Discovering Hamming Codes

July 18th, 2010 admin

Digital data, transmitted over a communication medium (wireless, optical fiber, copper wire), or stored in some storage medium (such as computer memory or hard disk), is prone to bit-flips and errors. For example, if the message “10110101000101010″ means “BILL JOHN” and communication channel noise flips a bit, the message received may be “10010101000101010″, meaning, “KILL JOHN”. Now, that could create a problem. The problem also exists in data that is sitting untouched on a digital storage medium. Have you ever noticed that if you open some photo file on your computer, after years of storage, they develop strange colors and often do not display fully? This could be due to some bit errors in the stored 1s and 0s that represent the image file data. Read the rest of this entry »

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Fascinating course on Justice by Michael Sandel

June 20th, 2010 admin

Here is a link to video lectures from Harvard University’s course on Justice, taught by Professor Michael Sandel. (Watch the introductory video which should start automatically, and then look for the Episode list to the bottom right of the page. 12 hour long lectures – but worth the time.)

http://www.justiceharvard.org/

It contains some fascinating discussions on morals, philosophy, rights and justice. Professor Sandel has a very interesting teaching style, where he almost helps the students discover right vs. wrong, rather than just teaching it to them. Also, he has an extraordinary delivery style – careful and sincere. It is clear that he is actively participating in the discussion himself; he tailors the material such that it conveys all the crucial points while at the same time allowing the journey to these crucial points to be shaped by the students in the classroom. The class itself is comprised of over a thousand students, hanging on to every word from the teacher, and is a sight to behold.

A must watch. More accurately, a must think.

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Thoughts on the mathematical constant e

May 16th, 2010 admin

e for exponential

The mathematical constant e shows up in strange places. Moreover, its significance is not as easy to grasp as that of the other famous constant, \pi, because there is no easy physical object in whose context to imagine it. For example, \pi is the ratio of the circumference to the diameter of a circle. Yes, it is irrational, but if you can get over that mystery (or ignore it for the time being), it is straightforward to imagine what \pi is. Every circle does seem to have a certain circleness, which makes them all look the same. It is intuitively not hard to agree with the hunch that every circle has an unchanging ratio between the circumference and the diameter; and it makes sense to keep that ratio handy and give it a name.

The constant e is considerably more elusive. It appears, at first, to be a number you would not go hunting after. You just happen to stumble upon in during one of your mathematical excursions; it seems interesting enough that you then pick it up and put in in your pocket for some potential use later. After stumbling upon the same thing along other mathematical excursions, in hindsight, it does seem to be something rather useful. Something you should have gone looking for. Read the rest of this entry »

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We, the people …

May 2nd, 2010 admin

Reference for the population figure: http://www.google.com/publicdata?ds=wb-wdi&met=sp_pop_totl&tdim=true&dl=en&hl=en&q=world+population

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We made a garden trellis with PVC piping

May 2nd, 2010 admin

Figure1: Basic plan showing the material required

We have two 4′x8′ (4 feet by 8 feet) raised beds, which we use for vegetable plants. Kavita has been asking me to either buy or build a trellis for her climbing plants (cucumbers, tomatoes and eventually some types of squash and gourds). I read several websites online and decided to build a simple trellis using PVC piping. It took one trip to the local Home Depot, and then about 2 hours of work. The cost for the material was under $10 (I already had all the tools needed).

We decided to build one and test it out before getting carried away and building more. We decided that we would roughly want the trellis to be 4 feet wide by 5 feet high. At the Home Depot we did some quick calculations based on the basic design we had in mind and came up with a total of about 29 feet of PVC tube. The calculation is shown in Figure 1.

Figure 2: Materials and Tools for the project (4-way, + shaped, PVC connector missing)

The PVC pipes are sold in 10′ pieces. We got 3 pieces. We also got some string (I tried polypropylene string since I did not know any better, we’ll see how that works out).

Figure 2 shows most of the material and tools. The one caveat is, since I took this picture after completing the project, the one 4-way 1/2″ PVC pipe connector used at the center of the frame is missing from the picture. I had extra connectors of the other type, so I could use them for the picture. Also, one other thing that is missing from the picture is a power drill and drill bits. I used a 3/16″ drill bit to drill evenly spaced holes in the pipes to draw the string through, to create a framework.

Figure 3: Trellis plan with the stringing shown

Figure 4: Framework ready, stringing is yet to be completed

The spacing between the holes and how the trellis is supposed to look eventually is shown in Figure 3.

The thing that took the most time was measuring and marking the PVC pipes, cutting them to the right size with the saw, then measuring and marking the locations for the holes for the string to go through and then drilling the holes with the power drill. Since the PVC pipe keeps rolling about, making it stable before drilling is important. I just used an old rag to wrap around the pipe in order to hold it somewhat still.

Once the pieces were all ready, putting the trellis together took less than 10 minutes. There was no need for glue, since the connectors fit quite snugly. Figure 4 shows the trellis laid out on the lawn (with only one piece of string drawn through, Kavita will work on getting the rest of the mesh this evening).

We are not sure how well this will hold up, how long it will last etc. I will update the post with some pictures on the trellis in action, later.

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If you cannot be a Maradona, you can certainly be a Marrow Donor

April 30th, 2010 admin

Kavita (my wife) and I recently learned about bone marrow donation, and why it is important to register with the National Bone Marrow Donor registry. Kavita registered at a drive that was being conducted at a charity event being organized in the area. Through her I came to know about SaveVinod.com. I learned that is very difficult to find a bone marrow match (1 in 100,000) and it is therefore important to keep the database of potential donors as large as possible. Further, some ethnic groups have very few listed donors – Indians (South Asians) is one such under represented group. Read the rest of this entry »

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The Mathematics of Mortgage, Overpayment and Refinancing Decisions

October 7th, 2009 admin

With mortgage interest rates at historically low values refinancing home loans is an option currently being investigated by many here in the US. I, too, considered the same issue recently and discovered that this is not an easy decision to make. I developed a spreadsheet to figure out if this was a good idea. You can download this spreadsheet by clicking on this link (Microsoft Excel 2003). In general, the spreadsheet was also intended to show how loan repayment terms are set, how banks make money on loans, when overpaying monthly payments makes sense etc. Feel free to use the spreadsheet and improve upon it or tailor it to your situation. The rest of this article is a tutorial on how to make decisions about mortgages, how mortgages work in general, whether overpayment of the monthly payment makes sense, and what to consider when refinancing. The focus will be on the mathematical aspects of the decision making. Read the rest of this entry »

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What should I do with my used PVC shower curtain liner?

July 19th, 2009 admin

When replacing the PVC shower curtain liner today, I was wondering what kind of plastic it was and whether it was recyclable.

Here is what I learnt about the various types of plastics. The following list is from Wikipedia’s article on Plastics.

  1. PET (PETE), polyethylene terephthalate: Commonly found on 2-liter soft drink bottles, water bottles, cooking oil bottles, peanut butter jars.
  2. HDPE, high-density polyethylene: Commonly found on detergent bottles, milk jugs.
  3. PVC, polyvinyl chloride: Commonly found on plastic pipes, outdoor furniture, siding, floor tiles, shower curtains, clamshell packaging.
  4. LDPE, low-density polyethylene: Commonly found on dry-cleaning bags, produce bags, trash can liners, and food storage containers.
  5. PP, polypropylene: Commonly found on bottle caps, drinking straws, yogurt containers, Lego building blocks.
  6. PS, polystyrene: Commonly found on “packing peanuts”, cups, plastic tableware, meat trays, take-away food clamshell containers
  7. OTHER, other: This plastic category, as its name of “other” implies, is any plastic other than the named #1–#6, Commonly found on certain kinds of food containers, Tupperware, and Nalgene bottles.

Read the rest of this entry »

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Have people forgotten Shiva?

July 19th, 2009 admin

Hinduism has a notion of trinity – three forces that drive the universe. The trinity consists of the creator, the sustainer and the destroyer (personified respectively by Brahma, Vishnu and Shiva). I do not claim to know the spiritual aspect of this concept. However, the applicability of this concept to the physical things in our lives is almost obvious. Everything physical comes into being, serves its purpose during its lifetime and is (or rather, should be) eventually destroyed. These three forces must guide each other in an eternal cycle, rather than in a linear progression. That which is destroyed, must contribute to the creation, and that which is created must be destroyable. This is not philosophy; this is just the principle of equilibrium and balance. Read the rest of this entry »

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On the role of the media in sports in India

September 13th, 2008 admin

Some things are only visible from the corner of the eye; they vanish when you try to look at them directly. Similarly, I believe, the best approach to religion  is not a headlong dive to grab its elusive essence, but rather, an indirect infusion of those ideas and ideals via a more concrete medium. One such concrete medium, which India seems to have never given much chance to, is sports. My friend, Akshay, sent me an article by Professor V. Raghunathan (author of the book “Games Indians Play: Why we are the way we are”) on why India’s performances in sports in general and Olympics in particular falls way short of what one would expect from a nation of over a billion people. The article is called “Games Indians Don’t Win“. Read the rest of this entry »

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