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

[Thecla]

TL;DR

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?

 

[DaveC426913]

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.

 

[pbuk]

A hardware realisation (one of a number built, of course, with LEGO):


A software simulation (again one of many):
http://rendell-attic.org/gol/TMapplet/index.htm

An explanation of Turing's abstract concepts:
https://plato.stanford.edu/entries/turing-machine/