[DSRP Evidence](https://dsrpevidence.org/)

# The solution of a problem relating to the geometry of position

## Details

**Authors** Leonhard Euler

**Year** 1736

**Publisher** Commentarii academiae scientiarum Petropolitanae

**Discipline** Mathematics

[Read it](https://scholarlycommons.pacific.edu/euler-works/53/)

## In authors' words

### What they set out to do (purpose)

Seven Bridges Problem

### What they found (results)

Created network theory.

## Commentary

### In short

Nodes in network theory are representative of identities.

### In more detail

Leonhard Euler incidentally discovered graph theory and spawned modern day network theory during his effort to solve one of the perplexing problems of 18th century Prussian society. In the “Seven Bridges of Königsberg” problem, there are two islands connected to the mainland by seven bridges. The problem was to determine if it was possible to go on a walk through the city that crossed each of the seven bridges once and only once. Euler, using the power of abstraction, discovered that the Königsberg problem had no solution but in doing so he launched modern network theory.

Today networks are a ubiquitous modeling tool that crosses the physical, natural, and social sciences, as well as business and commerce. Networks are both ubiquitous structures in nature and powerful tools of the mind for understanding nature better. Figure 2 illustrates a sampling of such networks: (left to right, top to bottom) abstract, political, food web, corruption, ecological, computer, corporate, disease,

conceptual, terrorism, social, and human trafficking. Taking Euler’s cue on the value of abstraction, what we see across all of these networks is simply that there are things, which are called nodes in network theory. Nodes represent things (identities) of all shapes and sizes, from abstract ideas, to people, to groups of people, animals, corporations, words, computers, terrorists, senators, and so on. If it’s a thing, it can be a node. In short, networks—both in the real world and in our mind are made up of things (identities) represented as nodes in the network. The nodes exist with other nodes, which they are differentiated from by virtue of their own nodeness. Those other nodes provide the backdrop or context for any individual node (identity). Indeed, in any given network, in order to fully define any given node, one must not only identify that node’s (label, name, status, etc) but also that of the other nodes it is with. Thus, the other nodes provide context for the node itself, and this occurs simultaneously for all nodes in the network.

DSRP Theory advances modern day network theory by offering a complete definition of any given node: what the node is (it’s distinguishing characteristics, ID, label, position, etc.) and also what the node isn’t (i.e., the other nodes it is with). This is critically important, because, as you will see, the mind does not merely form concepts based only on positive affirmations of a thing, but also on the negation of a thing. A car is not-a-duck and also not-a-refrigerator, but closer to its definition, it is also not-a-truck. The concepts we form exist within a network of similar and different concepts and are heavily dependent on the affirmation of identity but also the negation of it.

**Patterns it shows** D

**How to cite this** Leonhard Euler (1736). The solution of a problem relating to the geometry of position. Commentarii academiae scientiarum Petropolitanae.