“I think […] that mathematical ideas originate in empirics. But, once they are conceived, the subject begins to live a peculiar life of its own and is […] governed by almost entirely aesthetical motivations. In other words, at a great distance from its empirical source, or after much "abstract" inbreeding, a mathematical subject is in danger of degeneration.

John von Neumann - "The Mathematician" in The Works of the Mind (1947)Whenever this stage is reached the only remedy seems to me to be the rejuvenating return to the source: the reinjection of more or less directly empirical ideas.”

## Emergent Law Based Statistics

In our opinion “probability” is such a degenerated concept.

There is neither an objective way (without any assumptions) to arrive at a probability statement from observations nor does the probability statement predict any possible concrete observation.

The statement “the probability that it will rain tomorrow is equal to 60%” can neither be objectively verified nor objectively and finally be falsified.

To “reinject” empirical content at the fundament of statistical reasoning we replaced the concept of probability by the concept of “emergent laws”.

Emergent Laws are descriptions of patterns that were always observed.

“In every sequence of 10 days (following a rainy day) the relative frequency of rain was at least 60%.”

This is a deterministic law that states simply that some kind of (complex) observation has been always true until now. We can induce that only what **has always been true** can possibly **be true in general** and therefore creates the chance to make a falsifiable prediction: “Within the next 10 days (following a rainy day) the relative frequency of rain will be at least 60%.”

In case such a prediction is falsified once the falsified universal statement will remain false forever. If we could only find enough not falsified deterministic laws we could base empirical science on a very solid methodological fundament.

In the meantime we have discovered billions of emergent laws – statements about features of sequences of measurements (patterns) that have been always true until now. So we can claim that:

**There are enough emergent laws to base statistics on them.**

Using emergent laws as the fundamental concept in statistics leads to far reaching consequences. We found superior performance in predictive modelling and algorithmic decision making compared to probability based approaches. And we found applications that are simply not possible in the world of stochastic modelling. The perhaps most important one is the transfer of knowledge between databases.

**Knowledge Nets** - *Creation of Knowledge*

## Central Concepts

Click on *Concept* for more information.

#### Emergent Law

A statement about a feature of sequences of measurements that has always been true until now.

#### Inductive Filter

The process of removing falsified hypotheses permanently from the set of still true emergent laws. The result is the actual empirical knowledge.

#### T-Dominance

The decision principle of our approach: If you have the choice between two decision rules choose the rule that led after T decisions always to a better result.

#### Meta Laws

Emergent Laws about the stability and predictive performance of sets of “similar” laws and about features of other sets of similar objects we us to control the learning process. Meta …

#### Objects

Descriptions of algorithms that are able to select time-indices that show certain emergent features. They are the logical bridge into the future because they are popperian universalities in the sense …

#### KnowledgeNets

Sets of emergent laws that show the (well defined) complete set of relations of objects concerning one or several variables of interest.

#### Emergent Law Based Models

Knowledge stored in a KnowledgeNet is combined to solve prediction task evaluated with the usual metrics (Mean Absolute Prediction Error, AUC,…). The resulting models demonstrate a very high level of …

#### WorldViews

Knowledge stored in a KnowledgeNet is combined to show predictable features of several variables of interest. It shows interesting features of the world that have been always true until now. …

##### More Thorough Discussion and Presentation of our Approach

## Notebooks and Papers

### Notebooks

In this section we show preliminary results. Because our methods lead to very fast progress and lots of results we want to publish some of them without taking too much care on formal restrictions like ortography and so on. Please excuse possible errors in advance.

### Papers

Papers provide further information with a more detailed explanation of our approach.

## Contact

### We are looking for

- fellows, who want to use our methods and help to develop them.
- institutions or single persons, who could imagine to fund our scientific research.
- business partners.