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🤯 Your computer can’t calculate 0.1 + 0.2 correctly. And a similar rounding error once contributed to the deaths of 28 soldiers. Here’s why. 💻 Computers store numbers in binary, not decimal. Just like 1/3 becomes 0.3333… forever, numbers like 0.1 have repeating binary representations. IEEE 754 floating-point numbers...

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🚨 In the new episode of my AfterMath series, I ask: Can a computer reach the full capacity of the human mind? With the recent advances in AI, this has become a hot topic for debate. I focus on the area I know best: mathematics. And I further narrow it down to the question: Can a computer be as good as a human in dealing with natural numbers? (Numbers like 0,1,2,3,4, and so on.) I make an important distinction between Type I and Type II statements about natural numbers. Statements of Type I are about specific numbers (here computers excel), and statements of Type II are GENERAL statements that apply to ALL NUMBERS at once (such as Fermat's Last Theorem). Mathematics is about Type II statements, and in this domain computers hit a wall, which I'd like to call the "Turing Wall." The problem is that Type II statements can't be reduced to Type I statements as computer's memory is finite. To handle Type II statements, one has to use FORMAL SYSTEMS, in which we symbolically encode properties of natural numbers, so they could be programmed on a computer. Once we choose the axioms and the rules of inference, we can run a computer, and it will produce many true statements about natural numbers. However, Tarski's Undefinability Theorem, which I introduce in this episode (it is closely related to Gödel's Incompleteness Theorems but is even more relevant to these issues, in my opinion), shows that this way we can NOT get all true statements about natural numbers. In fact, the notion of "true statement" is not contained in a formal system. To introduce this notion in a given formal system, one has to choose a model of this formal system, and there are many inequivalent models. Large Language Models give mathematicians a great tool for research, but they can't be used effectively for the kinds of foundational questions of mathematics we are discussing here. At the end of the episode, I go back to the 3-dimensional sphere I talked about in Episode 2. I give a 4-dimensional spacetime demonstration of it, using... a balloon. 😃 In a future video, I am planning to discuss the 3-dimensional sphere in more detail with my friend . See the links to the entire episode below.⤵️⤵️

Edward Frenkel

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The City of Chicago booted my car because they confused my license plate with another vehicle. I have video of a dispatcher acknowledging the mistake. Let that sink in. A city system with the power to immobilize your vehicle, disrupt your workday, cost you money, embarrass you publicly, and force you into a bureaucratic nightmare could not even verify the correct plate before taking action. This is not just about me. This is about every Chicagoan — especially South Side residents — who may be dealing with careless enforcement, wrongful penalties, impossible customer service, and city systems that treat people like they are guilty until they can prove otherwise. When government makes a mistake, the burden should not fall on the resident to fight through confusion, delays, fees, lost time, and stress. Chicago needs accountability. I am calling for: ✅ Immediate removal of wrongful boots when city error is confirmed ✅ Full dismissal of any fees connected to mistaken enforcement ✅ Written confirmation and documentation of the city’s error ✅ A clear appeals process that does not punish residents for mistakes they did not make ✅ Better verification before boots are placed on vehicles ✅ Public reporting on wrongful booting incidents and city error rates ✅ Accountability for departments and contractors involved in repeated mistakes ✅ Faster response times when residents present evidence of city error ✅ Reimbursement for residents who lose money because of wrongful enforcement If the city can make this mistake with me, how many residents without a camera, a platform, or time to fight back are being forced to pay for mistakes they did not make? This is what happens when government has too much power and too little diligence. Chicago residents deserve competence. South Side families deserve respect. And no taxpayer should have to pay the price for the city’s failure to do its job correctly.

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