# We Can Define the Domain of Information Online and Thus Globally Uniformly

## Abstract

**:**

## 1. Introduction

## 2. Basics and Recommended Method for Global Definition of Digital Information

- Digital bits first encode numbers (Figure 1). The software must know the binary format of the numbers.
- Each number represents a selection from an ordered set or “domain” (Figure 1).
- A sequence of multiple numbers selects from multiple domains or a “multidimensional” domain (which is ordered along multiple dimensions). It is the domain of the numbers and so the domain of this piece of digital information.
- The elements of the domain can represent very different things, e.g., control codes for software, letters, indices, e.g., on entries of a table, of course also measurable values (Figure 2) and other data.

^{2}= 100 possibilities per number), then a sequence of six such numbers (e.g., mm coordinates of only 2 points in a 10 cm cube) selects from a domain with 10

^{(6×2)}or 1000 billion elements. So the size of the domain increases rapidly. It increases exponentially with its dimensionality, i.e., the length of the number sequence. In the case of multiple measurements, e.g., medical findings, the domain becomes extremely large. If such a domain is unambiguously defined online, it can be a powerful basis for reproducible information transport.

- (a)
- The original source of information (e.g., observation, measurement) should be reproducible.
- (b)
- We create a list of all independent, reproducible features (e.g., measurements, properties) that could be of interest to this application.
- (c)
- We try to search, reference, and reuse existing online definitions for quantifying each listed feature. If no suitable online definition is available, we must create a new online definition of our own. This definition can use and describe the natural order of the feature and select a natural unit, or it can define a new order of feature variants so that they are reproducibly (one-to-one resp. bijectively) mapped to the domain of a number (quantification). Then, they are selectable by the number (which digitally represents the feature). The defined order of application-specific features can later be automatically used for similarity comparison and search by universal numerical search engines [14].
- (d)
- The digital representations (numbers) of all listed features are uniquely combined and nested to form the number sequence that digitally conveys the information for that application.
- (e)
- All necessary definitions (of the features, of the representing numbers, of their combination, of the digital format of each number) are put online in standardized machine-readable form. The online definition starts with a version number of the standard and an efficient machine-readable specification of the binary format of the number sequence. This includes short links to the exact definitions of each number. The exact definition may be very detailed and may also include links to multilingual and multimedia explanations and to (the source code of) software for handling the number sequence. Online definitions can be reused and nested in subsequent online definitions. This enables the definition and handling of complex data structures.
- (f)
- After the online definition, the defined information can be reproducibly digitized and transported as DV in the form (1): “UL plus number sequence”, where UL efficiently refers to the online definition.

## 3. Example of Results

## 4. Discussion

#### 4.1. Short Conclusive Argumentation

- Information (e.g., digital information) is a selection (2) from an ordered set. I have called this set the “domain” of information. It is clear that numbers are selections from ordered sets and that digital bits encode sequences of numbers.
- Therefore, for a direct comparison (e.g., to check similarities in a similarity search), the domain (2) of the compared pieces of digital information (number sequences) should be the same.
- Therefore, it is consequent to consider number sequences as building blocks of digital information and to define the domain of a number sequence and its binary format globally. In the current infrastructure, this can be performed efficiently by a machine-readable online definition of digital information (number sequence).
- The proposed DV data structure (1) simply represents such a number sequence, preceded by the UL, which is required as a global identifier and efficient pointer to the online definition. To save energy and resources, the binary format of the DV (UL and number sequence) is optimized for efficiency.
- Details about a possible format of the UL were published [12]. Additional data are not necessary for the DV and were avoided. This is relevant for both efficiency and global uniqueness. In contrast, the (globally unique) online definition of the DV may contain efficient links to additional detailed descriptions and explanations.

#### 4.2. More Detailed Discussion

#### 4.3. The Domain of Information Is Essential

#### 4.4. About Existing Concepts of Information—Rethinking Is Necessary

#### 4.5. Disadvantages of the New DV Data Structure

- Today still unfamiliar even for experts

- Initial effort

- Online definition is unusual up to now and easy to underestimate

- Large project which initially requires investment

#### 4.6. Advantages of the New DV Data Structure

- Global digital information including definition

How is it ensured globally that every communication participant with software knows the format and definition of the exchanged digital information (number sequence)?

- Global digital information including identification

- Globally reproducible and precise digital information

- Globally comparable and searchable digital information

- Global digital information representation optimized for the application

- Global language-independent information transport

- Digital information for global AI and machine learning

- Digital information for global programming

- Digital information for efficient global work-sharing

- Digital information optimized for efficiency

- Rethinking (digital) information

- Semantics (combination of digital information) are better reproducible

- Improving international communication

#### 4.7. This Has an Impact on My World View

**Remark.**

## 5. Conclusions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Exemplary selection from the domain 0…15 by 4 bits of digital information. The binary coding and the meaning of each possible number 0…15 must be clear to the participants of the digital communication.

**Figure 2.**(

**a**) Correction and preservation of the position of the incisors is part of the orthodontic treatment goals. The dentition model of this patient is shown in (

**b**). The red arrows show the sum of the incisor widths. This is used to estimate their space requirements and is an example of an orthodontic measurement. Many such data (number sequences) must be combined for diagnosis and treatment planning. Globally defined data enables direct global comparison and efficient exchange of experience. More details about medical applications are available in former publications (e.g., [5,7,10]).

**Figure 3.**Example of a search for cupboards with 100 cm width. The numbers “Price, Width, Depth, Height” were defined as relevant (searchable and comparable) features of a cupboard. These 4 numbers select from a 4-dimensional domain. We can select another domain definition by clicking on “* i7” and view the defined DVs by clicking on “* i4”. Open data of the users are viewable after clicking on “* iu”.

**Figure 4.**Search result after search input of Figure 3. The smaller the absolute difference (d) of the width from 100 cm, the higher the rank in the search result. Therefore, the cupboards whose width (2nd number) is closest to 100 (with the smallest distance (d) from 100) are listed first. Globally (online) defined DVs (1) would allow global searches.

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**MDPI and ACS Style**

Orthuber, W. We Can Define the Domain of Information Online and Thus Globally Uniformly. *Information* **2022**, *13*, 256.
https://doi.org/10.3390/info13050256

**AMA Style**

Orthuber W. We Can Define the Domain of Information Online and Thus Globally Uniformly. *Information*. 2022; 13(5):256.
https://doi.org/10.3390/info13050256

**Chicago/Turabian Style**

Orthuber, Wolfgang. 2022. "We Can Define the Domain of Information Online and Thus Globally Uniformly" *Information* 13, no. 5: 256.
https://doi.org/10.3390/info13050256