A Data Science Central Community

There are numbers that are so large that there is no compact formula to represent them. Think of a number so large, that its number of digits is so large, that the number of digits of its number of digits is so large... and it goes on and on -- you get the idea.

Sure, if you are able to *define* such a number, then add one, or even 0.5, and you get an even bigger number. But this is not the point. The issue is to come up with such massive numbers in the first place. The biggest ones known to men are produced by unusual recursions, and such recursions can be used to test how powerful a computer is, when dealing with recursive algorithms.

Let's start with a very simple recursive function that quickly produces phenomenally large numbers:

This is known as the Ackermann function. The fact that the recursion always ends no matter what *n* and *m* are, is by itself surprising. Below is an extract of the steps needed to compute *A*(4,3).

Below is a table that shows the first few values of *A*(*m*, *n*) :

Despite the fantastic growth of this function, it is possible to define another one that dwarfs it.. The Ackermann numbers are incredibly modest compared to Graham's number. Even though there is no hope of ever being able to compute a tiny tiny fraction of its digits, the last 500 digits are known::

Whether these digits are random or not is another question. Click here for more information.

**Other interesting fact**

Most numbers can not even be defined. The ones such as 3/4, Pi, the solution of log x = x -1,. or Euler's constant, that can be represented by a formula, represent a tiny proportion of all numbers - such a tiny proportion that its Lebesgue measure is zero. In short, the vast majority of numbers can not be computed, and not even defined. The big number mentioned here is computable, though no computer will every be powerful enough to compute its digits (these digits are far far more numerous, by many orders of magnitude, than all the atoms in the universe.)

To read more articles from the author, click here.

**DSC Resources**

- Services: Hire a Data Scientist | Search DSC | Classifieds | Find a Job
- Contributors: Post a Blog | Ask a Question
- Follow us: @DataScienceCtrl | @AnalyticBridge

Popular Articles

© 2021 TechTarget, Inc. Powered by

Badges | Report an Issue | Privacy Policy | Terms of Service

**Most Popular Content on DSC**

To not miss this type of content in the future, subscribe to our newsletter.

- Book: Applied Stochastic Processes
- Long-range Correlations in Time Series: Modeling, Testing, Case Study
- How to Automatically Determine the Number of Clusters in your Data
- New Machine Learning Cheat Sheet | Old one
- Confidence Intervals Without Pain - With Resampling
- Advanced Machine Learning with Basic Excel
- New Perspectives on Statistical Distributions and Deep Learning
- Fascinating New Results in the Theory of Randomness
- Fast Combinatorial Feature Selection

**Other popular resources**

- Comprehensive Repository of Data Science and ML Resources
- Statistical Concepts Explained in Simple English
- Machine Learning Concepts Explained in One Picture
- 100 Data Science Interview Questions and Answers
- Cheat Sheets | Curated Articles | Search | Jobs | Courses
- Post a Blog | Forum Questions | Books | Salaries | News

**Archives:** 2008-2014 |
2015-2016 |
2017-2019 |
Book 1 |
Book 2 |
More

**Most popular articles**

- Free Book and Resources for DSC Members
- New Perspectives on Statistical Distributions and Deep Learning
- Time series, Growth Modeling and Data Science Wizardy
- Statistical Concepts Explained in Simple English
- Machine Learning Concepts Explained in One Picture
- Comprehensive Repository of Data Science and ML Resources
- Advanced Machine Learning with Basic Excel
- Difference between ML, Data Science, AI, Deep Learning, and Statistics
- Selected Business Analytics, Data Science and ML articles
- How to Automatically Determine the Number of Clusters in your Data
- Fascinating New Results in the Theory of Randomness
- Hire a Data Scientist | Search DSC | Find a Job
- Post a Blog | Forum Questions

## You need to be a member of BigDataNews to add comments!

Join BigDataNews