# The Scientific Method/Print Version

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Philosophy of Science

The history of science and scientific thought is long and varied. In these chapters, we will look at the history and the philosophy behind science.

# Introduction to Science

## Science

Modern science is broken into so many divergent branches that it's almost inconceivable to think that they are all related. However, despite the varied subject matter, all scientific disciplines are tied together through their use of a common method, the scientific method. The scientific method is mostly a philosophical exercise that is used to refine human knowledge.

## Precepts of the Method

Different disciplines may employ the general scientific method in slightly different ways, but the major precepts are the same:

- Verifiability
- Any result should be provable. Any person (with the proper training and equipment) must be able to reproduce and verify any scientific result.
- Predictability
- Any scientific theory should enable us to make predictions of future events. The precision of these predictions is a measure of the strength of the theory.

- Falsifiability
- Falsifiability is an important notion in science and the philosophy of science. For an assertion to be falsifiable it must be logically possible to make an observation or do a physical experiment that would show the assertion to be false. It is important to note that "falsifiable" does
*not*mean false. Some philosophers and scientists, most notably Karl Popper, have asserted that no empirical hypothesis, proposition, or theory can be considered scientific if no observation could be made which might contradict it. Note that if an assertion is falsifiable its negation can be unfalsifiable, and vice-versa. For example, "God does exist" is unfalsifiable, while its negation "God doesn't exist" is falsifiable. Any scientific theory must have criteria under which it is deemed invalid. Should predictions and verifications fail completely, the theory must be abandoned. - Fairness
- Data needs to be analyzed as a whole or as a representative sample. We cannot pick and choose what data to keep and what to discard. Also, we cannot focus our attention on data that proves or disproves a particular hypothesis, we must account for all data even if it invalidates the hypothesis.

## Stages of the Method

We will get into more detail in the following chapters, but the basic steps to the scientific method are as follows:

- Observe a natural phenomenon
- Make a hypothesis about the phenomenon
- Test the hypothesis

Once the hypothesis has been tested, if it is true we can work to find more evidence, or we can find counter-evidence. If the hypothesis is false, we create a new hypothesis and try again.

The important thing to note here is that the scientific process is never-ending. No result is ever considered to be perfect, and at no point do we stop looking at evidence.

### Example: Newton and Einstein

Isaac Newton, a brilliant physicist, developed a number of laws of motion and mechanics that we still use today. For many many years the laws of Newton were considered to be absolute fact. Many years later, a physicist known as Albert Einstein noticed that in certain situations Newton's laws were incorrect. Especially in cases where the object under consideration is moving at speed nearing the speed of light.Einstein helped to create a new theory, the theory of relativity, that corrected those errors. Even though Einstein was a brilliant scientist, modern physicists are developing new theories because there are some small errors in Einstein's theories. Each new generation of physicists helps to reduce the errors of the previous generations.

### The Complete Method

The complete scientific method, as it is generally known is:

- Define the question
- Gather data and observations
- Form hypothesis
- Perform experiment and collect data
- Interpret data and draw conclusions

Notice that the first step is to define the question. In other words, we can not look for an answer if we do not know what the question is first. Once we have the question, we need to observe the situation and gather appropriate data. We need to gather *all* data, not just selectively acquire data to support a particular hypothesis, or to make analysis more simple.

Once we have our data, we can analyze it to determine a hypothesis. In many cases a hypothesis is a mathematical relationship between the data points. However, it is not necessary to use mathematics at any point with the scientific method. Once we have our hypothesis, we need to test it. Testing is a complicated process, and will be the focus of the second section in this book. We collect data from our tests, and attempt to fit that data to our hypothesis. At this point, we need to ask, is the hypothesis right or wrong? Or, if it is not completely wrong nor completely right, we need to ask if this hypothesis is better then the previous hypothesis? If this hypothesis is not quite right, we can modify it and perform the tests again.

Once we have completed tests and verified our hypothesis, we need to draw conclusions from that. What does our hypothesis mean, in the bigger picture? What kinds of relationships between the data can we find? What further problems does this hypothesis cause? What would it take to prove this hypothesis wrong?

# Components of the Method

## Principles

The laws of nature as we understand them are the bases for all empirical sciences. They are the result of postulates (specific laws) that have passed experimental verification resulting in principles that are widely accepted and can be re-verified (using observation or experimentation).

## World View (Axioms, Postulates)

The word "axiom" comes from the Greek word αξιωμα (axioma), which means that which is deemed worthy or fit or that which is considered self-evident.

To "postulate" is to assume a theory valid due to be based on an a given set of axioms, resulting on the creation of a new axiom, this is so due to be self evident, "axiom," "postulate," and "assumption" are used interchangeably.

Generally speaking, axioms are all the laws that are generally considered true but largely accepted on faith, they cannot be derived by principles of deduction nor demonstrable by formal proofs—simply because they are starting assumptions, other examples include personal beliefs, political views, and cultural values. An axiom is the basic precondition underlying a theory.

Another thing one should be aware is that some fields of science predate the scientific method, for instance alchemy is now part of chemistry and physics and math was created even before we had numbers, one should have particular attention that in some fields the definitions or nomenclature may be out dated or be so for historical reasons, due to their use since before the definition of scientific method, and that mathematics uses not only the scientific method but also logical deductions, that result in theorems.

Take for instance the use of the word "axiom" in mathematics, this particular field has gone by several changes, especially in the 19th century, but due to historic reasons an "axiom" in mathematics does have a particular meaning.

Euclid's geometry, is based on a system of axioms that look self-evident. So, in physics, Euclid's geometry was used as natural (and the only) choice, the complete theory could be drawn from the axioms, resulting in the whole geometry to be considered to be true and self evident. This changed in the early 19th century, Gauss, Johann Bolyai, and Lobatchewsky, each independently, took a different approach. Beginning to suspect that it was impossible to prove the Parallel Postulate, they set out to develop a self-consistent geometry in which that postulate was false. In this they were successful, thus creating the first non-Euclidean geometry. By 1854, Bernhard Riemann, a student of Gauss, had applied methods of calculus in a ground-breaking study of the intrinsic (self-contained) geometry of all smooth surfaces, and thereby found a different non-Euclidean geometry.

It remained to be proved mathematically that the non-Euclidean geometry was just as self-consistent as Euclidean geometry, and this was first accomplished by Beltrami in 1868. With this, non-Euclidean geometry (both Lobatchewsky and Lobatchewsky) was established on an equal mathematical footing with Euclidean geometry. But this raised issues, "what geometry is true?". Even more, "does the latest question make sense?". All three geometries are based on different system of axioms, all are consistent.

Physics has helped answer these questions. While Euclid's geometry is used on Newtons' mechanics (normal distance), Riemann's geometry became fundamental for Einstein's theory of relativity. Moreover, Lobatchewsky's geometry was used later in quantum mechanics. So, question "Which one of these theories is correct for our physical space?" was answered in the surprising way: "All geometries represents physical space, but on a different scale".

All this influences what to think about axioms. From end of 19th century - beginning 20th century, math didn't appeal to the "self-evidence" of the axioms. It takes the freedom to freely choice axioms. What does, math say, that *if the axioms are true, then the theory is followed from the axioms*. Correspondence to the real world should be established separately. Axioms doesn't provide any guarantee.

- Example of conflict of mathematics/theoretical physics and the scientific method

The best example lies with *quantum mechanics*. Many facets of quantum mechanics are merely mathematical models explaining the behavior and interaction between subatomic particles. One of the major stumbling blocks in quantum mechanics lies within one its' fundamental theories: quantum superposition (all particles exist in all states at the same time). There are many interpretations of this, the standard being the Copenhagen interpretation. This states, basically, that the act of measuring (or observing) the state of a particle collapses the superposition effect, altering it's state to the value defined by the measurement. This shows that the superposition effect, while being one of the most widely accepted and fundamental principles of quantum mechanics, can never actually be directly observed, even if it is possible for experiments to be devised to corroborate the theory.

## Theory

Consists in a set of statements or principles devised to provide an explanation to a group of facts or phenomena. For instance a mathematical theorem; in the mathematical field we have to be careful on how we apply the definition since a theorem may be considered an axiom in itself, they can be accepted as valid until proved false (due to the infinite nature of numbers, it is common to propose limits to sets to provide validation), and other mathematical theorems may depend or be created over each others assumption of validity.

### Hypothesis

The hypothesis, or the **model** is a way for us to make sense of the data. We try to fit the data into some kind of model, and that model is our hypothesis.

### Predictions

A key component to the scientific method is the ability to predict. We can make predictions about something, and then test those predictions to see if they are correct. If the predictions are true, it's likely that the hypothesis is correct.

### Theorems

Are not part of the scientific method but may be a cause of some confusion. Most theorems have two components, called the hypotheses and the conclusions. The proof of the theorem is a logical argument demonstrating that the conclusions are a necessary consequence of the hypotheses, in the sense that if the hypotheses are true then the conclusions must also be true, without any further assumptions. The concept of a theorem is therefore fundamentally deductive, in contrast to the notion of a scientific theory, which is empirical.

## Verification

The fundamental step of turning an hypothetical relation into a principle, by validating it with real world data. Any verified hypothesis becomes a principle.

### Observations

an act or instance of viewing or noting a fact or occurrence for some scientific or other special purpose.

### Experiments

Experiments are key to the scientific method. Without experiments, any conclusions are just conjecture. We need to test our observations (to ensure the observations are unbiased and reproducible), we need to test our hypothesis, and then we need to test the predictions we make with our hypothesis.

Setting up of a proper experiment is important, and we will discuss it at length in section 2.

### Reasoning

#### Induction

#### Deduction

#### Abduction

Scientific Experiments

Science is driven by experimentation, where hypotheses must be tested and verified. In these chapters, we will look at how to perform a proper scientific experiment.

# Independent and Dependent Variables

## Relationships Between Variables

In any experiment, the object is to gather information about some event, in order to increase one's knowledge about it. In order to design an experiment, it is necessary to know or make an educated guess about *cause and effect* relationships between what you change in the experiment and what you are measuring. In order to do this, scientists use established theories to come up with a **hypothesis** before experimenting.

## Hypothesis

A hypothesis is a conjecture, based on knowledge obtained while formulating the question, that may explain any given behavior. The hypothesis might be very specific or it might be broad. "DNA makes RNA make protein" or "Unknown species of life dwell in the ocean," are two examples of valid hypothesis.

When formulating a hypothesis in the context of a controlled experiment, it will typically take the form a prediction of how changing one variable effects another, bring a variable any aspect, or collection, open to measurable change. The variable(s) that *you* alter intentionally in function of the experiment are called **independent variables**, while the variables that do not change by intended direct action are called **dependent variables**.

A hypothesis says something to the effect of:

Changing independent variable X should do something to dependent variable Y.

For example, suppose you wanted to measure the effects of temperature on the solubility of table sugar (sucrose). Knowing that dissolving sugar doesn't release or absorb much heat, it may seem intuitive to guess that the solubility does not depend on the temperature. Therefore our hypothesis may be:

Increasing or decreasing the temperature of a solution of water does not affect the solubility of sugar.

## Isolation of Effects

When determining what independent variables to change in an experiment, it is very important that you **isolate the effects** of each independent variable. You do not want to change more than one variable at once, for if you do it becomes more difficult to analyze the effects of each change on the dependent variable.

This is why experiments have to be designed very carefully. For example, performing the above tests on tap water may have different results from performing them on spring water, due to differences in salt content. Also, performing them on different days may cause variation due to pressure differences, or performing them with different brands of sugar may yield different results if different companies use different additives.

It is valid to test the effects of each of these things, if one desires, but if one does not have an infinite amount of money to experiment with all of the things that could go wrong (to see what happens if they do), a better alternative is to design the experiment to avoid potential pitfalls such as these.

### Corollary to Isolation of Effects

A corollary to this warning is that when designing the experiment, you should choose a set of conditions that maximizes your power to analyze the effects of changes in variables. For example, if you wanted to measure the effects of temperature and of water volume, you should start with a *basis* (say, 20oC and 4 fluid ounces of water) which is easy to replicate, and then, keeping one of the variables constant, changing the other one. Then, do the opposite. You may end up with an experimental scheme like this one:

Test number Volume Water (fl. oz.) Temperature (oC) 1 4 20 2 2 20 3 8 20 4 4 5 5 4 50

Once the data is gathered, you would analyze tests number 1, 4, and 5 to get an idea of the effect of temperature, and tests number 1, 2, and 3 to get an idea of volume effects. You would **not** analyze all 5 data points at once.