### Overview

The SOCR group at the University of Michigan is developing novel theoretical foundation to extend the notion of time to the complex plane. This approach lifts the concept of*time*from a positive real number representing event ordering to a 2D complex-time (kime) comprising a pair of coordinates (time, phase). This approach enables powerful data-driven analytical strategies for large longitudinal data. The 5D spacekime analytics utilize information measures, entropy KL divergence, PDEs, Dirac’s

*bra-ket*operators, and the Fourier transform. This fundamentals of data science research project explores time-complexity and inferential uncertainty in modeling, analysis and interpretation of large, heterogeneous, multi-source, multi-scale, incomplete, incongruent, and longitudinal data.

### Kime-series (kimesurfaces)

In 4D spacetime, classical time-series are represented as real-valued functions defined over the positive real time domain. In the 5D spacekime manifold, time-series curves extend to kime-series, which are represented geometrically as surfaces. The animation to the right illustrates one such kime-series at one fixed spatial location. At any given kime, i.e., for a pair of arguments kime-magnitude (*t*) and the kime-phase (φ), the height of the kime-surface represents the intensity of the kime-series, which is coded in rainbow color. Notice the parametric kime grid superimposed on the surface of the kime-series. There are kime-phase aggregating operators that can be used to transform standard time-series curves to spacekime kime-surfaces that can be modeled, interpreted, and predicted using advanced spacekime analytics.

### About Spacekime

##### Complex Time (kime)

Over 100 years ago, the ideas of many polymaths materialized into unifying
the notions of space and time into a integrated 4D Minkowski space-time.
Kaluza and Klein were the first to ask what may be the implications of adding
a special tiny (non-traversable) fifth dimension. Later the work of Wesson, Bars,
and the 5D space-time-matter consortium generalized this idea.
The SOCR team has now extending the interpretation of the universe as a 5D space-kime
manifold where time is no longer a positive unidirectional concept, but a complete
field of the complex numbers. This leads to extensions of classical concepts like
*time, events, and spacetime metric*, to their more general counterparts,
* kime, kevents, and spacekime metric tensor*.
This generalization resolves some of the problems of time and enables
the formulation of time-dependent properties as process characteristics derived using
the 2D kime. Additionally, the quantum mechanical notions of particle and wavefunction
are extended to datasets and data science analytics.

##### Spacekime details

The time-complexity and inferential-uncertainty textbook provides detailed formulation of the spacekime manifold and its applications to data science and longitudinal health analytics.

##### Spacekime data analytics

The lifting of the 4D spacetime into the 5D spacekime manifold has profound implications on
the collection, modeling, interpretation, and analytics of all longitudinal information.

Two specific implications include:

- Reduction of the need for large-samples to estimate specific population characteristics; and
- Improvement of the subsequent data analytics performed on spacekime-transformed data.

##### Spacekime Project Goals

This project aims to answer some deep and fundamental questions like:

- How to translate centuries of fundamental mathematical and physics ideas to data science?
- Can large-sample theory be replaced by low-samples with some prior knowledge?
- Is the universe really four-dimensional?
- What if there is no arrow of time and we can traverse spacetime in any direction?
- Would lifting the spacetime dimension lead to differences in the interpretation of information and improvement of the resulting data-driven inference?