Have a Turing Machine? Can it solve linear algebraic equations?

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The Turing Machine, conceptualized in the 1930s, serves as a foundational model for computation, illustrating that any computational task can be performed by a machine, albeit potentially more slowly than modern computers. It is important to note that a Turing Machine is not a physical entity but rather a theoretical framework that can be realized in countless ways. Every computer built to date can be viewed as a specific implementation of this model. While programming a Turing Machine may resemble using Assembly language, the latter is significantly more complex. Discussions also touch on creative interpretations of Turing Machines, including unconventional ideas like using goldfish as components in a hypothetical computer. Resources for further exploration include software simulations and detailed explanations of Turing's concepts.
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Has anybody built one?
I don't understand the Turing Machine. Amazingly this hypothetical device, designed in the 1930s can do everything the most powerful computers can do today, but it would just take much longer. Has anybody ever built one just to solve a simple linear algebraic equation? How long would the tape be to feed into the device to solve this equation?
 
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1. A Turing machine is not really a thing - it's more like a set of principles. Those principles can be implemented into a physical device in a pretty much infinite number of ways.
2. Every computer ever built is one form of implementation that meets the requirements to be a Turing machine.

The closest thing you might find to programming a Turimg machine might be Assembly language - though even that is much more complex.

I have - on my mental drawing board - a computer made of goldfish. Goldfish are the memory and processor.
 

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