Links

1. A profile of the the prolific Lowell Wood (Bloomberg).

It chronicles the story of an F student, as he accumulated more inventions than Thomas Alva Edison.

This habit [of obsessive reading] goes back at least five decades. “I went to hear Linus Pauling lecture when I was a student,” Wood says. “Afterward I waited until everybody else went away, and then I asked him frankly, ‘How do you come up with these huge number of wonderful ideas?’ He said, ‘There’s really nothing to it all. You just read, and you remember what you read.’”

“It’s frankly illiterate to not be optimistic. We’re going to see a blossoming across essentially every front, unprecedented in human technological history. This is not something that’s hoped for. This is baked in the cake.”

2. On the folly of Big Science awards (NYT)

Dr. Allison’s work is surely impressive. But it occurred alongside and in dialogue with a number of related findings. Researchers analyzed the citations that led to Dr. Allison’s drug and concluded that it relied on work conducted by 7,000 scientists at 5,700 institutions over a hundred-year period. Yet only he was recognized. 

And there’s yet another problem. By honoring breakthroughs, award committees reinforce the misconception that science is all about discoveries, when the cornerstone of science is replication and corroboration of results, which ensure that a finding is real and not a false lead.

3.  Shinichi Mochizuki and the Impenetrable Proof (Nature)

Three years on, Mochizuki's proof remains in mathematical limbo — neither debunked nor accepted by the wider community. Mochizuki has estimated that it would take a maths graduate student about 10 years to be able to understand his work, and Fesenko believes that it would take even an expert in arithmetic geometry some 500 hours. So far, only four mathematicians say that they have been able to read the entire proof.

Splitting Up: A Python Program

I've been discussing the common, but not quite trivial problem of settling bills among a bunch of friends, in a couple of posts.

Here is a rudimentary (but fully functional) Python program which implements the algorithms.

One needs to create a 2 or 3 column csv file (INPUTFILE), and send it to the program. Here is the header portion of the program, which describes how one interacts with the program, in more detail.

# Given a set of contributions (and optionally expemptions) creates a list of pair-wise
# transactions which "settles" all accounts
#
# example : python splitup.py INPUTFILENAME
#
# : if INPUTFILENAME not provided then looks for csv file "input_table"
#
# : INPUTFILE = csv file containing 2 or three columns, for example
#
# Two column example: NAME, CONTRIBUTION
# Person1, 10
# Person2, 20
# Person3, 5
# Person4, 15
# Person5, 10
#
#
# Three column example: NAME, CONTRIBUTION, AND EXPEMPTION
# Person1, 10, 0
# Person2, 20, 5
# Person3, 5, 0
# Person4, 15, 5
# Person5, 10, 0

Try it out!

PS: I am still in the process of learning Python, and my coding style is admittedly funky.

Links

1. Alexander Coward at Berkeley Math "blows the whistle":

This question is one that I asked, and in response it was made very clear to me what is meant by the norms of the department. It means teach from the textbook. It means stop emailing students with encouragement, handwritten notes and homework problems, and instead assign problems from the textbook at the start of the semester. It means stop using evidence-based practices like formative assessment. It means micro-manage the Graduate Student Instructors rather than allowing them to use their own, considerable, talent and creativity. And most of all it means this: Stop motivating students to work hard and attend class by being engaging, encouraging and inspiring, by sharing with them a passion for the beauty and wonder of mathematics, but instead by forcing them into obedience with endless busywork in the form of GPA-affecting homework and quizzes and assessments, day after day, semester after semester. 

In a nutshell: Stop making us look bad. If you don't, we'll fire you.

 2. Bruce Carlson of the "My history can beat up your politics" has a beautiful answer to the question, "Which is harder to amend: The US constitution or the Bible?"

3. Nature editorial on "science communication" (pdf), and the harassment of scientists who speak out on public forums. The particular case in question here concerns GM crops.

These headlines focused on Kevin Folta, a University of Florida researcher, because USRTK leaked his e-mails to three journalists. Two of them co-posted a PLOS blog (now removed), while the third wrote a front-page New York Times news story highlighting a $25,000 donation from Monsanto to Folta’s institution. In both cases, the reporters cherrypicked sentences from several thousand e-mails, highlighting Folta’s communications with Monsanto, often out of context, to insinuate that he is an industry shill—and thus presumably unfit to talk to the public. 

Folta broke no laws. The Monsanto funds were a donation to his university’s Foundation outreach program. They were tied neither to him directly nor to his research. His conflict of interest disclosures were wholly compliant with his university’s rules. He never used industry funds for personal gain. Yes, he did have interactions with companies, and he is involved in a communications program that receives funding from industry (as well as from numerous private individuals, foundations, farmer bureaus and the US Pork Board, etc). None of this is shocking or, indeed, unusual.

Splitting Up: An algorithm

In a previous post, we considered an algorithm for settling accounts between friends who are splitting up a dinner bill.

At the end of the "pre-processing" step, we have a list of names (say ['p1', 'p2', 'p4', 'p3'])and a list of corresponding net contributions (x = [2, 7, -4, -5]), which add to zero.

We now consider the problem of generating the transaction list. The first thing to do is to sort contributions from highest to lowest.

Here, we would have, [p2, 7], [p1, 2], [p4, -4], and [p3, -5].

We now consider a transaction between the first and last members of the list. Once consummated, one of the members will be "settled", and hence out of reckoning for the rest of the calculation.

In this case, p3 pays p2 $5, and is out! (Transaction 1)

We then re-sort the remaining members to get, [p2, 2], [p1, 2], and [p4, -4].

Again we consider a transaction between the first and last members of the list.

In this case, p4 pays p2 $2, and is p2 is done! (Transaction 2)

We then re-sort the remaining members to get, [p1, 2], and [p4, -2], which can be settled by:

In this case, p4 pays p1 $2, and everyone is done.

It is easy to see that since at least one member drops out of contention during each transaction, we will need N-1 transactions at most.

We can write this up as an algorithm:

1. sort xi. set n = N.
2. consider transaction between x1 and xn.
3. if x1>abs(xn), transaction = pn pays $abs(xn) to p1, and is removed from the list. n = n - 1
4. elseif x1
5. elsife x1=abs(xn), transaction = pn pays x1 to p1, and both p1 and pn are removed from the list. n = n - 2
6. Sort remaining xi.
7. Repeat steps 3 through 6 until n = 0.

Introducing Unsolved Mathematical Mysteries in Grade School

I came across this excellent (and provocatively titled) article, "Unsolved problems with Common-Core", which suggests interesting exercises to students all the way from kindergarten to high-school.

These exercises then form a gateway to a big, usually unsolved, mathematical conjecture or hypothesis.

Here is an example for kindergarten/1st grade:

Can you color the map of Africa with four colors so that no two countries that touch are filled in with the same color?

This is followed by:

The unsolved problem: without trying all possibilities, can you tell when a map can be colored in with 3 colors so that no two countries that touch are filled in with the same color?

Fascinating stuff!