Preston Green III, University of Connecticut and Suzanne Eckes, University of Wisconsin-Madison

In April 2025, the Supreme Court will hear arguments about whether the nation’s first religious charter school can open in Oklahoma. The St. Isidore of Seville Catholic Virtual School would be funded by taxpayer money but run by a local archdiocese and diocese.

The case is often discussed in terms of religion, and a decision in the school’s favor could allow government dollars to directly fund faith-based charter schools nationwide. In part, the justices must decide whether the First Amendment’s prohibition on government establishing religion applies to charter schools. But the answer to that question is part of an even bigger issue: Are charters really public in the first place?

As two professors who study education law, we believe the Supreme Court’s decision will impact issues of religion and state, but could also ripple beyond – determining what basic rights students and teachers do or don’t have at charter schools.

Dueling arguments

In June 2023, the Oklahoma Statewide Virtual Charter School Board approved St. Isidore’s application to open as an online K-12 school. The following year, however, the Oklahoma high court ruled that the proposal was unconstitutional. The justices concluded that charter schools are public under state law, and that the First Amendment’s establishment clause forbids public schools from being religious. The court also found that a religious charter school would violate Oklahoma’s constitution, which specifically forbids public money from benefiting religious organizations.

On appeal, the charter school is claiming that charter schools are private, and so the U.S. Constitution’s establishment clause does not apply.

Moreover, St. Isidore argues that if charter schools are private, the state’s prohibition on religious charters violates the First Amendment’s free exercise clause, which bars the government from limiting “the free exercise” of religion. Previous Supreme Court cases have found that states cannot prevent private religious entities from participating in generally available government programs solely because they are religious.

In other words, while St. Isidore’s critics argue that opening a religious charter school would violate the First Amendment, its supporters claim the exact opposite: that forbidding religious charter schools would violate the First Amendment.

Are charters public?

The question of whether an institution is public or private turns on a legal concept known as the “state action doctrine.” This principle provides that the government must follow the Constitution, while private entities do not have to. For example, unlike students in public schools, students in private schools do not have the constitutional right to due process for suspensions and expulsions – procedures to ensure fairness before taking disciplinary action.

Charter schools have some characteristics of both public and private institutions. Like traditional public schools, they are government-funded, free and open to all students. However, like private schools, they are free from many laws that apply to public schools, and they are independently run.

Because of charters’ hybrid nature, courts have had a hard time determining whether they should be considered public for legal purposes. Many charter schools are overseen by private corporations with privately appointed boards, and it is unclear whether these private entities are state actors. Two federal circuit courts have reached different conclusions.

In Caviness v. Horizon Learning Center, a case from 2010, the 9th Circuit held that an Arizona charter school corporation was not a state actor for employment purposes. Therefore, the board did not have to provide a teacher due process before firing him. The court reasoned that the corporation was a private actor that contracted with the state to provide educational services.

In contrast, the 4th Circuit ruled in 2022 that a North Carolina charter school board was a state actor under the equal protection clause of the Fourteenth Amendment. In this case, Peltier v. Charter Day School, students challenged the dress code requirement that female students wear skirts because they were considered “fragile vessels.”

The court first reasoned that the board was a state actor because North Carolina had delegated its constitutional duty to provide education. The court observed that the charter school’s dress code was an inappropriate sex-based classification, and that school officials engaged in harmful gender stereotyping, violating the equal protection clause.

If the Supreme Court sides with St. Isidore – as many analysts think is likely – then all private charter corporations might be considered nonstate actors for the purposes of religion.

But the stakes are even greater than that. State action involves more than just religion. Indeed, teachers and students in private schools do not have the constitutional rights related to free speech, search and seizure, due process and equal protection. In other words, if charter schools are not considered “state actors,” charter students and teachers may eventually shed constitutional rights “at the schoolhouse gate.”

Amtrak: An alternate route?

When courts have held that charter schools are not public in state law, some legislatures have made changes to categorize them as public. For example, California passed a law to clarify that charter school students have the same due process rights as traditional public school students after a court ruled otherwise.

Likewise, we believe states looking to clear up charter schools’ ambiguous state actor status under the Constitution can amend their laws. As we explain in a recent legal article, a 1995 Supreme Court case involving Amtrak illustrates how this can be done.

Lebron v. National Railroad Passenger Corporation arose when Amtrak rejected a billboard ad for being political. The advertiser sued, arguing that the corporation had violated his First Amendment right to free speech. Since private organizations are not required to protect free speech rights, the case hinged on whether Amtrak qualified as a government agency.

The court ruled in the plaintiff’s favor, reasoning that Amtrak was a government actor because it was created by special law, served important governmental objectives, and its board members were appointed by the government.

Courts have applied this ruling in other instances. For example, the 10th Circuit Court ruled in 2016 that the National Center for Missing and Exploited Children was a governmental agency and therefore was required to abide by the Fourth Amendment’s protection from unreasonable search and seizure.

Currently, we believe charter schools fail the test set out in the Amtrak decision. Charter schools do serve the governmental purpose of providing educational choice for students. However, charter school corporations are not created by special law. They also fall short because most have independent boards instead of members who are appointed and removed by government officials.

However, we would argue that states can amend their laws to comply with Lebron’s standard, ensuring that charter schools are public or state actors for constitutional purposes.

Preston Green III, John and Maria Neag Professor of Urban Education, University of Connecticut and Suzanne Eckes, Susan S. Engeleiter Professor of Education Law, Policy and Practice, University of Wisconsin-Madison

This article is republished from The Conversation under a Creative Commons license. Read the original article.

Rutvik Desai, University of South Carolina

Generative AI systems like large language models and text-to-image generators can pass rigorous exams that are required of anyone seeking to become a doctor or a lawyer. They can perform better than most people in Mathematical Olympiads. They can write halfway decent poetry, generate aesthetically pleasing paintings and compose original music.

These remarkable capabilities may make it seem like generative artificial intelligence systems are poised to take over human jobs and have a major impact on almost all aspects of society. Yet while the quality of their output sometimes rivals work done by humans, they are also prone to confidently churning out factually incorrect information. Skeptics have also called into question their ability to reason.

Large language models have been built to mimic human language and thinking, but they are far from human. From infancy, human beings learn through countless sensory experiences and interactions with the world around them. Large language models do not learn as humans do – they are instead trained on vast troves of data, most of which is drawn from the internet.

The capabilities of these models are very impressive, and there are AI agents that can attend meetings for you, shop for you or handle insurance claims. But before handing over the keys to a large language model on any important task, it is important to assess how their understanding of the world compares to that of humans.

I’m a researcher who studies language and meaning. My research group developed a novel benchmark that can help people understand the limitations of large language models in understanding meaning.

Making sense of simple word combinations

So what “makes sense” to large language models? Our test involves judging the meaningfulness of two-word noun-noun phrases. For most people who speak fluent English, noun-noun word pairs like “beach ball” and “apple cake” are meaningful, but “ball beach” and “cake apple” have no commonly understood meaning. The reasons for this have nothing to do with grammar. These are phrases that people have come to learn and commonly accept as meaningful, by speaking and interacting with one another over time.

We wanted to see if a large language model had the same sense of meaning of word combinations, so we built a test that measured this ability, using noun-noun pairs for which grammar rules would be useless in determining whether a phrase had recognizable meaning. For example, an adjective-noun pair such as “red ball” is meaningful, while reversing it, “ball red,” renders a meaningless word combination.

The benchmark does not ask the large language model what the words mean. Rather, it tests the large language model’s ability to glean meaning from word pairs, without relying on the crutch of simple grammatical logic. The test does not evaluate an objective right answer per se, but judges whether large language models have a similar sense of meaningfulness as people.

We used a collection of 1,789 noun-noun pairs that had been previously evaluated by human raters on a scale of 1, does not make sense at all, to 5, makes complete sense. We eliminated pairs with intermediate ratings so that there would be a clear separation between pairs with high and low levels of meaningfulness.

We then asked state-of-the-art large language models to rate these word pairs in the same way that the human participants from the previous study had been asked to rate them, using identical instructions. The large language models performed poorly. For example, “cake apple” was rated as having low meaningfulness by humans, with an average rating of around 1 on scale of 0 to 4. But all large language models rated it as more meaningful than 95% of humans would do, rating it between 2 and 4. The difference wasn’t as wide for meaningful phrases such as “dog sled,” though there were cases of a large language model giving such phrases lower ratings than 95% of humans as well.

To aid the large language models, we added more examples to the instructions to see if they would benefit from more context on what is considered a highly meaningful versus a not meaningful word pair. While their performance improved slightly, it was still far poorer than that of humans. To make the task easier still, we asked the large language models to make a binary judgment – say yes or no to whether the phrase makes sense – instead of rating the level of meaningfulness on a scale of 0 to 4. Here, the performance improved, with GPT-4 and Claude 3 Opus performing better than others – but they were still well below human performance.

Creative to a fault

The results suggest that large language models do not have the same sense-making capabilities as human beings. It is worth noting that our test relies on a subjective task, where the gold standard is ratings given by people. There is no objectively right answer, unlike typical large language model evaluation benchmarks involving reasoning, planning or code generation.

The low performance was largely driven by the fact that large language models tended to overestimate the degree to which a noun-noun pair qualified as meaningful. They made sense of things that should not make much sense. In a manner of speaking, the models were being too creative. One possible explanation is that the low-meaningfulness word pairs could make sense in some context. A beach covered with balls could be called a “ball beach.” But there is no common usage of this noun-noun combination among English speakers.

If large language models are to partially or completely replace humans in some tasks, they’ll need to be further developed so that they can get better at making sense of the world, in closer alignment with the ways that humans do. When things are unclear, confusing or just plain nonsense – whether due to a mistake or a malicious attack – it’s important for the models to flag that instead of creatively trying to make sense of almost everything.

If an AI agent automatically responding to emails gets a message intended for another user in error, an appropriate response may be, “Sorry, this does not make sense,” rather than a creative interpretation. If someone in a meeting made incomprehensible remarks, we want an agent that attended the meeting to say the comments did not make sense. The agent should say, “This seems to be talking about a different insurance claim” rather than just “claim denied” if details of a claim don’t make sense.

In other words, it’s more important for an AI agent to have a similar sense of meaning and behave like a human would when uncertain, rather than always providing creative interpretations.

Rutvik Desai, Professor of Psychology, University of South Carolina

This article is republished from The Conversation under a Creative Commons license. Read the original article.

John Etnyre, Georgia Institute of Technology

When you look at your surrounding environment, it might seem like you’re living on a flat plane. After all, this is why you can navigate a new city using a map: a flat piece of paper that represents all the places around you. This is likely why some people in the past believed the earth to be flat. But most people now know that is far from the truth.

You live on the surface of a giant sphere, like a beach ball the size of the Earth with a few bumps added. The surface of the sphere and the plane are two possible 2D spaces, meaning you can walk in two directions: north and south or east and west.

What other possible spaces might you be living on? That is, what other spaces around you are 2D? For example, the surface of a giant doughnut is another 2D space.

Through a field called geometric topology, mathematicians like me study all possible spaces in all dimensions. Whether trying to design secure sensor networks, mine data or use origami to deploy satellites, the underlying language and ideas are likely to be that of topology.

The shape of the universe

When you look around the universe you live in, it looks like a 3D space, just like the surface of the Earth looks like a 2D space. However, just like the Earth, if you were to look at the universe as a whole, it could be a more complicated space, like a giant 3D version of the 2D beach ball surface or something even more exotic than that.

While you don’t need topology to determine that you are living on something like a giant beach ball, knowing all the possible 2D spaces can be useful. Over a century ago, mathematicians figured out all the possible 2D spaces and many of their properties.

In the past several decades, mathematicians have learned a lot about all of the possible 3D spaces. While we do not have a complete understanding like we do for 2D spaces, we do know a lot. With this knowledge, physicists and astronomers can try to determine what 3D space people actually live in.

While the answer is not completely known, there are many intriguing and surprising possibilities. The options become even more complicated if you consider time as a dimension.

To see how this might work, note that to describe the location of something in space – say a comet – you need four numbers: three to describe its position and one to describe the time it is in that position. These four numbers are what make up a 4D space.

Now, you can consider what 4D spaces are possible and in which of those spaces do you live.

Topology in higher dimensions

At this point, it may seem like there is no reason to consider spaces that have dimensions larger than four, since that is the highest imaginable dimension that might describe our universe. But a branch of physics called string theory suggests that the universe has many more dimensions than four.

There are also practical applications of thinking about higher dimensional spaces, such as robot motion planning. Suppose you are trying to understand the motion of three robots moving around a factory floor in a warehouse. You can put a grid on the floor and describe the position of each robot by their x and y coordinates on the grid. Since each of the three robots requires two coordinates, you will need six numbers to describe all of the possible positions of the robots. You can interpret the possible positions of the robots as a 6D space.

As the number of robots increases, the dimension of the space increases. Factoring in other useful information, such as the locations of obstacles, makes the space even more complicated. In order to study this problem, you need to study high-dimensional spaces.

There are countless other scientific problems where high-dimensional spaces appear, from modeling the motion of planets and spacecraft to trying to understand the “shape” of large datasets.

Tied up in knots

Another type of problem topologists study is how one space can sit inside another.

For example, if you hold a knotted loop of string, then we have a 1D space (the loop of string) inside a 3D space (your room). Such loops are called mathematical knots.

The study of knots first grew out of physics but has become a central area of topology. They are essential to how scientists understand 3D and 4D spaces and have a delightful and subtle structure that researchers are still trying to understand.

In addition, knots have many applications, ranging from string theory in physics to DNA recombination in biology to chirality in chemistry.

What shape do you live on?

Geometric topology is a beautiful and complex subject, and there are still countless exciting questions to answer about spaces.

For example, the smooth 4D Poincaré conjecture asks what the “simplest” closed 4D space is, and the slice-ribbon conjecture aims to understand how knots in 3D spaces relate to surfaces in 4D spaces.

Topology is currently useful in science and engineering. Unraveling more mysteries of spaces in all dimensions will be invaluable to understanding the world in which we live and solving real-world problems.

John Etnyre, Professor of Mathematics, Georgia Institute of Technology

This article is republished from The Conversation under a Creative Commons license. Read the original article.