Category: Analysis

Source: The Conversation – UK – By Wei Xing, Assistant Professor, School of Mathematical and Physical Sciences, University of Sheffield

OpenAI’s latest research paper diagnoses exactly why ChatGPT and other large language models can make things up – known in the world of artificial intelligence as “hallucination”. It also reveals why the problem may be unfixable, at least as far as consumers are concerned.

The paper provides the most rigorous mathematical explanation yet for why these models confidently state falsehoods. It demonstrates that these aren’t just an unfortunate side effect of the way that AIs are currently trained, but are mathematically inevitable.

The issue can partly be explained by mistakes in the underlying data used to train the AIs. But using mathematical analysis of how AI systems learn, the researchers prove that even with perfect training data, the problem still exists.

The way language models respond to queries – by predicting one word at a time in a sentence based on probabilities – naturally produces errors. The researchers in fact show that the total error rate for generating sentences is at least twice as high as the error rate the same AI would have on a simple yes/no question, because mistakes can accumulate over multiple predictions.

In other words, hallucination rates are fundamentally bounded by how well AI systems can distinguish valid from invalid responses. Since this classification problem is inherently difficult for many areas of knowledge, hallucinations become unavoidable.

It also turns out that the less a model sees a fact during training, the more likely it is to hallucinate when asked about it. With birthdays of notable figures, for instance, it was found that if 20% of such people’s birthdays only appear once in training data, then base models should get at least 20% of birthday queries wrong.

Sure enough, when researchers asked state-of-the-art models for the birthday of Adam Kalai, one of the paper’s authors, DeepSeek-V3 confidently provided three different incorrect dates across separate attempts: “03-07”, “15-06”, and “01-01”. The correct date is in the autumn, so none of these were even close.

The evaluation trap

More troubling is the paper’s analysis of why hallucinations persist despite extensive post-training efforts (such as providing extensive human feedback to an AI’s responses before it is released to the public). The authors examined ten major AI benchmarks, including those used by Google, OpenAI and also the top leaderboards that rank AI models. This revealed that nine benchmarks use binary grading systems that award zero points for AIs expressing uncertainty.

This creates what the authors term an “epidemic” of penalising honest responses. When an AI system says “I don’t know”, it receives the same score as giving completely wrong information. The optimal strategy under such evaluation becomes clear: always guess.

The researchers prove this mathematically. Whatever the chances of a particular answer being right, the expected score of guessing always exceeds the score of abstaining when an evaluation uses binary grading.

The solution that would break everything

OpenAI’s proposed fix is to have the AI consider its own confidence in an answer before putting it out there, and for benchmarks to score them on that basis. The AI could then be prompted, for instance: “Answer only if you are more than 75% confident, since mistakes are penalised 3 points while correct answers receive 1 point.”

The OpenAI researchers’ mathematical framework shows that under appropriate confidence thresholds, AI systems would naturally express uncertainty rather than guess. So this would lead to fewer hallucinations. The problem is what it would do to user experience.

Consider the implications if ChatGPT started saying “I don’t know” to even 30% of queries – a conservative estimate based on the paper’s analysis of factual uncertainty in training data. Users accustomed to receiving confident answers to virtually any question would likely abandon such systems rapidly.

I’ve seen this kind of problem in another area of my life. I’m involved in an air-quality monitoring project in Salt Lake City, Utah. When the system flags uncertainties around measurements during adverse weather conditions or when equipment is being calibrated, there’s less user engagement compared to displays showing confident readings – even when those confident readings prove inaccurate during validation.

The computational economics problem

It wouldn’t be difficult to reduce hallucinations using the paper’s insights. Established methods for quantifying uncertainty have existed for decades. These could be used to provide trustworthy estimates of uncertainty and guide an AI to make smarter choices.

But even if the problem of user preferences could be overcome, there’s a bigger obstacle: computational economics. Uncertainty-aware language models require significantly more computation than today’s approach, as they must evaluate multiple possible responses and estimate confidence levels. For a system processing millions of queries daily, this translates to dramatically higher operational costs.

More sophisticated approaches like active learning, where AI systems ask clarifying questions to reduce uncertainty, can improve accuracy but further multiply computational requirements. Such methods work well in specialised domains like chip design, where wrong answers cost millions of dollars and justify extensive computation. For consumer applications where users expect instant responses, the economics become prohibitive.

The calculus shifts dramatically for AI systems managing critical business operations or economic infrastructure. When AI agents handle supply chain logistics, financial trading or medical diagnostics, the cost of hallucinations far exceeds the expense of getting models to decide whether they’re too uncertain. In these domains, the paper’s proposed solutions become economically viable – even necessary. Uncertain AI agents will just have to cost more.

However, consumer applications still dominate AI development priorities. Users want systems that provide confident answers to any question. Evaluation benchmarks reward systems that guess rather than express uncertainty. Computational costs favour fast, overconfident responses over slow, uncertain ones.

Falling energy costs per token and advancing chip architectures may eventually make it more affordable to have AIs decide whether they’re certain enough to answer a question. But the relatively high amount of computation required compared to today’s guessing would remain, regardless of absolute hardware costs.

In short, the OpenAI paper inadvertently highlights an uncomfortable truth: the business incentives driving consumer AI development remain fundamentally misaligned with reducing hallucinations. Until these incentives change, hallucinations will persist.

Wei Xing does not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.

– ref. Why OpenAI’s solution to AI hallucinations would kill ChatGPT tomorrow – https://theconversation.com/why-openais-solution-to-ai-hallucinations-would-kill-chatgpt-tomorrow-265107

Source: The Conversation – UK – By Craig Beall, Associate Professor in Experimental Diabetes, University of Exeter

The link between diabetes and dementia is becoming increasingly clear. New research shows how blood sugar problems affect brain health and vice versa. Here are ten evidence-based insights into how the two conditions are related.

1. Diabetes raises the risk of dementia

People with diabetes are about 60% more likely to develop dementia than those without, and frequent episodes of low blood sugar are linked to a 50% higher chance of cognitive decline.

2. Insulin resistance affects the brain too

Insulin resistance – the major cause of type 2 diabetes – happens when cells stop responding properly to insulin. This means that too much sugar, in the form of glucose, is left in the blood, leading to complications.

It usually affects the liver and muscles, but it also affects the brain. In Alzheimer’s, this resistance may make it harder for brain cells to use glucose for energy, contributing to cognitive decline.

3. A brain sugar shortage in dementia

The brain is only 2% of our body weight, but uses about 20% of the body’s energy. In dementia, brain cells appear to lose the ability to use glucose properly.

This mix of poor use of glucose and insulin resistance is sometimes unofficially called type 3 diabetes.

4. Alzheimer’s can raise diabetes risk

People with Alzheimer’s often have higher fasting blood glucose, even if they don’t have diabetes. This is a form of pre-diabetes. Animal studies also show that Alzheimer’s-like changes in the brain raise blood glucose levels.

Also, the highest genetic risk factor for Alzheimer’s, the APOE4 genetic variant, reduces insulin sensitivity by trapping the insulin receptor inside the cell, where it cannot be switched on properly.

5. Blood vessel damage links both conditions

Diabetes damages blood vessels, causing complications in the eyes, kidneys and heart. The brain is also at risk. High or varying blood glucose levels can injure vessels in the brain, reducing blood flow and oxygen delivery.

Diabetes can also weaken the brain’s protective barrier, letting harmful substances in. This leads to inflammation. Reduced blood flow and brain inflammation are strongly linked to dementia.

6. Memantine: a dementia drug born from diabetes research

Memantine, used to treat moderate to severe Alzheimer’s symptoms, was originally developed as a diabetes medication. It didn’t succeed in controlling blood glucose, but researchers later discovered its benefits for brain function. This story shows how diabetes research may hold clues for treating brain disorders.

7. Metformin might protect the brain

Metformin, the most widely used diabetes drug, does more than just lower blood glucose. It gets in to the brain and may lower brain inflammation.

Some studies suggest that people with diabetes who take metformin are less likely to develop dementia, and those who stop taking it may see their risk increase again.

Trials are testing its effects in people without diabetes.

8. Weight-loss injections may reduce plaque buildup

GLP-1 receptors agonist drugs, such as semaglutide (Ozempic, Wegovy), lower blood glucose and support weight loss. Records show that people with diabetes on these drugs have a lower dementia risk. Comparing GLP1 drugs to metformin, studies have found that they were even more effective than metformin at reducing dementia risk.

Two major trials, Evoke and Evoke Plus, are testing oral semaglutide in people with mild cognitive impairment or early mild Alzheimer’s.

9. Insulin therapy might help the brain

Since insulin resistance in the brain is a problem, researchers have tested insulin sprays given through the nose. This method delivers insulin straight to the brain while reducing effects on blood sugar.

Small studies suggest these sprays may help memory or reduce brain shrinkage, but delivery methods remain a challenge. Sprays vary in how much insulin reaches the brain, and long-term safety has not yet been proven.

10. SGLT2 inhibitors may lower dementia risk

New evidence suggests that compared to GLP-1 receptor agonists, SGLT2 inhibitors, (a type of diabetes drug) are superior at reducing dementia risk, including Alzheimer’s and vascular dementia, in people with type 2 diabetes. These tablets lower blood sugar by increasing sugar removal in urine. This study builds on early evidence suggesting they lower dementia risk by reducing inflammation in the brain.

This growing body of evidence suggests that managing diabetes protects more than the heart and kidneys, it also helps preserve brain function.

Questions remain whether diabetes drugs only reduce the diabetes-associated dementia risk or whether these drugs could also reduce risk in people without diabetes.

However, diabetes research has been very successful in creating at least 13 different classes of drugs, multiple combination therapies, giving rise to at least 50 different medicines. These reduce blood sugar, improve insulin sensitivity and reduce inflammation. A “side-effect” may be better preservation of brain health during ageing.

Craig Beall currently receives funding from Diabetes UK, Breakthrough T1D, Steve Morgan Foundation Type 1 Diabetes Grand Challenge, Medical Research Council, NC3Rs, Society for Endocrinology and British Society for Neuroendocrinology.

Natasha MacDonald receives funding from Diabetes UK.

– ref. Ten ways diabetes and dementia are linked – https://theconversation.com/ten-ways-diabetes-and-dementia-are-linked-264393

Source: The Conversation – UK – By Cynthia Johnston, Senior Lecturer in History of the Book, School of Advanced Study, University of London

The Nature of Gothic, at the Blackburn Museum and Art Gallery, explores the history of decorative borders over hundreds of years. It covers the period from the late medieval age to the Arts and Crafts Movement of the late 19th and early 20th centuries.

In the late medieval period, manuscripts that were produced in northern Europe often featured decorative borders that framed the text of both religious and secular works. These borders featured motifs from the classical world such as swirling acanthus leaves, Greek meanders and intricate patterns which interlace flowers, leaves and vines.

From the early decades of the 13th century these largely naturalistic forms, used to enhance the visual appeal of the page, began to be used more widely. They were added to the front of books and important sections within them, such as the beginnings of individual psalms or chapters of the Bible.

These naturalistic frames provided platforms tangible enough for figures, animals and grotesques to be placed upon. These characters often present an alternative reality to the verses of the psalms or Aristotle’s Libri Naturales that they decorate.

The meaning and intent of these spaces is yet to be fully understood. The battle of a miniature knight versus a fully armed snail, for example, might be interpreted as the moral fight against evil in the margins of the psalm. But the meaning of a tiny man pushing another in a wheel barrow adjacent to the beginning of Aristotle’s Libri Naturales is less clear.

Read more:
Why medieval manuscripts are full of doodles of snail fights

The great enthusiasm for the illustrated grotesques (hybrid creatures which combine human and fantastical animal forms) in these peripheral spaces began in northern France. Texts produced by the monastic schools which emerged with the rise of scholasticism in the late 12th century often carried this type of decoration.

I have been collaborating with the Blackburn museum for over a decade, and have curated this exhibition alongside Anthea Purkis, its curator of art. This exhibition features some early examples of this technique from manuscripts held by the museum as well as examples on loan from the British Library.

In the exhibition

Although the names of very few medieval artists whose work appeared in manuscripts are known, Blackburn Museum and the British Library both hold examples of the intricate and sophisticated work of two known illuminators.

They are Mâitre Françoise, who ran his business in Paris in the third quarter of the 15th century, and Herman Scheere – perhaps the most renowned illuminator in London in the 15th century.

From his workshop on London Bridge, Scheere produced flowing extravagant frames for the pages of his books. His book the Bedford Psalter and Hours, (loaned by the British Library and on display in the exhibition) was commissioned by the younger brother of King Henry V. This aristocratic commission demonstrates the success of Scheere’s business and the appetite for the decorated border.

Some 15th century examples from northern Europe also show the influence of Islamic art on northern European aesthetics. A 15th-century Qur’an manuscript from the John Rylands Library and Research Centre in Manchester is on display in the exhibition. muh .aqqāq script is used for Arabic primary text while the interlinear script in Persian and Eastern Turkish is in minuscule naskh script. This reflects the various communities for whom the book was intended.

The beginnings of the chapters of the Qur’an manuscript, the ṣuwwar, are surrounded by borders filled with flowing abstract forms. They’re reminiscent of, but not imitative of, the natural world. This decorative tradition would have cross pollinated with western European cultures through trade and conflict.

Examples of Persian calligraphy also demonstrate the persistence of the trend for decorative borders at this time. The Rylands’ Persian MS 10, an album completed before 1785–1786AD, features an entwined Arabic calligraphy composition formed from two slogans Tawakkaltu bi-maghfirat al-Muhaymin (I entrust myself to the forgiveness of the Guardian) in black, and Huwa al-Ghafūr Dhū-al-Raḥmah (He is the All-Forgiving Lord of Mercy) in red thuluth script. Two dark indigo blue borders bear delicate silver and gold foliage surrounding a wide margin embellished with vibrant floral flourishes.

Migration to the printed page

In 15th century Germany, Johannes Gutenberg invented the moveable-type printing press. His new technology produced a codex (an ancient manuscript text in book form) that looked like a traditional manuscript with regard to text and margins.

Rubrication – the decoration of letters in coloured inks – was added by hand to the first printed books. As the ability of printers to produce more nuanced illustrations accelerated, the decorated border survived and thrived. Indeed, its importance as part of the aesthetic in terms of how a book should look to an early modern reader drove forward innovations in technology.

The Blackburn Museum’s collection of early printed books is full of examples of the new technology of print accommodating the decorative frame.

Falling in and out of favour

The decorated frame fell out of favour in the 16th and 17th centuries. For western European readers it began to appear old fashioned. But it returned during the Industrial Revolution, thanks to the work of the Pre-Raphaelite movement.

Pre-Raphaelite artists reached back to the medieval period for their inspiration as well as artistic practice. Dante Gabriel Rossetti, William Morris, Sir Edward Coley Burne-Jones, Arthur Hughes and their associates set out to reject the values and industrial production of the 19th century. Medieval narratives found new audiences in Pre-Rapahelite art such as Arthur Hughes’ Sir Galahad, the Quest for the Holy Grail. In the subsequent Arts and Crafts Movement, books, ceramics, textiles and furniture were produced with minimal mechanical intervention. The medieval decorative frame thrived across various media.

William Morris’ hand-written copy of The Rubaiyat of Omar Khayyam provides a compelling example of the after-life of the medieval margin. On each page, the text is surrounded by a lush decorated border which is punctuated by cameos that were designed by Burne-Jones and painted by Charles Fairfax Murray.

The Nature of Gothic gives visitors the opportunity to compare the work of medieval masters of decorative art with the work produced by the Pre-Raphaelites and the Arts and Crafts Movement. Contemporary artist Jamie Holman and ceramicist Nehal Aamir also contribute modern interpretations of the decorated frame.

The result is a celebration of the verdant decorative frames which twist and turn through time, illuminating art of both the past and present.

The Nature of Gothic is at the Blackburn Museum and Art Gallery from September 13 to December 13.

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With thanks to Jake Benson for the translation of Persian 10.

Cynthia Johnston is employed by The Institute of English Studies, School of Advanced Study, University of London. She receives funding from Arts Council England. This exhibit has been supported by major loans from the British Library, the John Rylands Library and Research Centre, Manchester Art Gallery and the Liverpool Museums Trust among others.

– ref. New exhibition explores history of decorative borders: from medieval manuscripts to William Morris – https://theconversation.com/new-exhibition-explores-history-of-decorative-borders-from-medieval-manuscripts-to-william-morris-261785

Source: The Conversation – UK – By Shweta Singh, Assistant Professor, Information Systems and Management, Warwick Business School, University of Warwick

Generative AI promises to help solve everything from climate change to poverty. But behind every chatbot response lies a deep environmental cost.

Current AI technology requires the use of large datacentres stationed around the world, which altogether draw enormous amounts of power and consume millions of litres of water to stay cool. By 2030, datacentres are expect to consume as much electricity as all of Japan, according to the International Energy Agency, and AI could be responsible for 3.5% of global electricity use, according to one consultancy report.

The continuous massive expansion of AI use and its rapidly growing energy demand would make it much harder for the world to cut its carbon emissions by switching fossil fuel energy sources to renewable electricity.

So, we are left with pressing questions. Can we harness the benefits of AI without accelerating environmental collapse? Can AI be made truly sustainable – and if so, how?

We are at a critical juncture. The environmental cost of AI is accelerating and largely unreported by the firms involved. What the world does next could determine whether AI innovation aligns with our climate goals or undermines them.

At one end of the policy spectrum is the path of complacency. In this scenario, tech companies continue unchecked, expanding datacentres and powering them with private nuclear microreactors, dedicated energy grids or even reviving mothballed coal plants.

Some of this infrastructure may instead run on renewables, but there’s no binding requirement that AI must avoid using fossil fuels. Even if more renewables are installed to power AI, they may compete with efforts to decarbonise other energy uses. Developers may tout efficiency gains, but these are quickly swallowed by the rebound effect: the more efficient AI becomes, the more it is used.

At the other end lies a more radical possibility: a global moratorium or outright restriction on the most harmful forms of AI, akin to international bans on landmines or ozone-depleting substances.

This is politically improbable, of course. Nations are racing to dominate the AI arms race, not to pause it. A global consensus on bans is, at least for now, a mirage.

But in between complacency and prohibition lies a window – rapidly closing – for decisive, targeted action.

This could take many different forms:

1. Mandatory environmental disclosure:

AI companies could report how much energy, water and emissions are used to train and use their models. Having a benchmark helps to measure progress while improving transparency and accountability. While some countries have started to impose greater corporate sustainability reporting requirements, there is significant variation. While mandatory disclosures alone won’t reduce consumption directly, they are an essential starting point.

2. Emissions labelling for AI services:

Just as carbon emissions labels on restaurant menus or supermarket produce can guide people to lower-impact options, users could be given a chance to know the footprint of their digital choices and AI providers, like efforts to measure the carbon footprint of websites. In the US, the blue Energy Star label, one of the country’s most recognisable environmental certifications, helps customers choose energy-efficient products.

Alternatively, AI providers could also temporarily reduce functionality to account for varying levels of renewable energy available that powers them.

3. Usage-based pricing tied to impact:

Existing carbon pricing aims to ensure that heavy users should pay their environmental share. Research shows that this works best when carbon is priced across the economy for all companies, rather than just specifically targeted at individual sectors. Yet much depends on digital tech providers fully accounting for such environmental burdens in the first place.

4. Sustainability caps or “compute budgets”:

This would especially target non-essential or commercial entertainment applications. Organisations may limit their employees’ usage similar to how they restrict heavy office printing or indeed corporate travel. As companies begin to measure and manage their indirect supply chain emissions, energy and water footprints from using AI may require new business policies.

5. Water stewardship requirements in water-stressed regions:

A simple regulation here would be to ensure no AI infrastructure depletes local aquifers unchecked.

Market forces alone will not solve this. Sustainability won’t emerge from goodwill or clever efficiency tricks. We need enforceable rules.

Consumer awareness isn’t enough

Awareness does help. But expecting individuals to self-regulate in a system designed for ease-of-use is naive. “Only use AI when needed” might soon be like “Don’t print this email” a decade or two ago – well-meaning, often ignored and utterly insufficient.

The world is building an AI-powered future that consumes like an industrial past. Without guardrails, we risk creating a convenience technology that accelerates environmental collapse.

Maybe AI will one day solve the problems we couldn’t, and our concerns about emissions or water will seem trivial. Or maybe we just won’t be around to worry about them.

The way we engage with AI now – blindly, cautiously, or critically – will shape whether it serves a sustainable future, or undermines it. Policymakers should treat AI as it would any other wildly profitable resource-intensive industry, with carefully thought through regulation.

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Frederik Dahlmann receives funding from National Institute for Health & Care Research (NIHR).

Shweta Singh does not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.

– ref. Regulating AI use could stop its runaway energy expansion – https://theconversation.com/regulating-ai-use-could-stop-its-runaway-energy-expansion-258425

Source: The Conversation – UK – By Marieke Riethof, Senior Lecturer in Latin American Politics, University of Liverpool

Four out of five members of Brazil’s supreme court have voted to convict the former president, Jair Bolsonaro, for plotting a military coup after losing the 2022 election to his left-wing rival, Luiz Inácio Lula da Silva. Bolsonaro has been sentenced to more than 27 years in prison, though his lawyers say they will appeal the decision.

Seven of Bolsonaro’s allies have also been convicted on charges related to the coup attempt. Five of these people – Walter Braga Netto, Mauro Cid, Paulo Sérgio Nogueira de Oliveira, Augusto Heleno Ribeiro and Almir Garnier Santos – come from a military or navy background. Bolsonaro’s former justice minister, Anderson Torres, and the former director of Brazil’s intelligence agency, Alexandre Ramagem, have been convicted too.

This is the first time in Brazil’s long history of political instability that a coup attempt has led to a conviction. It is also symbolically important that the only woman on the panel, Judge Carmen Lúcia, cast the deciding vote. Bolsonaro has an established track record of making denigrating comments about women.

The date of the verdict is equally important. It was delivered on September 11, which coincides with the 52nd anniversary of the 1973 Chilean military coup. This shows how far democracy in the region has come since an era when much of South America was under military rule.

Alexandre de Moraes, the supreme court judge who led the Bolsonaro trial, alluded to this in August. He said that Brazil’s 1988 constitution established the judiciary’s independence by restricting “interference by the armed forces, whether official or semi-official, in Brazilian politics”.

These constitutional guarantees mean that politicians like Bolsonaro cannot undermine democratic institutions with impunity.

The coup attempt took place on January 8 2023, less than a week after Lula was inaugurated as Bolsonaro’s successor. Echoing the attack on the US Capitol building in Washington two years earlier, hundreds of Bolsonaro supporters stormed the national congress, presidential palace and supreme court in the capital, Brasília.

They left a trail of destruction. Although the protests appeared initially to be a spontaneous act, investigations soon unearthed evidence that the event had been planned by Bolsonaro and his allies.

A history of dictatorship and threats against democracy have cast a long shadow over Brazilian politics. A right-wing military dictatorship ruled the country between 1964 and 1985. It began when the armed forces overthrew the democratically elected president, João Goulart, amid an economic crisis and fears about a turn to the left. The US government of the time supported the coup.

Brazil established a National Truth Commission in 2012, which spent two years investigating the thousands of cases of torture, extrajudicial killings, enforced disappearances and other violations that occurred during this period. However, there have been no convictions.

Under pressure from mass demonstrations and an economic crisis, the military gradually relaxed repression in the 1980s and allowed political parties to form. Brazil has been under civilian control since then. But the armed forces began to play a significant political role again during Bolsonaro’s presidency.

General Hamilton Mourão, his vice-president, served in the military during the dictatorship. And various other military figures were appointed to powerful positions in government. Bolsonaro also regularly celebrated the dictatorship and downplayed its human rights violations.

There were various examples of democratic backsliding under Bolsonaro. He, for example, questioned the legitimacy of democratic election results in 2022 – comments that saw him barred from running in elections for seven years.

Within this context, the decision to convict Bolsonaro of an attempted coup is a strong sign that Brazil’s democratic institutions have been able to withstand threats to democracy and the rule of law. It is a signal that attempts to undermine the country’s democratic institutions will not go unpunished.

Beyond Brazil’s borders

Bolsonaro’s conviction resonates beyond Brazil. During his presidency, Bolsonaro positioned Brazil as a close ideological ally to Donald Trump, who was then in his first presidential term.

Trump referred to Bolsonaro’s trial as a “witch hunt” as the court case progressed. He hit Brazil with 50% tariffs, framing them as retaliation for Bolsonaro’s prosecution. Reacting to the guilty verdict, Trump said it was “very surprising” and compared it to his own judicial struggles.

Lula has spoken out against US interference in Brazilian politics, calling the idea that “Trump can dictate rules for a sovereign country like Brazil” unacceptable.

The Brazilian foreign affairs ministry has also criticised the US secretary of state, Marco Rubio, for interfering in the country’s sovereignty and democracy. In a social media post, Rubio called the conviction “unjust” and said the US “will respond accordingly to this witch hunt”.

Looking ahead, Brazil’s next presidential elections are in 2026. Unless Bolsonaro manages to appeal his conviction and election ban, he will not be running again for the foreseeable future. Although Lula has not formally announced his candicacy he would be the front-runner.

But if there is a run-off, which would most likely be with right-wing politician and former army captain Tarcísio de Freitas, the race will probably be very close. There is a risk that the conviction will turn Bolsonaro into a martyr, which would strengthen politicians like de Freitas, who identify themselves with Bolsonaro’s politics.

Ahead of his conviction, around 40,000 Bolsonaro supporters protested in Rio de Janeiro and São Paulo. These demonstrations indicate continuing support. However, regardless of what happens next, the supreme court’s decision makes it much less likely that challenges to democracy will succeed in Brazil.

Marieke Riethof does not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.

– ref. Bolsonaro’s conviction marks a historic moment in Brazil’s political history – https://theconversation.com/bolsonaros-conviction-marks-a-historic-moment-in-brazils-political-history-265210