The Essence of the Difference Between Analog and Digital Information

This essay was originally written in Japanese by the author and translated using DeepL. It may contain translation issues.

Index

Continuous and Discrete: Unease with Textbook Definitions
Digital information is identification information defined by humans
The key point is whether concepts are associated with the information
Being discrete does not mean it is digital information
Digital information divorced from concepts has no meaning
Computers do not operate in binary

Continuous and Discrete: Unease with Textbook Definitions

What is the fundamental difference between analog and digital information?

Many people would likely answer, “Analog information is continuously changing information, while digital information is discrete information.” Of course, that is probably the textbook answer.

But is that truly the essential difference between analog and digital information?

Even with continuous information, if we extract only a single instant, we cannot question its changeability; thus the distinction between continuous and discrete holds no meaning. The step-second hand of a quartz analog watch rotates along a discrete trajectory.

Well, you could dismiss that as nitpicking, but when teaching students the difference between analog and digital information at work, I just couldn’t bring myself to explain it as “continuous vs. discrete.”

However, over the past few years, as I’ve worked on documenting the curriculum I’ve developed, it has become clear to me that the fundamental difference between analog and digital information lies elsewhere.

The clue was contained within the main theme of my lessons. It is the following idea:

The principle of the computer as a device is independent of its physical implementation and exists within the human spiritual activity of thought.

As we delve deeper into this theme, it becomes clear that what distinguishes analog information from digital information is whether the information is the information itself or symbolic information representing a corresponding concept.

The reason this fact is hard to see is that we refuse to look at the spiritual activity of humans, who are both the creators of digital information and its subjects of perception.

Depending on the context in which it is discussed, the definition of digital information can vary significantly.

To avoid misunderstanding, we confirm that our approach here is not to examine how digital information should be defined, but rather to consider the fundamental essence of the difference between analog and digital information.

Since we are considering the fundamental principles, this analysis should be applicable to any context.

Digital information is identification information defined by humans

The logic devices that make up digital computers can be realized using gears and cams, or implemented with electronic switches. At the start of every computer class, I always build logic devices with my students using the mechanism of a seesaw.

For example, the seesaw’s property where one side lowers as the other rises can be regarded as the function of NOT logic. However, this is merely a “regarding”—it is simply humans projecting NOT logic onto the seesaw’s motion using their own thinking. The seesaw’s motion itself is simply a board attached to a pivot rotating by a fixed angle.

Defining the lever’s up and down positions as 0 or 1 means identifying the lever’s state as an identifier and associating the concept of 0 or 1 with that identifier. Prior to these definitions, only the lever’s up-and-down movement exists. Only after associating the identifier with the concept can we derive the concept of 0 or 1 from the lever’s up or down state.

It is human thought that assigns meaning to the lever’s state.

Let’s confirm this clearly here. The logical state 0 and the logical state 1 are concepts. Concepts belong to humans.

Defining the lever’s up or down state means identifying the lever’s position as an identifier and associating the concepts 0 or 1 with that identifier. Prior to this, only the lever’s up-and-down motion exists. Only after we can associate the identifier with the concept can we derive the concepts 0 or 1 from the lever’s up or down state.

This is digital information. And it resembles something.

By learning letters, we associate the concept of the phoneme éɪ with the symbol A. This act is no different from defining 0 or 1 for the lever’s up/down position. Therefore, letters on paper are also digital information.

When we recognize the symbol A, we represent the concept of the phoneme éɪ. Similarly, when we recognize the state of the seesaw lever being up, we represent the concept of 0 or 1 that we defined beforehand.

Thus, even signs associated with concepts lacking physical objects are digital information. I would like to confirm here that digital information is not solely the abstraction of analog information.

Some might think, “Isn’t this discussion getting too hung up on whether information is symbolized or not?” But this consideration is unavoidable.

Though I treated it as a joke at the outset, the completely unchanging water level in a glass is analog information, and the angle formed by the stopped hands of a broken clock on its face is analog information as well. The essence of analog information is that it is quantitative information.

This makes it clear that changing information does not automatically become digital information simply by being sampled. Sampling and quantization are not essential requirements for digital information.

To jump to digital information, a mechanism is required to link the phenomena expressed there to specific concepts, and we are examining this mechanism as a symbolization system here.

The key point is whether concepts are associated with the information

By now, I believe the following has become clear.

Analog information: The quantitative information itself constitutes the intended information. Information that exists in this manner is analog information.
Digital information: The information itself is an identifier = ID, and has no meaning in and of itself. The concept linked to that identifier is the intended information. Thus, information where information and concept form a pair is digital information.

Analog information

Degree of light and dark, degree of color tone, angle, mass, volume, distance, etc.

Quantitative information → the information itself
＊Quantitative changes directly result in information degradation.

Digital information

Characters, numbers, symbols, identification patterns, etc. (functioning as ID information linked to specific concepts)

ID information
→ Concepts uniquely linked to an ID through human thought
＊If the ID information can be identified, the corresponding unique concept can be obtained without degradation.

How about that? This has cleared up the lingering doubts nicely.

Some might think, “But isn’t analog information just numerical data?” After all, rulers have markings, clock faces have numbers, and measuring cylinders have graduations—all making it easy to extract analog information as numerical values.

Admittedly, this can be confusing. However, the moment the extracted information is converted into numerical form, it becomes digital information.

There, a conversion process is performed: an appropriate unit quantity is prepared for the analog quantity to be sampled, and the quotient obtained by dividing by that unit is extracted as information. At this point, numerical information has not yet been objectified as a sign, but since the concept of numbers is represented to the observer, this is clearly digital information.

The reason this habit of treating information that should be digital as analog has become established is that the corresponding numerical identifier is not objectified unless the observer records the read value as a number.

There is an intuitive analog measurement method called “eyeballing,” and comparing it to the above concept should make it easier to understand.

Being discrete does not mean it is digital information

Considering this, it becomes clear that the notion of digital information being discrete because it is discrete is putting the cart before the horse.

Digital information is discrete because its essence is that of an identifier. It is not the other way around.

For example, the codes 41₁₆ and 42₁₆, representing A and B in ASCII, have no inherent relationship between them. They could be entirely different numbers, or they might not even need to be numbers at all; they just need to function as patterns for identifying phoneme concepts.

Assigning ordinal numbers to character codes to represent the ABC sequence serves to express a higher-level conceptual system rather than merely an alphabet set, which itself becomes another element for consideration.

Digital information divorced from concepts has no meaning

The beads of an abacus, characters on paper, magnetic information patterns, bit patterns in memory—all are digital information. On the abacus, the position of the beads is linked to the concept of number. Characters on paper point to the concept of phonemes or meaning associated with their form. The same holds true for magnetic patterns and bit patterns.

We know that one bead (ichidama) raised on each digit of the abacus represents 1. Two beads represent 2. And if the five-bead (godama) is raised, it signifies 5. We understand that together with the value indicated by the one bead, this represents one digit in the decimal system.

This is because we already possess the concept of the abacus’s definition, which has been shaped over the course of history, allowing us to understand it. Human thought links the fixed patterns created by the state of each bead with numerical concepts. The way these fixed patterns and numerical concepts are uniquely linked mirrors the way integer values are used as identifiers.

Thus, digital information itself is like an identifier or ID, holding no meaning in and of itself. For that information to have meaning, the identifier must be linked to a concept. It is human thought that makes this connection.

This means that digital information without human involvement holds no meaning whatsoever.

This fact holds profound significance for understanding computer technology.

Even digital information meaningful to humans is merely a meaningless pattern to computers. The concepts linked to that pattern exist only within humans.

In this sense, the notion that computers operate in binary is also an illusion.

Computers do not operate in binary

Only humans view binary bit patterns as numerical concepts; to computers, they are merely patterns. Computers associate the numerical concepts of 0 and 1 with specific states in memory, treating their sequence as binary numbers for operation. This is no different from moving beads on an abacus to perform calculations. Computers process it strictly as a pattern.

Humans prepare programs as consistent procedures that ensure these patterns are manipulated according to binary arithmetic rules, then instruct computers to execute them. Computers manipulate the “patterns” exactly as the program directs. There is no inherent meaning within this manipulation itself. The meaning of the operation exists outside the computer as the programmer’s thoughts: “Operating on that pattern in this way produces a pattern consistent with binary arithmetic.”

Some might think, “If you can recognize that logic by reading the program, then that logic must exist inside the computer.” But this is only because they overlook the fact that the entity “reading the program” is the reader’s own spiritual activity.

The program itself contains no logic; it consists solely of a collection of discrete procedural units. Only humans, as thinking beings, can integrate these discrete procedural units, grasp them as a coherent program, and connect them to the concept of purpose.

When a program—that is, a set of discrete procedures—is executed, a certain pattern remains as a trace in memory as a result.

This is everything that actually happens inside a computer.

By somehow deciphering these traces, humans recall the numerical concepts associated with their patterns and represent them within themselves, thereby endowing the information with meaning as the result of binary operations.

No matter how advanced an AI may be, it cannot be an exception to this.

So what exactly is the nature of the sophisticated responses generated by AI? While this digresses from the main topic here, I believe this examination—centered on the mental activities of humans, who are the agents of information generation and cognition—will serve as a powerful tool for elucidating the essence of computer technology and generative AI.

I am publishing an original ICT education curriculum based on this perspective below. Those interested are welcome to refer to it.

Shaping the spine of the ICT curriculum in Waldorf education

For Waldorf education, learning ICT technology represents a frontier. In Rudolf Steiner's time, there was not even a hint of computer technology, and the development of a curriculum for learning ICT technology is entrusted to us.I wanted to create a plan with a clear vision for how to structure ICT technology curricula and teaching methods as Waldorf education—which places human beings at the center of learning about the essence of things—and how to connect that learning to the use of personal computers and literacy education.