when they developed ideas behind the division of labor. Dividing labor is taken for granted; however, when agrarian cultures moved towards developing trade and cities, everyone did not have the time to farm. By dividing labor, people could focus and become highly competent at something. In addition, division of labor allows some of the Egyptians to develop the pyramids.

Management In China and the West

In China, Sun Tzu and his “Art of War” lays down many ideas related to management. Ideas behind resources management, inspiring the people, and examining oneself are all addressed in this classic. Countless managers have read and received inspiration from this practical book.

The Han dynasty of China (206 BC – 220 AD) also contributed to management through its development of bureaucracy. The large governmental system that was important at this time helped the dynasty control and monitor the people while also providing opportunities to people good enough to pass the various civil servant exams.

The Greeks and the Romans have also made their contributions to management. The Greeks also developed division of labor, or perhaps they borrowed the idea from the Egyptians with who they had frequent contact through trade. The Romans gave the world standardization. Standardizing everything allowed the Romans to produce things much faster for conquest. The Romans could pave the world because the roads were generally built the same way, saving time and resources.


Management will continue to play a role in the world as the world becomes more complex. Therefore, it will be interesting to see what the next generation of innovations will be.

brain inscription on cardboard box under flying paper pieces

Challenges to Decision-Making

Decisions are a critical part of the life of people, whether teachers or leaders. Even though this is an important skill, many people struggle with making decisions about important and even mundane matters. In this post, we will look at several challenges to making decisions.

Sunk Cost

There are times when a decision is made, and after some time, all parties involved begin to realize it was a bad decision. The challenge in this context is that since time and resources have already been devoted to this bad choice, maybe if everyone is patient, things will begin to work out. Generally, this is not the case.


Organizations and schools make this kind of mistake all the time. For example, a new curriculum or technology is adopted by the school. It is clear that this software or tech is not working, but a commitment has already been made. Such a situation can lead to a great deal of frustration among faculty and staff.


Nobody can predict the future. When it is unclear in terms of what to expect, it can lead to analysis paralysis, which essentially means that leadership or the teacher tries not to make a decision until new evidence arises. Unfortunately, new evidence is normally not forthcoming except that there is now less time to decide, and options begin to disappear because of lost time.

Since there is no way to be 100% sure of anything, the next best approach may be to make small incremental decisions and or take a step forward and be bold and see what happens. Neither of these alternatives is attractive, but there are times when a decision must be made.

Temporal Constraint

Due to procrastination, there are times when there is not enough time to decide. Again, some teachers and leaders what as long as possible and then go with the only viable option when they are forced to decide. When this happens, the teacher can blame the context for what happened when the reality is that they did not want to make a decision. There is no better excuse than a lack of time in many situations.

Time can be an ally in decision-making if used for thinking rather than for avoiding making a decision. Too often, people fall for the temptation of letting circumstances dictate their choices.

Limits of Reasoning

While thinking is good, there are limits to what reasoning can accomplish. There is no way to collect all data and process all possibilities when it is time to decide. Eventually, there comes the point where a teacher has thought enough about a decision and must make a decision. However, not too many people fall for the trap of limited reasoning as reasoning is not generally encouraged in this day and age.


People are often more comfortable with situations in which their own ideas and beliefs agree with the decision to be made. For example, a group of teachers may agree on something because they share similar backgrounds and thus have a similar perspective on a matter. This is an example of confirmation bias in which a person looks for information in agreement with their own position. Such examples can include people who agree with you or information that supports your position.

Bias is not always bad. If a decision needs to be made quicker, then a group of people with similar views can agree fast. However, suppose the goal is a creative or innovative solution. In that case, a diverse group is more likely to challenge and stretch each other to a novel idea.


The final barrier to decision-making is conflict. Most people want to avoid conflict as it can lead to disharmony and other problems. However, people will not agree in the decision-making process, and they often like their idea at the expense of other people’s ideas.

There are two forms of conflict. Process conflict is disagreements about doing something and is not about an individual. Relationship conflict is personal and involves attacks on the person rather than the process or idea. Process conflict can lead to better processes, but once it becomes personal, it can collapse the decision-making process. It is difficult for many people to separate themselves from their shared ideas, but learning to do this is highly beneficial for the decision-making experience.


Decisions need to be made alone and in groups. Whatever the case may be, there are impediments to the decision-making process that people need to be aware of. The ideas presented here are just some of the challenges awaiting people who need to make up their minds about something.

man sitting in front of three computers

Decision-Making and the Brain

Decision-making generally takes place in one of two ways. The two ways are the reflective system and the reactive system. The reflective system is the analytical way of making decisions and is often characterized as methodical and logical. Although the thought process is carefully laid out when using the reflective system, the downside is that reflecting is much slower than reacting. Therefore although often viewed as superior, the reflective system is not always the optimal choice.

Two Systems

The reactive system is intuitive and relies more on emotions when compared to the reflective system. Although much faster than the reflective system, the reactive system is much less accurate and or careful. As such, the benefit of reactive is when spending is needed, and the complexity of the problem is not significant. Children tend to rely more on the reactive system as they lack the cognitive ability and experience to ponder reflectively.


The system that people use often depends on their emotional states. When people are calm, and at peace, they are more likely to use the reflective system. However, if people are angry, sad, happy, etc., they may use the reactive system. We have all been in situations where our emotions control us when dealing with students. This may be an example of the reactive system taking over reasonably. The choice of which system is also associated with personality as some prefer one style over another regardless of their emotional state.

Different decisions can rely on different systems. If a teacher faces a routine decision, they may choose to use the reactive system to make a fast decision. If the situation is novel and unusual, the teacher may adopt a reflective approach. This is one reason why experienced teachers can work faster. The speed is based on using prior knowledge to make a quick, insightful decision that reactively while a new teacher has to reflect on every single experience because they are all so novel.

Types of Decisions

Decisions that are repeated frequently and based on rules are called programmed decisions. These can include things such as when to take a break, how much time to give for a test, etc. The ability to autopilot these decisions comes from experience.

Non-programmed decisions are decisions in a context in which clear criteria are not available. Examples of non-programmed decisions in the classroom may include equipment breakdowns, accepting new students, etc. This implies that reflection will be necessary to decide in this unclear situation.


The point here was not to try and make a case that one form of decision-making is superior to the other. Each system has its pros and cons and what really determines what’s best is the context in which the decision needs to be made. There is little time for reflecting if there is a fire in the class. In addition, it is equally harmful to determine students’ grades reactively.

woman in red long sleeve writing on chalk board

Responsibilities and Skills of Teachers

Every job has its list of responsibilities and skills required for the position. This post will look at some of the common skills and responsibilities associated with teaching.


Teachers are expected to spend a large amount of their time making daily and long-term lesson plans. Developing these plans can include setting long-term goals, short-term objectives, procedures, assignments, and more. However, Once plans are developed, they have to be implemented, which involves coordinating students’ behavior and, at times, working with people outside of the class for various reasons.


Teachers have to constantly observe the behavior of their students and make adjustments to what plans or goals they have in mind. For example, if students are struggling, the teacher needs to slow down and reteach. Suppose the problem is not comprehension but a rather poor attitude. In that case, the teacher needs to modify how they enforce rules.

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Teachers also have to track resources such as paper, pencils, books, time, etc. These things must be observed while also trying to move forward in the curriculum and maintain learning.

Professional Development

Teachers also must stay abreast of the latest developments in their field. This includes changes and innovation in teaching and in one’s area of expertise. Different fields change at different speeds, but all teachers have to stay current to help students to be prepared for the workforce and or college.

Staying current in one’s profession is not overly time-consuming. The real challenge is doing this along with the other responsibilities of teaching and the demands of one’s life outside the classroom.

Skills of Teachers

The skills of teachers can be broken down into three categories

  • Technical skills
  • Human relation skills
  • Conceptual skills

Technical skills are essentially the expertise of the teacher. For example, a math teacher knows math and can use it practically. In addition, teachers must have technical knowledge of teaching, such as familiarity with pedagogy and various approaches to instruction. Generally, a teacher must have a high degree of technical skill because they are a teacher to others.

Human relation skills are the ability to work with other people. Teachers need to have ways to connect with students to inspire enthusiasm and growth. In addition, teachers also need to maintain relationships with other teachers, parents, and the administration. Working with others is often dicey, and surprisingly, teachers can often struggle to maintain a cordial relationship with their peers, students, and community members.

Conceptual skills relate to planning and seeing the big picture. Developing this skill comes with experience. For example, new teachers often cannot see beyond developing daily lesson plans, while more experienced teachers can plan months or semesters at a time. Conceptual skills become more important if a teacher moves more in the direction of leadership after a few years in the classroom.


Teaching is a challenging field in that it calls on a person to keep track of several important tasks while also developing themselves and working with others. Since doing this is no easy task, perhaps that is why so many teachers can find their jobs challenging.

crop businessman giving contract to woman to sign

Teachers as Classroom Managers

Henry Mintzberg (1973) researched what business managers do within companies. His results indicated that managers have three primary roles, which are…

  • Interpersonal
  • Informational
  • Decisional

We will examine each of these roles within the context of a teacher as a classroom manager.

Interpersonal Roles

The interpersonal role of a manager involves dealing with many people during a given day. Managers serve as figureheads, and this involves such tasks as greeting guests, participating in various ceremonies/formal activities, and being the general face of whatever they are in charge of. Teachers are frequently involved in figurehead-type roles as classroom managers. For example, teachers are often responsible for flag ceremonies in the morning, participating in graduation, responding to guess who comes to the classroom, etc. As such, teachers have a lot in common with business managers in the role of figurehead.


A second interpersonal role for managers is that of liaison. The liaison role involves maintaining connections outside of the group or unit that the manager is in charge of. It also involves connecting people within the organization with those outside and keeping track of information gained through external and internal relationships. For teachers, serving as a liaison is not as common in my experience. Often the student has access to the same people like the teacher. One exception may be if a teacher helps a student obtain a job or get into a college by providing connections to such opportunities.

A final interpersonal role of managers as a leader. The leader role involves training, motivating, and communicating with subordinates. When most people think of managers, this may be the first thing that comes to mind. This is also a primary function for teachers as they are expected to lead the classroom and communicate expectations with students.

Informational Roles

The informational role defines itself and involves obtaining pertaining data relating to the goals of the manager’s team. One role that falls under this category is that of a monitor. The manager is supposed to gather information from various sources to improve decision-making, among other things. Teachers also have to play this role as one of their primary functions is communicating what they have learned with their students. Teachers and managers who like knowledge or expertise will generally struggle with their role as a manager.

A second informational role is that of a disseminator of information. As mentioned with the teacher, the manager gathers information to share it. There are various lines of communication such as telephone, email, chat, etc. Whatever channel(s) is chosen is just how the manager shares information. We have already discussed how teachers spend the majority of their time sharing information, so we do not need to add much but to mention that it is important to consider how the information is shared in that do the students understand.

Lastly, managers serve as spokespersons, which means sharing information with people outside the unit or team. Sharing information like this can involve speaking with superiors, members of the community, etc. For teachers, the role of spokesperson may involve sharing concerns of their students with administration or with other teachers. Students sometimes like to raise concerns about things that the teacher can speak about because the teacher has a higher status. Thus the spokesperson role may be an advocacy position for a classroom teacher.

Decisional ROles

The final collection of roles of managers involves decisions. A manager is also an entrepreneur, which involves taking the initiative in projects and delegating responsibilities. Teachers are often implementing new ideas and teaching approaches in their classroom, and when possible, they will delegate responsibilities to students.

Managers also must handle conflicts and other emergencies. These conflicts can be among coworkers, with people outside the team, and even with the manager themself. As such, diplomatic skills are an important aspect of a manager’s skill set. Teachers may deal with even more conflicts than managers, given the age of the students. Both managers and teachers have in common the must know how to handle conflict and surprises.

Managers are also resource allocators, and this involves sharing not necessarily information but tangibles things such as budget resources, determining schedules, and setting wages. Teachers also serve as resource allocators as they determine who gets to use the computers, when it’s time to play, what rewards students get for good behavior, and much more. Care must be given to resource allocation as hints of unfairness and favoritism can lead to conflict.

The final role of a manager is that of a negotiator. This role is often paired with many of the other roles already mentioned. For example, the manager may negotiate as a spokesperson for their team, negotiate a conflict between subordinates, etc. For teachers, the same ideas apply. Teachers have to negotiate for themselves, their students, and with parents as just some examples.


From the examples presented here, we can see that teachers as classroom managers have a lot in common with managers in the business world. Both teachers and manger need to perform roles that involve interpersonal skills, informational skills, and decision-making skills. As such, a knowledge of management in the context of business could help teachers in their classrooms.

scientists experimenting in the laboratory

Acid & Bases

We will take a look at some simple ideas related to acid bases

Acids and bases are classified by the chemical behavior of their molecules. Acids usually have a sour taste, are covalent electrolytes, and turn litmus paper red. Citric acid is one example of an acid many of us have encountered as it is commonly found in citrus fruits such as oranges. At a technical level, acids donate a H+ ion during a chemical reaction.


On the other hand, Bases tend to have a better taste, are slippery when mixed with water, and turn litmus paper blue. Soap is one example of the use of a base in everyday life. Bases accept an H+ ion during a chemical reaction at a technical level. When acids and bases are mixed, they generally neutralize each other and produce water as a by-product.

Most acids and bases are aqueous solutions, which means they are found in a liquid state. However, some liquids do not neatly fall into the category of acid or base. Water is an example of this, and the term used to describe this is amphoteric. This means that water will sometimes donate an H+ ion or accept an H+ ion depending on the context. For this reason, water is often added to acids/bases to dilute the concentration of either one.

Water is also considered neutral on the pH scale commonly used to identify acids and bases. The Ph scale stands for potential hydrogen scale and measures the amount of hydronium ion in the solution. Lower numbers on the pH scale indicate higher levels of hydronium.

Most fruits and vegetables are considered to have low pH, thus considered base or alkaline, and they include the following

  • Avocados
  • Persimmon
  • lentils
  • Olives, black
  • Honeydew melon
  • Mangoes, ripe
  • Honeydew

Foods that are acidic in nature include the following

  • Most dairy
  • Citrus fruits
  • Meat
  • Sweeteners
  • Alcohol

There are lots of websites that promote such things as an alkaline diet. However, this is generally highly controversial, and the experts do not seem to agree about the benefits of eating alkaline foods.


Understanding acids/bases and their behavior can be important, especially in everyday life. Acid and bases serve a vital role in many different substances and can be helpful or harmful depending on the context.

activity adventure aerial air

Gases, Pressure, & Laws

It is common in chemistry to have to deal with gases. Naturally, scientists have uncovered various laws that describe how gases act. This post will look at concepts such as pressure and the development of various laws related to gases and pressure.

Pressure and Units

Pressure is defined as (force / area). To make this practical, scientists have found that our bodies are constantly exposed to 14.7 pounds of pressure per square inch by the air around us. Our bodies are so used to this constant external pressure that without it breathing would be difficult, if not impossible.

There are various units of measurement of pressure. The Pascal, named after Blaise Pascal, is newtons per meter square. However, Pascals are rarely used by scientists. Another common unit is standard atmospheric pressure or atm for short, which is the average amount of pressure exerted by air at sea level. As a fact, one atm is the equivalent of 101,325 pascals.


One more unit for pressure is the torr, which is 1 /760th of an atm. In terms of measuring pressure, it is common to use a barometer, and a barometer measures pressure using millimeters of mercury or mmHg. The units on a barometer are almost the same as for the torr.

Laws Related to Gases

There are several laws related to gases. For example, Boyle’s law states an inverse relationship between pressure and volume with the assumption that temperature is constant. In other words, when the pressure goes up, the volume will go down and vice versa. Boyle’s law was developed by Robert Boyle, an Irish scientist from the 17th century.

Breathing is based on Boyle’s law. When we breathe, inhaling causes the volume of our lungs to grow, which leads to a drop in pressure. The pressure drop is what allows air to flow into the lungs. The opposite takes place when we exhale. Our lungs become smaller, raising the pressure and forcing the air out of our bodies.

Charles’s laws are somewhat of a variation on Boyle’s law. This law was developed by Jacques Charles, a French scientist of the 18th century. Charles law states that if pressure is constant, then temperature and volume are proportional. In other words, when the temperature goes up or down, then the volume will go up or down.

An interesting by-product of Charles’ law is the idea behind absolute zero. Essentially, as we lower the temperature, the volume of a gas will shrink. However, gas is made of matter, and it can’t go to zero. This implies that there is a lower limit to temperature, and this lower limit is called absolute zero and is -273.15 C.

As shown below, the combined gas law combines Boyle and Charles’ law into one equation.

(p * v) / T

Pressure times volume captures a value to describe a gas in a particular context. However, we use the equation to solve for unknown values, so it is more appropriate to show it as follows.

(p1 * v1) / T1 = (p2 * v2) / T2


People generally dislike pressure, but the pressure is literally needed for life, at least when it comes to gases. Thanks to the work of many excellent scientists, we have a better understanding of how gases behave in the world around us.

bird s eye view of group of people

Crowds and Theories on Collective Behavior

This post will look at various types of crowds that we often find ourselves a part of at different times. In addition, we will look at two theories that attempt to explain the collective behavior that happens when crowds form.


A crowd is a group of people who are close to each other. There are several types of crowds. A casual crowd is a group of people who are together but not really interacting with each such as what one would find in a shopping mall. In the shopping mall, there are lots of people, but the interaction among the people is often limited to small groups.

A conventional crowd is a group of people who come together for a scheduled event. A common example of a conventional crowd would be people coming together for a religious service. In such an environment, the people have a general-purpose. There is generally more interaction because of the unity that a religious experience can often bring people.


An expressive crowd is a crowd that is together for an emotional purpose. Examples of expressive crowds can include such things as weddings and funerals. Lastly, an acting crowd is a crowd that comes together for a specific purpose or goal, such as a sporting event. Of course, these categories are artificial, and maybe an event may not fit neatly in anyone exclusively, but they do provide a way to organize large groups of people.

When people find themselves in crowds, they often exhibit the group’s norms, which is called collective behavior. For example, a perfectly rational individual will begin to act emotionally in a charismatic religious experience or will become violent within the context of a riot.

Emergent Theory

Several theories have attempted to explain how norms in crowds develop. Emergent norm theory states that people react to the crowd they are in with their own norms, which change as the crowd responds to different stimuli. For example, suppose people are angry and frustrated with the government. In that case, the group may believe that breaking and burning things is acceptable. Outsiders consider this lawbreaking, but for the people within the crowd, this is justifiable behavior in the face of injustice. In other words, the emergent theory attempts to explain that the behavior of a crowd is not irrational and unpredictable but rather a logical response to the current situation.

An example of such behavior can be found in the protesting in the US. People got together and began to break into buildings and steal and destroy property. Things individuals would have never done by themselves were brazenly done in a justified manner due to the perception of injustice.

Value-Added Theory

Value-added theory states that several conditions must be present for collective behavior as found in a crowd can take place.

  1. The first is structural conduciveness which means that people are aware of a problem and begin to gather together.
  2. The second is a structural strain which is people developing frustration over the unsolved problem.
  3. Third is growth and spread of disbelief which means the problem is clearly defined and blame is placed on an individual or group.
  4. The fourth condition is called precipitating factors, which is a trigger event that leads to collective behavior.
  5. The fifth condition is mobilization which involves the emergence of leaders to guide the crowd.
  6. The final condition is social control, and this involves the process of ending the collective behavior.

The protesting that has taken place in the US can also be explained from the perspective of value-added theory. A group of people gather together over a perceived injustice, they begin to get angry, they blame the people in positions of power, some starts to break, burn or steal something, more people follow this example and chaos breaks out, only after a time are the authorities able to end the carnage.

These conditions do not have to happen linearly, but most must be present for collective behavior to begin. For example, leaders can emerge at the beginning rather than the fifth condition.


The theories above try to explain from different viewpoints a phenomenon that most of us have experienced: the loss of self when moving in a crowd. The behavior of such crowds does not have to be negative, but it is negative behavior that is easier to notice compared to positive action. In whatever case, these theories do provide some insight into what can be a blessing or a curse.

graduated cylinders with yellow liquid

Solutes, Solvents, & Molality

A solution in chemistry is a homogenous mixture of two or more substances. The substances that are found in a solution can further be broken down into two types, and these are solute and solvent. The solute is the substance(s) dissolved into a solution. A solvent is a substance into which a solute is dissolved. In other words, solutes generally disappear into solvents. An example would be pouring salt into water. The salt is the solute, and the water is the solvent, and it appears that the salt disappears when added to water.

There is a limit to how much solute can be dissolved into a solvent. The term for this is solubility. Solubility varies from substance to substance but as an example, salt has a solubility of 35.9 grams per 100 grams of water. This means that you can dissolve 35.9 grams of salt in 100 grams of water. Any more salt, and there will be no more dissolving. The technical term when a solute can no longer dissolve in a solution is saturation, and the solution is now saturated.


Solubility is also affected by temperature. For a gas, the solubility increase as the temperature is lowered. However, the solubility of a gas increases with an increase in pressure. For solids, solubility actually increases with temperature.


The concentration measures the amount of substance in a given volume. Concentration is measured by a unit called molarity. Molarity is the proportion of the moles of solute to the liters of solution. For example, suppose I have 150 grams of calcium nitrate, and I dissolve this into 1 liter of water. In that case, I can calculate the molarity as follows.

  1. Determine the amu of calcium nitrate
    1. This is calculated by finding the number of amu, which in this case is 164.10 amu
  2. Convert the amu to moles
    1. This is done by placing the original grams as the numerator of a fraction and the amu as the denominator, which is
    2. 150/164.10 = 0.9141 moles
  3. Use the ratio
    1. Our answer is simple it is moles to solution as shown below
    2. 0.9141 moles / 1 liter = 0.9141 M

Freezing and Boiling

A final point to mention is a term called freezing point depression. This involves mixing solutes and solutions that can change the freezing point of the substance. What is taking place is that when a solute is added to a solution, it now requires more energy to freeze the new substance. This is why salt is thrown on roads during icy days. The salt lowers the temperature at which ice can form, thus making the roads safer. However, there is a limit, and if it becomes cold enough, the salt will no longer have the desired effect.

Another factor involves the boiling point. Solutes increase the temperature that is needed for boiling to occur.


Solutes and solvents are among many terms used in chemistry to define the behavior of substances in a certain context. It is amazing how complex the world is and how there is always so much more that can be learned in various knowledge domains.

cn tower in toronto

Demographic Theories

People have tried to explain population growth and decline for centuries. A major topic of controversy today is how to deal with an ever-increasing population. This post will look at several theories that try to address population growth.

Malthusian Theory

Thomas Malthus is famous for claiming that the Earth would lose its ability to sustain an ever-growing population. In his theory, Malthus claims three factors would limit the growth of humans on Earth. These three factors are war, famine, and disease. Malthus defined these three factors as “positive checks” because they increase mortality.

Malthus also defined “preventive checks” or factors that reduced fertility. These factors were birth control and celibacy. As resources were depleted, Malthus theorized that they would begin to fight wars, generally leading to famine and disease. As the fighting over resources continued, people would limit the children they have or even forgo marriage and having children together.


Malthus’s predictions turned out to be incorrect. There have been technological improvements that he could never have foreseen. These improvements in technology have not only increased food production but have also included treatments for diseases that used to kill.

However, Malthus was correct about preventive checks. In the western world and some parts of Asia (Japan, China, Singapore, and Thailand). Fertility rates have plummeted as people focus on careers and other things rather than raising a family. The general trend of the world is an increase in people, but this may change with time.

Zero Population Growth

A variation on Malthus theory was developed by Paul Ehrlich. Ehrlich states that the environment and not food supply is the factor that determines the planet’s population. As more and more people abuse the environment, it endangers the human population.

Ehrlich’s solution to this problem is zero population growth which, as its name implies, that the number of births equals the number of deaths. No practical way has been found to do this, but this demographic theory is often associated with conspiracy theories of how the elite wants to limit population growth.

Cornucopian Theory

The opposite of Malthus and Ehrlich’s position would be cornucopian theory. This theory posits that human ingenuity can resolve whatever problems humans face. It is possible to cite human ingenuity examples that develop after a crisis, such as vaccinations. However, often by the time the breakthrough is implemented, the catastrophe has already done significant damage has already been done.

Not even the Black Death of the medieval period completely wiped out humanity. The cornucopian theory is always correct until something happens on Earth that wipes out human existence.

Demographic Transition Theory

Demographic transition theory takes a modeling approach to demographic change. Population growth follows four predictable stages in this theory, as explained below.

Stage 1: Births, deaths, and infant mortality are high with low life expectancy.

Stage 2: Birth rates are high while infant mortality and death drops with an increase in life expectancy

Stage 3: Birthrates decline for the first time while death rates continue their decline, life expectancy continues to increase

Stage 4: Birth and death rates keep falling, life expectancy peaks, the population stabilizes, and may start to decline.

These stages are often associated with industrialization. Many countries enter stage 2 when they begin to industrialize. A fully developed country is often found in stage 3, while a post-industrial country could be found in stage 4.


The question that perhaps everyone is wondering is perhaps how much more can the population grow on this planet? It may be impossible to know for sure. Every time it appears the Earth has reached its limit, new resources are discovered, and there is a boost in technology that makes it easier to continue life with whatever resources are available. A question such as this is one that experts will wrestle with for a long time.

computer program language text

More Selecting and Transforming with dplyR

In this post, we are going to learn some more advance ways to work with functions in the dplyr package. Let’s load our libraries


Our dataset is the gapminder dataset which provides information about countries and continents related to gdp, life expectancy, and population. Here is what the data looks like as a refresher.

## Rows: 1,704
## Columns: 6
## $ country   <fct> "Afghanistan", "Afghanistan", "Afghanistan", "Afghanistan", …
## $ continent <fct> Asia, Asia, Asia, Asia, Asia, Asia, Asia, Asia, Asia, Asia, …
## $ year      <int> 1952, 1957, 1962, 1967, 1972, 1977, 1982, 1987, 1992, 1997, …
## $ lifeExp   <dbl> 28.801, 30.332, 31.997, 34.020, 36.088, 38.438, 39.854, 40.8…
## $ pop       <int> 8425333, 9240934, 10267083, 11537966, 13079460, 14880372, 12…
## $ gdpPercap <dbl> 779.4453, 820.8530, 853.1007, 836.1971, 739.9811, 786.1134, …


You can use the colon symbol to select multiple columns at once. Doing this is a great way to save time when selecting variables.

## # A tibble: 1,704 x 3
##    lifeExp      pop gdpPercap
##      <dbl>    <int>     <dbl>
##  1    28.8  8425333      779.
##  2    30.3  9240934      821.
##  3    32.0 10267083      853.
##  4    34.0 11537966      836.
##  5    36.1 13079460      740.
##  6    38.4 14880372      786.
##  7    39.9 12881816      978.
##  8    40.8 13867957      852.
##  9    41.7 16317921      649.
## 10    41.8 22227415      635.
## # … with 1,694 more rows

You can see that by using the colon we were able to select the last three columns.

There are also arguments called “select helpers.” Select helpers help you find columns in really large data sets. For example, let’s say we want columns that contain the string “life” in them. To find this we would use the contain argument as shown below.

## # A tibble: 1,704 x 1
##    lifeExp
##      <dbl>
##  1    28.8
##  2    30.3
##  3    32.0
##  4    34.0
##  5    36.1
##  6    38.4
##  7    39.9
##  8    40.8
##  9    41.7
## 10    41.8
## # … with 1,694 more rows

Only the column that contains the string life is selected. There are other help selectors that you can try on your own such as starts_with, ends_with and more.

To remove a variable from a dataset you simply need to put a minus sign in front of it as shown below.

gapminder %>%
        select(-lifeExp, -gdpPercap)
## # A tibble: 1,704 x 4
##    country     continent  year      pop
##    <fct>       <fct>     <int>    <int>
##  1 Afghanistan Asia       1952  8425333
##  2 Afghanistan Asia       1957  9240934
##  3 Afghanistan Asia       1962 10267083
##  4 Afghanistan Asia       1967 11537966
##  5 Afghanistan Asia       1972 13079460
##  6 Afghanistan Asia       1977 14880372
##  7 Afghanistan Asia       1982 12881816
##  8 Afghanistan Asia       1987 13867957
##  9 Afghanistan Asia       1992 16317921
## 10 Afghanistan Asia       1997 22227415
## # … with 1,694 more rows

In the output above you can see that life expectancy and per capa GDP are missing.


Another function is the rename function which allows you to rename a variable. Below is an example in which the variable “pop” is renamed “population.”

gapminder %>%
        select(country, year, pop) %>%
## # A tibble: 1,704 x 3
##    country      year population
##    <fct>       <int>      <int>
##  1 Afghanistan  1952    8425333
##  2 Afghanistan  1957    9240934
##  3 Afghanistan  1962   10267083
##  4 Afghanistan  1967   11537966
##  5 Afghanistan  1972   13079460
##  6 Afghanistan  1977   14880372
##  7 Afghanistan  1982   12881816
##  8 Afghanistan  1987   13867957
##  9 Afghanistan  1992   16317921
## 10 Afghanistan  1997   22227415
## # … with 1,694 more rows

You can see that the “pop” variable has been renamed. Remember that the new name goes on the left of the equal sign while the old name goes on the right of the equal sign.

There is a shortcut to this and it involves renaming variables inside the select function. In the example below, we rename the pop variable population inside the select function.

gapminder %>%
        select(country, year, population=pop)
## # A tibble: 1,704 x 3
##    country      year population
##    <fct>       <int>      <int>
##  1 Afghanistan  1952    8425333
##  2 Afghanistan  1957    9240934
##  3 Afghanistan  1962   10267083
##  4 Afghanistan  1967   11537966
##  5 Afghanistan  1972   13079460
##  6 Afghanistan  1977   14880372
##  7 Afghanistan  1982   12881816
##  8 Afghanistan  1987   13867957
##  9 Afghanistan  1992   16317921
## 10 Afghanistan  1997   22227415
## # … with 1,694 more rows


The transmute function allows you to select and mutate variables at the same time. For example, let’s say that we want to know total gdp we could find this by multplying the population by gdp per capa. This is done with the transmute function below.

gapminder %>%
        transmute(country, year, total_gdp = pop * gdpPercap)
## # A tibble: 1,704 x 3
##    country      year    total_gdp
##    <fct>       <int>        <dbl>
##  1 Afghanistan  1952  6567086330.
##  2 Afghanistan  1957  7585448670.
##  3 Afghanistan  1962  8758855797.
##  4 Afghanistan  1967  9648014150.
##  5 Afghanistan  1972  9678553274.
##  6 Afghanistan  1977 11697659231.
##  7 Afghanistan  1982 12598563401.
##  8 Afghanistan  1987 11820990309.
##  9 Afghanistan  1992 10595901589.
## 10 Afghanistan  1997 14121995875.
## # … with 1,694 more rows


With these basic tools it is now a little easier to do some data analysis when using R. There is so much more than can be learned but this will have to wait for the future.

shallow focus photo of man holding floor brush ceramic figurine

Data Aggregation with dplyr

In this post, we will learn about data aggregation with the dplyr package. Data aggregation is primarily a tool for summarizing the information you have collected. Let’s start by loading our packages.


dplyr is for the data manipulation while gapminder provides us with the data. We will learn the following functions from the dplyr package

  • count()
  • summarize
  • group_by()
  • top_n()


The count function allows you to count the number of observations in your dataset as shown below.

gapminder %>%
## # A tibble: 1 x 1
##       n
##   <int>
## 1  1704

The output tells us that there are over 1700 rows of data. However, the count function can do much more. For example, we can also count values in a specific column. Below, we calculated how many rows of data we have by continent.

gapminder %>%
## # A tibble: 5 x 2
##   continent     n
##   <fct>     <int>
## 1 Africa      624
## 2 Americas    300
## 3 Asia        396
## 4 Europe      360
## 5 Oceania      24

The output speaks for its self. There are two columns the left is continent and the right is how many times that particular continent appears in the dataset. You can also sort this data by adding the argument called sort as shown below.

gapminder %>%
        count(continent, sort =TRUE)
## # A tibble: 5 x 2
##   continent     n
##   <fct>     <int>
## 1 Africa      624
## 2 Asia        396
## 3 Europe      360
## 4 Americas    300
## 5 Oceania      24

There is another argument we can add and this is called the weight or wt argument. The wt argument adds up the values of the population in our example and we can now see how many respondents there were from each continent. Below is the code an example

gapminder %>% 
        count(continent, wt=pop, sort=TRUE)
## # A tibble: 5 x 2
##   continent           n
##   <fct>           <dbl>
## 1 Asia      30507333901
## 2 Americas   7351438499
## 3 Africa     6187585961
## 4 Europe     6181115304
## 5 Oceania     212992136

You can see that we now know how many people from each continent were in the dataset.


The summarize function takes many rows of data and reduce it to a single output. For example, if we want to know the total number of people in the dataset we could run the code below.

gapminder %>%
## # A tibble: 1 x 1
##     total_pop
##         <dbl>
## 1 50440465801

You can also continue to add more and more things you want to know be separating them with a comma. In the code below, we add to it the average GDP.

gapminder %>%
        summarize(total_pop=sum(pop), average_gdp=mean(gdpPercap))
## # A tibble: 1 x 2
##     total_pop average_gdp
##         <dbl>       <dbl>
## 1 50440465801       7215.


The group by function allows you to aggregate data by groups. For example, if we want to know the total population and the average gdp by continent the code below would help to learn this.

gapminder %>%
        group_by(continent) %>%
        summarize(total_pop=sum(pop), mean_gdp=mean(gdpPercap)) %>%
## # A tibble: 5 x 3
##   continent   total_pop mean_gdp
##   <fct>           <dbl>    <dbl>
## 1 Asia      30507333901    7902.
## 2 Americas   7351438499    7136.
## 3 Africa     6187585961    2194.
## 4 Europe     6181115304   14469.
## 5 Oceania     212992136   18622.

It is also possible to group by more than one column. However, to do this we need to create another categorical variable. We are going to use mutate to create a categorical variable that breaks the data into two parts. Before 1980 and after 1980. Then we will group by country and whether the mean of the gdp was collected before or after 1980. Below is the code

gapminder %>%
        mutate(before_1980=if_else(year < 1980, "yes","no")) %>%
        group_by(country, before_1980) %>%
## # A tibble: 284 x 3
## # Groups:   country [142]
##    country     before_1980 mean_gdp
##    <fct>       <chr>          <dbl>
##  1 Afghanistan no              803.
##  2 Afghanistan yes             803.
##  3 Albania     no             3934.
##  4 Albania     yes            2577.
##  5 Algeria     no             5460.
##  6 Algeria     yes            3392.
##  7 Angola      no             2944.
##  8 Angola      yes            4270.
##  9 Argentina   no             9998.
## 10 Argentina   yes            7913.
## # … with 274 more rows


The top_n function allows you to find the most extreme values when looking at groups. For example, we could find which countries has the highest life expectancy by continent. The answer is below

gapminder %>%
        group_by(continent) %>%
        top_n(1, lifeExp)
## # A tibble: 5 x 6
## # Groups:   continent [5]
##   country   continent  year lifeExp       pop gdpPercap
##   <fct>     <fct>     <int>   <dbl>     <int>     <dbl>
## 1 Australia Oceania    2007    81.2  20434176    34435.
## 2 Canada    Americas   2007    80.7  33390141    36319.
## 3 Iceland   Europe     2007    81.8    301931    36181.
## 4 Japan     Asia       2007    82.6 127467972    31656.
## 5 Reunion   Africa     2007    76.4    798094     7670.

As an example, Japan has the highest life expectancy in Asia. Canada has the highest life expectancy in the Americas. Naturally you are not limited to the top 1. This number can be changed to whatever you want. For example, below we change the number to 3.

gapminder %>%
        group_by(continent) %>%
        top_n(3, lifeExp)
## # A tibble: 15 x 6
## # Groups:   continent [5]
##    country          continent  year lifeExp       pop gdpPercap
##    <fct>            <fct>     <int>   <dbl>     <int>     <dbl>
##  1 Australia        Oceania    2002    80.4  19546792    30688.
##  2 Australia        Oceania    2007    81.2  20434176    34435.
##  3 Canada           Americas   2002    79.8  31902268    33329.
##  4 Canada           Americas   2007    80.7  33390141    36319.
##  5 Costa Rica       Americas   2007    78.8   4133884     9645.
##  6 Hong Kong, China Asia       2007    82.2   6980412    39725.
##  7 Iceland          Europe     2007    81.8    301931    36181.
##  8 Japan            Asia       2002    82   127065841    28605.
##  9 Japan            Asia       2007    82.6 127467972    31656.
## 10 New Zealand      Oceania    2007    80.2   4115771    25185.
## 11 Reunion          Africa     1997    74.8    684810     6072.
## 12 Reunion          Africa     2002    75.7    743981     6316.
## 13 Reunion          Africa     2007    76.4    798094     7670.
## 14 Spain            Europe     2007    80.9  40448191    28821.
## 15 Switzerland      Europe     2007    81.7   7554661    37506.
brown wooden floor

Transform Data with dplyr

In this post, we will be exposed to tools for wrangling and manipulating data in R.

Let’s begin by loading the libraries we will be using. We will use the dplyr package and the gapminder package. dplyr is for manipulating the data and gapminder provides the dataset.


You can look at the data briefly by using a function called “glimpse” as shown below.

## Rows: 1,704
## Columns: 6
## $ country   <fct> "Afghanistan", "Afghanistan", "Afghanistan", "Afghanistan", …
## $ continent <fct> Asia, Asia, Asia, Asia, Asia, Asia, Asia, Asia, Asia, Asia, …
## $ year      <int> 1952, 1957, 1962, 1967, 1972, 1977, 1982, 1987, 1992, 1997, …
## $ lifeExp   <dbl> 28.801, 30.332, 31.997, 34.020, 36.088, 38.438, 39.854, 40.8…
## $ pop       <int> 8425333, 9240934, 10267083, 11537966, 13079460, 14880372, 12…
## $ gdpPercap <dbl> 779.4453, 820.8530, 853.1007, 836.1971, 739.9811, 786.1134, …

You can see that we have six columns or variables and over 1700 rows of data. This data provides information about countries and various demographic statistics.


The select function allows you to grab only the variables you want for analysis. This becomes exceptionally important when you have a large number of variables. In our next example, we will select 4 variables from the gapminder dataset. Below is the code to achieve this.

gapminder %>% 
        select(country,continent, pop, lifeExp)
## # A tibble: 1,704 x 4
##    country     continent      pop lifeExp
##    <fct>       <fct>        <int>   <dbl>
##  1 Afghanistan Asia       8425333    28.8
##  2 Afghanistan Asia       9240934    30.3
##  3 Afghanistan Asia      10267083    32.0
##  4 Afghanistan Asia      11537966    34.0
##  5 Afghanistan Asia      13079460    36.1
##  6 Afghanistan Asia      14880372    38.4
##  7 Afghanistan Asia      12881816    39.9
##  8 Afghanistan Asia      13867957    40.8
##  9 Afghanistan Asia      16317921    41.7
## 10 Afghanistan Asia      22227415    41.8
## # … with 1,694 more rows

The strange symbol %>% is called a “pipe” and allows you to continuously build your code. You can also save this information by assigning a name to an object like any other variable in r.

country_data<-gapminder %>% 
        select(country,continent, pop, lifeExp)


The arrange verb sorts your data based on one or more variables. For example, let’s say we want to know which country has the highest population. The code below provides the answer.

country_data %>%
## # A tibble: 1,704 x 4
##    country               continent   pop lifeExp
##    <fct>                 <fct>     <int>   <dbl>
##  1 Sao Tome and Principe Africa    60011    46.5
##  2 Sao Tome and Principe Africa    61325    48.9
##  3 Djibouti              Africa    63149    34.8
##  4 Sao Tome and Principe Africa    65345    51.9
##  5 Sao Tome and Principe Africa    70787    54.4
##  6 Djibouti              Africa    71851    37.3
##  7 Sao Tome and Principe Africa    76595    56.5
##  8 Sao Tome and Principe Africa    86796    58.6
##  9 Djibouti              Africa    89898    39.7
## 10 Sao Tome and Principe Africa    98593    60.4
## # … with 1,694 more rows

To complete this task we had to use the arrange function and place the name of the variable we want to sort by inside the parentheses. However, this is not exactly what we want. What we have found is the countries with the smallest population. To sort from largest to smallest you must use the desc function as well and this is shown below.

country_data %>%
## # A tibble: 1,704 x 4
##    country continent        pop lifeExp
##    <fct>   <fct>          <int>   <dbl>
##  1 China   Asia      1318683096    73.0
##  2 China   Asia      1280400000    72.0
##  3 China   Asia      1230075000    70.4
##  4 China   Asia      1164970000    68.7
##  5 India   Asia      1110396331    64.7
##  6 China   Asia      1084035000    67.3
##  7 India   Asia      1034172547    62.9
##  8 China   Asia      1000281000    65.5
##  9 India   Asia       959000000    61.8
## 10 China   Asia       943455000    64.0
## # … with 1,694 more rows

Now, this is what we want. China claims several of the top spots. The reason a country is on the list more than once is that the data was collected several different years.


The filter function is used to obtain only specific values that meet the criteria. For example, what if we want to know the population of only India in descending order. Below is the code for how to do this.

country_data %>%
        arrange(desc(pop)) %>%
## # A tibble: 12 x 4
##    country continent        pop lifeExp
##    <fct>   <fct>          <int>   <dbl>
##  1 India   Asia      1110396331    64.7
##  2 India   Asia      1034172547    62.9
##  3 India   Asia       959000000    61.8
##  4 India   Asia       872000000    60.2
##  5 India   Asia       788000000    58.6
##  6 India   Asia       708000000    56.6
##  7 India   Asia       634000000    54.2
##  8 India   Asia       567000000    50.7
##  9 India   Asia       506000000    47.2
## 10 India   Asia       454000000    43.6
## 11 India   Asia       409000000    40.2
## 12 India   Asia       372000000    37.4

Now we have only data that relates to India. All we did was include one more pipe and the filter function. We had to tell R which country by placing the information above in the parentheses.

filter is not limited to text searches. You can also search based on numerical values. For example, what if we only want countries with a life expectancy of 81 or higher

country_data %>%
        arrange(desc(pop)) %>%
        filter(lifeExp >= 81)
## # A tibble: 7 x 4
##   country          continent       pop lifeExp
##   <fct>            <fct>         <int>   <dbl>
## 1 Japan            Asia      127467972    82.6
## 2 Japan            Asia      127065841    82  
## 3 Australia        Oceania    20434176    81.2
## 4 Switzerland      Europe      7554661    81.7
## 5 Hong Kong, China Asia        6980412    82.2
## 6 Hong Kong, China Asia        6762476    81.5
## 7 Iceland          Europe       301931    81.8

You can see the results for yourself. It is also possible to combine multiply conditions for whatever functions are involved. For example, if I want to arrange my data by population and country while also filtering it by a population greater than 100,000,000,000 and with a life expectancy of less than 45. This is shown below

country_data %>%
        arrange(desc(pop, country)) %>%
        filter(pop>100000000, lifeExp<45)
## # A tibble: 5 x 4
##   country continent       pop lifeExp
##   <fct>   <fct>         <int>   <dbl>
## 1 China   Asia      665770000    44.5
## 2 China   Asia      556263527    44  
## 3 India   Asia      454000000    43.6
## 4 India   Asia      409000000    40.2
## 5 India   Asia      372000000    37.4


The mutate function is for manipulating variables and creating new ones. For example, the gdpPercap variable is highly skewed. We can create a variable of gdpercap that is the log of this variable. Using the log will help the data to assume the characteristics of a normal distribution. Below is the code for this.

gapminder %>% 
        select(country,continent, pop, gdpPercap) %>%
## # A tibble: 1,704 x 5
##    country     continent      pop gdpPercap log_gdp
##    <fct>       <fct>        <int>     <dbl>   <dbl>
##  1 Afghanistan Asia       8425333      779.    6.66
##  2 Afghanistan Asia       9240934      821.    6.71
##  3 Afghanistan Asia      10267083      853.    6.75
##  4 Afghanistan Asia      11537966      836.    6.73
##  5 Afghanistan Asia      13079460      740.    6.61
##  6 Afghanistan Asia      14880372      786.    6.67
##  7 Afghanistan Asia      12881816      978.    6.89
##  8 Afghanistan Asia      13867957      852.    6.75
##  9 Afghanistan Asia      16317921      649.    6.48
## 10 Afghanistan Asia      22227415      635.    6.45
## # … with 1,694 more rows

In the code above we had to select our variables again and then we create the new variable “log_gdp”. This new variable appears all the way to the right in the dataset. Naturally, we can extend our code by using our new variable in other functions as shown below.


This post was longer than normal but several practical things were learned. You now know some basic techniques for wrangling data using the dplyr package in R.

tax documents on the table

Types of Government

In this post, we will look at different types of government.


Anarchy is defined as an absence of government. In practice, anarchies are for the short-term because eventually, from the chaos of a lack of government comes some sort of structure, whether it’s a dictator or king or some other form of government. There is always some ambitious, strong man looking to fill a power vacuum in a place of chaos.

Often after revolutions, there is a state of anarchy. The French Revolution was one example of chaos being the order until Robespierre came to power. The Russian Revolution of the early 20th century is yet another example. In both examples, there was a short period of chaos followed by a strong totalitarian reaction.


Monarchy is a government in which one person is in charge until they die or give up power. Often, the role of a monarch is hereditary but necessarily always. There is also a common claim of divine or supernatural approval. This was often the case in Europe, where monarchs frequently courted papal approval of their rule.


There are generally two types of monarchs. Absolute monarchs have complete power to do as they see fit. This still of government is rare because people generally do not appreciate being under the whim of anybody to such a degree. Many kings from medieval Europe were absolute monarchs.

The challenge of being an absolute monarch is not when things are going well. When there is peace and everybody is happy, the monarch gets all the credit because they are absolutely in charge. However, when things fall apart, the monarch also gets all the blame because they are absolutely in charge.

In addition, people, whether a monarch or not, can be capricious and unpredictable. If the monarch shows inconsistencies or weaknesses, people may try to remove them to protect themselves and their gains within the country. For example, Henry VI of England was removed several times because of the weakness of his character and mental instability. In other words, having this level of power is not as great as it seems.

Another form of monarchy is a constitutional monarchy. In this form of government, the monarch’s power is limited by the constitution. You would think that having a constitution limiting a monarch’s power would irritate them, and it has in some instances. However, the benefit of a constitution is that giving up some power can help a monarch stay in the position of privilege that they have because everything that goes wrong is not completely their fault. Many monarchies today are constitutional monarchies such as Great Britain, and often these monarchs are above politics, which makes it difficult to complain about them as they stay out of governmental decision-making for the most part.

However, even giving up power can lead to a monarchy being removed. Louis XVI of France and Czar Nicholas II of Russia both made reforms before being overthrown. On the other hand, the British monarchy has been stable for decades. therefore, there is no single strategy that can protect a government


Oligarch is government by a small elite. OFten these elites are rather sneaky and work behind the scenes. One reason for this is they do not want to be held responsible if something goes wrong. AS such, it is hard to tell when a country’s government is an oligarchy.

Members of an oligarchy tend to excel at one aspect of society or another. For example, they may be wealthy businessmen, military strongmen, or clergy members. Due to its mysterious nature, it is difficult for others to rise to membership in this exclusive and secretive club.


Dictatorship is power held by a single person. A dictator is different from a monarch because their power is not hereditary, and dictators often arise from a revolution to overthrow another government, so they avoid the word king even if they have the same powers. In other words, they are a king, but that word is not socially acceptable.

Dictators are normally charismatic leaders who rise to power on the back of the people. Once in place, they are looking to find ways to stay in power and are often worst than the people they overthrew. Pol pot of Cambodia killed millions of his own people, Hitler of Germany killed millions of Jews, Idi Amin ran his country into the ground. Each of these totalitarian dictators sought to control as much of the lives of the people under them as they could.


The most popular form of government is democracy. Democracy involves giving all citizens an equal voice in the government. These citizens then elect leaders to represent their interest in the government. In practice, this sounds great, but sometimes it can be frustrating.

People looking for a positi0n of power know that perception is more important than truth. As a result, it is common for politicians in democracies to try and find ways to manipulate their constituencies. Outlandish claims are made in the media; overt and covert lying occurs. All this is done in the name of democracy.

However, this only happens because the citizens often neglect to educate themselves about what is going on. Therefore, people cast votes for controversial topics they have not thoroughly investigated. The point here is not to criticize any position but to wonder if people have really thought about the position they support instead of the one they do not support.


Every form of government has its strengths and weaknesses. Therefore, there is no real benefit in raising one form over another. This is because governments are built upon people. If the people or not good, it doesn’t matter how good the government is.

crop laboratory technician examining interaction of chemicals in practical test modern lab

Moles in Chemistry


In this post we will have a brief introduction to moles in chemistry. This fundamental concepts is a part of Stoichiometry which is another important aspect of chemistry.

In chemistry an atomic mass unit (amu) is the mass of a proton or neutron in an atom. This number has been calculated to be.

1.66 X 10-24 g

Knowing this number we can calculate how much a single atom weighs. For example, if we want to calculate the weight in grams of oxygen, we know know that helium has an atomic weight of 4. This means that

The amu cancel each other. This number becomes important because if we take the amu of 1 atom of helium (or any element) in grams and divide by the mass of one atom in grams we get the following number no mattter which element we use.

This number above is how many atoms in 4 grams of helium. This number is called Avogadro’s constant but it also referred to as a mole. Knowing this value, it is possible to calculate the mass of single mole of a molecule. For example, if we want to know the mass of a single mole of glucose we would calculate the amu as shown below.

The mass is as follows

Element# of AtomsamuTotal
Carbon 612.0172.06
Total = 180.18 amu

This output tell us that one mole of glucose is 180.18 grams. We can use this information in other ways such as determining how many moles are in a certain number of grams of a substance. If we have 15 grams of magnesium chloride MgCl2. We can calculate how many moles are in this substance as shown below

Step 1 Calculate the amu of the molecule

Mass of MgCl2 = 24.31 amu + 2 * (35.45 amu) = 95.21 amu

Step 2 Determine Conversion Reltionship

1 Mole of MgCl2 = 95.21 grams MgCl2

Step 3 Convert from grams to Moles

We now know that there are about 0.158 moles in 15 grams of magnesium chloride. But we could take this a step further by determining how many molecules are in 15 grams of magnesium chloride as shown below

0.158 * 6.02 * 1023 = 9.84 * 1022

The first number is the number of moles in 15 grams of magnesium chloride and and the second number is one mole.

There are many variations on the calculations that were done here but this is enough to serve as an introduction.

gray concrete building

Authority Types

Various countries and governments have developed different forms of authority to maintain power and stability. This post will look at three common forms of authority found throughout the world.

Traditional Authority

As its name implies, traditional authority relies on tradition to maintain its power. Examples of traditional authority usually include monarchies such as those found in Europe at one time. People support the leader because this support has been given for a long time.

The actual leader often does not have power beyond people’s respect for them. The leader can often have a figurehead-type status while others exercise overt power. For example, it is common in many countries with traditional authority to have the monarch avoid politics and serve a ceremonial role.


A variation of traditional authority is called patrimonialism. Patrimonialism is a strong-man character who has a strong administration and military support. Some may see this as a form of military-backed dictatorship. The people under the supreme leader only have their privileges through their obedience and loyalty to the supreme leader.

Charismatic Authority

Charismatic authority generally involves an individual who gains power through the strength of their personality more than on any other single reason. Often this will happen during a time of crisis in which people are looking for help and or protection. One example of this would be Napolean Bonaparte, who rose to power in France after the French Revolution.

However, charismatic leaders often do not last long. There may be several reasons for this. The crisis may worsen, the leader’s shortcomings become more apparent over time, or someone even more popular arises to threaten the leader. These are not the only reasons, but they play a part in the demise of charismatic leaders. For example, Napolean’s shortcomings as a general were the primary reason for his downfall. Though one of the greatest generals ever, he was not perfect, and often leaders are expected to never fail.

Rational-Legal Authority

Rational-legal authority emphasizes laws, rules, regulations, and the office of authority rather than the individual person. Countries with constitutions are often inspired by rational-legal authority. For example, the United States is a strong example of rational-legal authority. They have a constitution and a new president every 4 to 8 years. The power lies within the office, and there is no idea of a single absolute authority but rather an emphasis on “we the people.”

With the focus on laws, all the lawmakers have to do is make illegal things legal and legal things illegal, and there will not be as much push-back from the people because they believe in the rule of law. Examples of this from the United States can include any controversial topic such as sexuality, taxes, reproductive rights, etc. Each of these examples involves actions that were legal, then illegal, or vice versa. In summary, whoever defines the laws appears to have the power in a rational-legal framework.


Countries require leadership, and leaders can have various forms of authority. The examples provided here are just some of the commonly seen options. Naturally, it would be an oversimplification to think that leaders and countries could not mix the examples above. For example, Cesar was charismatic and spent a lot of time passing various laws. The real point here is to be aware of these various styles.

scientist in laboratory

Chemical Equations

Chemical reactions involves the rearrangement of atoms to beget new chemicals. Often these reactions are captured succinctly in what is called a chemical equation. For example, if we want to show how carbon reacts with oxygen to make carbon dioxide we would write the follow chemical equation.


The plus sign means “reacts with” and the arrow means “to make”. Therefore, we can write this chemical equation in English by saying

Carbon reacts with oxygen to make carbon dioxide

Chemical equations need to balance. If you look at the example above, there are the same number of atoms for each element on each side. The example above is rather simple, however, sometimes it is a little trickeier to tell if an chemical equation is balanced.

In the reaction above we have to look carefully to see if the chemical equation is balanced. Starting on the left we have 1 carbon and 4 hydrogens. Next, there is a 2 which means that we multipl everything by 2 that is next to it. In other words, we do not have 2 oxygen atoms but rather 4 (2 x 2 = 4). After the arrow, we have 1 carbon and 2 oxygen atoms and after the plus sign we have 4 hydrogen atoms (2 x 2 = 4) and 2 oxygen (2 x 1 = 2). If we line everything up you can see that this equation is balanced.

Left SideRight Side
C 1 x 1 = 1 1 x 1 = 1
H 4 x 1 = 4 2 x 2 = 4
O 2 x 2 = 4 2 + (2 x 1) = 4

There are times when you need to balance a chemical equation. This can get really challlenging but we will do a simple example below.

The chemical equation above is not balance as you can see below

Left SideRight Side
H 1 x 2 = 2 1 x 1 = 1
Cl 1 x 2 = 2 1 x 1 = 1

The table above is one process in balancing an equation. We need both sides to equal each other and the simplest way to do this is to multiple the right side by two and we get the following table.

Left SideRight Side
H 1 x 2 = 2 2 x 1 = 2
Cl 1 x 2 = 2 2 x 1 = 2

Below is what our balanced chemical equation looks like.

As mentioned previous, placing the 2 in front of the molecule means multiply everything by 2. Such an example like this is really simple but provides a basic understanding of this process.


Chemical equations can be really fun to deal with once you understand how this works. In the beginning, it can be truly frustrating but perseverance will make the difference.

water drop

Physical & Chemical Changes in Chemistry

In this post, we will focus most of our attention on physical changes in chemistry with a brief look at chemical changes.


Physical change is a change to a substance that does not alter the chemical composition. For example, boiling water is a physical change. Generally, physical changes are easy to reverse, such as when steam is cooled to become liquid water.


Chemical change is a change that alters the chemical composition of a substance. An example would be various forms of cooking, such as frying potatoes to make french fries. Unlike physical changes, chemical changes are much harder to reverse. Just as it is impossible to turn french fries back into raw potatoes.

A specific type of physical change is called phase change. There are several different types of phase changes, as listed below.

  • melting
  • vaporizing
  • freezing
  • condensing
  • sublimation

Many of these are obvious, but they will be explained for clarity. Melting involves a substance moving from a solid to a liquid. Vaporizing takes place as a substance moves from liquid to gas. A substance that moves from a gas to a liquid is called condensing. Freezing is the process of a liquid becoming a solid. Sublimation is a solid moving straight to a gas.

The first four-phase changes are commonly seen in water. Ice melts to become liquid water, water boils/evaporates (vaporizes) to become steam. Water freezes to become ice; in the early morning, it is common in many places to see water on plants due to condensation. Sublimation is tricker to see on a day-to-day basis. The most common example involves carbon dioxide, aka dry ice, which is a favorite tool for Halloween. Other substances that sublimate include arsenic, iodine, and naphthalene (used for mothballs).

Phase changes are related to the kinetic theory of matter, which we will now turn our attention to.

Kinetic Theory of Matter

The kinetic theory of matter states that Molceults have space between them and are in constant random motion. We can say that the more heat, the faster the motion because more energy is present. For solid, the molecules can vibrate, but that is essentially it. All solids are vibrating, such as tables, chairs, desks, etc. However, the vibration is random, and thus the vibrations cancel each other.

Liquids can clearly move about, and this is why they cannot keep a single shape but is formed by their circumstances. This also applies to gasses. The real difference between the various phases is the space around molecules and the speed at which they are moving. When energy is added, molecules move apart and move faster. This explains a solid becoming a liquid and a liquid a gas.

Water breaks many rules in relation to the Kinetic theory of matter. When water freezes, instead of the molecules getting closer together, they actually push out and are thus less dense than water. This is one reason why ice floats and why you would find frozen ice on the top of a lake. The ice floats to the top, and by being on top, it insulates the animals inside the lake from the cold above.


Physical changes play a major role in all of our lives. The phase changes of water are used for various purposes in everyday life. It is beneficial to understand these concepts as they are so commonly encountered.

family walking on path

Family Stages and School

Family is a term that is used but not necessarily agreed upon. In this post, we will look at views on family and the stages of family. Understanding the stages of family life will help teachers try to help parents.

Defining Marriage & Family

Family often begins with marriage, and defining marriage has been controversial for years now. Traditional marriage in the West generally involves people of the opposite sex who have some sort of a public ceremony. A family that is formed through marriage is called a family of procreation. Marriage can also be more complex. Some support having multiple partners, which is called polygamy or polyandry (multiple wives or husbands).


Despite being around since the beginning of time, people do not agree on what family is. One definition sees family as the blood relations a person has. However, many people do not grow up with blood relatives and thus may see adoptive parents or friends as family. Sociologists try to deal with this by speaking about a family of orientation which is the family in which one is born or raised.

Stages of a Family

There are seven common stages that a family goes through. Stage 1 is the marriage family and is usually childless. The couple is essentially newlyweds and has not had any children yet. Stage 2 is the procreation stage and involves having newborns to toddlers. This stage is a huge transition as the responsibility of parenthood has descended on a young couple.

Stage 3 is the preschooler family and goes from toddlers until 6 years of age. Generally, kids are not yet in school and spend most of their time at home or daycare. Stage 4 is the school-age family and goes from age 6-13. At this stage, children are in school, are more independent, and the parents can focus more on their jobs and career.

Stage 5 is the teenage family and goes from age 13-20. The children are adults who lack experience and need to be guided by their parents. As they push the limits, parents can begin to worry greatly about the young adults in their house. Stage 6 is the launching family and involves young adults leaving home. This can be extremely emotional as children leave home and parents have to deal with the separation from adult children. Lastly, stage 7 is the empty nest family, which is a family in which the children have grown up and moved away. Now that their children are adults, parents are left with a huge transition as they try to find other ways to invest their time.

Families and Education

The stages are useful but not always accurate. It is common to have children in various age categories simultaneously. For example, have a toddler and a teenager in the same house. Is such a family a preschooler or teenager family? It may not be clear, but perhaps the stage is tied to the individual child instead of the entire family.

For teachers, the stages of the family often involve them dealing with families from at least the stages 2-6. Parents will be in different stages with different children, which may impact whatever children the teacher is dealing with. For example, suppose a 10 year has an older sibling who is leaving for college. In that case, this could cause behavioral problems as the students struggle to accept this separation. In addition, if a 7-year-old now has a baby brother, this could also lead to problems as they adjust to less attention from their parents. These two examples don’t even consider the fracturing of a family through a divorce or the commonly found experience of single parents.


Teachers and families have to work together to help children. This is an idea that seems to have been forgotten over the years. With the challenges of moving through each stage of family life, teachers need to be aware and understand as they try to support the home.

clear glass apparatus on white table

Dalton’s Atomic Theory

John Dalton was an 18th-century scientist who made several significant contributions to his field. One of his most prominent works was his Atomic theory. Dalton’s Atomic theory is a major concept in the study of chemistry. In this post, we will look at this theory and share some of the misunderstandings that Dalton had at his time.

Atomic Theory

Dalton’s Atomic Theory has four propositions to it.

  1. All matter is made of atoms that cannot be divided or destroyed
  2. All atoms of an element are identical in all their properties
  3. Compounds are formed by a combo of two or more different kinds of atoms
  4. A chemical reaction is a rearrangement of the atoms in the substance

There is little to explain here. Part one states that atoms cannot be divided or destroyed. In other words, the atom is the fundamental unit of the universe. Part 2 states that all atoms are identical in their properties, which implies that every atom of an element has the same number of protons, neutrons, and electrons.


The third component states that compounds are formed by two or more different atoms. For example, one compound would be H2O which is water. Since there are two elements in H2O, it meets the definition of a compound. We also call such a compound a molecule. Component four states that a chemical reaction is a rearrangement of the atoms in the substance. An example of this would be digestion which involves significant chemical changes to the food.

Problems with Dalton’s Theory

Despite the brilliance of Dalton’s theory, several problems have arisen as researchers have continued to explore the mysteries of chemistry. For example, the first proposition of Dalton states that atoms cannot be divided or destroyed. Both of these claims are false. We now know that atoms are made of protons, neutrons, and electrons. In addition, atoms can be destroyed, which happens at any nuclear power plant through fission. Nuclear fission involves neutrons hitting atoms which causes them to split.

Dalton was also incorrect regarding his second proposition about the same atoms having the same properties. With the discovery of the neutron, it became clear that atoms may have the same chemical properties but not the same physical properties. The reason for this is that having a different number of neutrons affects the atom’s weight. When atoms of the same element have different neutrons, we call these isotopes.


Dalton’s work in the study of atoms is something to be praised. It is understandable that perhaps he got some things wrong. The purpose of science is to grow and improve over time, and this means that sometimes great scientists are right, but they must also be wrong.

Principal Component Analysis with Python VIDEO

Principal component analysis is a tool for reducing the number of variables in a dataset without losing too much information. This is a great way to summarize information or to simplify things for a more complex analysis. The video provides a simple example of how to do this.


crowd of people black and white photo

Terms Related to Social Stratification

Social stratification is the ranking of individuals using various factors such as wealth, income, education, etc. While I was preparing this post, I could not find any evidence of a classless society. In fact, some of the sources claimed that no such society as a classless one has existed. This implies that stratification is a natural part of human existence whether people like it or not.


What causes this is not always apparent. For some reason, people often like to exalt themselves and be above others. There is a tendency in some people to desire control and dominance. Sometimes people are chosen to be the leader or in a higher social position by others in the society. Leaders often fall into this category and can include politicians, clergy, and kings. Others gain a higher status through hard work, and people admire and appreciate this. For example, Napolean was able to rise through the ranks of the military due to his brilliant leadership and eventually became emperor.

There are also examples in history of people gaining power not just for selfish reasons but for personal protection from one’s enemies. Ceaser was truly driven by a desire to rule, but he also had enemies who were waiting for him to lose power so they could attack him through various legal means. Therefore, Ceasar looked for ways to maintain the leadership of provinces and be consul of Rome to maintain his legal immunity. Even when taking power, he generally would grant amnesty to enemies to avoid stirring up more enmity. However, as he became more powerful, he just became even scarier to the other elites who simply murdered him one day.

The best it appears people can hope for without being cynical is a world in which the elite and upper class refrain from abusing and mistreating the people below. There is also little historical evidence of elite restraint as there is almost no evidence of a classless society. Different people put in different amounts of work, and some find different ways to cheat their way, and thus there will always be differences between the ranking of people.

Caste System

There are several terms related to social stratification. The caste system is one. With the caste system, people are born into a certain level of society, and they are stuck there forever. There is no social mobility. Examples of this can be found in India, Feudal Japan, and Medieval Europe.

Marriages between caste are frowned upon or even illegal. For example, a friend from India told me how they got married. She was from the warrior caste, while her future husband was from the priestly caste. Since they were Christian, they did not think they were bound by the tradition of the caste system and for married. Being it was a Christian community, everyone was okay with it; however, several people were still worried that something “bad” might happen to the newlywed couple because of the country’s cultural background. India abolished the caste system, but its roots are still strong in some situations.

Class System and Meritocracy

The class system is a more flexible style of social stratification in which people belong to one of many different classes based on their wealth, education, etc. Examples of classes can include upper, middle, and lower classes. Unlike the caste system, which discourages marriage, the class system does not generally condemn marriages of people from different classes.

Meritocracy is social stratification based on effort. At best, meritocracy has been partially implemented in many places. No matter how hard humans try, people are just good at findings ways of getting through the system without equal work. This leads to frustration by those who “play by the rules.” Another problem is that some people will achieve a great deal in one area, but this area is not valued as important by society.

Highly educated people often have amazing expertise in minute details of life that are not generally valued by the larger society in terms of prestige and financial remuneration. This can lead to frustration and desires to challenge the social stratification. At times, some of the strongest proponents of a classless society are people who do not have the status they believe they deserve.


Stratification is always going to be a problem. This is because people will always find ways to move up the social hierarchy through honest hard work and abuse the system for personal gain. Unfortunately, people may lose status due to mistakes or injustice, and those who are higher up may mistreat those who are lower, which is not fair or right again.

Data Visualization with Altair VIDEO

Python has a great library called that Altair that makes it really easy to make various data visualizations. The primary strength of this particular library is how easy it is to use and to also create interactive plots. The video below provides an introduction to using this innovative tool.



CASE WHEN statements are similar to if-then statements in other programming languages. These statements are used to have SQL execute certain behaviors as determine by the criteria that is set in the statement. In the video below, we will go through several examples of how to use CASE WHEN statements in SQL.


Making Groupwork Work

For many students, working in groups can be a serious challenge. Different people have different temperaments regarding communication, work style, and ability to cooperate. It can be difficult to have success when a student is compelled to work in groups.This post will provide three tips for improving the group work experience of students.

Example Projects

Perhaps one of the best ways to get students going when it comes to completing group work is to show them how other students have dealt with this problem/project in the past through showing examples. When students see examples, it helps them process what is possible and what the expectations are for earning a certain grade.


Often the struggle with groups is trying to determine what to do. This is usually the first impediment to the project. Examples of prior work help a group determine which ideas they have are reasonable as they try to pivot off what the teacher has shown them as potential projects.

Checkpoints & Communication

It is often common for teachers to assign the entire project and only collect or comment on the final submitted project. This is a high-stakes approach that can lead to frustration when cooperation is not happening for many people working in groups. This is one reason why many students want to work alone to control everything.

A better approach is to break the project into pieces and provide feedback and support at each checkpoint. Students are provided with an opportunity to check in with the teacher as a group and feedback before the final submission. In addition, this also allows the teacher to communicate with students about expectations and address any problems that may have arisen proactively. Sometimes, students will just suffer in their group until the last minute. However, the teacher can guide the group towards success rather than failure and frustration by breaking the project into smaller pieces with frequent feedback and communication. 

Separate Grading

Freeloading is a common problem in group projects. There are always students who believe in doing minimum and even nothing when working in a group. This practice may be one of the main reasons students dislike group work. The project often becomes a solo project in which the smart student does everything. One way to deal with this problem is through separate grading.

Instead of giving one grade that is exactly the same for all members, a teacher can give separate grades based on the contribution of individual members. Often, two grades are provided, one for the entire group project and a second grade for the individual contribution. Doing this makes group members individually accountable for their part.

HOw the individual grade is calculated can vary. Some teachers lick to have peer evaluations as part of the final grade in which members of a group evaluate each other’s contributions. This works in cultures that accept conflict more. However, in more collectivist settings, students will often mark everyone high to maintain harmony even if there is evidence that many did not contribute.

Another approach involves the teacher marking the specific contribution of the individual members. However, there must be some sort of rubric for this to work. Essentially, every group must follow the same process for the teacher to mark them similarly. In other words, the group project becomes a collection of individual assignments that are lumped together as a project. Doing this would limit the flexibility of each group with the tradeoff of higher accountability.


Groupwork has a place in the classroom. It allows students to develop communication skills, compromise, and work in less-than-ideal situations. However, the teachers must find ways to help students succeed in the context of group work so that everyone can perform.

photo of clear glass measuring cup lot

Terms Related to Matter

Matter is the physical stuff that everything around us is generally made of. Trees, birds, water, etc., are all examples of matter. Since almost everything is considered matter, scientists have naturally found ways to classify matter to better understand it.

Types of Matter

One way matter is classified whether it is a pure substance or a mixture. A pure substance is a substance that has the same properties throughout out it. An example of a pure substance would be salt or sugar. Both of the substances are only made of salt or sugar, and the properties of these two substances are the same if you have one or the other in a sample.


On the other hand, a mixture is a combination of two or more substances. For example, if you have salt and pepper inside the same shaker, this is a mixture. This is because separating the salt and the pepper from each other is possible. Separating pure substances is generally not possible physically. However, pure substances can further be broken down into elements and compounds.

Elements are fundamental substances that cannot be broken down into simpler substances. The periodic table contains all known elements. Examples include oxygen, sodium, carbon, etc. Compounds are pure substances that are made of two or more elements. Compound examples include salt, sugar, carbon dioxide, etc.

More on Mixtures

Returning to mixtures, there are two types of mixtures: homogenous and heterogeneous. Homogenous mixtures have the same composition throughout the sample. Examples include milk and sugar water. In both of these examples, the substances that make up the mixture are evenly spread throughout the sample.

Heterogeneous mixtures have different compositions in parts of the sample. A classic example of this is salad dressing. When salad dressing is allowed to sit, it separates clearly into the various substances/homogenous mixture that it is made up of. This is why salad dressing must be shaken before it is enjoyed.

Law of mass conservation

Antoine Lauren de Lavoisier developed the law of mass conservation, which states that in any chemical or physical process, the total mass of everything involved must remain the same. This means that if you start with 5 kg of wood and burn it, there will still be 5kg of matter in a different form. You might see a pile of ashes that weighs less but what happens is that some of the matter was converted to gases and smoke in the burning process. Essentially, matter can be created or destroyed but can only be converted or broken down.


No pun intended, but matter matters. For students, it is important to develop an understanding of concepts related to chemistry. Doing so may help at least some of them prepare for whatever occupation they may have in the future.

close up photo of a diagram with drawing compass

Scientific Measurement

When it comes to measurement in research. There are some rules and concepts a student needs to be aware of that are not difficult to master but can be tricky. Measurement can be conducted at different levels. The two main levels are categorical and continuous.

Categorical measurement involves counting discrete values. An example of something measured at the categorical level is the cellphone brand. A cellphone can be Apple or Samsung, but it cannot be both. In other words, there is no phone out there that is half Samsung and half Apple. Being an Apple or Samsung phone is mutually exclusive, and no phone can have both qualities simultaneously. Therefore, categorical measurement deals with whole numbers, and generally, there are no additional rules to keep in mind.

However, with continuous measurement, things become more complicated. Continuous measurement involves an infinite number of potential values. For example, distance and weight can be measured continuously. A distance can be 1 km or 1.24 km, or 1.234. It all depends on the precision of the measurement tool. The point to remember now is that categorical measurement often has limit values that can be used while continuous has an almost limitless set of values that can be used.


Since the continuous measurement is so limitless, there are several additional concepts that a student needs to mastery. One, the units involved must always be included. At least one reason for this is that it is common to convert units from one to the other. However, with categorical data, you generally will not convert phone units to some other unit.

A second concern is to be aware of the precision and accuracy of your measurement. Precision has to do with how fine the measurement is. For example, you can measure something the to the tenth, the hundredth, the thousandth, etc. As you add decimals, you are improving the precision. Accuracy is how correct the measurement is. If a person’s weight is 80kg, but your measurement is 63.456789kg, this is an example of high precision with low accuracy.

Another important concept when dealing with continuous measurement is understanding how many significant figures are involved. The ideas of significant figures are explored below.

Significant figures

Significant figures are digit that contributes to the precision of a measurement. This term is not related to significance as defined in statistics related to hypothesis testing.

An example of significant figures is as follows. If you have a scale that measures to the thousandth of a kg, you must report measurements to the thousandths of a kg. For example, 2 kg is not how you would report this based on the precision of your tool. Rather, you would report 2.000kg. This implies that the weight is somewhere between 1.995 and 2.004 kg. This is really important if you are conducting measurements in the scientific domain.

There are also several rules in regards to determining the number of significant figures, and they are explained below

  1. All non zeros are significant
    1. Example-123 are all non-zeros and thus are all significant in this case
  2. A zero is significant if it is between two significant numbers
    1. example-1023. The 0 is in between 1 and 2 and is thus significant
  3. Zeros are significant if it is at the end of a number and to the right of the decimal
    1. Example 2.00: Here, the 0’s are to the right of the decimal, which makes them significant

Each of the examples discussed so far has been individual examples. However, what happens when numbers are added or multiplied. The next section covers this in detail

Significant Figures in Math


When adding and subtracting measurements, you must report the measurement results with the less precise measurement.

  • example
  • 115kg – 16.234kg = 98.766kg, but the least precise measurement is 115kg, so we round the answer to 99 kg. This is because our precision is limited to one’s place.


When multiply or dividing measurements report results with the same number of significant figures as the measurement with the fewest significant figures

  • example 1
  • 16.423 m / 101 m = 0.16260396 m

This number is too long. The second number, 101, has three significant figures, so our answer will have 3 significant figures, 0.163m. The zero to the left of the decimal is insignificant and does not count in the total.

  • example 2
  • 8.0 cm * 3.208 = 25.664 cm2 or 26cm2 the first number has two significant digits, so the answer can only have two significant figures, which leads to an answer of 26cm2.

Converting Units

Finally, there are rules for converting units as well. To convert units, you must know the relationship that the two units have. For example, there are 2.54 cms per inch. Often this information is provided for you, and simply apply it. Once the relationship between units is known, it is common to use the factor label method for conversion. Below is an example.

To solve this problem, it is simply a matter of canceling the numerator of one fraction and the denominator of another fraction because, in this example, they are the same. This is shown below.

Essentially there was no calculation involved. Understanding shortcuts like this saves a tremendous amount of time. What is really important is that this idea applies to units as well. Below is an example.

In the example above, we are converting inches to meters. We know that there is 2.54cm in 1 inch. We set up our fractions as shown above. The inches cancel because they are in the numerator of one fraction and the denominator of another. The only unit left is cm. We multiply across and get our answer. Since 24.0cm has the fewest number of significant figures are the answer will also have three significant figures, and that is why its 61.0cm

Scientiifc Nottation

There can be problems with following the rules of significant figures. For example, if you want to convert meters to centimeters. There can be a problem.

The answer should only have three significant figures, but our answer has one significant figure. We need to move two zeros to the right of the decimal.

This is done with scientific notation as shown vbelow.

This simple trick allows us to keep the number of signifcant figures that we need without hhanging the value of then umber.

Below is an example of how to do this with a really small number that is a decimal.


This post explains some of the rules involved with numbers in scientific measurement. These rules are critical in terms of meeting expectations for communicating quantitative results.

a pen over a paper with a bar chart

Creating Bar Graphs in LaTex

LaTex is a highly flexible typesetting program that seems to be capable of almost anything. Here, we will learn how to make bar graphs use this language.

Simple Bar Graph

Below is the code and the bar graph for simple bar graph.

Here is what is happening in the code

  1. Line 1-2 we declare our document class and load the only package we need which is pgfplots.
  2. Line 3-5 we declare the various environments needed
  3. Line 6-12 are all the details we need to create the axis on which our data will be.
  4. Line 7 gives the title of the graph
  5. Line 8 makes the graph a bar graph
  6. Line 9 places the numbers above the bars in the bar graph to make it easier to read. This line also controls how thick the bars are
  7. Line 10 sets the names for the x-axis
  8. Line 11 makes sure each bar only has one name
  9. Line 13 creates the plot. Inside the curly braces you have in parentheses the name of the group and the frquency.
  10. The rest of the code closes the enviornments

Multiple Bars

In the code below we will add several bar graphs to one plot and also add a legend. The code is mostly the same below.

The new information is in lines 12-15. These lines contain the information for the legend. The at argument tells where to put the legend at, anchor tells LaTex how to hold it and the column sep determines the width of the column.


The next important information is in lines 19-23. Here is were we add additional bars. The arguments in side still tell LaTex what color the numbers above the bar should be as well as the color of the bar graphs. The coordinates is were you can hand code the values for the x axis.

The final example will use raw data already available in LaTex to make a bar graph.

Using Data

Below is the code followed by the bar plot

New information is found first in lines 4-9. Here we use a command called “pgfplotstableread” in order to create the table. The table is found in lines 5-9. The first row sets the columns of the table and lines 6-8 is our actual data. In line 9 we give our table a name called “mydata.” It is important to note that this table will not appear in your pdf. Rather this table is just for storing information.If you want to show the table you need to make a table the traditional way.

Line 15 has the names of the groups in our data which were animal names. The next major change is in line 18. Here, we use the “addplot” command to add a table with the x as animal and the y as weight. Next to this information in curly braces is the name of the dateset called mydata.

If you look at the table you can see that we have information on the animals weight and speed but the bar plot only shows weight. In Line 19 there was some code in red which means that it was not compiled. By removing the percent sign we can run all the code and get the following.

The idea of adding to a bar plot remains the same. Just create another instance of the command and run it.


Making bar plots in LaTex is another convenient tool. It allows you to manipulate the data inside LaTex rather then having to pull images from your folder. If your data is stable and not going to change this might be worth while.