## Abstract

The big data in biology is often associated with Heisenberg Uncertainty principle, Schrodinger Cat, Halting problem and the Incompleteness theorem. Theoretical computer science like never before has combined with other branches of natural sciences that include, astronomy, biology (genomics in particular), physics, chemistry, material science, and social media like, Facebook, Twitter, and YouTube, to tackle the problem of Big Data. The present work is in context with the “uncertain” elements of big data, given the high level of accuracy and reproducibility of the generation of such data. The question primarily raised in this paper is, whether there is any physical existence of such uncertainty, or the analogy is entirely metaphysical in nature, the way economists use the principles of statistical mechanics. In biology how this uncertainty is going to affect our future health and environment-related predictions is analyzed using public domain analytic tools.

## Heissenberg

What Einstein’s $$E=mc^2$$ is to relativity theory, Heisenberg’s uncertainty principle is to quantum mechanics—not just a profound insight, but also an iconic formula that even non-physicists recognize. The principle holds that we cannot know the present state of the world in full detail, let alone predict the future with absolute precision.

## Niel’s Bohr

his 1933 lecture “Light and life” , Niels Bohr applied an analogous uncertainty concept in biology to argue that a living being would be killed by detailed physical investigation, so there is “complementarity” between the simultaneous existence of life and the possibility of describing it scientifically.

## Biopsy - A Biomedical Example of poking a system

There are some reports that says biopsies do cause spread of cancer cells, but at least one 2004 study found a correlation between “fine-needle aspiration and an increase in the incidence of sentinel node metastases.” While the two studies cannot be directly compared — one involves pancreatic cancer, the other breast cancer — the methods and analysis involved in both are similar, yet the researchers reach conflicting conclusions. http://www.medicaldaily.com/cancer-biopsy-wont-spread-tumors-data-may-be-unconvincing-317136

## The 1927 Uncertainity formulation

Heisenberg inferred his formulation in 1927 via his famous thought experiment in which he imagined measuring the position of an electron using a gamma-ray microscope. The formula he derived was $\epsilon(q)\eta(p) \ge \frac{h}{4\pi}$

## Heisenberg offered no proof

Heisenberg offered no direct proof for this version of his principle, and expressed his ideas “only informally and intuitively”, says physicist Jos Uffink of the University of Minnesota in Minneapolis.

## Heisenberg’s error-disturbance relation

The relation can be formulated as $$\epsilon(q)\eta(p) \ge |<[A, B]>|$$ where $$\epsilon(A)$$ is the measurement precision of an observable A and $$\eta(B)$$ is the disturbance that this measurement induces on another observable B.

## Implications of the error-disturbance interpretation

The interesting implication stems from states for which measures of error and disturbance can be both zero $$\epsilon(A)=\eta(B)=0$$, while at the same time the estimated lower bound on them is non-zero. This motivates a state-independent approach in which the error-disturbance trade-off is evaluated for a set of states that “calibrate” the measurement apparatus.

## Encapsulating the strangeness

Encapsulating the strangeness of quantum mechanics is a single mathematical expression. According to every undergraduate physics textbook, the uncertainty principle states that it is impossible to simultaneously know the exact position and momentum of a subatomic particle — the more precisely one knows the particle’s position at a given moment, the less precisely one can know the value of its momentum.

## A translation of the uncertainty principle in Big Data

Werner Heisenberg showed that as things get small, you cannot know everything precisely. Well, it turns out, as things get big, we can get confused, too.

## Uncertainty in large and small scales

Under scale, we lose precision. Big is hard! Time, meaning, mutual understanding, dependencies, staleness, and derivation all become a challenge. Heisenberg pointed out that at a small scale, uncertainty is a fact of life. In computing at a large scale, uncertainty is also a fact of life.http://queue.acm.org/detail.cfm?id=1988603

## $$\delta t =0 ?$$

Simultaneity does not exist at a distance. Information speed is bound by speed of light (EPR paradox tells otherwise) . By the time we see a distant object in the night sky, it may have changed. Similarly, by the time we receive a message from a distant computer, the data contained in that system may have changed.By the time we hear about a bad news a good thing might have happened.

## How certain are you of those search results?

library(gtrendsR)
## Warning: package 'gtrendsR' was built under R version 3.4.2
trend <- gtrends(c("Bigdata","Genomics","Bioinformatics","Systems Biology"))
## Warning in fun(libname, pkgname): No TZ information found. Falling back to
## UTC.
plot(trend)
## Warning in as.POSIXlt.POSIXct(x): unknown timezone 'zone/tz/2017c.1.0/
## zoneinfo/Asia/Kolkata'