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Human Ingenuity vs. the Computer’s Halting Problem

In a dialogue with a friendly skeptic, I suggested an explanation he found astounding but it’s the only possible one

When studying computer science a student invariably learns about the infamous halting problem. The problem states there is no general algorithm that can determine for every deterministic computer program whether that program will halt or not. This struck me as absurd when I first learned of the problem. Surely a whizkid like myself could design a simple algorithm to track the program’s memory and catch when it started repeating itself and determined it would not halt. Once convinced the problem was indeed provably unsolvable, I then thought the problem must show that humans are not computers. This is because it seems intuitive that for every program, if I watch it enough and think about it carefully enough, I should be…

Schrodinger's cat

Does Schrödinger’s Cat Think Quantum Computing Is a Sure Thing?

It might lead to more security, though not to thinking computers

Some hope that a move to quantum computing—qubits instead of bits, analog instead of digital—will work wonders, including the invention of the true thinking computer. In last week’s podcast, futurist George Gilder and computer engineer Robert J. Marks looked at, among other things, what’s really happening with quantum computing: https://episodes.castos.com/mindmatters/Mind-Matters-108-George-Gilder.mp3 (The quantum computing discussion begins at 15:04.) Robert J. Marks: What’s your take on quantum computing? It seems to me that there’s been glacial progress in the technology. George Gilder (pictured): I think quantum computing is rather like AI, in that it moves the actual problem outside the computational process and gives the illusion that it solved the problem, but it’s really just pushed the problem out. Quantum computing is…

Communist Party Monument, Pyongyang, North-Korea

Computer Science Explains Why Communism Can’t Work

Successful communism is not only morally and practically flawed, it is mathematically impossible

Communism has been the target of many criticisms. The strongest deal with the mismatch between central planning and individuals’ desires for their lives and with the horrific human rights record of communist nations. Some scholars place the toll in human life due to communism at above 100 million in the 20th century. Those are criticisms of the practicality and ethics of communism. But is it also intrinsically flawed at a fundamental mathematical level? It turns out that the answer is yes. The basic idea behind central planning is this: If the central government makes most decisions that, in a freer society, individuals or small communities would make for themselves, more efficiency will follow—and, as a result, more prosperity. It doesn’t…


Why Your Computer Will Never Talk to You

As a jokester recently demonstrated, even “shirts without stripes” is a fundamental, unsolvable problem for computers

At first, “shirts without stripes” might not seem like much of an issue but it turns out that many important and interesting problems for computers fundamentally reduce to this “halting problem.” And understanding human language is one of these problems.

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An array of symbols from the National Archives, Hämeenlinna, Finland

Artificial Intelligence Must Be Possible! Really…?

Many arguments for strong artificial intelligence depend on an ideological commitment to explicit, unproven theories about the universe

Not only is it valid to ask whether artificial intelligence is impossible but the argument can be pursued on a scientific basis with quantifiable, empirical evidence.

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Water droplet on glossy surface of freshness orange and red apple
Apples and oranges in shadows

Why I Doubt That AI Can Match the Human Mind

Computers are exclusively theorem generators, while humans appear to be axiom generators

My primary reason for doubting that AI can match human intelligence is that the difference between mind and machine is a difference of kind, not of quantity. Understanding the distinction will help us exploit the abilities of each to their maximum potential.

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If Computers Thought Like Fruit Flies, They Could Do More

But even with more sophisticated buzz, there remain "non-computable" things that a computer cannot be programmed to think

Recently, researchers discovered that fruit flies use a filter similar to a computer algorithm to assess the odors that help them find fruit, only the flies’ tools are more sophisticated: When a fly smells an odor, the fly needs to quickly figure out if it has smelled the odor before, to determine if the odor is new and something it should pay attention to,” says Saket Navlakha, an assistant professor in Salk’s Integrative Biology Laboratory. “In computer science, this is an important task called novelty detection. Computers use a Bloom filter for that, Navlakha, an integrative biologist, explains: When a search engine such as Google crawls the Web, it needs to know whether a website it comes across has previously…


Human intelligence as a halting oracle

Jonathan Bartlett proposes to model the human mind as a halting oracle
A common objection to Bartlett’s idea is that humans cannot be halting oracles because we embed any unsolvable math problem as the halting condition for a loop and a human cannot tell us whether the loop will halt or not. This objection misses the fact that there is a range of oracles between plain Turing machines and a complete halting oracle. Read More ›