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Apple's paper, "The Illusion of Thinking: Understanding the Strengths and Limitations of Reasoning Models via the Lens of Problem Complexity," aims to reveal the shortcomings of Large Reasoning Models (LRMs). While its observations contain some truth, the conclusions it draws are deeply flawed.
Here’s why this study fails to deliver—and how its errors pile up into a misleading narrative.
Problem #1: Cumulative Error Probability—Not a Flaw, Just Reality
LRMs generate outputs via neural networks, where each token carries a tiny error probability. In complex tasks like the Tower of Hanoi with 13 disks, the model needs ~81,910 tokens (2^13 - 1 moves × 10 tokens/move). Even with 99.99% per-token accuracy, the odds of a perfect solution plummet to ~0.44%. Apple paints this as a fatal weakness, but it’s not unique to AI—humans also stumble in long, repetitive tasks due to cumulative errors. This is simply how probabilistic systems work, not a groundbreaking flaw.
Problem #2: Misjudging Abstraction as a Failure
When faced with massive problems, LRMs shift to describing algorithms rather than executing every step—a move Apple criticizes as a defect. But this is a strength, not a failure. The model recognizes its error rate spikes with length (because it was trained on many problems of various complexity) and adapts by offering a high-level solution, much like a human would. Users want answers, not exhaustive breakdowns, but Apple’s rules rigged the game from the start.
Problem #3: Apple Hobbled The Models From Working As Intended
Apple spotlights token limits as a critical flaw, but this is a red herring. For Tower of Hanoi, an LRM could perfectly solve it by executing code—yet Apple disallowed this. ChatGPT, Claude, and Google Gemini can write and execute code to solve complex problems that their neural network cannot — but Apple’s test skipped this practical strategy, forcing models into an unrealistic bind. Reasoning isn’t about flawlessly churning out thousands of steps; it’s about planning and adapting. By obsessing over token constraints, Apple dodges the real issue: Can LRMs reason beyond raw computation? Their setup can’t answer that.
Problem #4: A Puzzle, Not a Proving Ground
The Tower of Hanoi is a toy problem with a neat, known solution—hardly a test of real-world reasoning. True reasoning tackles planning, task decomposition, self-correction, ambiguity, trade-offs, and creativity, not just scripted steps. By hinging their study on this contrived puzzle, Apple sacrifices relevance and generalizability. It’s like rating a chef by how well they boil water—measurable, but meaningless.
Flip the problem around: if the LRMs did solve a 13-ring Tower of Hanoi puzzle, would that prove they are capable of human-level reasoning? No, it would only prove the model had grown by a few orders of magnitude. Larger models can solve arbitrarily longer puzzles, but this only provides the raw computing ability, not their reasoning ability.
Conclusion: A Study Chasing Headlines, Not Truth
Apple’s "The Illusion of Thinking" flags real issues but trips over its own logic. Cumulative errors are overstated, abstraction is misread, token limits are a non-issue, and the puzzle choice undermines it all. This isn’t a decisive strike against LRMs—it’s a misfire. If we’re serious about testing reasoning, we need tasks rooted in reality, not academic gimmicks. The illusion here lies in the study, not the models.
It's been risible watching statists here struggling over recent months to get their heads around the Atlas Network think tank—and what exactly think tanks do.
What troubles them most perhaps is the word "think" in the description. Many have forgotten how to.
Nonetheless, to help them understand, the think tank Students for Liberty sets out to explain what they do.
The story goes back to 1945, when a war hero wanted to save his country—and a Nobel Prize winner told him to forget about politics.
This isn't just about a pin. It's about how ideas travel from university classrooms to presidential palaces. And why every student needs to understand this journey—because you're living through it right now.
In 1945, World War II just ended. F.A. Hayek, teaching at the London School of Economics, meets Antony Fisher—a combat aviator and war hero. Fisher had read Hayek's The Road to Serfdom and was terrified about Britain's socialist direction. "I want to enter politics," Fisher declared.
Hayek stopped him cold. "The political battle isn't won in the political arena," he explained. "It's fought—and ultimately won—by intellectuals." Politicians follow public opinion. But intellectuals? They shape it.
Fisher listened. Instead of running for political office, he founded the UK's Institute of Economic Affairs. For decades, IEA scholars published papers, hosted debates, and educated a generation about free markets. The result? Britain elected Margaret Thatcher.
Legend has it that in her first Cabinet meeting, Thatcher slammed down Hayek's book Constitution of Liberty—published by the IEA—and declared: "This is what we believe!" Ideas had become policy. Intellectuals had changed a nation.
This wasn't an accident. Hayek had studied how ideas spread. It's like a pyramid:
Scholars develop ideas ...
... Intellectuals* spread them
... Media amplifies them
... Politicians adopt them
Every revolution starts at the top of that pyramid.
Now look at American universities today (and this is fairly universal everywhere):X Professors teaching government as the solution to everythingX Students defending socialism (70% of Gen Z consider voting socialist)X 53% of graduates feel unqualified for jobs in their fieldX Ideology of resentment toward achievementOur Local Coordinators host events, educate peers, and develop as leaders worldwide.In 2024 alone: 3,881 events reaching 150,000+ people.One person who helped SFL in Argentina? An economist named Javier Milei.Milei didn't just wear our pin—he partnered with us.He attended our events, explained our mission on TV, and mentored pro-liberty students across Argentina.Why? Because he understood: to change politics, you first have to change culture.
Take Ethan Yang. Started with "no leadership experience, no professional skills. Just a small libertarian club that met in the basement of our dining hall."As a Students for Liberty coordinator, his Freedom of Information Act request helped halt the Biden administration's social-media censorship. The case reached the Supreme Court.A federal judge called the Biden Administration's collusion with/threats to Big Tech "the most massive attack against free speech in US history."Stopped by one student. One request. Supreme Court case.That's the power of the pyramid when it works for liberty.
Here's what every student needs to understand:You're not just getting a degree.You're being shaped by ideas that will define the next fifty years.The question isn't whether ideas will spread from campus—it's which ideas will spread.Milton Friedman explains the point: "Our basic function is to develop alternatives to existing policies, to keep them alive until the politically impossible becomes the politically inevitable."Before Milei became president, he was attending SFL events.That pin? It represents a movement that changed a country.Tired of feeling outnumbered, silenced, or lost in campus groupthink?The College Survival Kit is your first step into this global movement.Learn how real change begins—with students who refuse to stay silent: DOWNLOAD YOURS HERE.
"President Trump has deployed the National Guard, along with several hundred marines, to Los Angeles — despite the objections of California Governor Gavin Newsom. ... the first time a president has invoked this authority since Lyndon Johnson sent them in to protect civil rights protesters in Alabama in 1965... The circumstances in Trump’s case are dramatically different, and it’s far from clear that his decision meets the legal standard for federalising Guard troops. ... The protests over the weekend weren’t even particularly large, numbering in the hundreds, rather than the thousands, most of whom were demonstrating peacefully. ...Trump’s response was unprecedented in recent American history. ...
"Trump might see several advantages to engineering a dramatic showdown in a city and state run by his political enemies.
"He also probably wants to posture for his base as a tough and decisive leader. ... The incentive to pander to his base might be particularly strong in this case because the underlying issue is immigration. ... but his administration has struggled to deport anything like th[e millions promised] By sending the marines to Los Angeles to stop protesters from blocking ICE vans, perhaps Trump is seeking to symbolically compensate for the gap between rhetoric and reality.
"There are other plausible explanations which are far more disturbing. Is Trump hoping that inflaming tensions will provoke a violent response from Angelenos extreme enough to justify seizing further emergency powers? Or could it be a trial balloon: an opportunity for Trump to gauge how much authoritarianism he can get away? That would fit the pattern of the rest of his second term, during which he has sent deportees to a prison in El Salvador without trial, and ignored a judge’s explicit order to turn back deportation flights that were already in the air. ...
"Something similar might be going on here. While senior White House aide Stephen Miller has explicitly used the word 'insurrection' to describe events in Los Angeles, Trump has so far stopped short of using the i-word. ...Even so, this sets a precedent: that marines can be sent to sites of domestic unrest. And this might make the public and the press a bit less rattled if Trump ever does invoke the Insurrection Act in the future.
"Trump, though, tends to act on impulse. Few presidents have been lessconsistent in their decision making: administration officials and advisors come and go, the President’s moods change, and everyone has to scramble to keep up. But while he fumbles in the dark, acting on instinct, many of those instincts are deeply authoritarian. Testing how far he can push the limits of presidential power is par for the course."~ Ben Burgis from his op-ed 'Trump is testing Los Angeles'
