Two days ago, July 16th 2019, it was announced on BBC World Service that Bank of England will issue £50 bank notes with the portrait of Alan Mathison Turing, the good mathematician who saved millions of lives with his and his fiancee Joan Clarke’s work on breaking the German Enigma encryption during World War Two as portraited in the movie The Imitation Game.

# Category Archives: Mathematics

# Mathematics #8: Radio

On June 15th 2019 I completed my work in Mathematics Research with a very naïve claim that GNOME Internet Radio Locator beats Turing’s test in Artificial Intelligence with a Gettier counter-example argument, since there is no way to know if the radio streaming is broadcasting recorded or live.

See https://www.gnome.org/~ole/gnome-internet-radio-locator/gnome-internet-radio-locator.html and http://www.ping.uio.no/~oka/Aamot-Turing-Gettier-2020.pdf

My conclusion: The only way to gain new recommendations from a human being is to meet new people, expand your Social Graph, like I wrote in http://math.aamot.org/Global/SocialGraphs.pdf or listen to radio for new ideas.

I choose to meet new people.

# Mathematics #7: Haversine

In August 2015 I went to Berkeley, California and wrote a paper on a new web site called Piperpal. You can read about my work on the web site at https://www.piperpal.com/doc/2.0/piperpal-2.0.pdf

Given two geographical coordinates P(glat,glon) and Q(latpoint,longpoint), you can calculate the distance *r* between P and Q in meters with the following Haversine formula:

111.045*DEGREES*(ACOS(COS(RADIANS(latpoint))*COS(RADIANS(glat))*COS(RADIANS(longpoint)-RA DIANS(glon))+SIN(RADIANS(latpoint))*SIN(RADIANS(glat))))

Check with other sources before you implement Haversine distance in your computer program.

# Mathematics #6: Social Recommendations

In April 2015 I wrote a paper called Social Recommendations in Mathematics on a new social recommendation engine and the problems we face with modern Artificial Intelligence with lack of input from unknown people.

# Mathematics #5: Practical Machine learning with R

I was in the US for 3 weeks on the Visa Waiver program in 2015 and stayed at a friendly AirBnB host in Berkeley nearby the UC Berkeley campus.

While I was in Berkeley I decided to check out the course offerings at the UC Berkeley Extension student program and found the class COMPSCI X460 – Practical Machine Learning (With R) interesting.

I sent an email to UC Berkeley Extension team who showed me the web site where it was written that I as a tourist is permitted to study for recreation without credits at UC Berkeley Extension. If you want to study with credits in the US, you need a student VISA known as F-1.

http://extension.berkeley.edu/static/studentservices/policies/#international

- Your enrollment into UC Berkeley Extension course(s) must solely be for recreational purposes;
- Your course(s) must only be incidental to your visit as a tourist to the U.S., and must not be the main purpose of your visit;
- Your course(s) must not equal or exceed 18 instructional hours per week;
- Your course(s) must not equal or exceed:
- For courses numbered X300-499: 8 semester units a term; or
- For courses numbered X or XB 1-299: 12 semester units per term (including concurrent enrollment courses); and,
- Your course(s) must not be used for credit toward a degree, diploma, certificate or other program completion award.

I attended the first introduction class at UC Berkeley Extension in the Golden Bear Center, but didn’t continue with the class since I was in the US on the Visa Waiver program for 90 days and was going to return to Norway the day after the introduction class.

The curriculum for Practical Machine learning (With R) was Max Kuhn and Kjell Johnson’s Applied Predictive Modeling, but I could not find the text book in the campus book store. The book is available on Amazon.

Extra curriculum was Hastie, Tibshirani and Friedman’s Elements of Statistical Learning.

In the first introduction class I learnt about the R programming language, how to install RStudio and the various R packages from CRAN.

# Mathematics #4: Google’s PageRank

I am reading the linear algebra book “Google’s PageRank and Beyond – The Science of Search Engine Rankings” by Amy N. Langville & Carl D. Meyer on the math behind Google’s search engine.

In Chapter 4 the PageRank equation is presented.

$\pi^T = \pi^T ( \alpha S + ( 1 – \alpha ) E )$

# Mathematics #3: Publishing

If you intend to publish Mathematics, you can either submit the article to a peer-reviewed journal such as Bulletin of the AMS or arXiv, or self-publish.

If you plan to publish on your own, I recommend getting a book on TeX and install a TeX distribution on a free operating system such as Debian GNU/Linux, Fedora Linux, or Ubuntu.

If you plan to publish Mathematics on the World Wide Web, learn TeX and MathJax.

$Q.E.D.$

# Mathematics #2: The Social Rules

The Social Rules theorem is an extension of The Social Theorem, published in “Social Graphs in Mathematics” (2009) available from http://math.aamot.org/Global/SocialGraphs.pdf

Whenever a person meets another person, a vertice on the social graph, they will either ignore each other, talk to each other, occassionally talk to a new person, or be introduced to a person that isn’t yet in a vertice on their social graph, by a person on the social graph.

# Mathematics #1: The Social Theorem

Yesterday I wrote my first letter to John Nash.

The Social Theorem (from my article “Social Graphs in Mathematics“, on Paul Erdős, John Nash, and Bertrand Russell, not surprisingly rejected by Notices of the American Mathematical Society in 2009 because it didn’t end with a conclusion, and then printed on my own cost and distributed) goes something like this:

Whenever a mathematician meets another mathematician in a point on the social graph, they will either ignore each other, produce a new proof, occasionally a new mathematician, or deﬁne a new conjecture.

My conclusion in 2014 after visiting MIT is:

**Expand your social graph.**