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Harlan Brothers
Works at Brothers Technology, LLC
Attended Berklee College of Music
Lives in Branford, CT
930 followers|28,716 views


Harlan Brothers

• Psychology/Sociology  - 
Progress on an actual thinking cap - the application of transcranial direct current stimulation can enhance the ability to learn, or if the current is reversed, impede learning.

#learning   #tDCS  
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Harlan Brothers

• General/Interdisciplinary  - 
The popular concept of the "language of jazz" takes on scientific meaning in a new article in PLOS ONE.  An fMRI study shows that when jazz musicians "trade fours," areas of the brain related to language syntax are activated.  The article below contains a link to the research paper.   #music   #neuroscience  
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Harlan Brothers

commented on a video on YouTube.
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O frabjous day! Callooh! Callay!...  What a delightful idea for a documentary!  Top notch production.  Look forward to the release.
Congratulations, +Roger Bagula!  Just saw your "Borromean links cage" featured in the American Mathematical Society's promotional mailing under the title "Exploring the World of Mathematics and Art with Mathematical Imagery."
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Well liked because we have a good eye for beauty :D
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Hi, +Peter Edenist.  The rules make sense!  They are particularly important at a time when knowledge has become so easily available and simultaneously deep - vetting both its accuracy and its sources can be a challenge.  Thank you (and the OP) for the blog entry from the Columbia math department.  It certainly fills out the picture to see that there are parallel lines of research unfolding.  At least the author, Peter Woit, gives the Natalie Wolchover article the "thumbs-up."

I particularly like the Witten quote, which has a timeless quality: "The field is still developing very fast, and it is difficult to guess what will happen or what the lessons will turn out to be."  
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Have him in circles
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Harlan Brothers

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In honor of Pi Day, here's an animation of some surprising music derived from the digits of pi:

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+Richard Green has created an excellent animation illustrating a result of mine that links Pascal's triangle and the constant e.  Thanks, Richard!  A short proof of the result can be found here:'s_Triangle.pdf

A more detailed treatment that includes an interesting connection to the Barnes G-Function appears in The Mathematical Gazette, Vol. 96, No. 535, 2012; pages 145-148.

Pascal's triangle and the number e

Pascal's triangle is a triangular array of integers, the first few rows of which are shown in the picture. Apart from the flanking strips of 1s, each entry is the sum of the two entries above it. There are many well known patterns among the entries of Pascal's triangle. Two of these patterns are (a) that the sum of the entries in the n-th row is equal to 2^n, and (b) that the alternating sum of entries in the n-th row is equal to 0. For example, if n = 4, this means (a) that 1+4+6+4+1 = 2^4 = 16, and (b) that 1-4+6-4+1 = 0.

A less studied sequence associated with Pascal's triangle is the product of the entries in each row. This sequence, which appears as A001142 in The On-Line Encyclopedia of Integer Sequences ( begins 
1, 1, 2, 9, 96, 2500, 162000, 26471025, ...
Let us denote the entries of this sequence by p(1), p(2), p(3), and so on. The remarkable property of the sequence, illustrated in the picture, is that as n becomes large, the value of p(n-1)p(n+1)/(p(n)^2) converges, albeit slowly, to the number e. The number e, which is approximately 2.718281828459045, is a famous irrational number, and is important because it is the base of the natural logarithm.

This post is based on a post by +Richard Elwes, which you can find here ( The result itself is due to +Harlan Brothers. +Alexander Bogomolny has written up a nice proof of the result here (

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Congratulations - wtg, Harlan!
A touching tribute to one of the greatest minds of our times, Benoit Mandelbrot - an extraordinary human being whose warm and generous spirit is missed by many.
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Harlan Brothers

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Check out this beautiful app for Leap Motion by +Nathan Selikoff!
Hello, Friends. I thought I'd share a collaboration between me and pi. I tried to let pi do most of the work...  

#Pi #Music
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Inventor, Composer, Mathematician, Technologist, Educator
Inventing, Composing, Mathematics, Programming, Communication
  • Brothers Technology, LLC
    Founder, 1992 - present
    Brothers Technology creates a broad range of intellectual property for license and sale. Current projects range from commercial encryption techniques to novel consumer devices and educational tools.
  • The Country School
    Director of Technology, 2002 - 2011
    Greatly advanced the use of technology through infrastructure upgrades, software training, and installation of interactive educational systems. Other roles included teacher, school administrator, advisor, and network administrator.
  • Yale Mathematics Department
    Consultant, 2001 - 2007
    - Edited the planned 20th anniversary edition of The Fractal Geometry of Nature for Benoit Mandelbrot - Collaborated with Michael Frame and Benoit Mandelbrot at the NSF funded Yale University Fractal Geometry Workshops - Conducted workshop and lab on the subject of fractal music - Trained educators in the subject of fractal geometry and in the use of specialized software - Developed fractal-based mathematics curricula for students in middle school through college
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Branford, CT
Boston, MA - New York City
Inventor, Composer, Mathematician, Technologist, Educator

I'm an inventor, composer, mathematician, educator, and founder of Brothers Technology, LLC.  I served as Director of Technology at The Country School for nine years. I've got six U.S. patents and have published numerous research papers related to number theory and fractal geometry.  I enjoy performing and composing in many styles including jazz, pop, and Brazilian music.

Over the course of six years, I had the honor and the pleasure of working with Michael Frame and Benoit Mandelbrot at the NSF funded Yale University Fractal Geometry Workshops. The workshops served to train educators in the subject of fractal geometry with the goal of developing fractal-based mathematics curricula for students in middle school through college.

Latest projects include a provably secure, patent pending encryption system, an automatic interior mailbox light, and an interactive, multimedia birthday app for iPhone called iKandl.

If you're in my circles and have an iPhone or iPad, let me know and I'll send you a free upgrade code for the eco-friendly iKand Birthday App!  It ain't Angry Birds, but it *IS* fun and has the advantage of making other people smile!

Bragging rights
...not all rights need to be exercised.
  • Berklee College of Music
  • Gateway Community College
Basic Information
Other names
Harlan J. Brothers
Harlan Brothers's +1's are the things they like, agree with, or want to recommend.
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