Reversing Entropy

Project Euler 1

December 11th, 2011

I took a look at the first problem on the Project Euler site earlier this afternoon:

This asks you to find the sum of the natural numbers that are less than 1000 and are multiples of 3 or 5.

I decided that Haskell’s filter function and a lambda would make this problem trivially easy to solve. In GHCi:

Prelude> let sumMultiplesOf3Or5 max = sum(filter(\x -> (mod x 3 == 0) || (mod x 5 == 0))[1 .. max - 1])
Prelude> sumMultiplesOf3Or5 1000
233168

As I played around with other values for max, something unexpected appeared before my eyes. A pattern of repeated digits begins to emerge in the sums of the multiples of 3 and 5 less than 10 to the power of i as i increases.

Prelude> map sumMultiplesOf3Or5 (map (\i -> 10 ^ i) [1..6])
[23,2318,233168,23331668,2333316668,233333166668]

Something similar happens with the sums of the multiples of 3 or 5 less than 20, 200,…,30,300, and so on:

Prelude> map (\j -> map sumMultiplesOf3Or5 (map (\i -> j * 10 ^ i) [1..6])) [1..9]
[[23,2318,233168,23331668,2333316668,233333166668],[78,9168,931668,93316668,9333166668,933331666668],[195,20850,2098500,209985000,20999850000,2099998500000],[368,37268,3732668,373326668,37333266668,3733332666668],[543,57918,5829168,583291668,58332916668,5833329166668],[810,83700,8397000,839970000,83999700000,8399997000000],[1133,114218,11432168,1143321668,114333216668,11433332166668],[1428,148668,14926668,1493266668,149332666668,14933326666668],[1845,188550,18895500,1889955000,188999550000,18899995500000]]

Reformatted:

[[23,2318,233168,23331668,2333316668,233333166668], -- [10,100,1000,10000,100000,1000000]
[78,9168,931668,93316668,9333166668,933331666668], -- [20,200,2000,20000,200000,2000000]
[195,20850,2098500,209985000,20999850000,2099998500000], -- and so on
[368,37268,3732668,373326668,37333266668,3733332666668],
[543,57918,5829168,583291668,58332916668,5833329166668],
[810,83700,8397000,839970000,83999700000,8399997000000],
[1133,114218,11432168,1143321668,114333216668,11433332166668],
[1428,148668,14926668,1493266668,149332666668,14933326666668],
[1845,188550,18895500,1889955000,188999550000,18899995500000]]

I’m not sure if this continues indefinitely. I wonder if similar patterns emerge with numbers in different bases. I’m curious about trying multiples of numbers other than 3 or 5. At this point, I’ve really no idea why this happens, but my curiosity is aroused.

I’m also really impressed with Haskell, a language that I barely know. The only other time I’ve used functional programming seriously is with C# and VB.Net for LINQ, of which I am a huge fan.

Posted in Mathematics, Programming | No Comments »

GHCN Monthly and MS Access

December 4th, 2011

For some of the last few evenings, I have been learning about MS Access’s data import functionality in order to interrogate the data of the Global Historical Climatology Network-Monthly dataset. This dataset holds records of temperature readings dating back to the beginning of the eighteenth century from more than seven thousand stations around the globe.

GHCN Monthly

The data are in text files with a fixed width format. It’s very straightforward to set up the import format (although there are many columns!) and save the import specification so that future datasets can be imported as they are released with ease. The largest data files have almost half a million rows, yet Access can import the data in a few seconds. The resulting table of readings of average, minimum and maximum temperatures for each month for each station has more than one million rows. I have not experimented with adding indexes yet but, in spite of this, I can run queries that are not painfully slow.

Now that I have the data into an Access database, I hope to start analysing the data. I have produced a couple of charts for a single station but am yet to run any serious calculations. I have read of a similar project at:

A Quick and Dirty Analysis of GHCN Surface Temperature Data

The algorithm that caerbannog (the blogger) uses in his C++ program to smooth the data and calculate averages is fairly simple. Something similar should be possible (or even easy) using the MS Office tools.

Ultimately, my aim for this is to make this the basis of an ICT lesson or project. As caerbannog notes “Never in history has science been more accessible to the general public than it is now.” The quantities of data that can be accessed for free are as enormous as the power of the computers that are now cheaply available. I hope that my students will be inspired to look deeply into the issue and this will help develop their sense of empirical curiosity.

Posted in Computers, Environment, Mathematics, Science, Teaching | No Comments »

Mouse Utopia

August 17th, 2011

I’ve just read an interesting piece on a scientist who tried to create a utopia for mice and his results.

http://www.cabinetmagazine.org/issues/42/wiles.php

Science fiction writers have often presented a pessimistic vision of the future, where overpopulation is the problem and nihilism and violence are the consequences. That authors take this route is understandable as a functioning society is not much of a backdrop for a story. Also, despair is easier than hope.

It’s heartening that the scientist in the piece to which I link above was disappointed by the pessimistic fiction that he inspired. Whatever happens to our population and environment, we’re going to have to keep on keeping on.

In spite of the recent ugliness in the streets of London, I still feel that urban living and constantly being surrounded by other people is infinitely to be preferred to living like Robinson Cruesoe.

Posted in Environment, Philosophy | No Comments »

New Niece in Cheltenham

August 16th, 2011

At the weekend, we went over to Cheltenham to meet our new niece, Annabel Elizabeth Woodward.

2011-08-13 Cheltenham

Tags: Cheltenham Niece
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Sardinia Beach Holiday

August 7th, 2011

2011-07-30 to 2011-08-07 Sardinia

Tags: Sardinia Beach Holiday
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Generics in VB.Net

June 14th, 2011

Taking a lead (again) from Java generic types for beginners, I decided to experiment with generic types in VB.Net. The ICT Cool blog covers the idea behind generics and the MSDN documentation on generic types in VB.Net gives more details on the topic, so I won’t repeat what has been explained elsewhere.

My code shows how generics can make code more robust by enforcing compile time type checking. The type safety of the various objects can be checked in Visual Studio by hovering the mouse over any of the variables in the code. This brings up a pop up that says the type of the object. Many of the lines of the main sub have been commented out because the project would not build otherwise. Try uncommenting them to see the errors that the IDE finds.

The code also shows that generic types allow coders to build and use type safe, polymorphic collections. Put simply, we can create a list (for example) that will only allow us to add an object of any type, so long as it implements an interface given at the time of construction.

GenericsInLists

Posted in Computers, Programming | 2 Comments »

String Manipulation with the Decorator Pattern

June 12th, 2011

Inspired by the Java program to sort and reverse a string at ICTCool.com, I decided to try to solve the problem using Java and the Decorator Pattern.

StringDecoratorDemo.tar.gz

My solution required considerably more lines of code than the code at ICT Cool. For a problem as simple as this, using the Decorator Pattern is probably overkill. However, the advantage of this pattern is that multiple decorators can be stacked up at run time in any order that we choose. Also, if we wanted to add more operations later, we simply add a new class, which is cleanly separate from the other operations.

I’ve written the program using NetBeans, which creates quite a few files other than the source files, which are in src. To run the program, cd to the dist directory and type java -jar StringDecoratorDemo.jar.

Posted in Computers, Programming, Teaching | 1 Comment »

Wedding in Sardinia

May 22nd, 2011

We’ve just returned from a very short trip to Sardinia for the wedding of Valeria and Gilberto. The wedding and reception took place in the lovely seaside town of Cala Gonone.

2011-05-21 Cala Gonone

No trip to Barbagia is complete without hearing the Cantu a Tenores. At the ceremony and the reception, the singers formed a circle several times to serenade us all.