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Assad Ebrahim
Commercial Mathematician
Commercial Mathematician

Assad's posts

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Inter-planetary Radar NASA's Jet Propulsion Lab has used ground-based microwave radar to locate the lost lunar satellite Chandrayaan-1, still orbiting the moon 273,000 miles away. The tiny satellite, just 5x5x5 feet, was still in the same polar orbit as it had been at last contact in August 2009. Four hours of observation showed an object crossing the radar beam twice, which, at 2h and 8m matched exactly Chandrayaan's expected orbital period.


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Mathematics of Gerrymandering Districts - 'Cracking' and 'packing' are two techniques that can be used by a political party to create districts that ensure continued dominance.  They work by reducing the efficiency of opposition voters by grouping them into minority districts for e.g. 40% of the local vote (cracking) or into supermajority districts for e.g. 60% of the vote (packing).  In the first case, all opposition votes are essentially wasted, while in the second, all votes above 50% are wasted. 

Computer algorithms have made these techniques relatively easy to implement, and with devastating effect, prompting a Supreme Court review of the legality of using mathematics to introduce clear disparities in voter efficiency. 

While Mathematics itself is independent of ethics, its applications are not.  At stake is the legality of an algorithm specifically designed to erode democracy.

Article: Noah Feldman, Bloomberg, 22 Nov 2016.

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Coding - An expository article "Coding from Pre-School" has now been written to accompany the release of Turtle Logo in Forth, v1.2, for Windows.
Free download (with auto-installer) available from here:

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Coding - The Turtle Logo drawing program I wrote in Forth last month for my 4-year old daughter can now be freely downloaded from here:   We've added quite a number of usability features including recordable macros so that we only have to create one cloud, one tree, one bird...  Take it for a spin, especially if you have young children!  It works on any version of Windows and has an auto-installer for ease.

The power of the Forth language is that the program is just ~500 lines of code.  For those who would like to modify, extend, or just browse the code, full source is provided (GNU License). 

If you decide to give it a try, just follow the instructions after downloading.  Feel free to comment or ask for help here!

The original post is here:

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Data Visualization - The Fallen of World War II, by Neil Halloran, is a new type of documentary -- a data documentary, with narration, and a musical score. But for the point it makes -- this is all that is needed: the scale of death in WWII, and the long peace that has followed. Highly recommended.

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Coding - Wrote a Turtle Logo drawing program this weekend for little Jasmine (aged 4 years).  It's 300 lines of Forth code, draws interactively on Windows, and generates 80's-style block-y graphics. 
    The user interface is an infinite loop processing 5 single-key instructions---forward, rotate CW, rotate CCW, change color, and go-home (for when Turtle gets lost!)---simple enough for a 4-year old to execute, but with enough complexity to create pretty things together. 
    Was delighted to hear her announce, "Daddy, this is more fun than my tablet, because I can make something with it!"  Fun times, and the start of algorithmic thinking.  She has plans already for more features... :)

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Autonomous Vehicles - Autonomous passenger vehicles (no steering wheel and no pedals) are an interesting proposition for the ride-sharing and ride-hailing market, offering the possibility of Transportation-as-a-Service.  Ford has announced plans to get there in five years (by 2021).

LA Times story:

Ford's official statement:

Goal-achievement - Michael Uslan, accredited university comic book course creator and originator of the Batman movie franchise, offers:  "First, sometimes you have to take calculated risks and roll the dice, or risk growing old and having to say, “I could have been…."  Secondly, you must believe in yourself and in your work.  And, don’t then forget to market yourself. Use both sides of your brain.  Third, you must have a high threshold for frustration.  You must knock on doors until your knuckles bleed. Doors will slam in your face. You must pick yourself up, dust yourself off, and knock again.  Finally, follow whatever your passion is. Do something you love!"

Michael's story is a masterpiece of inspiration, from how he wangled his way to teaching the first accredited university literature course on comic books, and then worked his way to originating and producing the Batman movie franchise,

You can read the full text here:

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Mathematics - There is a tradition in mathematics that says "Read the Masters!" Thanks to the Mathematical Association of America, this is now easier: gathered in one place are masterful expositions of mathematics, from 1925 to the present, written by winners of the Chauvenet Prize.

Where "Read the Masters!" originated:
"Euler learned at the feet of Johann Bernoulli, who had Euler 'read the masters'.  Euler read difficult mathematics and Bernoulli helped him when he got stuck.  In his later years, I propose that Euler was able to teach in the style under which he himself had learned.  He had learned guided by the principle 'Read the masters'.  He taught under the style 'Read me, read me.  I am Euler and I am your teacher in all things.' (Edward Sandifer, How Euler Did It, Euler as a Teacher, Part 2, Feb 2010)

Laplace on Euler (1749-1827): "Read Euler, read Euler.  He is the master of us all." (quoted as a personal communication by Gugliemo Libri, Journal des Savants, p.51, 1846)

Neils Abel (1826), when asked how he got his expertise, replied, "It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils." (Letter to Bernt Holmboe, quoted by Oystein Ore, Abel: Mathematician Extraordinaire, 1957)

[1] The Chauvenet Prize Archive

[2] Edward Sandifer: Euler as Teacher, part 2:
Full Archive:

[3] Euler biography, and Laplace's quote:

[4] Neils Abel, his student years:

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Mathematics - Super excited to see the release last year of "The Princeton Companion to Applied Mathematics (2015) edited by Nicholas Higham (the numerical analyst).  This second, 1000 page collection follows the outstanding example of the "Princeton Companion to Mathematics" (2008) edited by Fields Medalist Timothy Gowers, which is one of the best surveys of current (last 50 years) of mathematics at the graduate / research level.  Nick's collection promises to be an absorbing read!

For the Princeton University Press announcement, with downloadable table of contents, preface, etc.

For the original recommendation, see the thread here:
Surveys of Current (last 50 years) Mathematics at Graduate / Research level?
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