Thursday, February 2, 2017

How to explain Threads

People new to programming might have hard time  understanding what are "threads". How are they different from "programs"?  There's a simple metaphor you can use to explain  the concept of "threads":

Your  program is like a labyrinth.  You can't walk "through it", you must follow the paths that exist. There are many branches in those paths you can take. You can go forwards and you can reverse your direction to return to an earlier point. You can pick things up to carry with you while inside the labyrinth, maybe just some information, maybe take photographs.

The program has run its course when you return back to the entry-point and exit. You still have the things you picked along the route, the photographs you took etc. Those are your output. What you took with you into the labyrinth was your input, say a map which guided your choice of turns at the branch-points.

The above  is single-threading. You moving inside the labyrinth is like the program-counter in your program's execution environment pointing to different locations in the program being "run". (Yes you can run in a labyrinth too, you must if a Minotaur is chasing).

Now leash multiple visitors into the same labyrinth, more or less at the same time, concurrently . They will choose their own paths according to their own maps. They might communicate with each other by leaving notes on the walls for others to read. Some visitors might overwrite notes written by others, probably not a very good practice but certainly possible. This is multi-threading: Multiple visitors in the labyrinth at the same time. Each visitor walking inside the labyrinth is one thread.

Why are  they called "threads"?  I can think of one reason. In the Minotaur-myth Theseus entered the labyrinth with a  ball of thread.  He tied the start of the thread to the entry point of the labyrinth. Then he unwound the thread as he moved deep into the Labyrinth. After he found the Minotaur and killed it he needed a way to find his way back out. He simply followed the unwound thread.

Copyright © 2017 Panu Viljamaa. All rights reserved

Monday, January 30, 2017 IV

The previous episodes II, III describe how to use with three argument-types: Array, Object and Function.  These extensions to Function.prototype provide support for and take advantage of Functional Programming (a.k.a "FP") in JavaScript.

It is kind of fitting that additional support for Functional Programming in JavaScript should be provided as additional methods of the JavaScript class Function. Don't you think?

This blog-post describes some additional features not previously covered and the fpmap() -library as a whole. The described features are now implemented in the "fpmp" download available from npm and GitHub, see links below.


JavaScript standard can be used to execute a given function once once for each of the array-elements and get back an array containing the results of each such call:

  var arr = [1,2,3];
  var a2  = (double);  // -> [2, 4, 6] 

Above "double" is a function which returns its argument times two.  Writing such code I occurred to me  to ask did I write it correctly. Or should I have instead written:

  var a3 = (arr);  // ???

Luckily I had it correct no problem. I usually don't' make errors like that I congratulated myself. But then I started thinking, is there any rule-of-thumb I could use to easily remember the correct order? Is there perhaps something obviously wrong in the "wrong order" ?

I couldn't find anything obviously wrong with it. So I started thinking, why does it have to matter which way I put it? If both ways would produce the same result then I could more easily remember the simplest rule: Order doesn't matter!  If something seems good either way, we shouldn't have to think much about which way to do it.

So, went to work and implemented the function "fpmap()".  Calling it to first install,  it now allows me to write:

  var a3 = (arr); // -> [2,4,6] 


This made me feel almost like I had discovered complex numbers!  Why?  Because it seemed the possible ways of using the same operation, with different types of arguments had now greatly expanded. It was almost like jumping out of line to the plane around it! Let me explain...

With [1,2,3].map(double) the "recipient" must always be an Array, and it seems argument-type must be Function, to make it useful in general. Regardless of what type the Array elements are, you can then always put in as argument some function that accepts those array-elements as argument.

With[1,2,3]) it came obvious to ask a follow-up question: What if I use something else as argument, perhaps an Object like:  "{x: 1, y: 2})" ?  Is there something useful such an expression could do?  YES OF COURSE. It can iterate over the fields of the argument-object, like  {x:1, y:2}.

You could't really do such an expansion with, unless you start adding the method "map()" to all built-in prototypes in JavaScript. That is a possibility but there's no need for that if we can make treat different types of arguments in different ways. The area of the standard library that needs to be extended this way stays smaller, and you choose and alternative method-name to use as desired. You can install it as  Function . prototype . map9() if you wish to use a more unique name

With this re-arrangement there  seems to be no reason why the argument could not be a non-Array "object". Which leads to the further question: What else?  What are the argument-types that could be passed to Function .prototype .map, to accomplish something useful, some economies of the amount of code you must write, read, and understand?  What should be  the behavior of 'map' with such possible argument-types?


The previous blog-posts described  three argument-types so far: Array, (non-Array) Object, Function. Yes. can also take a function as its argument, the result being the "composition" of the two functions. And you can compose a whole series, a "pipeline" if you will:  funkA . map(funkB) . map(funkC) ;

But turns out there are still a few more argument-types with different, useful  behavior. In the end, currently "fpmap" now supports the following behaviors on the following six (6) argument-types:

A) Array

Like standard but with recipient and the argument-types switched.

B) Object

Similar to Arrays but iterates over named properties of the object rather than array indexes.

C) Function

Implements function-composition. Like:  var result =  funkA . map(funkB) . map(funkC) ;

D) RegExp

Returns a function which can be used to Iterate over all matches of a given Regular Expression for any string-argument.

E) Number

Returns a function which when given an initial argument will call the source-function with it, then call it again with the results and so on N times, where N is the number that was given as argument to fmap(N). Naturally requires that the source-function result-type is the same as its argument type. Useful for creating numeric series like Fibonacci's but also for building arbitrary recursive data-structures.

F) String

Iterates by repeatedly calling a function that incrementally consumes parts of the argument string, in effect parsing it according to the language specified by the recipient-function.


What unites the different argument types described above is they are all used in the same manner, as argument to So it's kind of easy to remember how to use them, if not exactly what each of them exactly does.  But that you can look up from documentation.

For detailed documentation of the above and other features of fpmap() see the unit-tests-file fpmap_test.js. Tests don't lie. The code of  the tests serve as examples of how to use fpmap() with different arguments, and what to expects as result. There's also explanatory comments. The of course is a good source for documentation  as well.

Could there  still be other additional, useful argument-types besides the above? Possibly. But the above is a good start.



Copyright © 2017 Panu Viljamaa. All rights reserved unless otherwise noted.
Reuse of source-code in this blog-post is allowed under the terms of 
Creative Commons Attribution 4.0 International (CC BY 4.0) -license 

Thursday, January 19, 2017 III

This is starting to sound like the band Chicago. First they came up with the album "Chicago", then "Chicago II",  then "Chicago III", and so on.  I want to assure you this is the last blog-post in my series of "" -blog-posts.  But this needs to be written ...

If you want to catch up with the previous episodes, they are  and II.


So can take as argument either an Array OR any (non-Array) object, and knows how to handle them appropriately. This raises the question are there any other argument-types it could beneficially handle in a similar or at least somewhat coherent manner? What if we gave it a Function as an argument? What should that do? That is the subject of this 3rd blog-post in this series, which I aim to make short, not a double-album ...

We can look for answer on what should do when given a Function argument by looking at the  type-signatures of the two previously provided extensions:
  • (Array)   ->   Array
  • (Object)  ->  Object
From the above, an answer suggests itself:
  • (Function)  ->  Function

I think it is clear that should return a function, to preserve commonality with the other two cases.  But what function?  Notice this should be a method of any function, taking as argument some other function. What should the resulting function do, in general?   What's the most basic way to use two existing functions to produce a third function as a result?

To make the question more concrete, if
  funkA . map (funkB) -> funkC

then how should we produce funkC from funkA and funkB?

The best answer I believe is "Function Composition".  The argument to funkC is first passed to funkA, whose result is then passed as argument to funkB, whose result is then returned  finally as the result of funkC.

Note that this puts some constraint on the type signatures of functions funkA and funkB to be combined: It must be possible to call the second function funkB with the result of the first function funkA. We  need to be aware of this constraint when we go about our jolly ways of combining functions.

However there is one thing we can do to make different functions more "recombinable": Allow a function to return undefined IF it does not know how to handle its argument - OR if it more simply wants to state the answer is undefined.  For instance if you try to divide something by zero it makes a lot of sense to say the answer is undefined.

If we allow for undefined results then the combination rule can be amended as follows:
IF the first function funkA returns undefined, the second function funkB is NOT called with it and  the result of funkC will be undefined as well.


The first example below shows how it is possible to "map a function to itself". This is possible IF the argument-type and result-type of the function are the same:

  var times8 =
  ok (times8 (1) === 8 );
  ok (times8 (2) === 16);

The function double() expects a number as argument and returns a number that is double the argument, so this is clearly the case here. And clearly there is no limit as to how many times we can combine such a function with itself. The external inputs just keeps traveling though the "pipeline" created by the combination, doubling in value at each stage. You can think of the above example as there "amplifiers" connected in series to produce and 8-fold increase in the volume of our album " III".

The second  example shows how we can take advantage of the "Do not pass undefined information on" -amendment we gave to our function-composition rule.

Function "odd()" returns its argument number if it is odd, else it returns undefined. If we combine it with the function double() we get double the argument for every odd number, and undefined for every even number given as argument. From that the following ensues:

  var doubleOdds     =;
  ok (doubleOdds(0) === undefined);
  ok (doubleOdds(1) === 2);
  ok (doubleOdds(2) === undefined);
  ok (doubleOdds(3) === 6);

 function odd (n)
 { if (n % 2) {return n}
 function double (n)
 { return n * 2;
 function odd (n)
 { if (n % 2) {return n}
 function even (n)
 { if (n % 2 === 0) { return n;}
 function ok (b)
 { if (!b)
   { throw "assert failed";


The full  source-code and tests for which implements the examples in this and previous blog-posts is available at GitHub and also at the Node.js npm -repository. The latter means that if you have Node.js installed you can get the code simply by executing:
  • npm install fpmap
If you plan to use this code on client-side JavaScript and don't have Node.js installed you can get it by downloading from GitHub (see "6. LINKS" below). The GitHub  -page also shows you more extensive test examples than above, so it may be worth a look.


So what have we now?  We have a function you can use wherever you use functions, to  transform and filter both Arrays and Objects. And by passing in a function as argument you can now do also "function composition".

To avoid any ambiguity,  let's refer to the implementation of discussed in this and previous blog-posts as "fpmap". Since that name now exists in the global npm-registry, it's a fairly good unique name for it.

One potential issue you might have against using fpmap is that it requires an addition to the JavaScript built-in object Function.prototype. This is potentially problematic if multiple sources provide similar additions to the same built-in objects of JavaScript. Something named might even be part of the EcmaScript -standard one day, who knows.

To make potential name-conflicts less of a problem, our implementation "fpmap" will cause an error if you try to install it but it detects that Function.prototype already has the property "map" . You will then see an error so you will immediately know there's a conflict.

What you can do then is install "fpmap" under a different name, say "map2". We propose other writers of base-object extensions should follow the same convention:  Never assign a property to built-in JavaScript objects if they already have it,  and always provide a way for the client to choose the name they want to install the extension as. The -file on GitHub gives an example of how to install "fpmap" under a different method-name in Function.prototype.



Copyright © 2017 Panu Viljamaa. All rights reserved unless otherwise noted.
Reuse of source-code in this blog-post is allowed under the terms of 
Creative Commons Attribution 4.0 International (CC BY 4.0) -license 

Wednesday, January 11, 2017 II


In the previous blog-post titled  I proposed  that Functions in JavaScript should have  the method "map()" like Arrays do, allowing you to process each element with a function instead of the longer and more complicated for-in -statement.  is called like: The proposed

Apart from the syntactic difference of reversing the roles of argument and recipient, also removes all undefined elements from the result. That makes it suitable for not only transforming every element of an array, but also for filtering out some of them.

In this  follow-up I present one more feature differentiating from Its ability to iterate over non-Array Objects.



The new behavior in version-2 is exemplified by the following few lines of code The function ok() is my simple ad hoc assert-utility which  throws an error if called with anything untrue.
 var o  = {x:1, y:2, z:3};
 var o2 = (o);

 ok (o2.x === 1         );
 ok (o2.y === undefined );
 ok (o2.z === 3         );

 function odd (n)
 { if (n % 2) {return n}

 function ok (b)
 { if (!b)  
   { throw "assert failed";


You might write a function that takes as argument an object with fields x, y, z whose values must be numbers, representing a point in three-dimensional space. You then might want to write a short routine that checks that x, y and z really are numbers, all of them. 

Assuming your argument is named 'coordinates' you could write checker-code like:

  // var coordinates = {x:1, y:2, z:3};
  for (var p in  coordinates)
  { assertIsNumber (coordinates, p); 

But aren't you tired of writing for-loops already?  

Having installed, you can write the equivalent of the above as:

  // var coordinates = {x:1, y:2, z:3}; (coordinates);

In both cases the checker-function could be defined as:

function assertIsNumber (n)
{  if (typeof n === "number") return;
   throw "Not a number: " + n;


Below you see the JavaScript code for installation, tests, and implementation of this new improved version:

// ------------------  cut here -------------------------

// 1. INSTALLATION: = map2;

// 2. TESTS:
test_map2 (); 

function test_map2 ()
 // 2.A:  FOR ARRAYS:
 var a  = [1,2,3];
 var a2 =;

 ok (a2[0] === 1);
 ok (a2[1] === 3);
 ok (a2.length  === 2);

 // 2.B:  FOR OBJECTS:
 var o  = {x:1, y:2, z:3};
 var o2 = (o);

 ok (o2.x === 1        );
 ok (o2.y === undefined);
 ok (o2.z === 3        );

 var coordinates =  {x:1, y:2, z:3}; (coordinates);

 // Next would fail because y-value is not a number:
 // ({x:1, y:"s"} );

 return;  // from test_map2()

 function ok (b)
 { if (!b)  
   { throw "assert failed";

 function assertIsNumber (n)
 { if (typeof n === "number") 
{ return n;
   throw "not a number: " + n;


function map2 (objectOrArray, thisArg)
  var resultA, resultB;
  if (objectOrArray.constructor === Array)
  { return (this, objectOrArray, thisArg);
  return (this, objectOrArray, thisArg);

    function map2_object (anObject, thisArg)
    { var result  = new anObject.constructor(); 
      for (var p in anObject)
      { var v = this (anObject[p], p, anObject) ;
        if (v !== undefined)
        { result  [p] = v;
      return result;
    } // end map2_object()

    function map2_array (anArray, thisArg)
    { resultA = []  (anArray, this, thisArg);
      resultB = [];
      for (var j=0; j < resultA.length; j++)
      { var e = resultA[j];
        if (e !== undefined)
{ resultB . push(e);  
return resultB;
     } // end map2_array()

   } // end map2()

// ------------------  cut here -------------------------


Copy the code from Section 3. to the start of your JavaScript-file. After that you can call  'map()' on any function with any []  OR any {} as argument.

What name to use to install this function as a method in Function.prototype is of course up to you. In my own projects I've chosen to install it as 'map' because of  its close proximity in  behavior to the already standard


Iterating over non-arrays is a frequent task in JavaScript. The for-in statement which does it however quickly becomes tedious to write, again and again. JavaScript does have the which makes it simpler to iterate over Arrays. can not be used for non-arrays because it is not! But with you can perform the more general task of calling map() on a Function, to process Objects and Arrays alike.

Yes, we are aware there is also, but that is not quite the same as For one thing it doesn't remove undefined values and it only works on instances of Map. And it returns undefined.

For more about, see my previous blog-post

Copyright © 2017 Panu Viljamaa. All rights reserved unless otherwise noted.
Reuse of source-code in this blog-post is allowed under the terms of 
Creative Commons Attribution 4.0 International (CC BY 4.0) -license 

Thursday, January 5, 2017


This blog-post unofficially proposes a new standard API-function for JavaScript: While it may not become part of any official standard ever, you can use it to make your code simpler in some cases, by copying the code for it from below.

The specification for is simple because it is stated in terms of  the existing

  • IF for any array arrayX and function functionX the expression ( functionX, arg2 )  produces result arrayY, THEN ( arrayX,      arg2 )  must produce the same result except  without any undefined elements.


[1,2,3].map(doubleF);   // -> [2,4,6], standard[1,2,3]);   // -> [2,4,6], proposed
ifOddF .map([1,2,3]);   // -> [1,3]  , proposed

function doubleF (currentValue, index, array)
{ return currentValue * 2;

function ifOddF (currentValue, index, array)
{ if (currentValue % 2)
  { return currentValue;


Below shows a simple implementation of The first paragraph of code does the equivalent of what would do, if given the "recipient-function" as its argument. The 2nd code-paragraph removes undefined elements before returning the  result without them: = 
function ()
{ var args    = [] (arguments);  
  var args2   = [this].concat (args.slice(1));  
  var result1 = [].map.apply  (args[0], args2);  
  var result2 = [];  

  for (var j=0; j < result1.length; j++)  
  { var e = result1[j];    
    if (e !== undefined) 
    { result2.push(e);    
  return result2;


Below code-example shows the function filesOfCurrentDir()which  returns an array containing the absolute path-names of all files in the current directory in Node.js. We want to know what are the files apart from sub-directories. Node.js does not have a simple API for doing this, so we need to create our own.

Node.js does have the  function  Fs.readdirSync() for listing the elements of a directory-path given as argument. That returns an array of the names of the directory components including files and the sub-directories. But we want more than the names, we want path-names which uniquely identify their corresponding files.   

The solution is to create another function  ifFile() and call the standard function bind() with it as argument to return a derived function which will always call the original function with the 2nd argument of bind() as the first argument of  ifFile()That sounds complicated.  Therefore, it's worth the while to try to make everything else as simple as possible. We can use to help do that.   

The code for filesOfCurrentDir() below shows two ways of trying to get the files in the directory, the first of which doesn't quite work:

  var filesA = fileAndDirNames                         // A
.map (ifFile.bind (null, currentDir));  

Above uses the standard to call  a function derived with bind() from ifFile() for each file- and directory -name  in the current directory. We want the result to be an Array of the absolute path-names of files in the directory.

But there's a problem: ifFile() is meant to filter out  directory names by returning undefined if a path-name points to a directory. Therefore filesA now contains the absolute path-names of every file in the directory PLUS an undefined value for every sub-directory of it. 

We could easily write a loop for removing the undefined values. However we get that done automatically if we use instead, like this:     

var filesB = ifFile.bind (null, currentDir)            // B
                   .map  (fileAndDirNames);    

So one reason to use is that it does more, it removes undefined values automatically. Which is what you usually want, not much you can do with undefined array-elements. If you do want undefined array-elements you can always fall back on to give them to you. In Object Oriented Programming you can have your cake and eat it too!     

A more fundamental reason I prefer over its Array-cousin  in this case, is seen by comparing the code-structure of  the  two alternatives. The first one contains nested parenthesis, the second doesn't!

Trying to understand an expression that contains nested parenthesis is more difficult and laborious and easier to misunderstand. When reading the first example (A) from left to right you can't understand what the whole expression does without first understanding what the argument expression does, then you have to "back up" to restart calculating the value of the containing expression. 
Whereas reading the 2nd expression (B) from left to right you can parse and understand what each step independently does because there are no "inner expressions".  Just know that the data flows from left to right, like in a pipeline.

You could rewrite the first example to get rid of nested parenthesis by taking the inner expression out and storing it into a temporary variable which you then use as argument. But then you would have to make a similar "jump back" to recall what was the value you stored into the variable. And more variables means more locations that can hold a wrong value. There's a cost to every variable.

function filesOfCurrentDir ()

  var Path            = require('path');  
  var Fs              = require('fs')  ; 
  var currentDir      = __dirname      ;                
  var fileAndDirNames = Fs.readdirSync (currentDir);
  var filesA =  fileAndDirNames  
.map (ifFile.bind (null, currentDir));
  // Above ALMOST does it, but the array 'filesA' 
  // contains undefined for each sub-directory. 
  // Using we get rid of
  // those automatically. NOTE: Above call should
  // be removed after studying it and understanding 
  // why it does not work.       

  var filesB  = ifFile.bind (null, currentDir)       
                    .map  (fileAndDirNames);    
  return filesB ;

  function ifFile (currentDir, fileOrDirName)
    var path = Path.join(currentDir, fileOrDirName);
    if (Fs.lstatSync(path).isFile())    
    { return path;                    
    // else: return nothing, a.k.a undefined



The JavaScript API of Function would seem to be an obvious candidate for extension, for improved support for Functional Programming in JavaScript.

The downside of per-programmer extensions which add something to the basic JavaScript classes of course is that if everybody comes up with their own extension, there will be conflicts between the implementations.  But the extension proposed above is simple and  benefits of it substantive enough that I've found no reason not to use it.

Having available in addition to helps us get rid of nested argument-expressions without having to add extra temporary variables which would require more lines of code.

Stripping away undefined values allows us to use for not only transforming arrays but also for filtering out elements from the results of the transformation.

Note what the function presented here does is in no way dependent on what method-name of Function.prototype it is installed as. You can decide which method-name to use for it on a module-by-module basis. What an extension-function does is dependent on which prototype it is is installed in.


Copy the code-segment from Section 3. to the start of your JavaScript-file. After that you can call  'map()' on any function with any array as argument.


A newer  blog-post II  provides and describes an improved implementation for, with the ability to loop over non-arrays as well


If you 're not familiar with some of the external functions used in the code-example you can find their documentations here:


2. Function.prototype.bind:

3. fs.readdirsync:

4. fs.lstatsync:

Copyright © 2017 Panu Viljamaa. All rights reserved unless otherwise noted.
Reuse of code examples in this blog-post is granted under the terms of 
Creative Commons Attribution 4.0 International (CC BY 4.0) -license 

Friday, November 25, 2016

Getting the semantics right

In natural language "Getting the semantics right" means making sure other people understand you. It means picking the right words and putting them in right order, taking into account your intended audience of course.

In another sense you always  get the semantics "right" in natural language.  The semantics of a sentence is what it is, it is the perceived meaning of the sentence. There may be more or less of it however.  You don't choose the semantics, it chooses you .  Your sentence could be ambiguous, or (which is not the same thing) it could mean different things to different people. So yes, getting the semantics  wrong  means saying something that is either not understood at all, or easily misunderstood. ("Oh Lord, please don't let me …")

In programming "Getting the semantics right" is a more difficult thing. Not only do we have to pick the right statements to get our intention across to the machine.  We must INVENT new words, new APIs. The name of an API-method is like a word, a call to that API with some arguments is like a sentence.

Getting the semantics of new API-words and sentences right means their meaning, their effect must be easily understood in relation to other existing and new words and sentences and ways of using them. Getting the "API sentences" right is sometimes called "Fluent programming style" (

"Fluent" means easy to read, easy to understand, using exactly the right combination of words to convey your meaning with nuance and precision. Being fluent means using the language of your choice like a native speaker would.  In programming we must invent languages that _can be_  used fluently. But in programming there's more to it than just fluency because your API is creating a new language, there are no native speakers of it.

We could name our APIs arbitrarily, say with increasing numbers, API-1, API-2 etc.  Then "getting semantics right" would simply mean calling the right APIs. But we would never do that . Compilers do that. They turn our meaningful API-names into addresses of binary code entry-points.

Making API-method-names and  the possible ways of using them easy to understand means they must correspond to some real-world analogue. Example: "Search-Trees".  When they do  we can understand them in terms of that analogue, consistent with how we understand other words and sentence in terms of the same model. But it's not easy to come up with cohesive set of new words where understanding one term helps to understand the others.

In summary in programming getting semantics right means not only calling the right APIs but also coming up with API-method-names that are meaningful and consistent with other API-methods we "invent".  In programming there's more to "getting semantics right", than just picking the right words in right order. #fluent_programming

© 2016 Panu Viljamaa. All rights reserved

Wednesday, November 16, 2016

Why Programming Is Difficult

Programming is difficult because you can not understand a program piecemeal. You can not ultimately "Divide and Conquer" a program, although you must try your best.

You try to divide your program into independent "modules" to manage the complexity of understanding it.  But that can not fully solve the problem because what the program does is caused by interaction of its components.

There is no single component that would or could be "The Interaction". Each component must do its  part to interact with others.  In doing so it must assume something about those other parts. This makes it difficult to change any part of the program, changing it can break the assumptions other parts make about it.

Software Engineering is about trying to devise ways to divide programs into minimally dependent parts, and also to divide the problem of creating programs into multiple  more or less independent parts, and making it easy to understand what those parts are, and what are their dependencies, the interactions between them. That's a mouthful, right?  But that just indicates what a big task it is.

In the end that can not be done as well as we'd like  because each part must interact with others, it must encode assumptions about  other parts  to be able to  interact with them.

In this way Software Engineering is like other engineering disciplines. We're trying  to make programs stronger, less likely to collapse like house of cards, cheaper, faster, easier to maintain, adapt and reuse for different purposes.. There is no ultimate solution to this, only better solutions to be discovered. No Sorcerer's Stone. No mythical Silver Bullet to kill the "Beast of Interactions". But there is progress I believe, as we gain a better understanding of what Software Engineering is, what it can and cannot do.

© 2016 Panu Viljamaa. All rights reserved