Is my computer Turing Equivalent?

Well, here's a very quick answer: If your computer can do anything a Turing Machine can do, and if a Turing Machine can do anything your computer can do, then your computer is Turing Equivalent.

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The above is a nice quick answer, but is it satisfactory enough for you?

First of all, how do you know if your computer can do anything that any Turing Machine can do?

Well, if you had downloaded the Excel file from the Home Page of this website, and were able to simulate one or more Turing Machines on it, then your computer can certainly do what those Turing Machines did. If you had simulated the Universal Turing Machine on your computer, then you know that your computer can do anything that any Turing Machine can do.

This means that your computer is Turing Complete. (Well, actually we have to ignore the minor detail that a Turing Machine has infinite memory with its infinitely-long tape, and that your computer doesn't have infinite memory, but we won't quibble about that here now.)

Conversely, for anything that you can do on your computer, how do you know that there is a Turing Machine that can do it as well?

Before we answer this question, let me ask you this: What is it that makes your computer actually work?

In case you answered electricity, or keyboard, or mouse, or screen, etc. -- let me say that those are all good answers, but not the answer I'm looking for.

The correct answer here is: ALGORITHMS!

Without algorithms, your computer would be completely useless.

When you bought your computer, it probably came with an operating system. That's a program that somebody had to write. It has a series of instructions on what is to be displayed on the screen, what to do when you press a key on the keyboard, move the mouse, or do anything at all. This program consists of lots of instructions, and is therefore a big long algorithm.

You may have downloaded some really cool apps to run on your computer. These apps are nothing more than programs that someone had to write. In other words, they are also algorithms.

Some apps are really amazing, relying on the most sophisticated AI (Artificial Intelligence). Yet, these too are nothing more than just algorithms.

Yet, regardless of how sophisticated an algorithm may be, its ultimate purpose is just to manipulate some bits in the computer's memory. It may add numbers together, or subtract them, or multiply or divide them, or it may perform some logical operations on those bits. But that's all it can do.

Without algorithms, your computer wouldn't have the foggiest clue of what to do. It needs to be told what to do, or else it'll do absolutely nothing.

So, the question "Can anything done on my computer be done on the Turing Machine as well?" can be rephrased as "Can any algorithm that I run on my computer be implemented on a Turing Machine?"

The Church-Turing Thesis states that any algorithm can be implemented on a Turing Machine. (In other words, if there is an algorithm that can be used to compute a certain number, then that same number can also be computed by some Turing Machine.)

So, according to the Church-Turing Thesis, your computer is Turing Equivalent.