Why are Turing Machines the foundation of computers and artificial intelligence?

Turing’s ideas deal with one of the most unique, complex, and stubborn problems in philosophy, in our understanding of reasoning, the significance/reality of the Universe in general. However, so few people understand that, and even fewer care to explain it.

We need to mark our starting point. So, let us review some starting assumptions:

• Assumption: The world exists. Things exist. Things interact via laws of nature. We are born, learn the rules and use them for our benefit.
• Assumption: The world outside is complex; we will never know all the rules. For example, Einstein broke Newton’s laws. Today, no scientist believes we have found all of the laws of motion, even with relativity.
• Therefore, laws are not in our control, and we will never understand all the complexity of the Universe. Therefore, a machine will never be able to process all algorithms possible for known and unknown behaviors of nature.

And yet the universal computer exists. Quantum physicists, geologists, biologists, psychologists, elementary school kids, are using the same computers. The same Turing-complete computers. So how could limited universal computers exist, in an infinitely complex universe? Why don’t they need a quantum extension, biology module, elementary processor? There must be something wrong with the above assumptions. There is no way a limited machine can compute everything in the Universe.

How are Turing Complete / Universal Computers possible then? We need to step back a couple of thousand years. This problem is related to the fundamental problem of human reasoning, to the beginning of modern philosophy.

Let us start.

Before the Greeks, knowledge, science, and philosophy was about looking at nature. Things were there, and nobody questioned that. The Greeks were the first to see a problem there. The issue is that we talk about things, like chairs, water, fire, but some of these are changing all the time. Like Descartes noted later, wax is wax, whether liquid or solid. So what property makes it wax?

Incredibly, Greeks struggle with this idea, never reaching a satisfactory solution. That had to wait until Descartes.

We are all Descartian now, though we don’t know it, so the answer feels evident to us: Reality is not about things in the Universe first, but about our mind processing sensory data first, and then reasoning that things are there. Yes, your cup of tea there; it is in your mind. It could be one of many in the kitchen, you can not tell the specific cup apart. It does not matter, you do not see “the” cup. First, your mind receives eye sensor data, then reasons, and then decides there is “a” cup. Separating physicality from reasoning took 2,000 years from Thales to Descartes…
(Descartes, R. Meditations on first philosophy)

However, there are still issues with that notion. So yes, there is a cup of tea there. How does your mind detect teacups out of thousands of color points in your retina? How does your mind “see” a reach 3D environment from two flat blurry pictures coming from your eyes.

It was Socrates that figured out the basic nature of reasoning. He made his great discovery by asking simple “stupid” questions. For example, Socrates asked, what are straight lines?, points in space?, do parallel lines go to infinity?, infinity, where is that?, Beauty, Justice. So everyone knew about such. People with and without schooling. From any town. The same answers.

So Socrates (or Plato, as some people think he made Socrates up) found something that changed western thought forever. He found that all things share some universal forms/ideas (εἶδος/μορφή) that are not learned, they “are”, they are always there, in everything, somehow. You can not teach someone that parallel lines cross at 10 meters, and you do not need to teach beauty, circles, squares, justice, infinity. Greeks call these forms/ideas. Where do they come from?
(Plato Dialogues)

Where do forms/ideas come from? Immanuel Kant figured that, against what we believe, our mind is not born empty and learns the universe as we experience. In one of the most complex books ever written, Kant explained that is not possible. Or at least that is not how humans and most animals work. The basic framework of Arithmetic, Trigonometry, Space, effect and cause, Time, etc. is per-configured in our mind “a priory”; then, we use it to process data from the real world. Kant assumes that this “a priory” framework is needed to process sensory data in the first place. The implications of that are enormous.
( Kant, I. Critique of pure reason = “Study of not learned knowledge/logic/reasoning”)

So Descartes/Kant thesis seems to be that reality is made inside your mind by processing perception with some preprogrammed logic, with some preprogrammed templates, which Plato called ideas/forms.

So, how much of our reasoning is hard coded? What is the difference between parallel lines in my mind and “reality”? Can we ignore this framework and make another “artificially” say where “1+1=3”? Why do we need this framework? Is it just for survival, Darwinian purposes? Is it revealing the hand of a God ? … there is no answer to that yet.

So what does all that have to do with Turing and his machine?

Remember that in Turing’s times, 1930s, there were no computers and to this day few engineers know/care about Plato and Kant. So people imagined complex machines that could do logic or at least complex math, and that you would need special machines for different natural problems; a machine to crack the atom, another to process sociology data, another for a flight autopilot, and another to write documents.

But Turin had a different vision. Turing envisioned a Universal Machine. A machine that could process all of the above, everything conceivable. Now Turin was not a philosopher, but his 1950 paper “Computing Machinery and Intelligence” is one of the most frequently cited in modern philosophical literature.

So, Turing wondered, could there be a universal computing machine? He answered the question with the Turing machine. His Turing machine is not a mechanical prototype. It is a mind experiment. It isolates and solves a significant philosophical problem decisively.

A Turing machine is a machine similar to a teleprinter with a long piece of paper with symbols — any symbol. The device reads a sequence and then prints another. So Turing asked, can there ever be a resulting sequence for some input that no machine could compute? No, he wrote:

“It is possible to invent a single machine which can be used to compute any computable sequence. If this machine U is supplied with the tape on the beginning of which is written the string of quintuples separated by semicolons of some computing machine M, then U will compute the same sequence as M.”… and long explanation follows.

This was astonishing.

While Kant and Plato hinted of a defined framework of logic in our brain, Turin approached the problem from another/ simpler way. The physical brain is of finite size, hence the logic must be finite. From there, Turing discovered the Universal Computer. Not universal because it could process every sequence in nature, but universal because it can process any logical sequence a human can think of, because humans logic is finite and predefined.

So you might not want to believe that. Problem is: Take a computer, any modern computer language, and try to find a logical sequence in nature that cannot be programmed… you cannot. Any modern computer can run any logical sequence thinkable, because the computer’s ALU (Arithmetic Logic Unit) has all the logic humans use for arithmetic. There is no past arithmetic, current, or future, that a current computer cannot process.

Turing was the first human being to know universal computers were possible, how they would work, and the first to try building one. Indeed, one of the greatest minds in the world and Turing machines of the most outstanding ideas/inventions in the world.

“The idea behind digital computers may be explained by saying that these machines are intended to carry out any operations which could be done by a human computer. “(Turing, 1950, “Computing Machinery and Intelligence”)

“A man provided with paper, pencil, and rubber, and subject to strict discipline, is in effect a universal machine.” (Turing 1948: “Intelligent Machinery”, National Physical Laboratory Report)

“Turing’s ‘Machines’. These machines are humans who calculate. “(Wittgenstein, 1947, Remarks on the Philosophy of Psychology, Vol 1 )