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Mechanics (Essentials) - Class 11th

Course: mechanics (essentials) - class 11th   >   unit 2.

• Introduction to physics
• What is physics?

The scientific method

• Models and Approximations in Physics

Introduction

• Make an observation.
• Ask a question.
• Form a hypothesis , or testable explanation.
• Make a prediction based on the hypothesis.
• Test the prediction.
• Iterate: use the results to make new hypotheses or predictions.

Scientific method example: Failure to toast

1. make an observation..

• Observation: the toaster won't toast.

2. Ask a question.

• Question: Why won't my toaster toast?

3. Propose a hypothesis.

• Hypothesis: Maybe the outlet is broken.

4. Make predictions.

• Prediction: If I plug the toaster into a different outlet, then it will toast the bread.

5. Test the predictions.

• Test of prediction: Plug the toaster into a different outlet and try again.
• If the toaster does toast, then the hypothesis is supported—likely correct.
• If the toaster doesn't toast, then the hypothesis is not supported—likely wrong.

Logical possibility

Practical possibility, building a body of evidence, 6. iterate..

• Iteration time!
• If the hypothesis was supported, we might do additional tests to confirm it, or revise it to be more specific. For instance, we might investigate why the outlet is broken.
• If the hypothesis was not supported, we would come up with a new hypothesis. For instance, the next hypothesis might be that there's a broken wire in the toaster.

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Article • 5 min read

Using the Scientific Method to Solve Problems

How the scientific method and reasoning can help simplify processes and solve problems.

By the Mind Tools Content Team

The processes of problem-solving and decision-making can be complicated and drawn out. In this article we look at how the scientific method, along with deductive and inductive reasoning can help simplify these processes.

‘It is a capital mistake to theorize before one has information. Insensibly one begins to twist facts to suit our theories, instead of theories to suit facts.’ Sherlock Holmes

The Scientific Method

The scientific method is a process used to explore observations and answer questions. Originally used by scientists looking to prove new theories, its use has spread into many other areas, including that of problem-solving and decision-making.

The scientific method is designed to eliminate the influences of bias, prejudice and personal beliefs when testing a hypothesis or theory. It has developed alongside science itself, with origins going back to the 13th century. The scientific method is generally described as a series of steps.

• observations/theory
• explanation/conclusion

The first step is to develop a theory about the particular area of interest. A theory, in the context of logic or problem-solving, is a conjecture or speculation about something that is not necessarily fact, often based on a series of observations.

Once a theory has been devised, it can be questioned and refined into more specific hypotheses that can be tested. The hypotheses are potential explanations for the theory.

The testing, and subsequent analysis, of these hypotheses will eventually lead to a conclus ion which can prove or disprove the original theory.

Applying the Scientific Method to Problem-Solving

How can the scientific method be used to solve a problem, such as the color printer is not working?

1. Use observations to develop a theory.

In order to solve the problem, it must first be clear what the problem is. Observations made about the problem should be used to develop a theory. In this particular problem the theory might be that the color printer has run out of ink. This theory is developed as the result of observing the increasingly faded output from the printer.

2. Form a hypothesis.

Note down all the possible reasons for the problem. In this situation they might include:

• The printer is set up as the default printer for all 40 people in the department and so is used more frequently than necessary.
• There has been increased usage of the printer due to non-work related printing.
• In an attempt to reduce costs, poor quality ink cartridges with limited amounts of ink in them have been purchased.
• The printer is faulty.

All these possible reasons are hypotheses.

3. Test the hypothesis.

Once as many hypotheses (or reasons) as possible have been thought of, then each one can be tested to discern if it is the cause of the problem. An appropriate test needs to be devised for each hypothesis. For example, it is fairly quick to ask everyone to check the default settings of the printer on each PC, or to check if the cartridge supplier has changed.

4. Analyze the test results.

Once all the hypotheses have been tested, the results can be analyzed. The type and depth of analysis will be dependant on each individual problem, and the tests appropriate to it. In many cases the analysis will be a very quick thought process. In others, where considerable information has been collated, a more structured approach, such as the use of graphs, tables or spreadsheets, may be required.

5. Draw a conclusion.

Based on the results of the tests, a conclusion can then be drawn about exactly what is causing the problem. The appropriate remedial action can then be taken, such as asking everyone to amend their default print settings, or changing the cartridge supplier.

Inductive and Deductive Reasoning

The scientific method involves the use of two basic types of reasoning, inductive and deductive.

Inductive reasoning makes a conclusion based on a set of empirical results. Empirical results are the product of the collection of evidence from observations. For example:

‘Every time it rains the pavement gets wet, therefore rain must be water’.

There has been no scientific determination in the hypothesis that rain is water, it is purely based on observation. The formation of a hypothesis in this manner is sometimes referred to as an educated guess. An educated guess, whilst not based on hard facts, must still be plausible, and consistent with what we already know, in order to present a reasonable argument.

Deductive reasoning can be thought of most simply in terms of ‘If A and B, then C’. For example:

• if the window is above the desk, and
• the desk is above the floor, then
• the window must be above the floor

It works by building on a series of conclusions, which results in one final answer.

Social Sciences and the Scientific Method

The scientific method can be used to address any situation or problem where a theory can be developed. Although more often associated with natural sciences, it can also be used to develop theories in social sciences (such as psychology, sociology and linguistics), using both quantitative and qualitative methods.

Quantitative information is information that can be measured, and tends to focus on numbers and frequencies. Typically quantitative information might be gathered by experiments, questionnaires or psychometric tests. Qualitative information, on the other hand, is based on information describing meaning, such as human behavior, and the reasons behind it. Qualitative information is gathered by way of interviews and case studies, which are possibly not as statistically accurate as quantitative methods, but provide a more in-depth and rich description.

The resultant information can then be used to prove, or disprove, a hypothesis. Using a mix of quantitative and qualitative information is more likely to produce a rounded result based on the factual, quantitative information enriched and backed up by actual experience and qualitative information.

In terms of problem-solving or decision-making, for example, the qualitative information is that gained by looking at the ‘how’ and ‘why’ , whereas quantitative information would come from the ‘where’, ‘what’ and ‘when’.

It may seem easy to come up with a brilliant idea, or to suspect what the cause of a problem may be. However things can get more complicated when the idea needs to be evaluated, or when there may be more than one potential cause of a problem. In these situations, the use of the scientific method, and its associated reasoning, can help the user come to a decision, or reach a solution, secure in the knowledge that all options have been considered.

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Sat / act prep online guides and tips, the 6 scientific method steps and how to use them.

General Education

When you’re faced with a scientific problem, solving it can seem like an impossible prospect. There are so many possible explanations for everything we see and experience—how can you possibly make sense of them all? Science has a simple answer: the scientific method.

The scientific method is a method of asking and answering questions about the world. These guiding principles give scientists a model to work through when trying to understand the world, but where did that model come from, and how does it work?

In this article, we’ll define the scientific method, discuss its long history, and cover each of the scientific method steps in detail.

What Is the Scientific Method?

At its most basic, the scientific method is a procedure for conducting scientific experiments. It’s a set model that scientists in a variety of fields can follow, going from initial observation to conclusion in a loose but concrete format.

The number of steps varies, but the process begins with an observation, progresses through an experiment, and concludes with analysis and sharing data. One of the most important pieces to the scientific method is skepticism —the goal is to find truth, not to confirm a particular thought. That requires reevaluation and repeated experimentation, as well as examining your thinking through rigorous study.

There are in fact multiple scientific methods, as the basic structure can be easily modified.  The one we typically learn about in school is the basic method, based in logic and problem solving, typically used in “hard” science fields like biology, chemistry, and physics. It may vary in other fields, such as psychology, but the basic premise of making observations, testing, and continuing to improve a theory from the results remain the same.

The History of the Scientific Method

The scientific method as we know it today is based on thousands of years of scientific study. Its development goes all the way back to ancient Mesopotamia, Greece, and India.

The Ancient World

In ancient Greece, Aristotle devised an inductive-deductive process , which weighs broad generalizations from data against conclusions reached by narrowing down possibilities from a general statement. However, he favored deductive reasoning, as it identifies causes, which he saw as more important.

Aristotle wrote a great deal about logic and many of his ideas about reasoning echo those found in the modern scientific method, such as ignoring circular evidence and limiting the number of middle terms between the beginning of an experiment and the end. Though his model isn’t the one that we use today, the reliance on logic and thorough testing are still key parts of science today.

The Middle Ages

The next big step toward the development of the modern scientific method came in the Middle Ages, particularly in the Islamic world. Ibn al-Haytham, a physicist from what we now know as Iraq, developed a method of testing, observing, and deducing for his research on vision. al-Haytham was critical of Aristotle’s lack of inductive reasoning, which played an important role in his own research.

Other scientists, including Abū Rayhān al-Bīrūnī, Ibn Sina, and Robert Grosseteste also developed models of scientific reasoning to test their own theories. Though they frequently disagreed with one another and Aristotle, those disagreements and refinements of their methods led to the scientific method we have today.

Following those major developments, particularly Grosseteste’s work, Roger Bacon developed his own cycle of observation (seeing that something occurs), hypothesis (making a guess about why that thing occurs), experimentation (testing that the thing occurs), and verification (an outside person ensuring that the result of the experiment is consistent).

After joining the Franciscan Order, Bacon was granted a special commission to write about science; typically, Friars were not allowed to write books or pamphlets. With this commission, Bacon outlined important tenets of the scientific method, including causes of error, methods of knowledge, and the differences between speculative and experimental science. He also used his own principles to investigate the causes of a rainbow, demonstrating the method’s effectiveness.

Scientific Revolution

Throughout the Renaissance, more great thinkers became involved in devising a thorough, rigorous method of scientific study. Francis Bacon brought inductive reasoning further into the method, whereas Descartes argued that the laws of the universe meant that deductive reasoning was sufficient. Galileo’s research was also inductive reasoning-heavy, as he believed that researchers could not account for every possible variable; therefore, repetition was necessary to eliminate faulty hypotheses and experiments.

All of this led to the birth of the Scientific Revolution , which took place during the sixteenth and seventeenth centuries. In 1660, a group of philosophers and physicians joined together to work on scientific advancement. After approval from England’s crown , the group became known as the Royal Society, which helped create a thriving scientific community and an early academic journal to help introduce rigorous study and peer review.

Previous generations of scientists had touched on the importance of induction and deduction, but Sir Isaac Newton proposed that both were equally important. This contribution helped establish the importance of multiple kinds of reasoning, leading to more rigorous study.

As science began to splinter into separate areas of study, it became necessary to define different methods for different fields. Karl Popper was a leader in this area—he established that science could be subject to error, sometimes intentionally. This was particularly tricky for “soft” sciences like psychology and social sciences, which require different methods. Popper’s theories furthered the divide between sciences like psychology and “hard” sciences like chemistry or physics.

Paul Feyerabend argued that Popper’s methods were too restrictive for certain fields, and followed a less restrictive method hinged on “anything goes,” as great scientists had made discoveries without the Scientific Method. Feyerabend suggested that throughout history scientists had adapted their methods as necessary, and that sometimes it would be necessary to break the rules. This approach suited social and behavioral scientists particularly well, leading to a more diverse range of models for scientists in multiple fields to use.

The Scientific Method Steps

Though different fields may have variations on the model, the basic scientific method is as follows:

#1: Make Observations 

Notice something, such as the air temperature during the winter, what happens when ice cream melts, or how your plants behave when you forget to water them.

#2: Ask a Question

Turn your observation into a question. Why is the temperature lower during the winter? Why does my ice cream melt? Why does my toast always fall butter-side down?

This step can also include doing some research. You may be able to find answers to these questions already, but you can still test them!

#3: Make a Hypothesis

A hypothesis is an educated guess of the answer to your question. Why does your toast always fall butter-side down? Maybe it’s because the butter makes that side of the bread heavier.

A good hypothesis leads to a prediction that you can test, phrased as an if/then statement. In this case, we can pick something like, “If toast is buttered, then it will hit the ground butter-first.”

#4: Experiment

Your experiment is designed to test whether your predication about what will happen is true. A good experiment will test one variable at a time —for example, we’re trying to test whether butter weighs down one side of toast, making it more likely to hit the ground first.

The unbuttered toast is our control variable. If we determine the chance that a slice of unbuttered toast, marked with a dot, will hit the ground on a particular side, we can compare those results to our buttered toast to see if there’s a correlation between the presence of butter and which way the toast falls.

If we decided not to toast the bread, that would be introducing a new question—whether or not toasting the bread has any impact on how it falls. Since that’s not part of our test, we’ll stick with determining whether the presence of butter has any impact on which side hits the ground first.

#5: Analyze Data

After our experiment, we discover that both buttered toast and unbuttered toast have a 50/50 chance of hitting the ground on the buttered or marked side when dropped from a consistent height, straight down. It looks like our hypothesis was incorrect—it’s not the butter that makes the toast hit the ground in a particular way, so it must be something else.

Since we didn’t get the desired result, it’s back to the drawing board. Our hypothesis wasn’t correct, so we’ll need to start fresh. Now that you think about it, your toast seems to hit the ground butter-first when it slides off your plate, not when you drop it from a consistent height. That can be the basis for your new experiment.

#6: Communicate Your Results

Good science needs verification. Your experiment should be replicable by other people, so you can put together a report about how you ran your experiment to see if other peoples’ findings are consistent with yours.

This may be useful for class or a science fair. Professional scientists may publish their findings in scientific journals, where other scientists can read and attempt their own versions of the same experiments. Being part of a scientific community helps your experiments be stronger because other people can see if there are flaws in your approach—such as if you tested with different kinds of bread, or sometimes used peanut butter instead of butter—that can lead you closer to a good answer.

A Scientific Method Example: Falling Toast

We’ve run through a quick recap of the scientific method steps, but let’s look a little deeper by trying again to figure out why toast so often falls butter side down.

#1: Make Observations

At the end of our last experiment, where we learned that butter doesn’t actually make toast more likely to hit the ground on that side, we remembered that the times when our toast hits the ground butter side first are usually when it’s falling off a plate.

The easiest question we can ask is, “Why is that?”

We can actually search this online and find a pretty detailed answer as to why this is true. But we’re budding scientists—we want to see it in action and verify it for ourselves! After all, good science should be replicable, and we have all the tools we need to test out what’s really going on.

Why do we think that buttered toast hits the ground butter-first? We know it’s not because it’s heavier, so we can strike that out. Maybe it’s because of the shape of our plate?

That’s something we can test. We’ll phrase our hypothesis as, “If my toast slides off my plate, then it will fall butter-side down.”

Just seeing that toast falls off a plate butter-side down isn’t enough for us. We want to know why, so we’re going to take things a step further—we’ll set up a slow-motion camera to capture what happens as the toast slides off the plate.

We’ll run the test ten times, each time tilting the same plate until the toast slides off. We’ll make note of each time the butter side lands first and see what’s happening on the video so we can see what’s going on.

When we review the footage, we’ll likely notice that the bread starts to flip when it slides off the edge, changing how it falls in a way that didn’t happen when we dropped it ourselves.

That answers our question, but it’s not the complete picture —how do other plates affect how often toast hits the ground butter-first? What if the toast is already butter-side down when it falls? These are things we can test in further experiments with new hypotheses!

Now that we have results, we can share them with others who can verify our results. As mentioned above, being part of the scientific community can lead to better results. If your results were wildly different from the established thinking about buttered toast, that might be cause for reevaluation. If they’re the same, they might lead others to make new discoveries about buttered toast. At the very least, you have a cool experiment you can share with your friends!

Key Scientific Method Tips

Though science can be complex, the benefit of the scientific method is that it gives you an easy-to-follow means of thinking about why and how things happen. To use it effectively, keep these things in mind!

Don’t Worry About Proving Your Hypothesis

One of the important things to remember about the scientific method is that it’s not necessarily meant to prove your hypothesis right. It’s great if you do manage to guess the reason for something right the first time, but the ultimate goal of an experiment is to find the true reason for your observation to occur, not to prove your hypothesis right.

Good science sometimes means that you’re wrong. That’s not a bad thing—a well-designed experiment with an unanticipated result can be just as revealing, if not more, than an experiment that confirms your hypothesis.

Be Prepared to Try Again

If the data from your experiment doesn’t match your hypothesis, that’s not a bad thing. You’ve eliminated one possible explanation, which brings you one step closer to discovering the truth.

The scientific method isn’t something you’re meant to do exactly once to prove a point. It’s meant to be repeated and adapted to bring you closer to a solution. Even if you can demonstrate truth in your hypothesis, a good scientist will run an experiment again to be sure that the results are replicable. You can even tweak a successful hypothesis to test another factor, such as if we redid our buttered toast experiment to find out whether different kinds of plates affect whether or not the toast falls butter-first. The more we test our hypothesis, the stronger it becomes!

What’s Next?

Want to learn more about the scientific method? These important high school science classes will no doubt cover it in a variety of different contexts.

Test your ability to follow the scientific method using these at-home science experiments for kids !

Need some proof that science is fun? Try making slime

Melissa Brinks graduated from the University of Washington in 2014 with a Bachelor's in English with a creative writing emphasis. She has spent several years tutoring K-12 students in many subjects, including in SAT prep, to help them prepare for their college education.

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What is the Scientific Method: How does it work and why is it important?

The scientific method is a systematic process involving steps like defining questions, forming hypotheses, conducting experiments, and analyzing data. It minimizes biases and enables replicable research, leading to groundbreaking discoveries like Einstein's theory of relativity, penicillin, and the structure of DNA. This ongoing approach promotes reason, evidence, and the pursuit of truth in science.

Updated on November 18, 2023

Beginning in elementary school, we are exposed to the scientific method and taught how to put it into practice. As a tool for learning, it prepares children to think logically and use reasoning when seeking answers to questions.

Rather than jumping to conclusions, the scientific method gives us a recipe for exploring the world through observation and trial and error. We use it regularly, sometimes knowingly in academics or research, and sometimes subconsciously in our daily lives.

In this article we will refresh our memories on the particulars of the scientific method, discussing where it comes from, which elements comprise it, and how it is put into practice. Then, we will consider the importance of the scientific method, who uses it and under what circumstances.

What is the scientific method?

The scientific method is a dynamic process that involves objectively investigating questions through observation and experimentation . Applicable to all scientific disciplines, this systematic approach to answering questions is more accurately described as a flexible set of principles than as a fixed series of steps.

The following representations of the scientific method illustrate how it can be both condensed into broad categories and also expanded to reveal more and more details of the process. These graphics capture the adaptability that makes this concept universally valuable as it is relevant and accessible not only across age groups and educational levels but also within various contexts.

Steps in the scientific method

While the scientific method is versatile in form and function, it encompasses a collection of principles that create a logical progression to the process of problem solving:

• Define a question : Constructing a clear and precise problem statement that identifies the main question or goal of the investigation is the first step. The wording must lend itself to experimentation by posing a question that is both testable and measurable.
• Gather information and resources : Researching the topic in question to find out what is already known and what types of related questions others are asking is the next step in this process. This background information is vital to gaining a full understanding of the subject and in determining the best design for experiments. 
• Form a hypothesis : Composing a concise statement that identifies specific variables and potential results, which can then be tested, is a crucial step that must be completed before any experimentation. An imperfection in the composition of a hypothesis can result in weaknesses to the entire design of an experiment.
• Perform the experiments : Testing the hypothesis by performing replicable experiments and collecting resultant data is another fundamental step of the scientific method. By controlling some elements of an experiment while purposely manipulating others, cause and effect relationships are established.
• Analyze the data : Interpreting the experimental process and results by recognizing trends in the data is a necessary step for comprehending its meaning and supporting the conclusions. Drawing inferences through this systematic process lends substantive evidence for either supporting or rejecting the hypothesis.
• Report the results : Sharing the outcomes of an experiment, through an essay, presentation, graphic, or journal article, is often regarded as a final step in this process. Detailing the project's design, methods, and results not only promotes transparency and replicability but also adds to the body of knowledge for future research.
• Retest the hypothesis : Repeating experiments to see if a hypothesis holds up in all cases is a step that is manifested through varying scenarios. Sometimes a researcher immediately checks their own work or replicates it at a future time, or another researcher will repeat the experiments to further test the hypothesis.

Where did the scientific method come from?

Oftentimes, ancient peoples attempted to answer questions about the unknown by:

• Making simple observations
• Discussing the possibilities with others deemed worthy of a debate
• Drawing conclusions based on dominant opinions and preexisting beliefs

For example, take Greek and Roman mythology. Myths were used to explain everything from the seasons and stars to the sun and death itself.

However, as societies began to grow through advancements in agriculture and language, ancient civilizations like Egypt and Babylonia shifted to a more rational analysis for understanding the natural world. They increasingly employed empirical methods of observation and experimentation that would one day evolve into the scientific method . 

In the 4th century, Aristotle, considered the Father of Science by many, suggested these elements , which closely resemble the contemporary scientific method, as part of his approach for conducting science:

• Study what others have written about the subject.
• Look for the general consensus about the subject.
• Perform a systematic study of everything even partially related to the topic.

By continuing to emphasize systematic observation and controlled experiments, scholars such as Al-Kindi and Ibn al-Haytham helped expand this concept throughout the Islamic Golden Age . 

In his 1620 treatise, Novum Organum , Sir Francis Bacon codified the scientific method, arguing not only that hypotheses must be tested through experiments but also that the results must be replicated to establish a truth. Coming at the height of the Scientific Revolution, this text made the scientific method accessible to European thinkers like Galileo and Isaac Newton who then put the method into practice.

As science modernized in the 19th century, the scientific method became more formalized, leading to significant breakthroughs in fields such as evolution and germ theory. Today, it continues to evolve, underpinning scientific progress in diverse areas like quantum mechanics, genetics, and artificial intelligence.

Why is the scientific method important?

The history of the scientific method illustrates how the concept developed out of a need to find objective answers to scientific questions by overcoming biases based on fear, religion, power, and cultural norms. This still holds true today.

By implementing this standardized approach to conducting experiments, the impacts of researchers’ personal opinions and preconceived notions are minimized. The organized manner of the scientific method prevents these and other mistakes while promoting the replicability and transparency necessary for solid scientific research.

The importance of the scientific method is best observed through its successes, for example: 

• “ Albert Einstein stands out among modern physicists as the scientist who not only formulated a theory of revolutionary significance but also had the genius to reflect in a conscious and technical way on the scientific method he was using.” Devising a hypothesis based on the prevailing understanding of Newtonian physics eventually led Einstein to devise the theory of general relativity .
• Howard Florey “Perhaps the most useful lesson which has come out of the work on penicillin has been the demonstration that success in this field depends on the development and coordinated use of technical methods.” After discovering a mold that prevented the growth of Staphylococcus bacteria, Dr. Alexander Flemimg designed experiments to identify and reproduce it in the lab, thus leading to the development of penicillin .
• James D. Watson “Every time you understand something, religion becomes less likely. Only with the discovery of the double helix and the ensuing genetic revolution have we had grounds for thinking that the powers held traditionally to be the exclusive property of the gods might one day be ours. . . .” By using wire models to conceive a structure for DNA, Watson and Crick crafted a hypothesis for testing combinations of amino acids, X-ray diffraction images, and the current research in atomic physics, resulting in the discovery of DNA’s double helix structure .

Final thoughts

As the cases exemplify, the scientific method is never truly completed, but rather started and restarted. It gave these researchers a structured process that was easily replicated, modified, and built upon. 

While the scientific method may “end” in one context, it never literally ends. When a hypothesis, design, methods, and experiments are revisited, the scientific method simply picks up where it left off. Each time a researcher builds upon previous knowledge, the scientific method is restored with the pieces of past efforts.

By guiding researchers towards objective results based on transparency and reproducibility, the scientific method acts as a defense against bias, superstition, and preconceived notions. As we embrace the scientific method's enduring principles, we ensure that our quest for knowledge remains firmly rooted in reason, evidence, and the pursuit of truth.

The AJE Team

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A Guide to Using the Scientific Method in Everyday Life

The  scientific method —the process used by scientists to understand the natural world—has the merit of investigating natural phenomena in a rigorous manner. Working from hypotheses, scientists draw conclusions based on empirical data. These data are validated on large-scale numbers and take into consideration the intrinsic variability of the real world. For people unfamiliar with its intrinsic jargon and formalities, science may seem esoteric. And this is a huge problem: science invites criticism because it is not easily understood. So why is it important, then, that every person understand how science is done?

Because the scientific method is, first of all, a matter of logical reasoning and only afterwards, a procedure to be applied in a laboratory.

Individuals without training in logical reasoning are more easily victims of distorted perspectives about themselves and the world. An example is represented by the so-called “ cognitive biases ”—systematic mistakes that individuals make when they try to think rationally, and which lead to erroneous or inaccurate conclusions. People can easily  overestimate the relevance  of their own behaviors and choices. They can  lack the ability to self-estimate the quality of their performances and thoughts . Unconsciously, they could even end up selecting only the arguments  that support their hypothesis or beliefs . This is why the scientific framework should be conceived not only as a mechanism for understanding the natural world, but also as a framework for engaging in logical reasoning and discussion.

A brief history of the scientific method

The scientific method has its roots in the sixteenth and seventeenth centuries. Philosophers Francis Bacon and René Descartes are often credited with formalizing the scientific method because they contrasted the idea that research should be guided by metaphysical pre-conceived concepts of the nature of reality—a position that, at the time,  was highly supported by their colleagues . In essence, Bacon thought that  inductive reasoning based on empirical observation was critical to the formulation of hypotheses  and the  generation of new understanding : general or universal principles describing how nature works are derived only from observations of recurring phenomena and data recorded from them. The inductive method was used, for example, by the scientist Rudolf Virchow to formulate the third principle of the notorious  cell theory , according to which every cell derives from a pre-existing one. The rationale behind this conclusion is that because all observations of cell behavior show that cells are only derived from other cells, this assertion must be always true. 

Inductive reasoning, however, is not immune to mistakes and limitations. Referring back to cell theory, there may be rare occasions in which a cell does not arise from a pre-existing one, even though we haven’t observed it yet—our observations on cell behavior, although numerous, can still benefit from additional observations to either refute or support the conclusion that all cells arise from pre-existing ones. And this is where limited observations can lead to erroneous conclusions reasoned inductively. In another example, if one never has seen a swan that is not white, they might conclude that all swans are white, even when we know that black swans do exist, however rare they may be.  

The universally accepted scientific method, as it is used in science laboratories today, is grounded in  hypothetico-deductive reasoning . Research progresses via iterative empirical testing of formulated, testable hypotheses (formulated through inductive reasoning). A testable hypothesis is one that can be rejected (falsified) by empirical observations, a concept known as the  principle of falsification . Initially, ideas and conjectures are formulated. Experiments are then performed to test them. If the body of evidence fails to reject the hypothesis, the hypothesis stands. It stands however until and unless another (even singular) empirical observation falsifies it. However, just as with inductive reasoning, hypothetico-deductive reasoning is not immune to pitfalls—assumptions built into hypotheses can be shown to be false, thereby nullifying previously unrejected hypotheses. The bottom line is that science does not work to prove anything about the natural world. Instead, it builds hypotheses that explain the natural world and then attempts to find the hole in the reasoning (i.e., it works to disprove things about the natural world).

How do scientists test hypotheses?

Controlled experiments

The word “experiment” can be misleading because it implies a lack of control over the process. Therefore, it is important to understand that science uses controlled experiments in order to test hypotheses and contribute new knowledge. So what exactly is a controlled experiment, then? 

Let us take a practical example. Our starting hypothesis is the following: we have a novel drug that we think inhibits the division of cells, meaning that it prevents one cell from dividing into two cells (recall the description of cell theory above). To test this hypothesis, we could treat some cells with the drug on a plate that contains nutrients and fuel required for their survival and division (a standard cell biology assay). If the drug works as expected, the cells should stop dividing. This type of drug might be useful, for example, in treating cancers because slowing or stopping the division of cells would result in the slowing or stopping of tumor growth.

Although this experiment is relatively easy to do, the mere process of doing science means that several experimental variables (like temperature of the cells or drug, dosage, and so on) could play a major role in the experiment. This could result in a failed experiment when the drug actually does work, or it could give the appearance that the drug is working when it is not. Given that these variables cannot be eliminated, scientists always run control experiments in parallel to the real ones, so that the effects of these other variables can be determined.  Control experiments  are designed so that all variables, with the exception of the one under investigation, are kept constant. In simple terms, the conditions must be identical between the control and the actual experiment.     

Coming back to our example, when a drug is administered it is not pure. Often, it is dissolved in a solvent like water or oil. Therefore, the perfect control to the actual experiment would be to administer pure solvent (without the added drug) at the same time and with the same tools, where all other experimental variables (like temperature, as mentioned above) are the same between the two (Figure 1). Any difference in effect on cell division in the actual experiment here can be attributed to an effect of the drug because the effects of the solvent were controlled.

In order to provide evidence of the quality of a single, specific experiment, it needs to be performed multiple times in the same experimental conditions. We call these multiple experiments “replicates” of the experiment (Figure 2). The more replicates of the same experiment, the more confident the scientist can be about the conclusions of that experiment under the given conditions. However, multiple replicates under the same experimental conditions  are of no help  when scientists aim at acquiring more empirical evidence to support their hypothesis. Instead, they need  independent experiments  (Figure 3), in their own lab and in other labs across the world, to validate their results. 

Often times, especially when a given experiment has been repeated and its outcome is not fully clear, it is better  to find alternative experimental assays  to test the hypothesis. 

Applying the scientific approach to everyday life

So, what can we take from the scientific approach to apply to our everyday lives?

A few weeks ago, I had an agitated conversation with a bunch of friends concerning the following question: What is the definition of intelligence?

Defining “intelligence” is not easy. At the beginning of the conversation, everybody had a different, “personal” conception of intelligence in mind, which – tacitly – implied that the conversation could have taken several different directions. We realized rather soon that someone thought that an intelligent person is whoever is able to adapt faster to new situations; someone else thought that an intelligent person is whoever is able to deal with other people and empathize with them. Personally, I thought that an intelligent person is whoever displays high cognitive skills, especially in abstract reasoning. 

The scientific method has the merit of providing a reference system, with precise protocols and rules to follow. Remember: experiments must be reproducible, which means that an independent scientists in a different laboratory, when provided with the same equipment and protocols, should get comparable results.  Fruitful conversations as well need precise language, a kind of reference vocabulary everybody should agree upon, in order to discuss about the same “content”. This is something we often forget, something that was somehow missing at the opening of the aforementioned conversation: even among friends, we should always agree on premises, and define them in a rigorous manner, so that they are the same for everybody. When speaking about “intelligence”, we must all make sure we understand meaning and context of the vocabulary adopted in the debate (Figure 4, point 1).  This is the first step of “controlling” a conversation.

There is another downside that a discussion well-grounded in a scientific framework would avoid. The mistake is not structuring the debate so that all its elements, except for the one under investigation, are kept constant (Figure 4, point 2). This is particularly true when people aim at making comparisons between groups to support their claim. For example, they may try to define what intelligence is by comparing the  achievements in life of different individuals: “Stephen Hawking is a brilliant example of intelligence because of his great contribution to the physics of black holes”. This statement does not help to define what intelligence is, simply because it compares Stephen Hawking, a famous and exceptional physicist, to any other person, who statistically speaking, knows nothing about physics. Hawking first went to the University of Oxford, then he moved to the University of Cambridge. He was in contact with the most influential physicists on Earth. Other people were not. All of this, of course, does not disprove Hawking’s intelligence; but from a logical and methodological point of view, given the multitude of variables included in this comparison, it cannot prove it. Thus, the sentence “Stephen Hawking is a brilliant example of intelligence because of his great contribution to the physics of black holes” is not a valid argument to describe what intelligence is. If we really intend to approximate a definition of intelligence, Steven Hawking should be compared to other physicists, even better if they were Hawking’s classmates at the time of college, and colleagues afterwards during years of academic research. 

In simple terms, as scientists do in the lab, while debating we should try to compare groups of elements that display identical, or highly similar, features. As previously mentioned, all variables – except for the one under investigation – must be kept constant.

This insightful piece  presents a detailed analysis of how and why science can help to develop critical thinking.

In a nutshell

Here is how to approach a daily conversation in a rigorous, scientific manner:

• First discuss about the reference vocabulary, then discuss about the content of the discussion.  Think about a researcher who is writing down an experimental protocol that will be used by thousands of other scientists in varying continents. If the protocol is rigorously written, all scientists using it should get comparable experimental outcomes. In science this means reproducible knowledge, in daily life this means fruitful conversations in which individuals are on the same page. 
• Adopt “controlled” arguments to support your claims.  When making comparisons between groups, visualize two blank scenarios. As you start to add details to both of them, you have two options. If your aim is to hide a specific detail, the better is to design the two scenarios in a completely different manner—it is to increase the variables. But if your intention is to help the observer to isolate a specific detail, the better is to design identical scenarios, with the exception of the intended detail—it is therefore to keep most of the variables constant. This is precisely how scientists ideate adequate experiments to isolate new pieces of knowledge, and how individuals should orchestrate their thoughts in order to test them and facilitate their comprehension to others.   

Not only the scientific method should offer individuals an elitist way to investigate reality, but also an accessible tool to properly reason and discuss about it.

Edited by Jason Organ, PhD, Indiana University School of Medicine.

Simone is a molecular biologist on the verge of obtaining a doctoral title at the University of Ulm, Germany. He is Vice-Director at Culturico (https://culturico.com/), where his writings span from Literature to Sociology, from Philosophy to Science. His writings recently appeared in Psychology Today, openDemocracy, Splice Today, Merion West, Uncommon Ground and The Society Pages. Follow Simone on Twitter: @simredaelli

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This has to be the best article I have ever read on Scientific Thinking. I am presently writing a treatise on how Scientific thinking can be adopted to entreat all situations.And how, a 4 year old child can be taught to adopt Scientific thinking, so that, the child can look at situations that bothers her and she could try to think about that situation by formulating the right questions. She may not have the tools to find right answers? But, forming questions by using right technique ? May just make her find a way to put her mind to rest even at that level. That is why, 4 year olds are often “eerily: (!)intelligent, I have iften been intimidated and plain embarrassed to see an intelligent and well spoken 4 year old deal with celibrity ! Of course, there are a lot of variables that have to be kept in mind in order to train children in such controlled thinking environment, as the screenplay of little Sheldon shows. Thanking the author with all my heart – #ershadspeak #wearescience #weareallscientists Ershad Khandker

Simone, thank you for this article. I have the idea that I want to apply what I learned in Biology to everyday life. You addressed this issue, and have given some basic steps in using the scientific method.

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1.1: The Scientific Method

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• Laci M. Gerhart-Barley
• College of Biological Sciences - UC Davis

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Biologists, and other scientists, study the world using a formal process referred to as the scientific method . The scientific method was first documented by Sir Francis Bacon (1561–1626) of England, and can be applied to almost all fields of study. The scientific method is founded upon observation, which then leads to a question and the development of a hypothesis which answers that question. The scientist can then design an experiment to test the proposed hypothesis, and makes a prediction for the outcome of the experiment, if the proposed hypothesis is true. In the following sections, we will use a simple example of the scientific method, based on a simple observation of the classroom being too warm.

Proposing a Hypothesis

A hypothesis is one possible answer to the question that arises from observations. In our example, the observation is that the classroom is too warm, and the question taht arises from that observation is why the classroom is too warm. One (of many) hypotheses is “The classroom is warm because no one turned on the air conditioning.” Another hypothesis could be “The classroom is warm because the heating is set too high."

Once a hypothesis has been developed, the scientist then makes a prediction, which is similar to a hypothesis, but generally follows the format of “If . . . then . . . .” In our example, a prediction arising from the first hypothesis might be, “ If the air-conditioning is turned on, then the classroom will no longer be too warm.” The initial steps of the scientific method (observation to prediction) are outlined in Figure 1.1.1.

Testing a Hypothesis

A valid hypothesis must be testable. It should also be falsifiable, meaning that it can be disproven by experimental results. Importantly, science does not claim to “prove” anything because scientific understandings are always subject to modification with further information. To test a hypothesis, a researcher will conduct one or more experiments designed to eliminate one or more of the hypotheses. Each experiment will have one or more variables and one or more controls. A variable is any part of the experiment that can vary or change during the experiment. The control group contains every feature of the experimental group except it is not given the manipulation that tests the hypothesis. Therefore, if the results of the experimental group differ from the control group, the difference must be due to the hypothesized manipulation, rather than some outside factor. Look for the variables and controls in the examples that follow. To test the first hypothesis, the student would find out if the air conditioning is on. If the air conditioning is turned on but does not work, then the hypothesis that the air conditioning was not turned on should be rejected. To test the second hypothesis, the student could check the settings of the classroom heating unit. If the heating unit is set at an appropriate temperature, then this hypothesis should also be rejected. Each hypothesis should be tested by carrying out appropriate experiments. Be aware that rejecting one hypothesis does not determine whether or not the other hypotheses can be accepted; it simply eliminates one hypothesis that is not valid. Using the scientific method, the hypotheses that are inconsistent with experimental data are rejected.

While this “warm classroom” example is based on observational results, other hypotheses and experiments might have clearer controls. For instance, a student might attend class on Monday and realize they had difficulty concentrating on the lecture. One observation to explain this occurrence might be, “When I eat breakfast before class, I am better able to pay attention.” The student could then design an experiment with a control to test this hypothesis.

Exercise \(\PageIndex{1}\)

In the example below, the scientific method is used to solve an everyday problem. Order the scientific method steps (numbered items) with the process of solving the everyday problem (lettered items). Based on the results of the experiment, is the hypothesis correct? If it is incorrect, propose some alternative hypotheses.

• Observation
• Hypothesis (answer)
• The car battery is dead.
• If the battery is dead, then the headlights also will not turn on.
• My car won't start.
• I turn on the headlights.
• The headlights work.
• Why does the car not start?

C, F, A, B, D, E

The scientific method may seem overly rigid and structured; however, there is flexibility. Often, the process of science is not as linear as the scientific method suggests and experimental results frequently inspire a new approach, highlight patterns or themes in the study system, or generate entirely new and different observations and questions. In our warm classroom example, testing the air conditioning hypothesis could, for example, unearth evidence of faulty wiring in the classroom. This observation could then inspire additional questions related to other classroom electrical concerns such as inconsistent wireless internet access, faulty audio/visual equipment functioning, non-functional power outlets, flickering lighting, etc. Notice, too, that the scientific method can be applied to solving problems that aren’t necessarily scientific in nature.

This section was adapted from OpenStax Chapter 1:2 The Process of Science

Module 7: Exponents

Problem solving with scientific notation, learning outcome.

• Solve application problems involving scientific notation

A water molecule.

Solve Application Problems

Learning rules for exponents seems pointless without context, so let us explore some examples of using scientific notation that involve real problems. First, let us look at an example of how scientific notation can be used to describe real measurements.

Think About It

Match each length in the table with the appropriate number of meters described in scientific notation below. Write your ideas in the textboxes provided before you look at the solution.

Several red blood cells.

One of the most important parts of solving a “real-world” problem is translating the words into appropriate mathematical terms and recognizing when a well known formula may help. Here is an example that requires you to find the density of a cell given its mass and volume. Cells are not visible to the naked eye, so their measurements, as described with scientific notation, involve negative exponents.

Human cells come in a wide variety of shapes and sizes. The mass of an average human cell is about [latex]2\times10^{-11}[/latex] grams. [1] Red blood cells are one of the smallest types of cells [2] , clocking in at a volume of approximately [latex]10^{-6}\text{ meters }^3[/latex]. [3] Biologists have recently discovered how to use the density of some types of cells to indicate the presence of disorders such as sickle cell anemia or leukemia. [4]  Density is calculated as [latex]\frac{\text{ mass }}{\text{ volume }}[/latex]. Calculate the density of an average human cell.

Read and Understand:  We are given an average cellular mass and volume as well as the formula for density. We are looking for the density of an average human cell.

Define and Translate:   [latex]m=\text{mass}=2\times10^{-11}[/latex], [latex]v=\text{volume}=10^{-6}\text{ meters}^3[/latex], [latex]\text{density}=\frac{\text{ mass }}{\text{ volume }}[/latex]

Write and Solve:  Use the quotient rule to simplify the ratio.

[latex]\begin{array}{c}\text{ density }=\frac{2\times10^{-11}\text{ grams }}{10^{-6}\text{ meter }^3}\\\text{ }\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,=2\times10^{-11-\left(-6\right)}\frac{\text{ grams }}{\text{ meter }^3}\\\text{ }\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,=2\times10^{-5}\frac{\text{ grams }}{\text{ meter }^3}\\\end{array}[/latex]

If scientists know the density of healthy cells, they can compare the density of a sick person’s cells to that to rule out or test for disorders or diseases that may affect cellular density.

The average density of a human cell is [latex]2\times10^{-5}\frac{\text{ grams }}{\text{ meter }^3}[/latex]

The following video provides an example of how to find the number of operations a computer can perform in a very short amount of time.

Light traveling from the sun to the earth.

In the next example, you will use another well known formula, [latex]d=r\cdot{t}[/latex], to find how long it takes light to travel from the sun to Earth. Unlike the previous example, the distance between the earth and the sun is massive, so the numbers you will work with have positive exponents.

The speed of light is [latex]3\times10^{8}\frac{\text{ meters }}{\text{ second }}[/latex]. If the sun is [latex]1.5\times10^{11}[/latex] meters from earth, how many seconds does it take for sunlight to reach the earth?  Write your answer in scientific notation.

Read and Understand:  We are looking for how long—an amount of time. We are given a rate which has units of meters per second and a distance in meters. This is a [latex]d=r\cdot{t}[/latex] problem.

Define and Translate: 

[latex]\begin{array}{l}d=1.5\times10^{11}\\r=3\times10^{8}\frac{\text{ meters }}{\text{ second }}\\t=\text{ ? }\end{array}[/latex]

Write and Solve:  Substitute the values we are given into the [latex]d=r\cdot{t}[/latex] equation. We will work without units to make it easier. Often, scientists will work with units to make sure they have made correct calculations.

[latex]\begin{array}{c}d=r\cdot{t}\\1.5\times10^{11}=3\times10^{8}\cdot{t}\end{array}[/latex]

Divide both sides of the equation by [latex]3\times10^{8}[/latex] to isolate  t.

[latex]\begin{array}{c}\frac{1.5\times10^{11}}{3\times10^{8}}=\frac{3\times10^{8}}{3\times10^{8}}\cdot{t}\end{array}[/latex]

On the left side, you will need to use the quotient rule of exponents to simplify, and on the right, you are left with  t. 

[latex]\begin{array}{c}\text{ }\\\left(\frac{1.5}{3}\right)\times\left(\frac{10^{11}}{10^{8}}\right)=t\\\text{ }\\\left(0.5\right)\times\left(10^{11-8}\right)=t\\0.5\times10^3=t\end{array}[/latex]

This answer is not in scientific notation, so we will move the decimal to the right, which means we need to subtract one factor of [latex]10[/latex].

[latex]0.5\times10^3=5.0\times10^2=t[/latex]

The time it takes light to travel from the sun to Earth is [latex]5.0\times10^2[/latex] seconds, or in standard notation, [latex]500[/latex] seconds.  That is not bad considering how far it has to travel!

Scientific notation was developed to assist mathematicians, scientists, and others when expressing and working with very large and very small numbers. Scientific notation follows a very specific format in which a number is expressed as the product of a number greater than or equal to one and less than ten times a power of [latex]10[/latex]. The format is written [latex]a\times10^{n}[/latex], where [latex]1\leq{a}<10[/latex] and n is an integer. To multiply or divide numbers in scientific notation, you can use the commutative and associative properties to group the exponential terms together and apply the rules of exponents.

• Orders of magnitude (mass). (n.d.). Retrieved May 26, 2016, from https://en.wikipedia.org/wiki/Orders_of_magnitude_(mass) ↵
• How Big is a Human Cell? ↵
• How big is a human cell? - Weizmann Institute of Science. (n.d.). Retrieved May [latex]26, 2016[/latex], from http://www.weizmann.ac.il/plants/Milo/images/humanCellSize120116Clean.pdf ↵
• Grover, W. H., Bryan, A. K., Diez-Silva, M., Suresh, S., Higgins, J. M., & Manalis, S. R. (2011). Measuring single-cell density. Proceedings of the National Academy of Sciences, 108(27), 10992-10996. doi:10.1073/pnas.1104651108 ↵
• Revision and Adaptation. Provided by : Lumen Learning. License : CC BY: Attribution
• Application of Scientific Notation - Quotient 1 (Number of Times Around the Earth). Authored by : James Sousa (Mathispower4u.com) for Lumen Learning. Located at : https://youtu.be/san2avgwu6k . License : CC BY: Attribution
• Application of Scientific Notation - Quotient 2 (Time for Computer Operations). Authored by : James Sousa (Mathispower4u.com) for Lumen Learning. Located at : https://youtu.be/Cbm6ejEbu-o . License : CC BY: Attribution
• Unit 11: Exponents and Polynomials, from Developmental Math: An Open Program. Provided by : Monterey Institute of Technology and Education. Located at : http://nrocnetwork.org/dm-opentext . License : CC BY: Attribution

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Solving Everyday Problems with the Scientific Method: Thinking Like a Scientist (Second Edition)

This book describes how one can use The Scientific Method to solve everyday problems including medical ailments, health issues, money management, traveling, shopping, cooking, household chores, etc. It illustrates how to exploit the information collected from our five senses, how to solve problems when no information is available for the present problem situation, how to increase our chances of success by redefining a problem, and how to extrapolate our capabilities by seeing a relationship among heretofore unrelated concepts. One should formulate a hypothesis as early as possible in order to have a sense of direction regarding which path to follow. Occasionally, by making wild conjectures, creative solutions can transpire. However, hypotheses need to be well-tested. Through this way, The Scientific Method can help readers solve problems in both familiar and unfamiliar situations. Containing real-life examples of how various problems are solved — for instance, how some observant patients cure their own illnesses when medical experts have failed — this book will train readers to observe what others may have missed and conceive what others may not have contemplated. With practice, they will be able to solve more problems than they could previously imagine. In this second edition, the authors have added some more theories which they hope can help in solving everyday problems. At the same time, they have updated the book by including quite a few examples which they think are interesting. Readership: General public interested in self-help books; undergraduates majoring in education and behavioral psychology; graduates and researchers with research interests in problem solving, creativity and scientific research methodology.

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math tutorials for students majoring in the earth sciences

Scientific Notation - Practice Problems

Solving earth science problems with scientific notation, × div[id^='image-'] {position:static}div[id^='image-'] div.hover{position:static} introductory problems.

These problems cover the fundamentals of writing scientific notation and using it to understand relative size of values and scientific prefixes.

Problem 1: The distance to the moon is 238,900 miles. Write this value in scientific notation.

Problem 2: One mile is 1609.34 meters. What is the distance to the moon in meters using scientific notation?

`1609.34 m/(mi) xx 238","900 mi` = 384,400,000 m

Notice in the above unit conversion the 'mi' units cancel each other out because 'mi' is in the denominator for the first term and the numerator for the second term

Problem 4: The atomic radius of a magnesium atom is approximately 1.6 angstroms, which is equal to 1.6 x 10 -10 meters (m). How do you write this length in standard form?

 0.00000000016 m  

Fissure A = 40,0000 m Fissure B = 5,0000 m

This shows fissure A is larger (by almost 10 times!). The shortcut to answer a question like this is to look at the exponent. If both coefficients are between 1-10, then the value with the larger exponent is the larger number.

Problem 6: The amount of carbon in the atmosphere is 750 petagrams (pg). One petagram equals 1 x 10 15 grams (g). Write out the amount of carbon in the atmosphere in (i) scientific notation and (ii) standard decimal format.

The exponent is a positive number, so the decimal will move to the right in the next step.

750,000,000,000,000,000 g

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Softening the sharp edges in mathematics.

For everyone whose relationship with mathematics is distant or broken, Jo Boaler , a professor at Stanford Graduate School of Education (GSE), has ideas for repairing it. She particularly wants young people to feel comfortable with numbers from the start — to approach the subject with playfulness and curiosity, not anxiety or dread.

“Most people have only ever experienced what I call narrow mathematics — a set of procedures they need to follow, at speed,” Boaler says. “Mathematics should be flexible, conceptual, a place where we play with ideas and make connections. If we open it up and invite more creativity, more diverse thinking, we can completely transform the experience.”

“Mathematics should be flexible, conceptual, a place where we play with ideas and make connections," says Professor Jo Boaler. (Photo: Robert Houser Photography)

Boaler, the Nomellini and Olivier Professor of Education at the GSE, is the co-founder and faculty director of Youcubed , a Stanford research center that provides resources for math learning that has reached more than 230 million students in over 140 countries. In 2013 Boaler, a former high school math teacher, produced “How to Learn Math,” the first massive open online course (MOOC) on mathematics education. She leads workshops and leadership summits for teachers and administrators, and her online courses have been taken by over a million users. 

In her new book, Math-ish: Finding Creativity, Diversity, and Meaning in Mathematics , Boaler argues for a broad, inclusive approach to math education, offering strategies and activities for learners at any age. We spoke with her about why creativity is an important part of mathematics, the impact of representing numbers visually and physically, and how what she calls “ishing” a math problem can help students make better sense of the answer. 

What do you mean by “math-ish” thinking?

It’s a way of thinking about numbers in the real world, which are usually imprecise estimates. If someone asks how old you are, how warm it is outside, how long it takes to drive to the airport – these are generally answered with what I call “ish” numbers, and that’s very different from the way we use and learn numbers in school.

In the book I share an example of a multiple-choice question from a nationwide exam where students are asked to estimate the sum of two fractions: 12/13 + 7/8. They’re given four choices for the closest answer: 1, 2, 19, or 21. Each of the fractions in the question is very close to 1, so the answer would be 2 — but the most common answer 13-year-olds gave was 19. The second most common was 21. 

I’m not surprised, because when students learn fractions, they often don’t learn to think conceptually or to consider the relationship between the numerator or denominator. They learn rules about creating common denominators and adding or subtracting the numerators, without making sense of the fraction as a whole. But stepping back and judging whether a calculation is reasonable might be the most valuable mathematical skill a person can develop.

But don’t you also risk sending the message that mathematical precision isn’t important? 

I’m not saying precision isn’t important. What I’m suggesting is that we ask students to estimate before they calculate, so when they come up with a precise answer, they’ll have a real sense for whether it makes sense. This also helps students learn how to move between big-picture and focused thinking, which are two different but equally important modes of reasoning.

Some people ask me, “Isn’t ‘ishing’ just estimating?” It is, but when we ask students to estimate, they often groan, thinking it’s yet another mathematical method. But when we ask them to “ish” a number, they're more willing to offer their thinking.

Ishing helps students develop a sense for numbers and shapes. It can help soften the sharp edges in mathematics, making it easier for kids to jump in and engage. It can buffer students against the dangers of perfectionism, which we know can be a damaging mind-set. I think we all need a little more ish in our lives. 

You also argue that mathematics should be taught in more visual ways. What do you mean by that? 

For most people, mathematics is an almost entirely symbolic, numerical experience. Any visuals are usually sterile images in a textbook, showing bisecting angles, or circles divided into slices. But the way we function in life is by developing models of things in our minds. Take a stapler: Knowing what it looks like, what it feels and sounds like, how to interact with it, how it changes things — all of that contributes to our understanding of how it works. 

There’s an activity we do with middle-school students where we show them an image of a 4 x 4 x 4 cm cube made up of smaller 1 cm cubes, like a Rubik’s Cube. The larger cube is dipped into a can of blue paint, and we ask the students, if they could take apart the little cubes, how many sides would be painted blue? Sometimes we give the students sugar cubes and have them physically build a larger 4 x 4 x 4 cube. This is an activity that leads into algebraic thinking. 

Some years back we were interviewing students a year after they’d done that activity in our summer camp and asked what had stayed with them. One student said, ‘I’m in geometry class now, and I still remember that  sugar cube, what it looked like and felt like.’ His class had been asked to estimate the volume of their shoes, and he said he’d imagined his shoes filled with 1 cm sugar cubes in order to solve that question. He had built a mental model of a cube.

When we learn about cubes, most of us don’t get to see and manipulate them. When we learn about square roots, we don’t take squares and look at their diagonals. We just manipulate numbers.

I wonder if people consider the physical representations more appropriate for younger kids.

That’s the thing — elementary school teachers are amazing at giving kids those experiences, but it dies out in middle school, and by high school it’s all symbolic. There’s a myth that there’s a hierarchy of sophistication where you start out with visual and physical representations and then build up to the symbolic. But so much of high-level mathematical work now is visual. Here in Silicon Valley, if you look at Tesla engineers, they're drawing, they're sketching, they're building models, and nobody says that's elementary mathematics.

Click to enlarge: A depiction of various ways to calculate 38 x 5, numerically and visually. (Image: Courtesy of Jo Boaler)

There’s an example in the book where you’ve asked students how they would calculate 38 x 5 in their heads, and they come up with several different ways of arriving at the same answer. The creativity is fascinating, but wouldn’t it be easier to teach students one standard method?

That narrow, rigid version of mathematics where there’s only one right approach is what most students experience, and it’s a big part of why people have such math trauma. It keeps them from realizing the full range and power of mathematics. When you only have students blindly memorizing math facts, they’re not developing number sense. They don’t learn how to use numbers flexibly in different situations. It also makes students who think differently believe there’s something wrong with them. 

When we open mathematics to acknowledge the different ways a concept or problem can be viewed, we also open the subject to many more students. Mathematical diversity, to me, is a concept that includes both the value of diversity in people and the diverse ways we can see and learn mathematics. When we bring those forms of diversity together, it’s powerful. If we want to value different ways of thinking and problem-solving in the world, we need to embrace mathematical diversity.

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Scientists use generative AI to answer complex questions in physics

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When water freezes, it transitions from a liquid phase to a solid phase, resulting in a drastic change in properties like density and volume. Phase transitions in water are so common most of us probably don’t even think about them, but phase transitions in novel materials or complex physical systems are an important area of study.

To fully understand these systems, scientists must be able to recognize phases and detect the transitions between. But how to quantify phase changes in an unknown system is often unclear, especially when data are scarce.

Researchers from MIT and the University of Basel in Switzerland applied generative artificial intelligence models to this problem, developing a new machine-learning framework that can automatically map out phase diagrams for novel physical systems.

Their physics-informed machine-learning approach is more efficient than laborious, manual techniques which rely on theoretical expertise. Importantly, because their approach leverages generative models, it does not require huge, labeled training datasets used in other machine-learning techniques.

Such a framework could help scientists investigate the thermodynamic properties of novel materials or detect entanglement in quantum systems, for instance. Ultimately, this technique could make it possible for scientists to discover unknown phases of matter autonomously.

“If you have a new system with fully unknown properties, how would you choose which observable quantity to study? The hope, at least with data-driven tools, is that you could scan large new systems in an automated way, and it will point you to important changes in the system. This might be a tool in the pipeline of automated scientific discovery of new, exotic properties of phases,” says Frank Schäfer, a postdoc in the Julia Lab in the Computer Science and Artificial Intelligence Laboratory (CSAIL) and co-author of a paper on this approach.

Joining Schäfer on the paper are first author Julian Arnold, a graduate student at the University of Basel; Alan Edelman, applied mathematics professor in the Department of Mathematics and leader of the Julia Lab; and senior author Christoph Bruder, professor in the Department of Physics at the University of Basel. The research is published today in Physical Review Letters.

Detecting phase transitions using AI

While water transitioning to ice might be among the most obvious examples of a phase change, more exotic phase changes, like when a material transitions from being a normal conductor to a superconductor, are of keen interest to scientists.

These transitions can be detected by identifying an “order parameter,” a quantity that is important and expected to change. For instance, water freezes and transitions to a solid phase (ice) when its temperature drops below 0 degrees Celsius. In this case, an appropriate order parameter could be defined in terms of the proportion of water molecules that are part of the crystalline lattice versus those that remain in a disordered state.

In the past, researchers have relied on physics expertise to build phase diagrams manually, drawing on theoretical understanding to know which order parameters are important. Not only is this tedious for complex systems, and perhaps impossible for unknown systems with new behaviors, but it also introduces human bias into the solution.

More recently, researchers have begun using machine learning to build discriminative classifiers that can solve this task by learning to classify a measurement statistic as coming from a particular phase of the physical system, the same way such models classify an image as a cat or dog.

The MIT researchers demonstrated how generative models can be used to solve this classification task much more efficiently, and in a physics-informed manner.

The Julia Programming Language , a popular language for scientific computing that is also used in MIT’s introductory linear algebra classes, offers many tools that make it invaluable for constructing such generative models, Schäfer adds.

Generative models, like those that underlie ChatGPT and Dall-E, typically work by estimating the probability distribution of some data, which they use to generate new data points that fit the distribution (such as new cat images that are similar to existing cat images).

However, when simulations of a physical system using tried-and-true scientific techniques are available, researchers get a model of its probability distribution for free. This distribution describes the measurement statistics of the physical system.

A more knowledgeable model

The MIT team’s insight is that this probability distribution also defines a generative model upon which a classifier can be constructed. They plug the generative model into standard statistical formulas to directly construct a classifier instead of learning it from samples, as was done with discriminative approaches.

“This is a really nice way of incorporating something you know about your physical system deep inside your machine-learning scheme. It goes far beyond just performing feature engineering on your data samples or simple inductive biases,” Schäfer says.

This generative classifier can determine what phase the system is in given some parameter, like temperature or pressure. And because the researchers directly approximate the probability distributions underlying measurements from the physical system, the classifier has system knowledge.

This enables their method to perform better than other machine-learning techniques. And because it can work automatically without the need for extensive training, their approach significantly enhances the computational efficiency of identifying phase transitions.

At the end of the day, similar to how one might ask ChatGPT to solve a math problem, the researchers can ask the generative classifier questions like “does this sample belong to phase I or phase II?” or “was this sample generated at high temperature or low temperature?”

Scientists could also use this approach to solve different binary classification tasks in physical systems, possibly to detect entanglement in quantum systems (Is the state entangled or not?) or determine whether theory A or B is best suited to solve a particular problem. They could also use this approach to better understand and improve large language models like ChatGPT by identifying how certain parameters should be tuned so the chatbot gives the best outputs.

In the future, the researchers also want to study theoretical guarantees regarding how many measurements they would need to effectively detect phase transitions and estimate the amount of computation that would require.

This work was funded, in part, by the Swiss National Science Foundation, the MIT-Switzerland Lockheed Martin Seed Fund, and MIT International Science and Technology Initiatives.

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1.12: Scientific Problem Solving

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• Page ID 52325

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How can we use problem solving in our everyday routines?

One day you wake up and realize your clock radio did not turn on to get you out of bed. You are puzzled, so you decide to find out what happened. You list three possible explanations:

• There was a power failure and your radio cannot turn on.
• Your little sister turned it off as a joke.
• You did not set the alarm last night.

Upon investigation, you find that the clock is on, so there is no power failure. Your little sister was spending the night with a friend and could not have turned the alarm off. You notice that the alarm is not set—your forgetfulness made you late. You have used the scientific method to answer a question.

Scientific Problem Solving

Humans have always wondered about the world around them. One of the questions of interest was (and still is): what is this world made of? Chemistry has been defined in various ways as the study of matter. What matter consists of has been a source of debate over the centuries. One of the key areas for this debate in the Western world was Greek philosophy.

The basic approach of the Greek philosophers was to discuss and debate the questions they had about the world. There was no gathering of information to speak of, just talking. As a result, several ideas about matter were put forth, but never resolved. The first philosopher to carry out the gathering of data was Aristotle (384-322 B.C.). He recorded many observations on the weather, on plant and animal life and behavior, on physical motions, and a number of other topics. Aristotle could probably be considered the first "real" scientist, because he made systematic observations of nature and tried to understand what he was seeing.

Inductive and Deductive Reasoning

Two approaches to logical thinking developed over the centuries. These two methods are inductive reasoning and deductive reasoning . Inductive reasoning involves getting a collection of specific examples and drawing a general conclusion from them. Deductive reasoning takes a general principle and then draws a specific conclusion from the general concept. Both are used in the development of scientific ideas.

Inductive reasoning first involves the collection of data: "If I add sodium metal to water, I observe a very violent reaction. Every time I repeat the process, I see the same thing happen." A general conclusion is drawn from these observations: the addition of sodium to water results in a violent reaction.

In deductive reasoning, a specific prediction is made based on a general principle. One general principle is that acids turn blue litmus paper red. Using the deductive reasoning process, one might predict: "If I have a bottle of liquid labeled 'acid', I expect the litmus paper to turn red when I immerse it in the liquid."

The Idea of the Experiment

Inductive reasoning is at the heart of what is now called the " scientific method ." In European culture, this approach was developed mainly by Francis Bacon (1561-1626), a British scholar. He advocated the use of inductive reasoning in every area of life, not just science. The scientific method, as developed by Bacon and others, involves several steps:

• Ask a question - identify the problem to be considered.
• Make observations - gather data that pertains to the question.
• Propose an explanation (a hypothesis) for the observations.
• Make new observations to test the hypothesis further.

Note that this should not be considered a "cookbook" for scientific research. Scientists do not sit down with their daily "to do" list and write down these steps. The steps may not necessarily be followed in order. But this does provide a general idea of how scientific research is usually done.

When a hypothesis is confirmed repeatedly, it eventually becomes a theory—a general principle that is offered to explain natural phenomena. Note a key word— explain , or  explanation . A theory offers a description of why something happens. A law, on the other hand, is a statement that is always true, but offers no explanation as to why. The law of gravity says a rock will fall when dropped, but does not explain why (gravitational theory is very complex and incomplete at present). The kinetic molecular theory of gases, on the other hand, states what happens when a gas is heated in a closed container (the pressure increases), but also explains why (the motions of the gas molecules are increased due to the change in temperature). Theories do not get "promoted" to laws, because laws do not answer the "why" question.

• The early Greek philosophers spent their time talking about nature, but did little or no actual exploration or investigation.
• Inductive reasoning - to develop a general conclusion from a collection of observations.
• Deductive reasoning - to make a specific statement based on a general principle.
• Scientific method - a process of observation, developing a hypothesis, and testing that hypothesis.
• What was the basic shortcoming of the Greek philosophers approach to studying the material world?
• How did Aristotle improve the approach?
• Define “inductive reasoning” and give an example.
• Define “deductive reasoning” and give an example.
• What is the difference between a hypothesis and a theory?
• What is the difference between a theory and a law?

May 10, 2024

Brain Worms like the One in RFK, Jr.’s Head Are Actually a Global Problem

Experts explain how certain worms can infect the brain and why they are an important global public health problem

By Lauren J. Young

Magnetic resonance imaging (MRI) scan of an axial section through the brain of a 25-year-old patient showing cysts (purple) from a tapeworm infection.

Zephyr/Getty Images

Earlier this week news broke that independent presidential candidate Robert F. Kennedy, Jr., claimed to have once had a dead worm in his brain. Kennedy had been experiencing memory loss and mental fog, and he originally suspected these symptoms might be caused by a brain tumor. Brain scans in 2010 showed a cyst that his doctors said contained remains of a parasite. The findings and other health issues were revealed in a New York Times article based on a review of a deposition for his 2012 divorce, as well as an interview the outlet conducted with him.

The revelation drew attention in the worlds of politics and parasitology. “I woke up to all kinds of messages from friends in parasitology,” says Shira Shafir, an epidemiologist and an associate adjunct professor at the University of California, Los Angeles, in response to the news.

The species of the purported parasite in Kennedy’s brain was never identified, and he did not know where he got infected. A spokesperson told media outlets on Wednesday that Kennedy had traveled extensively to Africa, South America, and Asia and likely contracted the parasite on one of the trips. Several parasites can affect the central nervous system and potentially create cysts in brain tissue. While relatively uncommon in the U.S., such infections can be devastating in many parts of the world. For example, the World Health Organization estimates there are between 2.56 million and 8.3 million people around the globe living with neurocysticercosis, a brain infection caused by the pork tapeworm Taenia solium . “It's a really big deal in Latin America, sub-Saharan Africa, India and other parts of Asia. It’s a leading cause of acquired seizures,” says Clinton White, a parasitologist and infectious diseases professor at the University of Texas Medical Branch at Galveston. “Neurocysticercosis is a major disease, and it's kind of funny [these are] the circumstances in which people are paying attention to it.”

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Scientific American spoke with Shafir and White to discuss how parasitic worms may infect the brain, what symptoms they cause and how infections are diagnosed and treated.

[ An edited transcript of the interviews follows .]

What are parasitic worms, and which ones can infect the brain?

SHAFIR: We generally don’t have adult worms that end up in the brain. What does end up in the brain are parasites in their earlier developmental stages, such as eggs or larvae—or, for lack of a better word, baby worms. So generally the parasitic infections that can impact the brain are those of pathogens in early developmental stages, which, for the most part, accidentally make it into the brain.

I study a few parasitic infections that impact the central nervous system. The most common one is Taenia solium, the pork tapeworm. It has an incredibly complicated life cycle in which individuals get infected by consuming undercooked infected pork. [But] there is no chance that, through the consumption of undercooked pork itself, someone could develop neurocysticercosis.

Other species that I work on are Baylisascaris procyonis [the raccoon roundworm] and Angiostrongylus cantonensis [the rat lungworm], both of which can produce larvae that will travel through the [human] body in order to try and find the tissue that they prefer and that can accidentally end up in the brain. And they can cause some really significant neuropathological changes.

Walk me through the life cycle of Taenia solium . How does it infect humans?

SHAFIR: Definitively, pigs are the natural hosts. So pigs get infected with a tapeworm. When it is in the pig, it penetrates the intestinal wall and goes to the musculature. The musculature is obviously the part of pigs that people consume. So humans, if they consume uncooked or undercooked infected pork, can get infected with the intestinal form of the tapeworm. And then they will pass eggs in their feces, and if those eggs are consumed by pigs, the pigs get infected, and that kind of continues, on and on. But if, accidentally, another human or the infected human themself—because many people don’t have great hand hygiene—comes into contact with the fecal material and swallows the eggs, the eggs will then hatch, they will penetrate the intestinal wall, and they’ll circulate [in the bloodstream] to the musculature. They can then end up in any organ throughout the body, but most commonly they go to the subcutaneous tissues, as well as the brain and the eyes.

So if you eat raw pork, you get a tapeworm—that’s an intestinal problem. If you come into contact with fecal material from a person who has the intestinal tapeworm, that’s how you end up with this neurological manifestation.

What are the symptoms of neurocysticercosis?

WHITE: The disease from infection with T. solium in the tissues is called cysticercosis, and when it infects the brain, the disease is called neurocysticercosis . In most places [in the body] the larvae don’t cause a lot of problems and end up dying. Those that end up in the brain can survive for a few years, and they usually do not cause a lot of problems. The cysts, these little round, balloonlike structures, are about a centimeter in diameter and are clear, fluid-filled sacs. Sometimes the cysts can become big enough that if they get into the fluid around the brain, called the cerebrospinal fluid (CSF), they can get stuck at little openings in the brain and block the flow [of CSF]. That leads to hydrocephalus [swelling of the brain], and that’s often fatal unless the patient undergoes emergency surgery. But usually the cysts don’t cause a lot of problems—it’s the inflammatory response that you get when [the larvae] are starting to die and dying that can cause problems—particularly seizures.

SHAFIR: Once [the eggs of T. solium ] get to the musculature—either the musculature of the pig or the musculature of a person—they're going to “encyst,” which essentially is a cute little cuddly term for parasites rolling up into a ball and creating a protective structure. That process can happen in the brain. And depending on where in the brain [the cysts] are, they can disturb pretty important brain functions.

The [Centers for Disease Control and Prevention] actually has some really striking images of what it looks like when someone has neurocysticercosis. There are these cysts, or little balled-up eggs, in the brain—it has a very Swiss-cheese appearance.

Can the condition cause memory loss?

WHITE: No, it usually doesn’t directly cause much in the way of memory loss. If you do careful psychological tests, you may see some minor [memory] problems, but [this] wouldn’t be a common symptom. If someone has had frequent seizures, however, they can end up with memory loss. People wouldn’t describe brain fog or memory problems. As an aside, those are more typical of mercury poisoning. [ Editor’s Note: According to the New York Times , Kennedy has said he also experienced mercury poisoning around the time he had learned of his parasitic infection. Mercury exposure has been linked to central nervous system damage that can cause memory loss and Alzheimer’s disease .]

According to the New York Times, Kennedy claimed that the worm that infected him “ate a portion” of his brain. Can tapeworms “eat” brain tissue?

SHARIF: Discussions of eating brains are better left in zombie movies than in legitimate scientific discourse. The parasitic infections that impact the brain do not eat the brain. Now, that doesn’t mean that they cannot damage brain tissue. But that kind of inflammatory language indicates a lack of scientific literacy and is pretty concerning.

How is neurocysticercosis diagnosed and treated?

WHITE: The main diagnostics are imaging studies of the brain, such as a [computed tomography (CT)] scan or magnetic resonance imaging. Some of the findings on those scans can be confused with other things, however, so there are confirmatory tests that look for antibodies to the parasite. The CDC developed an excellent test that's very specific to the pathogen—a lot of the commercial tests are not that accurate. More recently, scientists have developed what's called a PCR test and an antigen detection test, and those are really quite helpful, particularly in severe cases. The treatment starts out with addressing the symptoms. If a patient has seizures, you should give them antiseizure medicine. If they have hydrocephalus, they may require neurosurgery. Anti-inflammatory steroids and antiparasitic drugs often hasten the demise of the parasites, and their use can be associated with somewhat fewer seizures. Sometimes it takes repeated treatments to kill them, but they do die. They don’t live forever even if you don’t treat them. There are cases [in which the larvae cause] calcified lesions that have been there for a long time in which you can get damage to a part of the brain called the hippocampus. This can be associated with seizures that are not relieved until you have surgery.

How common are these infections?

SHAFIR: Generally, cysticercosis [and neurocysticercosis are] far more common in low-income regions, including those in Latin America. We do a lot of work with communities from [there]. Because part of the tapeworm’s life cycle requires that individuals consume raw or undercooked pork and that [this meat is] allowed to be infected, we generally don’t see tapeworm transmission in the U.S. because of our robust [U.S. Department of Agriculture] inspection process. This means that the individuals who are getting infected are either from communities where it is common for pork to be infected or have traveled to those countries. Here in the U.S. we have about 1,000 hospitalizations each year —and those happen in the states where you have the greatest amount of international travel, such as New York, California, Texas and Illinois.

It is unfortunate that these parasitic infections, which disproportionately impact individuals in low- and middle-income countries, only get the attention and discussion when a high-profile individual gets infected. There are thousands of people throughout the world who are dealing with legitimate [problems] from these parasitic infections. We underfund research. We underfund the development of new treatments, which are not prioritized until they become front-page-worthy news because they’re impacting someone who is notable.

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‘you can solve anything’.

Priyanka Pillai wants to take on big problems — and has learned how good design can help

Christina Pazzanese

Harvard Staff Writer

Niles Singer/Harvard Staff Photographer

Part of the Commencement 2024 series

A collection of stories covering Harvard University’s 373rd Commencement.

Growing up in India, Priyanka Pillai witnessed the immense and varied struggles many impoverished people faced in their daily lives, such as getting prenatal care and protecting children from labor exploitation.

As an undergraduate in Bangalore studying industrial design, she wondered whether good design could help ease at least parts of these and other challenges. She came to Harvard Graduate School of Design two years ago and got her answer, discovering she could take on big problems “that you don’t even realize … could be tackled with design.”

Pillai wanted to do something to help address the refugee crisis in Uganda for her independent design engineering project. Those projects span two semesters and call for students seeking a master’s in design engineering (a joint GSD and John A. Paulson School of Engineering and Applied Sciences program) to identify complex, real-world problems and develop solution prototypes.

“For the first time, I truly felt like I was doing work that was very in touch with what GSD wants people to do, which is working with communities.”

Conducting fieldwork in Uganda, Pillai saw the difficulties that South Sudanese refugees were having reuniting with their families. The plight of those fleeing the ongoing civil war in the northeast African nation has become one of the largest refugee crises in the world, with more than half a million living in Uganda alone, mostly in camps.

More than 60 percent are children separated from parents who are looking for them, Pillai said, and need multiple layers of support. While non-governmental organizations (NGOs) are providing some assistance, much more help is needed.

“One thing that really stood out was agency. There’s currently a lack of agency when it comes to finding their family members on their own,” said Pillai, who graduates later this month. Many refugees use informal, ad hoc methods such as phone calls, WhatsApp, and photo sharing to try to find relatives.

“The second part, which is extremely critical, is that we need to move from a Western-centric way of finding a family member,” such as cataloguing names, ages, and date of separation done by NGOs, because it doesn’t capture vernacularor local geography, vital details that may speed up reunification, she said, noting that learning more about how to design for “the Indian context” and the Global South more generally was a key reason she came to Harvard.

“A lot of cultural nuances were missing in connection to the data to find missing family members,” she said. “And that’s the kind of solution that we’re moving toward.”

Given the ubiquity of cellphones there, Pillai and classmate Julius Stein designed and built an online platform for refugees to enter information about themselves using text, photos, and audio. The platform generates a series of questions that can lead to possible matches while minimizing the risk of exploitation by malign actors.

“For the first time, I truly felt like I was doing work that was very in touch with what GSD wants people to do, which is working with communities,” she said. “It was just a life-changing experience.”

Earlier this month, one startup Pillai is involved in, Alba, won an Ingenuity Award as part of the Harvard President’s Innovation Challenge. The team designed a special wipe so the visually impaired can better detect when their menstrual period has begun without relying on outside assistance.

In 2023, Pillai was part of a student project that won gold in the Spark International Design awards. The design team created Felt, a haptic armband that turns sound and visual clues into movement. The device assists people who are deaf blind to independently catch emotional nuances or subtexts in conversations, which often get lost in Braille or other translations.

During her time in the program, Pillai also jumped at the opportunity to take courses at the Harvard Kennedy School, Harvard Law School, and Harvard Graduate School of Education to learn more about things such as accessibility, ethical design, and negotiation.

“I knew that I was limiting myself because I didn’t know all these different things,” she said.

When not focused on her own studies, Pillai has been a teaching fellow for a design studio at GSD and at SEAS for a course led by her IDEP adviser, Krzysztof Gajos, Gordon McKay Professor of Computer Science.

“I love teaching,” she said. “It’s one of my favorite experiences.”

Reflecting on her time at GSD, Pillai has been deeply inspired by the faculty and her fellow students. This group from many different backgrounds with different interests and perspectives, working in many different disciplines, has been like a “dream” design studio where she’s been able to share and borrow ideas and practices from others and see how other fields look at things such as collaboration, sustainability and accessibility. It has been intellectually liberating to experience such fearlessness, she said, after years of feeling so “constrained” in her prior practice, which had been “rooted in ‘realistic goals.’”

“People tackling very huge issues that you don’t even realize 1) is a problem that could be tackled with design, and 2), they’re almost your age and they’re doing it somehow. That was very important to see,” she said.

“People really think that you can solve anything.”

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