A Mind at Play: An Interview with Martin Gardner

A Mind at Play: An Interview with Martin Gardner

KENDRICK FRAZIER

(Kendrick Frazier is editor of the Skeptical Inquirer and a fellow of the American Association for the Advancement of Science. He is editor of several anthologies, including Science Under Siege: Defending Science, Exposing Pseudoscience.)

Music of pi

Is IT enough, what about basic sciences?

Following is an article appeared in the 'open page'  section of  The Hindu. I believe that this is a significant one in the context of  the mad rush for IT and related career. It is written by Mr. Mukundarajan. ( Unfortunately there is no clue there as to what is he ) Read the full article here:

The IT industry has emerged as a major employer of technical and non-technical graduates. Because of the higher salaries, an IT job is chased and cherished by graduates. The manufacturing sector lacks the IT industry's financial muscle to compete in the job market.

We often hear captains of the IT industry complain that graduates are not industry-ready. That is, whatever their other accomplishments or merits, the graduates do not measure up to the expectations of the IT industry. The IT honchos never tire of lecturing the universities about the employability-deficit of the otherwise qualified candidates. Engineering graduates may be employable by the manufacturing sector, but not by the IT sector. Employability is measured vis-à-vis the IT industry's needs.

It has become fashionable for IT companies to berate the education system for not teaching the necessary ‘skills' to students. What are the ‘skills' the system reportedly fails to teach? Is it building that connection between learning and life that makes individuals liberal and compassionate in their outlook? Is it the development of a curious, questioning mind that can think out of the box and innovate? Is it a cultured and holistic perspective that views life in all its rich manifestations with wonder, eclecticism and empathy? Is it anything to do with nation building?

The answer is none of the above. The skills come packaged under a generic name ‘soft'. These are primarily the abilities to communicate, work in a team, solve problems (related to the industry), etc. The IT industry has co-opted universities and engineering colleges to teach ‘soft' skills to students to make them ready for IT careers. The focus seems to be on learning the skills to land an IT job from day one rather than learning science and technology. It is as if the purpose of technical education in India is to create a captive pool of industry — a ready workforce for our IT giants.

India may be an IT superpower but is a technological laggard. In a sense, the IT sector has hampered the growth of science and technology. It has always perplexed me why India cannot manufacture passenger and military aircraft with cent per cent indigenous content. India's ‘own' Light Combat Aircraft ‘Tejas' comes with an engine manufactured by the General Electric Company in the U.S. Self -sufficiency in defence production is far away.

No nation can hope to become a superpower without a qualitatively superior technological prowess. What is the contribution of the famed IITs to research and development? Are the IITs a springboard for higher education and plum jobs in the U.S? Should the mechanical, chemical, electrical IIT graduates be working as software engineers, consultants and knowledge workers instead of contributing to the growth and competitiveness of the core manufacturing sector?

Nobody wants to take away the freedom to choose one's profession. But when the government provides subsidised education with taxpayers' money, is it too much to expect something in return from the IIT alumni in the form meaningful research and technological innovations? Why can't we have a system where IIT graduates can be made to work in research laboratories for, say, three years? The government should offer free education to those IIT students who sign a contract to pursue a career in research and development.

This is not a jeremiad against the IT industry, which is a prolific employer and major contributor to foreign exchange reserves. The IT sector cannot be accused of ganging up on the manufacturing sector. We are proud that India is recognised as the IT capital of the world. But it is equally important for India to be one of the innovation hubs of the world to achieve not only technological self-sufficiency but also invent local solutions to the myriad problems like poverty, agricultural productivity, water conservation, and climate change. Basic science education should be given its due respect to foster a scientific temper and culture. We need bright and independent minds that can create great ideas in garages as well as in laboratories. It is the developing of ‘hard skills' in science and technology that will determine whether India is able to make its tryst with destiny to become a major power. The IT industry cannot be allowed to dictate what and how science and technology are taught in colleges. Higher education is too important to be tied to the apron strings of a single industry.

Mandelbrot Video

A music video for Jonathan Coulton’s song Mandelbrot Set by Pisut Wisessing made in Film 324: Cornell Summer Animation Workshop, taught by animator Lynn Tomlinson every summer for Cornell’s summer session, in the department of Theatre, Film & Dance.

Mathsblog Question (By Umesh)

Four people are digging a ditch of some pre-specified size, one after another, and finished a ditch. These four might have different speed in their work. Each of them might have worked for a different time and finished some portion of the work. It is observed that each of them dug for such time that, during that time the other three, working together, could have finished half the ditch. This is true for each of the workers.

Question: If they worked together, how faster they would have finished the ditch, when compared to the total time they took (i.e., sum of the individual time each worker spent)?

(For example, if, working one after another, they took 12 hours to finish the work, how much time it would have taken if they worked simultaneously?)

Let the ith person dig a length of xi meters in 1 hour and let him work for ti hours. Let d be the depth of the ditch. Then we have
\[{t_1} \times 1 + {t_2} \times 2 + {t_3} \times 3 + {t_4} \times 4 = d\]\[{t_1} + {t_2} + {t_3} + {t_4} = 12\]

It is observed that each of them dug for such time that, during that time the other three, working together, could have finished half the ditch. This is true for each of the workers.

Hence we must have 
\[{t_1}{\rm{ }}\left( {{x_2}{\rm{ }} + {\rm{ }}{x_3}{\rm{ }} + {\rm{ }}{x_4}} \right){\rm{ }} = {\rm{ }}\frac{d}{2}\]\[{t_2}({x_1} + {x_3} + {x_4}) = \frac{d}{2}\]\[{t_3}{\rm{ }}\left( {{x_1}{\rm{ }} + {\rm{ }}{x_2}{\rm{ }} + {\rm{ }}{x_4}} \right){\rm{ }} = {\rm{ }}\frac{d}{2}\]\[{t_4}{\rm{ }}\left( {{x_1}{\rm{ }} + {\rm{ }}{x_2}{\rm{ }} + {\rm{ }}{x_3}} \right){\rm{ }} = {\rm{ }}\frac{d}{2}\]
Adding the above equations
\[({t_2} + {t_3} + {t_4}){x_1} + ({t_1} + {t_3} + {t_4}){x_2} + ({t_1} + {t_2} + {t_4}){x_3} + ({t_1} + {t_2} + {t_3}){x_4} = 2d\]This Implies\[\left( {12 - {t_1}} \right){x_1} + \left( {12 - {t_2}} \right){x_2} + \left( {12 - {t_3}} \right){x_3} + \left( {12 - {t_4}} \right){x_4} = 2d\] That is\[12\left( {{x_1} + {x_2} + {x_3} + {x_4}} \right) - \left( {{t_1}{x_1} + {t_2}{x_2} + {t_3}{x_3} + {t_4}{x_4}} \right) = 2d\]This means\[12\left( {{x_1} + {x_2} + {x_3} + {x_4}} \right) = 3d\] and so finally we have\[\left( {{x_1} + {x_2} + {x_3} + {x_4}} \right) = \frac{d}{4}\] Now let us suppose that they can finish the job if they work together for t hours.This means \[t\left( {{x_1} + {x_2} + {x_3} + {x_4}} \right) = d\,\,\, \Rightarrow \,\,\,t\frac{d}{4} = d\,\,\, \Rightarrow \,\,\,t = 4\]

Post Script: Many readers of the mathsblog viewed my answer unwisely complicated. Some even went to the extent that those who study higher mathematics lack commonsense and they first make simple things complicate and then solve! The present problem was an Olympiad problem for small children of age six and my solution was stated to be something outside their reach. Subsequently alternate solutions were given by other people which were graded as the ideal ones and were indeed so. Before posting this here, I once again went through my earlier solution and tried to modify it to look natural. But on finishing the job I felt my second solution very artificial and threw it away. Poor me!

Mathsblog Question (by Hari Govindan)

The picture illustrates a regular hexagon with the side length equal to √3. Quadrilaterals XABC and QPXR are squares . What is the area of the shaded triangle CPS?

The side of the hexagon is square root of 3. So the width (GD) of the hexagon is \[\sqrt 3  \times \sqrt 3  = 3\]

From the right angled triangle ADX, we get, \[\cos 30 = \frac{{AD}}{{AX}}\]This implies \[AX = \frac{{AD}}{{\cos 30}} = \frac{{\frac{{\sqrt 3 }}{2}}}{{\frac{{\sqrt 3 }}{2}}} = 1\]Again,\[\sin 30 = \frac{{DX}}{{AX}} \Rightarrow DX = \frac{1}{2}\]Since the side of the equilateral triangle XCP is 1 its altitude \[EX = \frac{{\sqrt 3 }}{2}\]The altitude of the triangle CPS is SF, which is the same as GE (see figure)

But \[GE = GD - (DX + EX) = 3 - \left( {\frac{1}{2} - \frac{{\sqrt 3 }}{2}} \right) = \frac{{\left( {5 - \sqrt 3 } \right)}}{2}\]Finally, area of the triangle CPS is\[\frac{1}{2} \times {\rm{base }} \times {\rm{height}} = \frac{1}{2} \times 1 \times \frac{{5 - \sqrt 3 }}{2} = \frac{{5 - \sqrt 3 }}{4}\]

Mathsblog Question ( by Jasmine)

ABCD ഒരു സമചതുരമാണ്. അതിനുള്ളില്‍ P എന്ന ഒരു കുത്തിട്ടിരിക്കുന്നു. PCD-യും PDC-യും 15 ഡിഗ്രി വീതം. ത്രികോണം PAB സമഭുജത്രികോണമാണെന്ന് തെളിയിക്കുക.

DP -ക്ക് ലംബമായി AF വരക്കുക.

AF - ല്‍ കോണ്‍ FDG = 60 ഡിഗ്രി ആകത്തക്കവിധം G അടയാളപ്പെടുത്തുക. 

അപ്പോള്‍ കോണ്‍ AGD = 150 ഡിഗ്രി.

കോണ്‍ PDC = കോണ്‍ DPC = 15 ഡിഗ്രി ആയതിനാല്‍, Δ AGD, Δ DPC എന്നിവ സര്‍വസമങ്ങളാണ്.

ഇതില്‍ നിന്നും DP = DG എന്ന് ലഭിക്കും.

Δ DPG - ല്‍ കോണ്‍ FDG = 60 ഡിഗ്രി, കോണ്‍ DGF = 30 ഡിഗ്രി എന്നിങ്ങനെ ആയതിനാല്‍  DF = ½ DP എന്ന് ലഭിക്കുന്നു. അതായത് DF = PF.

ഇതില്‍ നിന്നും AF, DP യുടെ സമഭാജി ആണെന്ന് മനസ്സിലാക്കാം.

അങ്ങനെയെങ്കില്‍ AD = AP ആയിരിക്കുമല്ലോ. ഇതേപോലെ BC = BP എന്നും തെളിയിക്കാം. എല്ലാംകൂടി കൂട്ടിവായിച്ചാല്‍ AP = BP = AB ആയി.