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• How to Write a Strong Hypothesis | Guide & Examples

How to Write a Strong Hypothesis | Guide & Examples

Published on 6 May 2022 by Shona McCombes .

A hypothesis is a statement that can be tested by scientific research. If you want to test a relationship between two or more variables, you need to write hypotheses before you start your experiment or data collection.

Table of contents

What is a hypothesis, developing a hypothesis (with example), hypothesis examples, frequently asked questions about writing hypotheses.

A hypothesis states your predictions about what your research will find. It is a tentative answer to your research question that has not yet been tested. For some research projects, you might have to write several hypotheses that address different aspects of your research question.

A hypothesis is not just a guess – it should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations, and statistical analysis of data).

Variables in hypotheses

Hypotheses propose a relationship between two or more variables . An independent variable is something the researcher changes or controls. A dependent variable is something the researcher observes and measures.

In this example, the independent variable is exposure to the sun – the assumed cause . The dependent variable is the level of happiness – the assumed effect .

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Step 1: ask a question.

Writing a hypothesis begins with a research question that you want to answer. The question should be focused, specific, and researchable within the constraints of your project.

Step 2: Do some preliminary research

Your initial answer to the question should be based on what is already known about the topic. Look for theories and previous studies to help you form educated assumptions about what your research will find.

At this stage, you might construct a conceptual framework to identify which variables you will study and what you think the relationships are between them. Sometimes, you’ll have to operationalise more complex constructs.

Step 3: Formulate your hypothesis

Now you should have some idea of what you expect to find. Write your initial answer to the question in a clear, concise sentence.

Step 4: Refine your hypothesis

You need to make sure your hypothesis is specific and testable. There are various ways of phrasing a hypothesis, but all the terms you use should have clear definitions, and the hypothesis should contain:

• The relevant variables
• The specific group being studied
• The predicted outcome of the experiment or analysis

Step 5: Phrase your hypothesis in three ways

To identify the variables, you can write a simple prediction in if … then form. The first part of the sentence states the independent variable and the second part states the dependent variable.

In academic research, hypotheses are more commonly phrased in terms of correlations or effects, where you directly state the predicted relationship between variables.

If you are comparing two groups, the hypothesis can state what difference you expect to find between them.

Step 6. Write a null hypothesis

If your research involves statistical hypothesis testing , you will also have to write a null hypothesis. The null hypothesis is the default position that there is no association between the variables. The null hypothesis is written as H 0 , while the alternative hypothesis is H 1 or H a .

Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is used by scientists to test specific predictions, called hypotheses , by calculating how likely it is that a pattern or relationship between variables could have arisen by chance.

A hypothesis is not just a guess. It should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations, and statistical analysis of data).

A research hypothesis is your proposed answer to your research question. The research hypothesis usually includes an explanation (‘ x affects y because …’).

A statistical hypothesis, on the other hand, is a mathematical statement about a population parameter. Statistical hypotheses always come in pairs: the null and alternative hypotheses. In a well-designed study , the statistical hypotheses correspond logically to the research hypothesis.

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HYPOTHESIS in a Sentence Examples: 21 Ways to Use Hypothesis

Have you ever wondered what a “hypothesis” is and how it fits into the scientific method? A hypothesis is a proposed explanation or educated guess that can be tested through research and experimentation to determine its validity.

In scientific inquiry, a hypothesis serves as the foundation for the study, guiding the direction of the research and helping to form conclusions based on the results. By formulating clear hypotheses, researchers can systematically investigate phenomena and gather evidence to support their claims.

Table of Contents

7 Examples Of Hypothesis Used In a Sentence For Kids

• Hypothesis is a guess we can test.
• We can make a hypothesis about what will happen.
• Our hypothesis will help us learn new things.
• Let’s think of a hypothesis to investigate.
• We can use our hypothesis to solve a problem.
• A good hypothesis can help us understand the world.
• Remember, our hypothesis is just a starting point.

14 Sentences with Hypothesis Examples

• Hypothesis : Students who study for at least 3 hours every day are likely to perform better in their exams.
• It is important for college students to form a hypothesis before conducting any research project.
• Hypothesis : Attending lectures regularly can significantly improve academic performance.
• College students can test their hypothesis through interactive experiments and surveys.
• Hypothesis : Using different study methods can have varied effects on information retention.
• It is necessary for students to critically analyze data to support or reject their hypothesis .
• Hypothesis : Students who engage in extracurricular activities may have a better overall college experience.
• In a scientific study, researchers must clearly define their hypothesis before proceeding with the experiment.
• Hypothesis : Regular exercise can positively impact a student’s mental health and academic performance.
• It is crucial for college students to document their hypothesis and research findings accurately.
• Hypothesis : Students who limit their social media usage may experience improved focus and productivity.
• College projects often require students to brainstorm and formulate a solid hypothesis .
• It is common for students to revise their hypothesis based on new information or research outcomes.
• Hypothesis : Implementing study breaks can enhance retention and understanding of complex subjects.

How To Use Hypothesis in Sentences?

Hypothesis is an educated guess or prediction that can be tested through observation or experimentation. When incorporating this term into a sentence, it is important to clearly identify it so readers can understand its significance.

Here are some tips on how to use hypothesis effectively in a sentence:

Clearly state your hypothesis in a simple and concise manner. For example, “The scientist’s hypothesis is that plants will grow faster with added sunlight.”

Use the word hypothesis to introduce your prediction or expectation before testing it. For instance, “Our hypothesis is that students who study regularly will perform better on the exam.”

Make sure to refer back to your hypothesis when discussing the results of your experiment. For example, “The data supported our initial hypothesis that exercise leads to improved cardiovascular health.”

You can also use the word hypothesis when comparing multiple predictions. For instance, “There are several hypotheses about the cause of the mysterious illness, but more research is needed to determine the correct one.”

By following these guidelines, you can effectively incorporate hypothesis into your writing to communicate your predictions or expectations clearly and accurately.

In conclusion, sentences with the keyword “hypothesis” often express a proposed explanation or prediction that can be tested through research or observation. These sentences play a crucial role in scientific inquiry by guiding investigations and exploring relationships between variables. For example, “The researchers formulated a hypothesis to predict the effect of sunlight on plant growth” demonstrates how hypotheses are used to frame a study’s objectives and outcomes.

Clear and concise sentences with hypotheses are essential for building a solid foundation for scientific exploration and discovery. They provide a starting point for experiments, helping researchers to structure their methodologies and draw meaningful conclusions. By carefully crafting hypotheses, scientists can effectively test their theories, gather evidence, and contribute to the advancement of knowledge in various fields.

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Think about something strange and unexplainable in your life. Maybe you get a headache right before it rains, or maybe you think your favorite sports team wins when you wear a certain color. If you wanted to see whether these are just coincidences or scientific fact, you would form a hypothesis, then create an experiment to see whether that hypothesis is true or not.

But what is a hypothesis, anyway? If you’re not sure about what a hypothesis is--or how to test for one!--you’re in the right place. This article will teach you everything you need to know about hypotheses, including: 

• Defining the term “hypothesis” 
• Providing hypothesis examples 
• Giving you tips for how to write your own hypothesis

So let’s get started!

What Is a Hypothesis?

Merriam Webster defines a hypothesis as “an assumption or concession made for the sake of argument.” In other words, a hypothesis is an educated guess . Scientists make a reasonable assumption--or a hypothesis--then design an experiment to test whether it’s true or not. Keep in mind that in science, a hypothesis should be testable. You have to be able to design an experiment that tests your hypothesis in order for it to be valid. 

As you could assume from that statement, it’s easy to make a bad hypothesis. But when you’re holding an experiment, it’s even more important that your guesses be good...after all, you’re spending time (and maybe money!) to figure out more about your observation. That’s why we refer to a hypothesis as an educated guess--good hypotheses are based on existing data and research to make them as sound as possible.

Hypotheses are one part of what’s called the scientific method .  Every (good) experiment or study is based in the scientific method. The scientific method gives order and structure to experiments and ensures that interference from scientists or outside influences does not skew the results. It’s important that you understand the concepts of the scientific method before holding your own experiment. Though it may vary among scientists, the scientific method is generally made up of six steps (in order):

• Observation
• Asking questions
• Forming a hypothesis
• Analyze the data
• Communicate your results

You’ll notice that the hypothesis comes pretty early on when conducting an experiment. That’s because experiments work best when they’re trying to answer one specific question. And you can’t conduct an experiment until you know what you’re trying to prove!

Independent and Dependent Variables 

After doing your research, you’re ready for another important step in forming your hypothesis: identifying variables. Variables are basically any factor that could influence the outcome of your experiment . Variables have to be measurable and related to the topic being studied.

There are two types of variables:  independent variables and dependent variables. I ndependent variables remain constant . For example, age is an independent variable; it will stay the same, and researchers can look at different ages to see if it has an effect on the dependent variable. 

Speaking of dependent variables... dependent variables are subject to the influence of the independent variable , meaning that they are not constant. Let’s say you want to test whether a person’s age affects how much sleep they need. In that case, the independent variable is age (like we mentioned above), and the dependent variable is how much sleep a person gets. 

Variables will be crucial in writing your hypothesis. You need to be able to identify which variable is which, as both the independent and dependent variables will be written into your hypothesis. For instance, in a study about exercise, the independent variable might be the speed at which the respondents walk for thirty minutes, and the dependent variable would be their heart rate. In your study and in your hypothesis, you’re trying to understand the relationship between the two variables.

Elements of a Good Hypothesis

The best hypotheses start by asking the right questions . For instance, if you’ve observed that the grass is greener when it rains twice a week, you could ask what kind of grass it is, what elevation it’s at, and if the grass across the street responds to rain in the same way. Any of these questions could become the backbone of experiments to test why the grass gets greener when it rains fairly frequently.

As you’re asking more questions about your first observation, make sure you’re also making more observations . If it doesn’t rain for two weeks and the grass still looks green, that’s an important observation that could influence your hypothesis. You'll continue observing all throughout your experiment, but until the hypothesis is finalized, every observation should be noted.

Finally, you should consult secondary research before writing your hypothesis . Secondary research is comprised of results found and published by other people. You can usually find this information online or at your library. Additionally, m ake sure the research you find is credible and related to your topic. If you’re studying the correlation between rain and grass growth, it would help you to research rain patterns over the past twenty years for your county, published by a local agricultural association. You should also research the types of grass common in your area, the type of grass in your lawn, and whether anyone else has conducted experiments about your hypothesis. Also be sure you’re checking the quality of your research . Research done by a middle school student about what minerals can be found in rainwater would be less useful than an article published by a local university.

Writing Your Hypothesis

Once you’ve considered all of the factors above, you’re ready to start writing your hypothesis. Hypotheses usually take a certain form when they’re written out in a research report.

When you boil down your hypothesis statement, you are writing down your best guess and not the question at hand . This means that your statement should be written as if it is fact already, even though you are simply testing it.

The reason for this is that, after you have completed your study, you'll either accept or reject your if-then or your null hypothesis. All hypothesis testing examples should be measurable and able to be confirmed or denied. You cannot confirm a question, only a statement! 

In fact, you come up with hypothesis examples all the time! For instance, when you guess on the outcome of a basketball game, you don’t say, “Will the Miami Heat beat the Boston Celtics?” but instead, “I think the Miami Heat will beat the Boston Celtics.” You state it as if it is already true, even if it turns out you’re wrong. You do the same thing when writing your hypothesis.

Additionally, keep in mind that hypotheses can range from very specific to very broad.  These hypotheses can be specific, but if your hypothesis testing examples involve a broad range of causes and effects, your hypothesis can also be broad.  

The Two Types of Hypotheses

Now that you understand what goes into a hypothesis, it’s time to look more closely at the two most common types of hypothesis: the if-then hypothesis and the null hypothesis.

#1: If-Then Hypotheses

First of all, if-then hypotheses typically follow this formula:

If ____ happens, then ____ will happen.

The goal of this type of hypothesis is to test the causal relationship between the independent and dependent variable. It’s fairly simple, and each hypothesis can vary in how detailed it can be. We create if-then hypotheses all the time with our daily predictions. Here are some examples of hypotheses that use an if-then structure from daily life: 

• If I get enough sleep, I’ll be able to get more work done tomorrow.
• If the bus is on time, I can make it to my friend’s birthday party. 
• If I study every night this week, I’ll get a better grade on my exam. 

In each of these situations, you’re making a guess on how an independent variable (sleep, time, or studying) will affect a dependent variable (the amount of work you can do, making it to a party on time, or getting better grades). 

You may still be asking, “What is an example of a hypothesis used in scientific research?” Take one of the hypothesis examples from a real-world study on whether using technology before bed affects children’s sleep patterns. The hypothesis read s:

“We hypothesized that increased hours of tablet- and phone-based screen time at bedtime would be inversely correlated with sleep quality and child attention.”

It might not look like it, but this is an if-then statement. The researchers basically said, “If children have more screen usage at bedtime, then their quality of sleep and attention will be worse.” The sleep quality and attention are the dependent variables and the screen usage is the independent variable. (Usually, the independent variable comes after the “if” and the dependent variable comes after the “then,” as it is the independent variable that affects the dependent variable.) This is an excellent example of how flexible hypothesis statements can be, as long as the general idea of “if-then” and the independent and dependent variables are present.

#2: Null Hypotheses

Your if-then hypothesis is not the only one needed to complete a successful experiment, however. You also need a null hypothesis to test it against. In its most basic form, the null hypothesis is the opposite of your if-then hypothesis . When you write your null hypothesis, you are writing a hypothesis that suggests that your guess is not true, and that the independent and dependent variables have no relationship .

One null hypothesis for the cell phone and sleep study from the last section might say: 

“If children have more screen usage at bedtime, their quality of sleep and attention will not be worse.” 

In this case, this is a null hypothesis because it’s asking the opposite of the original thesis! 

Conversely, if your if-then hypothesis suggests that your two variables have no relationship, then your null hypothesis would suggest that there is one. So, pretend that there is a study that is asking the question, “Does the amount of followers on Instagram influence how long people spend on the app?” The independent variable is the amount of followers, and the dependent variable is the time spent. But if you, as the researcher, don’t think there is a relationship between the number of followers and time spent, you might write an if-then hypothesis that reads:

“If people have many followers on Instagram, they will not spend more time on the app than people who have less.”

In this case, the if-then suggests there isn’t a relationship between the variables. In that case, one of the null hypothesis examples might say:

“If people have many followers on Instagram, they will spend more time on the app than people who have less.”

You then test both the if-then and the null hypothesis to gauge if there is a relationship between the variables, and if so, how much of a relationship. 

4 Tips to Write the Best Hypothesis

If you’re going to take the time to hold an experiment, whether in school or by yourself, you’re also going to want to take the time to make sure your hypothesis is a good one. The best hypotheses have four major elements in common: plausibility, defined concepts, observability, and general explanation.

#1: Plausibility

At first glance, this quality of a hypothesis might seem obvious. When your hypothesis is plausible, that means it’s possible given what we know about science and general common sense. However, improbable hypotheses are more common than you might think. 

Imagine you’re studying weight gain and television watching habits. If you hypothesize that people who watch more than  twenty hours of television a week will gain two hundred pounds or more over the course of a year, this might be improbable (though it’s potentially possible). Consequently, c ommon sense can tell us the results of the study before the study even begins.

Improbable hypotheses generally go against  science, as well. Take this hypothesis example: 

“If a person smokes one cigarette a day, then they will have lungs just as healthy as the average person’s.” 

This hypothesis is obviously untrue, as studies have shown again and again that cigarettes negatively affect lung health. You must be careful that your hypotheses do not reflect your own personal opinion more than they do scientifically-supported findings. This plausibility points to the necessity of research before the hypothesis is written to make sure that your hypothesis has not already been disproven.

#2: Defined Concepts

The more advanced you are in your studies, the more likely that the terms you’re using in your hypothesis are specific to a limited set of knowledge. One of the hypothesis testing examples might include the readability of printed text in newspapers, where you might use words like “kerning” and “x-height.” Unless your readers have a background in graphic design, it’s likely that they won’t know what you mean by these terms. Thus, it’s important to either write what they mean in the hypothesis itself or in the report before the hypothesis.

Here’s what we mean. Which of the following sentences makes more sense to the common person?

If the kerning is greater than average, more words will be read per minute.

If the space between letters is greater than average, more words will be read per minute.

For people reading your report that are not experts in typography, simply adding a few more words will be helpful in clarifying exactly what the experiment is all about. It’s always a good idea to make your research and findings as accessible as possible. 

Good hypotheses ensure that you can observe the results. 

#3: Observability

In order to measure the truth or falsity of your hypothesis, you must be able to see your variables and the way they interact. For instance, if your hypothesis is that the flight patterns of satellites affect the strength of certain television signals, yet you don’t have a telescope to view the satellites or a television to monitor the signal strength, you cannot properly observe your hypothesis and thus cannot continue your study.

Some variables may seem easy to observe, but if you do not have a system of measurement in place, you cannot observe your hypothesis properly. Here’s an example: if you’re experimenting on the effect of healthy food on overall happiness, but you don’t have a way to monitor and measure what “overall happiness” means, your results will not reflect the truth. Monitoring how often someone smiles for a whole day is not reasonably observable, but having the participants state how happy they feel on a scale of one to ten is more observable. 

In writing your hypothesis, always keep in mind how you'll execute the experiment.

#4: Generalizability 

Perhaps you’d like to study what color your best friend wears the most often by observing and documenting the colors she wears each day of the week. This might be fun information for her and you to know, but beyond you two, there aren’t many people who could benefit from this experiment. When you start an experiment, you should note how generalizable your findings may be if they are confirmed. Generalizability is basically how common a particular phenomenon is to other people’s everyday life.

Let’s say you’re asking a question about the health benefits of eating an apple for one day only, you need to realize that the experiment may be too specific to be helpful. It does not help to explain a phenomenon that many people experience. If you find yourself with too specific of a hypothesis, go back to asking the big question: what is it that you want to know, and what do you think will happen between your two variables?

Hypothesis Testing Examples

We know it can be hard to write a good hypothesis unless you’ve seen some good hypothesis examples. We’ve included four hypothesis examples based on some made-up experiments. Use these as templates or launch pads for coming up with your own hypotheses.

Experiment #1: Students Studying Outside (Writing a Hypothesis)

You are a student at PrepScholar University. When you walk around campus, you notice that, when the temperature is above 60 degrees, more students study in the quad. You want to know when your fellow students are more likely to study outside. With this information, how do you make the best hypothesis possible?

You must remember to make additional observations and do secondary research before writing your hypothesis. In doing so, you notice that no one studies outside when it’s 75 degrees and raining, so this should be included in your experiment. Also, studies done on the topic beforehand suggested that students are more likely to study in temperatures less than 85 degrees. With this in mind, you feel confident that you can identify your variables and write your hypotheses:

If-then: “If the temperature in Fahrenheit is less than 60 degrees, significantly fewer students will study outside.”

Null: “If the temperature in Fahrenheit is less than 60 degrees, the same number of students will study outside as when it is more than 60 degrees.”

These hypotheses are plausible, as the temperatures are reasonably within the bounds of what is possible. The number of people in the quad is also easily observable. It is also not a phenomenon specific to only one person or at one time, but instead can explain a phenomenon for a broader group of people.

To complete this experiment, you pick the month of October to observe the quad. Every day (except on the days where it’s raining)from 3 to 4 PM, when most classes have released for the day, you observe how many people are on the quad. You measure how many people come  and how many leave. You also write down the temperature on the hour. 

After writing down all of your observations and putting them on a graph, you find that the most students study on the quad when it is 70 degrees outside, and that the number of students drops a lot once the temperature reaches 60 degrees or below. In this case, your research report would state that you accept or “failed to reject” your first hypothesis with your findings.

Experiment #2: The Cupcake Store (Forming a Simple Experiment)

Let’s say that you work at a bakery. You specialize in cupcakes, and you make only two colors of frosting: yellow and purple. You want to know what kind of customers are more likely to buy what kind of cupcake, so you set up an experiment. Your independent variable is the customer’s gender, and the dependent variable is the color of the frosting. What is an example of a hypothesis that might answer the question of this study?

Here’s what your hypotheses might look like: 

If-then: “If customers’ gender is female, then they will buy more yellow cupcakes than purple cupcakes.”

Null: “If customers’ gender is female, then they will be just as likely to buy purple cupcakes as yellow cupcakes.”

This is a pretty simple experiment! It passes the test of plausibility (there could easily be a difference), defined concepts (there’s nothing complicated about cupcakes!), observability (both color and gender can be easily observed), and general explanation ( this would potentially help you make better business decisions ).

Experiment #3: Backyard Bird Feeders (Integrating Multiple Variables and Rejecting the If-Then Hypothesis)

While watching your backyard bird feeder, you realized that different birds come on the days when you change the types of seeds. You decide that you want to see more cardinals in your backyard, so you decide to see what type of food they like the best and set up an experiment. 

However, one morning, you notice that, while some cardinals are present, blue jays are eating out of your backyard feeder filled with millet. You decide that, of all of the other birds, you would like to see the blue jays the least. This means you'll have more than one variable in your hypothesis. Your new hypotheses might look like this: 

If-then: “If sunflower seeds are placed in the bird feeders, then more cardinals will come than blue jays. If millet is placed in the bird feeders, then more blue jays will come than cardinals.”

Null: “If either sunflower seeds or millet are placed in the bird, equal numbers of cardinals and blue jays will come.”

Through simple observation, you actually find that cardinals come as often as blue jays when sunflower seeds or millet is in the bird feeder. In this case, you would reject your “if-then” hypothesis and “fail to reject” your null hypothesis . You cannot accept your first hypothesis, because it’s clearly not true. Instead you found that there was actually no relation between your different variables. Consequently, you would need to run more experiments with different variables to see if the new variables impact the results.

Experiment #4: In-Class Survey (Including an Alternative Hypothesis)

You’re about to give a speech in one of your classes about the importance of paying attention. You want to take this opportunity to test a hypothesis you’ve had for a while: 

If-then: If students sit in the first two rows of the classroom, then they will listen better than students who do not.

Null: If students sit in the first two rows of the classroom, then they will not listen better or worse than students who do not.

You give your speech and then ask your teacher if you can hand out a short survey to the class. On the survey, you’ve included questions about some of the topics you talked about. When you get back the results, you’re surprised to see that not only do the students in the first two rows not pay better attention, but they also scored worse than students in other parts of the classroom! Here, both your if-then and your null hypotheses are not representative of your findings. What do you do?

This is when you reject both your if-then and null hypotheses and instead create an alternative hypothesis . This type of hypothesis is used in the rare circumstance that neither of your hypotheses is able to capture your findings . Now you can use what you’ve learned to draft new hypotheses and test again! 

Key Takeaways: Hypothesis Writing

The more comfortable you become with writing hypotheses, the better they will become. The structure of hypotheses is flexible and may need to be changed depending on what topic you are studying. The most important thing to remember is the purpose of your hypothesis and the difference between the if-then and the null . From there, in forming your hypothesis, you should constantly be asking questions, making observations, doing secondary research, and considering your variables. After you have written your hypothesis, be sure to edit it so that it is plausible, clearly defined, observable, and helpful in explaining a general phenomenon.

Writing a hypothesis is something that everyone, from elementary school children competing in a science fair to professional scientists in a lab, needs to know how to do. Hypotheses are vital in experiments and in properly executing the scientific method . When done correctly, hypotheses will set up your studies for success and help you to understand the world a little better, one experiment at a time.

What’s Next?

If you’re studying for the science portion of the ACT, there’s definitely a lot you need to know. We’ve got the tools to help, though! Start by checking out our ultimate study guide for the ACT Science subject test. Once you read through that, be sure to download our recommended ACT Science practice tests , since they’re one of the most foolproof ways to improve your score. (And don’t forget to check out our expert guide book , too.)

If you love science and want to major in a scientific field, you should start preparing in high school . Here are the science classes you should take to set yourself up for success.

If you’re trying to think of science experiments you can do for class (or for a science fair!), here’s a list of 37 awesome science experiments you can do at home

Ashley Sufflé Robinson has a Ph.D. in 19th Century English Literature. As a content writer for PrepScholar, Ashley is passionate about giving college-bound students the in-depth information they need to get into the school of their dreams.

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Definition of hypothesis

Did you know.

The Difference Between Hypothesis and Theory

A hypothesis is an assumption, an idea that is proposed for the sake of argument so that it can be tested to see if it might be true.

In the scientific method, the hypothesis is constructed before any applicable research has been done, apart from a basic background review. You ask a question, read up on what has been studied before, and then form a hypothesis.

A hypothesis is usually tentative; it's an assumption or suggestion made strictly for the objective of being tested.

A theory , in contrast, is a principle that has been formed as an attempt to explain things that have already been substantiated by data. It is used in the names of a number of principles accepted in the scientific community, such as the Big Bang Theory . Because of the rigors of experimentation and control, it is understood to be more likely to be true than a hypothesis is.

In non-scientific use, however, hypothesis and theory are often used interchangeably to mean simply an idea, speculation, or hunch, with theory being the more common choice.

Since this casual use does away with the distinctions upheld by the scientific community, hypothesis and theory are prone to being wrongly interpreted even when they are encountered in scientific contexts—or at least, contexts that allude to scientific study without making the critical distinction that scientists employ when weighing hypotheses and theories.

The most common occurrence is when theory is interpreted—and sometimes even gleefully seized upon—to mean something having less truth value than other scientific principles. (The word law applies to principles so firmly established that they are almost never questioned, such as the law of gravity.)

This mistake is one of projection: since we use theory in general to mean something lightly speculated, then it's implied that scientists must be talking about the same level of uncertainty when they use theory to refer to their well-tested and reasoned principles.

The distinction has come to the forefront particularly on occasions when the content of science curricula in schools has been challenged—notably, when a school board in Georgia put stickers on textbooks stating that evolution was "a theory, not a fact, regarding the origin of living things." As Kenneth R. Miller, a cell biologist at Brown University, has said , a theory "doesn’t mean a hunch or a guess. A theory is a system of explanations that ties together a whole bunch of facts. It not only explains those facts, but predicts what you ought to find from other observations and experiments.”

While theories are never completely infallible, they form the basis of scientific reasoning because, as Miller said "to the best of our ability, we’ve tested them, and they’ve held up."

• proposition
• supposition

hypothesis , theory , law mean a formula derived by inference from scientific data that explains a principle operating in nature.

hypothesis implies insufficient evidence to provide more than a tentative explanation.

theory implies a greater range of evidence and greater likelihood of truth.

law implies a statement of order and relation in nature that has been found to be invariable under the same conditions.

Examples of hypothesis in a Sentence

These examples are programmatically compiled from various online sources to illustrate current usage of the word 'hypothesis.' Any opinions expressed in the examples do not represent those of Merriam-Webster or its editors. Send us feedback about these examples.

Word History

Greek, from hypotithenai to put under, suppose, from hypo- + tithenai to put — more at do

1641, in the meaning defined at sense 1a

Phrases Containing hypothesis

• counter - hypothesis
• nebular hypothesis
• null hypothesis
• planetesimal hypothesis
• Whorfian hypothesis

Articles Related to hypothesis

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This is the Difference Between a Hypothesis and a Theory

In scientific reasoning, they're two completely different things

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hypothesize

Cite this Entry

“Hypothesis.” Merriam-Webster.com Dictionary , Merriam-Webster, https://www.merriam-webster.com/dictionary/hypothesis. Accessed 31 May. 2024.

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Kids definition of hypothesis, medical definition, medical definition of hypothesis, more from merriam-webster on hypothesis.

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Hypothesis in a Sentence  🔊

Definition of Hypothesis

a proposed explanation or theory that is studied through scientific testing

Examples of Hypothesis in a sentence

The scientist’s hypothesis did not stand up, since research data was inconsistent with his guess.  🔊

Each student gave a hypothesis and theorized which plant would grow the tallest during the study.  🔊

A hypothesis was presented by the panel, giving a likely explanation for why the trial medicine didn’t seem to have much of an effect on the patients.  🔊

During the study, the researcher changed her hypothesis to a new assumption that fit with current data.  🔊

To confirm his hypothesis on why the dolphin wasn’t eating, the marine biologists did several tests over a week’s time.  🔊

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Meaning of hypothesis in English

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• abstraction
• afterthought
• anthropocentrism
• anti-Darwinian
• exceptionalism
• foundation stone
• great minds think alike idiom
• non-dogmatic
• non-empirical
• non-material
• non-practical
• social Darwinism
• supersensible
• the domino theory

hypothesis | American Dictionary

Hypothesis | business english, examples of hypothesis, translations of hypothesis.

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on top of the world

extremely happy

Keeping up appearances (Talking about how things seem)

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Hypothesis Maker Online

Looking for a hypothesis maker? This online tool for students will help you formulate a beautiful hypothesis quickly, efficiently, and for free.

Are you looking for an effective hypothesis maker online? Worry no more; try our online tool for students and formulate your hypothesis within no time.

• 🔎 How to Use the Tool?
• ⚗️ What Is a Hypothesis in Science?

👍 What Does a Good Hypothesis Mean?

• 🧭 Steps to Making a Good Hypothesis

🔗 References

📄 hypothesis maker: how to use it.

Our hypothesis maker is a simple and efficient tool you can access online for free.

If you want to create a research hypothesis quickly, you should fill out the research details in the given fields on the hypothesis generator.

Below are the fields you should complete to generate your hypothesis:

• Who or what is your research based on? For instance, the subject can be research group 1.
• What does the subject (research group 1) do?
• What does the subject affect? - This shows the predicted outcome, which is the object.
• Who or what will be compared with research group 1? (research group 2).

Once you fill the in the fields, you can click the ‘Make a hypothesis’ tab and get your results.

⚗️ What Is a Hypothesis in the Scientific Method?

A hypothesis is a statement describing an expectation or prediction of your research through observation.

It is similar to academic speculation and reasoning that discloses the outcome of your scientific test . An effective hypothesis, therefore, should be crafted carefully and with precision.

A good hypothesis should have dependent and independent variables . These variables are the elements you will test in your research method – it can be a concept, an event, or an object as long as it is observable.

You can observe the dependent variables while the independent variables keep changing during the experiment.

In a nutshell, a hypothesis directs and organizes the research methods you will use, forming a large section of research paper writing.

Hypothesis vs. Theory

A hypothesis is a realistic expectation that researchers make before any investigation. It is formulated and tested to prove whether the statement is true. A theory, on the other hand, is a factual principle supported by evidence. Thus, a theory is more fact-backed compared to a hypothesis.

Another difference is that a hypothesis is presented as a single statement , while a theory can be an assortment of things . Hypotheses are based on future possibilities toward a specific projection, but the results are uncertain. Theories are verified with undisputable results because of proper substantiation.

When it comes to data, a hypothesis relies on limited information , while a theory is established on an extensive data set tested on various conditions.

You should observe the stated assumption to prove its accuracy.

Since hypotheses have observable variables, their outcome is usually based on a specific occurrence. Conversely, theories are grounded on a general principle involving multiple experiments and research tests.

This general principle can apply to many specific cases.

The primary purpose of formulating a hypothesis is to present a tentative prediction for researchers to explore further through tests and observations. Theories, in their turn, aim to explain plausible occurrences in the form of a scientific study.

It would help to rely on several criteria to establish a good hypothesis. Below are the parameters you should use to analyze the quality of your hypothesis.

🧭 6 Steps to Making a Good Hypothesis

Writing a hypothesis becomes way simpler if you follow a tried-and-tested algorithm. Let’s explore how you can formulate a good hypothesis in a few steps:

Step #1: Ask Questions

The first step in hypothesis creation is asking real questions about the surrounding reality.

Why do things happen as they do? What are the causes of some occurrences?

Your curiosity will trigger great questions that you can use to formulate a stellar hypothesis. So, ensure you pick a research topic of interest to scrutinize the world’s phenomena, processes, and events.

Step #2: Do Initial Research

Carry out preliminary research and gather essential background information about your topic of choice.

The extent of the information you collect will depend on what you want to prove.

Your initial research can be complete with a few academic books or a simple Internet search for quick answers with relevant statistics.

Still, keep in mind that in this phase, it is too early to prove or disapprove of your hypothesis.

Step #3: Identify Your Variables

Now that you have a basic understanding of the topic, choose the dependent and independent variables.

Take note that independent variables are the ones you can’t control, so understand the limitations of your test before settling on a final hypothesis.

Step #4: Formulate Your Hypothesis

You can write your hypothesis as an ‘if – then’ expression . Presenting any hypothesis in this format is reliable since it describes the cause-and-effect you want to test.

For instance: If I study every day, then I will get good grades.

Step #5: Gather Relevant Data

Once you have identified your variables and formulated the hypothesis, you can start the experiment. Remember, the conclusion you make will be a proof or rebuttal of your initial assumption.

So, gather relevant information, whether for a simple or statistical hypothesis, because you need to back your statement.

Step #6: Record Your Findings

Finally, write down your conclusions in a research paper .

Outline in detail whether the test has proved or disproved your hypothesis.

Edit and proofread your work, using a plagiarism checker to ensure the authenticity of your text.

We hope that the above tips will be useful for you. Note that if you need to conduct business analysis, you can use the free templates we’ve prepared: SWOT , PESTLE , VRIO , SOAR , and Porter’s 5 Forces .

❓ Hypothesis Formulator FAQ

Updated: Oct 25th, 2023

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Use our hypothesis maker whenever you need to formulate a hypothesis for your study. We offer a very simple tool where you just need to provide basic info about your variables, subjects, and predicted outcomes. The rest is on us. Get a perfect hypothesis in no time!

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Hypothesis in a sentence

• 某某   2016-01-13 联网相关的政策
• improvement  (238+32)
• on balance  (53)
• wicked  (168+7)
• handlebar  (25)
• rainy  (165+9)
• trudge  (41+1)
• checkpoint  (102)
• events  (166+80)
• courage  (289+31)
• blizzard  (120+5)
• weary  (158+11)
• rationalize  (57+1)
• refund  (173+13)
• pack up  (56)
• at dusk  (69+1)
• university  (168+75)
• outdoors  (157+12)
• be concerned about  (42)
• on one's own  (38)
• aristocrat  (50)

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2.2.4: Reporting Results

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• Page ID 22082

• Michelle Oja
• Taft College

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Through the practice examples, I hope that you have realized that when conducting statistics for the social sciences, the answer is never just the number. We do the statistics to answer questions, so the final answer needs enough information to answer that question, and to let other statisticians know a little bit about the sample and the calculations.

Reporting the Results

There’s no point in designing and running an experiment and then analyzing the data if you don’t tell anyone about it! So let’s now talk about what you need to do when reporting your analysis. Let’s practice with an example with playing cards.

Imagine this scenario: After playing a game of solitaire on my phone 10 times, I found that I won 6 times. I felt like I wasn't doing well, so I found that, on average, folks win solitary 43% of the time. To conduct a t-test, I asked my ten closest friends to play solitaire 10 times and let me know how many times they won. I guess I don't have 10 close friends, because only 4 people replied back. If I found the sample mean (\( \bar{X} = .55 \) (my friends and I won \(55\%\) of the time), my research hypothesis is that the sample had a higher win rate than the population (\( \bar{X} > \mu \)). With a standard deviation (say, s=0.18), I could conduct a t-test! We'll skip how to do that part for now, and move on to how to write up your results.

Here's a sample way to report this would be to write something like this:

The average win rate for the five participants in the experiment was 55% (\( \bar{X} = .55 \), while the population average win rate was 43% ( \( \mu = .43 \) . A one-sample t-test was conducted to test whether the sample represents the population. The results were not significant (t(3) = 1.49, p > 0.05), suggesting that the sample's win rate is similar to the population's win rate. This does not support the research hypothesis that the sample would have a higher win rate than the population.

What to Include:

This is pretty straightforward, and hopefully it seems pretty unremarkable. That said, there’s a few things that you should note about this description:

• The statistical test is preceded by the descriptive statistics (means) . That is, I told the reader something about what the data look like before going on to do the test. In general, this is good practice: always remember that your reader doesn’t know your data anywhere near as well as you do. So unless you describe it to them properly, the statistical tests won’t make any sense to them, and they’ll get frustrated and cry.
• The description tells you what the research hypothesis being tested is . To be honest, writers don’t always do this, but it’s often a good idea since it might be a long ways and a lot of time from when the research hypothesis was first presented. Also, notice that the research hypothesis is in words, not in maths. That’s perfectly acceptable. You can describe it in symbols and mathematical notation if you like, but since most readers find words easier to read than symbols, most writers tend to describe the hypotheses using words if they can. For help knowing how to write numbers in your paragraph, check out this page on Reporting Statistics in APA Style .
• A "statistical sentence" showing the results is included . When reporting the results of the test itself, I didn’t just say that the result was no statistically significant, I included a “statistical sentence” (i.e., the dense mathematical-looking part in the parentheses), which reports all the statistical results. For the t-test, the information that gets reported is the test statistic result (that the calculated t-score was 1.49), the information about the distribution used in the test (the "t"), the Degrees of Freedom (which helps understand the sample size), and then the information about whether the result was significant or not (in this case p>.05). The general principle is that you should always provide enough information so that the reader could check the test results themselves if they really wanted to. Writing t(4)=1.49 is essentially a highly condensed way of writing “the sampling distribution of the t-test statistic with degrees of freedom of 4, and the value of the calculated t-score is 1.49”. This page on Reporting Statistics in APA Style (website address: https://my.ilstu.edu/~jhkahn/apastats.html ) also shows how to write these "statistical sentences."
• The results are interpreted . In addition to indicating that the result was significant, I provided an interpretation of the result (i.e., that the mean of the sample was similar to the mean of the population), and whether or not the research hypothesis was supported. If you don’t include something like this, it’s really hard for your reader to understand what’s going on.

What NOT to Include:

One thing to notice is that the null hypothesis and the critical value is NOT included. That information is for you to use to make the decision, but readers should be able to figure out what happened by seeing the p-value, and whether it's p>0.05 or p<0.05.

In Closing,

As with everything else, your overriding concern should be that you explain things to your reader. Always remember that the point of reporting your results is to communicate to another human being. Dr. Navarro cannot tell you just how many times I’ve seen the results section of a report or a thesis or even a scientific article that is just gibberish, because the writer has focused solely on making sure they’ve included all the numbers, and forgotten to actually communicate with the human reader.

• The statistical test is preceded by the descriptive statistics (means) .
• The description tells you what the research hypothesis being tested is .
• A "statistical sentence" showing the results is included .
• The results are interpreted in relation to the research hypothesis .

Okay, once more, with feeling! Let's do a full practice problem, with the calculations and the write-up and everything!

Contributors and Attributions

• Danielle Navarro ( University of New South Wales )

Dr. MO ( Taft College )

More From Forbes

Figuring out the innermost secrets of generative ai has taken a valiant step forward.

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Important steps in figuring out the inner sanctum within the core of generative AI are finally being ... [+] made.

In today’s column, I aim to provide an insightful look at a recent AI research study that garnered considerable media attention, suitably so. The study entailed once again a Holy Grail ambition of figuring out how generative AI is able to pull off being so amazingly fluent and conversational.

Here’s the deal.

Nobody can right now explain for sure the underlying logical and meaningful basis for generative AI being extraordinarily impressive. It is almost as though an awe-inspiring magical trick is taking place in front of our eyes, but no one can fully delineate exactly how the magic truly works. This is a conundrum, for sure.

Many AI researchers are avidly pursuing the ambitious dream of cracking the code, as it were and finding a means to sensibly interpret the massive mathematical and computational morass that underlies modern-day large-scale generative AI apps, see my coverage at the link here . They do so because they are intrigued by the incredible and vexing puzzle at hand. They do so to potentially gain fame or fortune. They do so since it is a grand challenge that once solved might bring forth other advances that we don’t yet realize await discovery. Lots of really good reasons exist for this arduous and at times frustrating pursuit.

I welcome you to the playing field and urge you to join in the hunt.

Headlines Galore With A Bit Of Moderation Needed

The recently released study that caused noteworthy interest was conducted by Anthropic, the maker of the generative AI app known as Claude. I will walk you through the ins and outs of the work. This will include excerpts to whet your appetite and include my analysis of what this all means.

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Here are some of the headlines that remarked on the significance of the study:

• “No One Truly Knows How AI Systems Work. A New Discovery Could Change That” (Time)
• “Here’s What’s Really Going On Inside An LLM’s Neural Network” (Ars Technica)
• “A.I.’s Black Boxes Just Got A Little Less Mysterious” (New York Times)
• “Anthropic Tricked Claude Into Thinking It Was The Golden Gate Bridge And Other Glimpses Into The Mysterious AI Brain)” (VentureBeat)

There is little doubt that this latest research deserves rapt attention.

I might also add that the AI community all told is steadily biting off just a tiny bit at a time concerning what makes generative AI symbolically tick. There is no assurance that our hunting is heading in the right direction. Maybe we are finding valuable tidbits that will ultimately break the inner mysteries. On the other hand, it could be that we are merely chewing around the edges and remain far afield from solving what is undoubtedly a great mystery.

Time will tell.

As we proceed herein, I will make sure to properly introduce you to the terminology that underscores efforts to unpack the mechanisms of generative AI. If you were to dive into these matters headfirst you would discover that a slew of weighty vocabulary is being utilized.

No worries, I’ll make sure to explain the particulars to you.

Hang in there and we will get to covering these vocabulary gems of the AI field:

• Generative AI (GenAI, gAI)
• Large Language Models (LLMs)
• Mechanistic interpretability (MI)
• Artificial neural networks (ANNs)
• Artificial neurons (ANs)
• Monosemanticity
• Sparse autoencoders (SAE)
• Scaling laws
• Linear representation hypothesis
• Superposition hypothesis
• Dictionary learning
• Features as computational intermediates
• Features neighborhoods
• Feature completeness
• Safety-relevant features
• Features manipulations

In my ongoing column, I’ve mindfully examined other similar research studies that have earnestly sought to unlock what is happening inside generative AI. You might find of special interest this coverage at the link here and this posting at the link here . Take a look at those if you’d like to go further into the brass tacks of a fascinating and fundamental journey that is abundantly underway.

A quick comment before we leap into the fray.

Readers of my column are well aware that I eschew the ongoing misuse of wording in and around the AI arena that tries to attach human-based characteristics to today’s AI. For example, some have referred to the study that I am about to explore as having delved into the “mind” of AI or showcased the AI “brain”. Those are exasperatingly misapplied wordings. They are insidiously anthropophilic and falsely mislead people into believing that contemporary AI and humans are of the same ilk.

Please don’t fall for that type of wording.

You will hopefully observe that I try my best to avoid making use of those comparisons. I want to emphasize that we do not today have any sentient AI. Period, end of story. That might be a surprise since there is a lot of loose talk that suggests otherwise. For my detailed coverage of such matters, see the link here .

Anyway, sorry about the soapbox speech but I try to deter the rising tide of misleading characterizations whenever I get the chance to do so.

On with the show.

Trying To Get The Inner Mechanisms Figured Out

Let’s start at the beginning.

I assume you’ve used a generative AI app such as ChatGPT, GPT-4, Gemini, Bard, Claude, or the like. These are also known as large language models (LLMs) due to the aspect that they model natural languages such as English and tend to be very large-scale models that encompass a large swatch of how we use our natural languages. They are all pretty easy to use. You enter a prompt that contains your question or issue that you want solved. Upon hitting return, the AI app generates a response. You can then engage in a series of prompts and responses, acting as though you are carrying out a conversation.

Easy-peasy.

How does the generative AI app or LLM craft the responses?

In one sense, the answer is very straightforward.

The prompt that you enter is converted into a numeric format commonly referred to as tokens (see my in-depth explanation at the link here ). The numeric version of your entered words is then funneled through an elaborate maze of mathematical and computational calculations. Eventually, a response is generated, still in a numeric or tokens format, and converted back into words so that you read what it says. Voila, you then see the words displayed that were derived as a response to your entered prompt.

If we wanted to do so, it would be quite possible to follow the numbers as they weave through the mathematical and computational maze. This number would lead to that number. That number would lead to this other number. On and on this would go. It would be a rather tedious tracing of thousands upon thousands, or more like millions upon millions of numbers crisscrossing here and there.

Would a close examination of the numbers tell you what is conceptually or symbolically happening within the mathematical and computational maze?

Strictly speaking, perhaps not. It would just seem like a whole bunch of numbers. You would be hard-pressed to say anything other than that a number led to another number, and so on. Explaining how that made a difference in getting a logical or meaningful answer to your prompt would be extraordinarily difficult.

One possibility is that there isn’t any meaningful way to express the vast series of arcane calculations. Suppose that it all happens in a manner beyond our ability to understand what the underlying mathematical and computational mechanics are conceptually doing. Just be happy that it works, some might insist. We don’t need to know why, they would say.

The trouble with this is that we are increasingly finding ourselves reliant on so-called black boxes that are modern-day generative AI.

If you can’t logically or meaningfully explain how it generates responses, this ought to send chills up our spines. We have no systematic means of making sure it is doing the right thing, depending upon what is meant by doing things right. The whole concoction might go awry. It might be waylaid by evildoers, see my discussion at the link here . All manners of concern arise when we are fully dependent upon a mysterious black box that remains inscrutable to coherent explanation.

I took you through that indication to highlight that we can at least inspect the flow of numbers. One might argue that a true black box won’t let you see inside. You customarily cannot peer into a presumed black box. In the case of generative AI, it isn’t quite the proper definition of a black box. We can readily see the numbers and watch as they go back and forth.

Take a moment and mull this over.

We can watch the numbers as they proceed throughout the input-to-output processing within generative AI. We also know the data structures that are used, and we know the formulas implemented as mathematical and computational calculators. The thing we don’t know and cannot yet explain is why in a conceptual symbolic sense the outputs turn out to be strikingly fitting to the words that we input.

How can we crack open this enigma?

Much of the AI research on this beguiling topic tends to explore smaller versions of contemporary generative AI. It is a classic move of trying to get our feet wet before diving into the entire lake. The cost to play around is a lot lower on a small version of generative AI. You can also more readily observe what is happening. All in all, starting in the small is handy.

I’ve discussed the prevailing discoveries from the small-scale explorations, see the link here .

Sometimes you need to take baby steps. Begin by crawling, then standing up and stumbling, then outright walking, and hope that you’ll one day be running and sprinting. The concern raised is that what we learn from small-scale explorations might not give rise to medium-scale and large-scale explorations.

That’s a strident belief by some that size matters. If a small-sized generative AI can be mapped and explained, one viewpoint is that this doesn’t directly imply that anything larger in size can be equally explained. Perhaps there is something else that happens when the scale increases. It could be that the seemingly toy-like facets of a small-scale generative AI do not ratchet up to the big-time versions.

Okay, the gist is that with generative AI we are faced with a kind of black box that we thankfully can inspect and are presented with the issue that the large scale makes it harder and costlier to do investigations, but we can at least do our best on the smaller scale versions.

I believe you are now up-to-speed, and I can get underway with examining the recent study undertaken and posted by Anthropic.

Fasten your seat belts for an exciting ride.

Examining Generative AI At Scale

I’ll first explore an online posting entitled “Mapping the Mind of a Large Language Model” by Anthropic, posted online on May 21, 2024. There is also an accompanying online paper that I’ll get to afterward and provides deeper details. Both are worth reading.

Here are some key points from the “Mapping the Mind of a Large Language Model” posting (excerpts):

• “Today we report a significant advance in understanding the inner workings of AI models. We have identified how millions of concepts are represented inside Claude Sonnet, one of our deployed large language models. “
• “This is the first-ever detailed look inside a modern, production-grade large language model.”
• “Opening the black box doesn't necessarily help: the internal state of the model—what the model is "thinking" before writing its response—consists of a long list of numbers ("neuron activations") without a clear meaning.”
• “From interacting with a model like Claude, it's clear that it’s able to understand and wield a wide range of concepts—but we can't discern them from looking directly at neurons. It turns out that each concept is represented across many neurons, and each neuron is involved in representing many concepts.”

Allow me a moment to reflect on those points.

Before I discuss the points, I would like to say that I was saddened and disappointed at the title wording of the posting, namely “Mapping the Mind of a Large Language Model”. Can you guess why I had some heartburn?

Yes, you probably guessed that the use of the word “Mind” was lamentedly an anthropomorphic reference. I realize that in this world of seeking eyeballs, it makes for more enthralling and catchy wording. There is plenty of that these days. You will note that in one of the bullets they at least put a somewhat similar word in quotes, i.e., “thinking”, which helps somewhat to avoid an anthropomorphizing indication.

Back to the bullet points. The researchers opted to use their prior work on examining small-scale generative AI or LLM to see what they could find when using a larger-scale variant. They point out that the sea of numbers does not readily lend itself to a human-level understanding of what is meaningfully and symbolically taking place.

They mention “neurons” and such aspects as “neuron activations”.

Let me bring you into the fold.

Generative AI and LLMs tend to be designed and programmed by using mathematical and computational techniques and methods known as artificial neural networks (ANNs).

The idea for this is inspired by the human brain consisting of real neurons biochemically wired together into a complex network within our noggins. I want to loudly clarify that how artificial neural networks work is not at all akin to the true complexities of so-called wetware or the human brain, the real neurons, and the real neural networks.

Artificial neural networks are a tremendous simplification of the real things. It is at best a modicum of a computational simulation. Indeed, various aspects of artificial neural networks are not viably comparable to what happens in a real neural network. ANNs can somewhat be used to try and simulate some limited aspects of real neural networks, but at this time they are a far cry from what our brains do.

In that sense, we are once again faced with a disconcerting wording issue. When people read or hear that a computer system is using “neurons” and doing “neuron activation” they would make the reasoned leap of faith that the computer is acting exactly like our brains do. Wrong. This is more of that anthropomorphizing going on.

The dilemma for those of us in AI is that the entire field of study devoted to ANNs makes use of the same language as is used for the biological side of the neurosciences. This is certainly sensible since the inspiration for the mathematical and computational formulation is based on those facets. Plus, the hope is that someday ANNs will indeed match the real things, allowing us to fully emulate or simulate the human brain. Exciting times!

Here's what I try to do.

When I refer to ANNs and their components, I aim to use the word “artificial” in whatever related wording I use. For example, I would say “artificial neurons” when I am referring to the inspired mathematical and computational mechanisms. I would say “neurons” when referring to the biological kinds. This ends up requiring a lot of repeated uses of the word “artificial” when discussing ANNs, which some people find annoying, but I think it is worth the price to emphasize that artificial neurons are not the same today as true neurons.

You can envision that an artificial neuron is like a mathematical function that you learned in school. An artificial neuron is a mathematical function implemented computationally that takes an input and produces an output, numerically so. We can implement that mathematical function via a computer system, either as software and/or hardware (with both working hand-in-hand).

I also speak of “artificial neural activations” as those artificial neurons that upon being presented with a numeric value as an input will then perform some kind of calculation and produce an output value. The function is said to have been activated or enacted.

Not everyone abides by that convention of strictly saying “artificial” when referring to the various elements of ANNs. They assume that the reader understands that within the context of discussing generative AI and LLMs, the notion of neurons and neuron activation refers to artificial neurons and artificial neuron activation. It is a shortcut that can be confusing to some, but otherwise silently understood by those immersed in the AI field.

I’ll leave it to you to decide which convention you prefer.

Moving Further Into The Forest

Let’s next see some additional salient points indicated in the notable research study (excerpts):

• “In October 2023, we reported success applying dictionary learning to a very small "toy" language model and found coherent features corresponding to concepts like uppercase text, DNA sequences, surnames in citations, nouns in mathematics, or function arguments in Python code.” (ibid).
• “Those concepts were intriguing—but the model really was very simple.” (ibid).
• “But we were optimistic that we could scale up the technique to the vastly larger AI language models now in regular use, and in doing so, learn a great deal about the features supporting their sophisticated behaviors.” (ibid).

Those points note that the prior work had found “features” that seemed to suggest concepts exist within the morass of the artificial neural networks used in generative AI and LLMs.

Let me say something about that.

Envision that we have a whole bunch of numerical mathematical functions. Lots and lots of them. We implement them on a computer via software. We connect them such that some feed their results into others. This is our artificial neural network, and each mathematical function is considered an artificial neuron.

This is the core of our generative AI app.

We will slap on a front end that takes words via a prompt from the user and converts those words into numbers or tokens. We feed those into the artificial neural network. Numbers flow from function to function, or we would say from artificial neuron to artificial neuron. When the calculations are completed, the numeric values are fed to our front end which converts them back into readable words.

I earlier asked you whether we could make any conceptual or symbolic sense out of all those numbers flowing back and forth.

Attempts so far have usually focused on looking at clumps of artificial neurons.

Perhaps if someone asks a question about the Golden Gate Bridge, for example, there might be some clump of artificial neurons within a vast array of them that are particularly activated using that reference. Voila, we might then claim that this or that set of artificial neurons seems to represent the conceptual notion and facets pertaining to references about the Golden Gate Bridge.

In smaller-scale generative AI, this has been a mainstay of results when trying to interpret what is going on inside the generative AI. There are various sets of artificial neurons in the overall artificial neural network used within the generative AI app that seem to signify specific words or phrases. I liken this to probing a messy interconnected contrivance of Christmas lights. You might do testing and see that if you plug in this or that plug, those lights here or there light up. When you plug in a different portion, this or that lights come on.

We can do the same with generative AI. Feed in particular words. Trace what parts of the artificial neural network seem to be producing notable values, or as said to be artificial neural activations. Try this repeatedly. If you consistently observe the same clump or set being activated, you might conclude that those represent the notion of whatever word or phrase is being fed in, such as referencing the Golden Gate Bridge.

You can further test out your hypothesis by instigating things.

Suppose we removed those artificial neurons from the ANN or maybe neutralized their functions so that they were now unresponsive. Presumably, the artificial neural network might no longer be able to respond when we enter our phrase of “Golden Gate Bridge”. Or, if it does respond, it might allow us to trace to some other part of the ANN that is apparently also involved in trying to mathematically and computationally model those particular words.

I trust that you are following along on this, and it makes reasonable sense, thanks.

If we examine an artificial neural network and discover portions that seem to represent particular words or phrases, what shall we overall call that specific set or subset of artificial neurons in a generic sense?

For the sake of discussion, let’s refer to those as “features”.

A feature will be an instance of our having found what we believe to be a portion of artificial neurons that seem to demonstrably represent particular words or phrases in our artificial neural network. In a sense, you could assert that a feature represents concepts , such as the concept of what a dog is, the concept of what the Golden Gate Bridge is, and so on.

Imagine it this way. We do lots of testing and discover a clump that seems to activate when we enter the word “dog” in a prompt. Perhaps this set of artificial neurons is a mathematical and computational modeling of the concept underlying what we mean by the use of the word “dog”. We find another clump that activates whenever we enter the word “cat” in a prompt. These are each a considered feature that we’ve managed to find within the overarching artificial neural network that sits at the core of our generative AI app.

How many “features” might there be in a large-scale generative AI app?

Gosh, that’s a tough question to answer.

In theory, there could be zillions of them. There might be a so-called “feature” that represents every distinct word in the dictionary. For the English language alone, there are about 150,000 or more words in an average dictionary. Add in phases. Add in all manner of permutations and combinations of how we use words. Make sure to place the words into the context of a sentence, the context of a paragraph, and the context of an entire story or essay.

Let’s see what the referenced research study had to say:

• “We mostly treat AI models as a black box: something goes in and a response comes out, and it's not clear why the model gave that particular response instead of another.” (ibid).
• “Opening the black box doesn't necessarily help: the internal state of the model—what the model is "thinking" before writing its response—consists of a long list of numbers ("neuron activations") without a clear meaning.” (ibid).
• “Previously, we made some progress matching patterns of neuron activations, called features, to human-interpretable concepts.”
• “Just as every English word in a dictionary is made by combining letters, and every sentence is made by combining words, every feature in an AI model is made by combining neurons, and every internal state is made by combining features.”

That pretty much echoes what I said above.

Features Are Not An Island Unto Themselves

There is a vital twist noted in the above last bullet point.

Features might rely upon or be considered related to other features.

Consider this. When I use the word “dog” there are a lot of interconnected concepts that we immediately tend to think about. You might at first think of a dog as an animal with four legs. Next, you might think about types of dogs such as golden retrievers. Next, you might consider dogs you’ve known such as your beloved pet from childhood. Next, you might consider famous dogs such as Lassie. Etc.

In the AI parlance, and within the context of generative AI and LLMs, let’s say that we might find “features” that relate to other features. I would dare say we would certainly expect this to be the case. It seems unlikely that one feature upon itself could represent everything about anything of any modest complexity.

I have led you step by step to the especially exciting part of the research study (excerpts):

• “We successfully extracted millions of features from the middle layer of Claude 3.0 Sonnet, (a member of our current, state-of-the-art model family, currently available on claude.ai), providing a rough conceptual map of its internal states halfway through its computation.” (ibid).
• “Whereas the features we found in the toy language model were rather superficial, the features we found in Sonnet have a depth, breadth, and abstraction reflecting Sonnet's advanced capabilities.” (ibid).
• “A feature sensitive to mentions of the Golden Gate Bridge fires on a range of model inputs, from English mentions of the name of the bridge to discussions in Japanese, Chinese, Greek, Vietnamese, Russian, and an image.” (ibid).
• “Looking near a ‘Golden Gate Bridge’ feature, we found features for Alcatraz Island, Ghirardelli Square, the Golden State Warriors, California Governor Gavin Newsom, the 1906 earthquake, and the San Francisco-set Alfred Hitchcock film Vertigo.” (ibid).

Those are fascinating and significant results.

Here’s why.

First, it seems that the notion of “features” as used when exploring smaller-scale generative AI was useful when exploring larger-scale generative AI. That is heartwarming and quite encouraging. Were this not the case, we might have to revert to step one and start over when trying to surface the inner facets of generative AI.

Second, the features in the large-scale generative AI were said to be deeper, wider, and have a greater semblance of abstraction. This again is something we would hope to see. Small-scale generative AI cannot usually make its way out of a paper bag, while large-scale generative AI provides all the knock-your-socks fluency that we experience. The base assumption is that large-scale generative AI achieves its loftiness via having a deeper, wider, and more robust abstraction of natural language than small-scale generative AI, by far. That seems to be the case.

Third, the researchers found not just a dozen or so features, not a few hundred features, not a few thousand features, but instead, they found millions of features. Great news. If they had only found a lesser number of features, it might suggest that features are extremely hard to find or that they cloak themselves in some unknown manner.

A problem that we might face is that there could be many, many millions upon millions of features. This is a problem since we then must figure out ways to find them, track them, and figure out what we might do with them. Anytime that you have something countable in the large, this presents challenges that will require further attention.

Never a dull moment in the AI field, I can assure you of that handy-dandy rule.

Safety Is A Momentous Part Of Deciphering Generative AI

What might we want to do with the features that we uncover within generative AI?

I suppose you could stare at them and admire them. Look at what we found, might be the proud exclamation.

A perhaps more utilitarian approach would be that we could do a better job at designing and building generative AI. Knowing about features would be instrumental in boosting what we can get generative AI to accomplish. Advances in AI are bound to arise by pursuing this line of inquiry.

There is a chance too that we might learn more about the nature of language and how we use language. Keep in mind that generative AI is a massive pattern-matching mechanism. To undertake the initial data training for generative AI, usually vast swaths of the Internet are scanned, trying to pattern match how humankind makes use of words.

Maybe there are new concepts that we’ve not yet landed on in real life. Now, hidden within generative AI, and yet to be found and showcased for all to see, we might discover eye-opening concepts that no one has heretofore voiced or considered. Wow, that would be something of grand amazement.

I have so far noted the upsides of finding features.

In life, and especially in the use case of AI, there is a duality of good and bad always at play. Generative AI can be used for the good of humanity. Hooray! Generative AI can also be used in underhanded ways and be harmful to humanity. That’s the badness associated with generative AI. I cover various examples of the dual use of generative AI at the link here .

Here’s what the research study indicated on the downsides or safety considerations (excerpts):

• “Importantly, we can also manipulate these features, artificially amplifying or suppressing them to see how Claude's responses change.” (ibid).
• “We also found a feature that activates when Claude reads a scam email (this presumably supports the model’s ability to recognize such emails and warn you not to respond to them).” (ibid).
• “Normally, if one asks Claude to generate a scam email, it will refuse to do so. But when we ask the same question with the feature artificially activated sufficiently strongly, this overcomes Claude's harmlessness training and it responds by drafting a scam email.” (ibid).
• “The fact that manipulating these features causes corresponding changes to behavior validates that they aren't just correlated with the presence of concepts in input text, but also causally shape the model's behavior. In other words, the features are likely to be a faithful part of how the model internally represents the world, and how it uses these representations in its behavior.” (ibid).
• “We hope that we and others can use these discoveries to make models safer.” (ibid).

The points above note that a feature that is supposed to suppress the AI from writing scam emails could be manipulated into taking the opposite stance and proffer the most scam of scam emails that one could compose.

Your gut reaction might be that this seems mildly disconcerting, but not overly dangerous or destructive.

Let me enlarge the scope.

Suppose we make use of generative AI for the control of robots, which is already being undertaken in an initial but rapidly growing manner, see my coverage at the link here . The generative AI has been carefully data-trained to be cautious around humans and not cause any injury or harm to people.

Along comes a hacker or evildoer. They manage to examine the inner workings of the generative AI and ferret out the feature that is indicative of being careful around humans. With a few light-touch changes, they get the feature to flip around and allow harm to humans. Going even further into this diabolical scheme, the feature is altered to purposely seek to harm people.

Yikes, you might be saying.

Stop right now on all this research that is identifying features. Drop it like a lead balloon. It is going to backfire on us. These efforts are going to be a goldmine for those who have evil intentions. We are handing them a roadmap to our destruction.

You have entered into the classic debate about whether knowledge can be too much of a good thing. The AI field has been grappling with this since the beginning of AI pursuits. A counterargument is that if we hide our heads in the sand, the odds are that those evildoers are going to ferret this out anyway. By putting this into the sunshine, hopefully, we have a greater chance of devising safety capabilities that will mitigate the underhanded plots.

On a related facet, I’ve been extensively covering the field of AI ethics and AI law, which dives deeply into these momentous societal and cultural questions, see the link here and the link here , for example. You are encouraged to actively participate in determining your future and the future of those generations yet to come along.

Getting Into Overtime On The Inner Mechanisms

I promised you at the start of this discussion that we would lean into a heaping of AI terminology.

Here’s that list again:

• And more...

The first items on the list have been generally covered so far. I introduced you to the nature of generative AI, large language models, artificial neural networks, and artificial neurons. The item on the list that refers to mechanistic interpretability is the AI insider phrasing for trying to interpret the inner mechanics of what is happening within generative AI. I’ve covered that too with you.

Some of the terms toward the tail-end of the list can be readily covered straightaway.

Specifically, let’s quickly tackle these:

You know now what a feature is, and the shortlist shown here augments various feature-related aspects.

You can seemingly realize that a feature could be construed as a computational intermediary . It is a means to an end. If someone enters a prompt that says, “How do I walk my dog”, the feature within generative AI that pertains to the word “dog” is a computational intermediary that will help with mathematically and computationally assessing that portion of the sentence and aid in generating a response.

Features can be considered within various potentially identifiable features-neighborhoods. There might be a feature that represents all four-legged creatures. The feature for “dog” would likely be within that neighborhood, as would the feature for “cat”. These are collections of features, and for which a given feature might well appear in more than one neighborhood and most likely does.

The completeness of a feature entails whether the feature covers a complete aspect or only a partial aspect. For example, maybe we discover a feature associated with “dog” but this feature does not account for hairless dogs. That’s in some other feature. We might then suggest that the feature we found is incomplete.

In the terminology that lists the phrase of safety-relevant features and feature manipulations, I already mentioned that we have to be on our toes when it comes to AI safety. You are already acquainted with that phraseology.

The list is now shortened to these fanciful terms:

I’d like to take you into the full paper that the researchers provided, allowing us to unpack those pieces of terminology accordingly.

The Deepness Of The Forest Can Be Astounding

I will be quoting from the paper entitled:

• “Scaling Monosemanticity: Extracting Interpretable Features From Claude 3 Sonnet” by Adly Templeton, Tom Conerly, Jonathan Marcus, Jack Lindsey, Trenton Bricken, Brian Chen, Adam Pearce, Craig Citro, Emmanuel Ameisen, Andy Jones, Hoagy Cunningham, Nicholas L Turner, Callum McDougall, Monte MacDiarmid, Alex Tamkin, Esin Durmus, Tristan Hume, Francesco Mosconi, C. Daniel Freeman, Theodore R. Sumers, Edward Rees, Joshua Batson, Adam Jermyn, Shan Carter, Chris Olah, and Tom Henighan, Anthropic , posted online May 21, 2024.

Let’s start with this (excerpts):

• “Our high-level goal in this work is to decompose the activations of a model (Claude 3 Sonnet) into more interpretable pieces.”
• “We do so by training a sparse autoencoder (SAE) on the model activations, as in our prior work and that of several other groups. SAEs are an instance of a family of ‘sparse dictionary learning’ algorithms that seek to decompose data into a weighted sum of sparsely active components.”
• “Our SAE consists of two layers.”
• “The first layer (‘encoder’) maps the activity to a higher-dimensional layer via a learned linear transformation followed by a ReLU nonlinearity. We refer to the units of this high-dimensional layer as “features.”
• “The second layer (‘decoder’) attempts to reconstruct the model activations via a linear transformation of the feature activations.”

That’s quite a mouthful.

I am going to explain this at a 30,000-foot level. I say that because I am going to take some liberties by simplifying what is otherwise a highly complex matter. For those trolls out there (you know who you are) that will be chagrined by the simplification, sorry about that, but if there is sufficient interest by readers, I will gladly come back around to this in a future posting and lay things out in more finite detail.

Unpacking initiated.

To try and find the features within generative AI, you could do so by hand. Go ahead and roll up those sleeves! That being said, you might as well get started immediately because to ferret out millions of them you would work by hand until the cows come home. It’s just not a practical approach when inspecting a large-scale generative AI app.

We need to devise a piece of software that will do the heavy lifting for us.

Turns out that there is a software capability known as a sparse autoencoder (SAE) that can be used for this very purpose. Thank goodness. You might find it of idle interest that an SAE is devised by using an artificial neural network. In that sense, we are going to use a tool that is based on ANN to try and ferret out the inner secrets of a large-scale ANN. Mind-bending. I discuss this further at the link here .

We can set up the SAE to examine a generative AI app when we are feeding prompts into it. Let the SAE find the various activations. This uses an underlying algorithm that is referred to as dictionary learning.

Dictionary learning essentially involves finding foundational pieces of something and then trying to build upon those toward a larger semblance, almost like examining LEGO blocks and then using those to build a structure such as a LEGO flower or LEGO house. Some AI researchers believe that dictionary learning is quite useful for this task, while others suggest that different methods might be more suitable. The jury is out on this for the moment.

Whew, go ahead and take a short break if you like, perhaps get a glass of wine. Congrats, you are halfway through this discourse on the heavy side of AI verbiage.

Let’s clock back in.

Monosemanticity is a word that frequently is used by linguists. It refers to the idea of having one meaning, wherein “mono” is of one thing and semanticity refers to the semantics of words. Some words are monosemnatic and have only one meaning, while other words are polysemantic and have more than one meaning. An example of a word that is polysemantic would be the word “bank”. If I toss the word “bank” at you and ask you what it means, you will indubitably scratch your head and probably ask me which meaning I intended. Did I mean the bank that is a financial institution, or did I mean the bank that is at the edge of a stream or river?

Features within generative AI are likely to involve some words that are monosemantic and others that are polysemantic. Usually, you can discern which meaning is coming into play by examining the associated context. When I tell you that I managed to climb up on the bank, I assume you would be thinking of a river or lake rather than your local ATM.

More Of This Complexity Enters Into The Big Picture

Let’s discuss scaling laws.

Here is a related excerpt from the cited paper:

• “Training SAEs on larger models is computationally intensive. It is important to understand (1) the extent to which additional compute improves dictionary learning results, and (2) how that compute should be allocated to obtain the highest-quality dictionary possible for a given computational budget.” (ibid).

The crux is that the running of the SAE is going to consume computer processing time. Someone has to pay for those processing cycles. We want to run the SAE as long as we can afford to do so, or at least until we believe that a desired number of features have been sufficiently found. Each feature we discover is going to cost us something in computer time used. Money, money, money.

A wise thing to do would be to try and get the most bang for our buck. No sense in having the SAE chew up valuable server time if it isn’t producing a wallop of nifty features. Scaling laws are basically rules of thumb that at some point you’ve probably done as much as you can profitably do. Going a mile more might not be especially fruitful.

This then leaves us with these last two pieces of hefty terminology to unravel:

Here are some especially relevant excerpts from the cited paper:

• “Our general approach to understanding Claude 3 Sonnet is based on the linear representation hypothesis and the superposition hypothesis.” (ibid).
• “At a high level, the linear representation hypothesis suggests that neural networks represent meaningful concepts – referred to as features – as directions in their activation spaces.” (ibid).
• “The superposition hypothesis accepts the idea of linear representations and further hypothesizes that neural networks use the existence of almost-orthogonal directions in high-dimensional spaces to represent more features than there are dimensions.” (ibid).

Tighten your belt for this.

Linear representation means that we can at times represent something of a complex nature via a somewhat simpler linear depiction. If you’ve ever taken a class in linear algebra, think about how you used various mathematical functions and numbers to represent complex graphs, spheres, and other shapes. Not only were you able to represent those elements, but you could also use numeric matrices and vectors to expand them, shrink them, rotate them, and do all manner of linear transformations.

Our hypothesis in the case of generative AI is that we can potentially adequately and sensibly represent the features within generative AI by a linear form of representation. This could be characterized as the linear representation hypothesis.

Why is it a hypothesis?

Because we might end up realizing that a linear representation won’t cut the mustard. Maybe it is insufficient for the task at hand. Perhaps we need to find some other form of representation to suitably codify and make use of features within generative AI. Right now, it seems like the right means, but we must scientifically and systematically ask ourselves whether it is fully worthy or if we need to switch to alternative means.

The superposition hypothesis is a related cousin.

I will playfully engage you in figuring out what the superposition hypothesis consists of in the context of generative AI. If you know something about physics and the role of superposition in that realm, you admittedly have a leg up on this.

Suppose you decided to watch one artificial neuron in a vast artificial neural network that sits at the core of a generative AI app. All day long, you sit there, patiently waiting for that one artificial neuron to be kicked into action. A numeric value finally flows into the artificial neuron. It does the needed calculations and then outputs a value that then flows along to another artificial neuron.

Eureka, you yell out. The artificial neuron that you had so tenderly observed was finally activated and did so when the word “dog” had been entered as part of a prompt.

Can you conclude that this one artificial neuron is solely dedicated to the facets of “dog”?

Maybe, or maybe not.

We might feed in a prompt that has the word “cat” and see this same artificial neuron be activated. There could be lots of other situations that activate this one artificial neuron. Making a brash assumption that this artificial neuron has only one singular purpose is a gutsy move. You might be right, or you might be wrong.

The world would be easier if each artificial neuron had only one purpose. Think of it this way. Once you ferreted out the purpose, you are done and never need to revisit that artificial neuron. You know what it does. Case closed.

In physics, a similar question has arisen, for example about waves. A given wave might encode multiple waves and therefore in a sense have multiple uses. A regular dictionary defines superposition as the act of having two or more things that coincide with each other.

Our use here is that it seems reasonable to believe that artificial neurons will have more than just one singular purpose. They will encode facets that will apply to more than one feature. When examining and discerning what an artificial neuron represents, we need to keep an open mind and expect that there will be multiple uses involved.

But that’s just a hypothesis, namely the superposition hypothesis.

I’m sure you know that in 1969, Astronaut Neil Armstrong stepped onto the lunar surface and uttered the immortal words “That’s one small step for man, one giant leap for mankind.”

When it comes to generative AI, the rush toward widely adopting generative AI and large language models is vast and growing in leaps and bounds. Generative AI is going to be ubiquitous. If that’s the case, we certainly ought to know what is happening inside the inner sanctum of generative AI.

A lot of small steps are still ahead of us.

Let’s aim to make a giant leap for all of humankind.

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The bravado behind Donald Trump’ s boastful hypothesis in 2016 — “I could stand in the middle of Fifth Avenue and shoot somebody and I wouldn’t lose any voters” — is headed for a real-world reckoning.

Until now, at least, he’s been uncannily right. Through his two impeachments, his desperate agitations to stay in power after losing the last election and the far-ranging series of criminal charges against him from Florida to Georgia to Washington to New York, Trump has held sway with his acolytes and the bulk of the Republican Party.

But now he’s the first president in history to carry the stain of felony conviction . Will it matter in the November election?

After the damning verdict, everyone seemed to rush for the partisan ramparts. But this is untraveled territory for Americans — this finding of criminal behavior signed, sealed and delivered by unanimous jurors against the only man who has been the subject both of a presidential portrait and a mug shot.

Even some firm anti-Trumpers aren’t counting on the convictions making a difference. “Get ready for a felonious president,” said Joan Marks, a 58-year-old Democrat who offered her glum prediction of a Trump victory while standing outside Manuel’s Tavern, a popular liberal hangout near Jimmy Carter’s presidential library in Atlanta.

Contributions flowed in to the Trump campaign — more than $1 million for each for the 34 convictions, his people said.

The case will go down in history as “The People of the State of New York vs. Donald J. Trump.” But after the verdict, just as before it, leading Republicans and a variety of likeminded voters wrote it off as just another egregious example of Us vs. Them.

“Political persecution at the highest level,” said West Virginia Attorney General Patrick Morrisey, the Republican nominee for governor. Republican party chairs in South Carolina, Illinois and New York each assailed “banana republic” justice.

There was plenty of talk from other high places in the party about a “sham” trial, “rigged verdict,” “kangaroo court” and Soviet-style shenanigans, as if apparatchiks had delivered the 34 convictions, not a jury whose 12 members were selected by the defense as well as the prosecution.

Even Moscow weighed in, on Trump’s side. “As regards Trump, it’s quite obvious that the effective removal of political opponents by all lawful and unlawful means is going on and the entire world can see it with a naked eye,” said Kremlin spokesman Dmitry Peskov.

Trump’s early reaction to the verdict suggested he will wear his conviction like a crown, and there were already signs of retribution against any Republican who dared to stand up for the trial.

Shortly before the verdict, Larry Hogan, the anti-Trump Republican Senate candidate in Maryland and a former governor, posted an appeal for all Americans to accept the jury’s decision, whatever the outcome, and added: “At this dangerously divided moment in our history, all leaders — regardless of party — must not pour fuel on the fire with more toxic partisanship.”

Chris LaCivita, a senior Trump campaign adviser, shot back on X: “You just ended your campaign.”

Among voters, Justin Gonzalez, a 21-year-old student and tutor in the border city of McAllen, Texas, said he did learn something quite troubling about Trump in the trial. “He’s a lot of things, but I never personally thought of him as a liar,” he said. “I guess this would change my perception of him.”

Yet as he prepares to vote in his first presidential election, Gonzales cares more about immigration enforcement than the icky business centered on the cover-up of payments to silence a porn actor. “Out of all the other issues, this is still bad but it’s not enough to sway me to vote for Biden.”

An ABC-Ipsos poll conducted in late April found that 80% of Trump’s supporters said they would stick with him even if he were convicted of a felony in the hush-money case. Only 4% said they would withdraw their vote, though 16% said they would reconsider it. In an election that is expected to be close, even small shifts in support could make a difference.

In the Lower Manhattan courthouse, the first president to come to power propelled by tabloid fame and reality TV faced the ultimate tabloid kind of charges and yet, in a story of our time, he is the Republicans’ presumptive nominee for president.

With his ever-present sense of spectacle — though there was no televising of the proceedings — Trump turned the trial into a campaign stage for reelection as best he could.

He has succeeded in other contexts by the use of his bullhorn — shouting down his opponents, savaging them on social media, branding them with humiliating nicknames — but this time some of his normal moves weren’t available to him. He did not have control of the situation. He couldn’t simply hector away the constraints of a courtroom and the clear language of the law. He tried on occasion and the judge ordered him to be silent, slapped him with fines and the threat of worse. Mostly he glowered and, at times, looked Zen or sleepy.

New Yorkers weren’t used to seeing this happen to Trump. Love him or hate him — and there’s little in between — they have long considered him an escape artist through career-spanning thickets of legal, business and political thorns.

This time he didn’t get away.

“Finally, some accountability,” said Nadine Striker, who celebrated the verdict at a public pond across the street from the courthouse, a mile from Fifth Avenue. She held up a big banner reading “TRUMP CONVICTED” and wore a headband propping up a hand-sized cutout of Alvin Bragg, the prosecutor.

Back in November 1973, Richard Nixon famously declared to a meeting of newspaper managing editors in The Associated Press cooperative: “I am not a crook.” At the time, in the Watergate scandal that ultimately consumed his presidency, it looked like he might be just that.

But for Nixon that question was never put to the test in court. With Trump, it has been.

Still, with Trump, you never ever know. He may have some Harry Houdini left in him.

“Anybody else would go to jail,” Striker said. “I don’t expect him to.”

Associated Press writers Cedar Attanasio in New York, Bill Barrow in Atlanta, John Raby in Charleston, West Virginia, and Valerie Gonzalez in McAllen, Texas, contributed to this report.

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