I'm not going to lie and say that I understand anything that Manovich is trying to portray, but I will attempt to define these key principles and not sound like a total idiot so here goes!

The principle of numerical representation states that new media objects are described using mathematical function.  When new media objects are created on computers, they generally originate in numerical form and new media becomes programmable through algorithmic manipulation.

The principle of Modularity is defined as the 'fractal structure of new media" meaning that new media elements are represented as collections of discrete samples.  These samples can be assembled into larger objects, but still maintain their separate identities. These are stored digitally so that it can be used in different media objects.  This makes me think of things like prezi presentations.  While it is one presentation, it consists of various multimedia elements that each are defined on their own, and can be edited or eliminated without difficulty.  I know that is really vague but I don't really understand much of it so bear with me.

Now using these two principles, we can now allow for the automation of many operations involved in media creation.  This means that one can modify or create a new media document by using templates or simple algorithms   Many programs on the computer, for whatever document that is being created have automated features set up that allow things to be automatically created without having to manual program it.  Just like any computer game or computer program, there are certain features that allow specific things to happen,  For example, in Microsoft Office Excel, certain mathematical functions are set up so that if you need a certain thing to happen you pick from an automatic formula and make adjustments where needed and it does all of it for you.  It needs for an interaction from the user, and then the automation of it kicks in.

Variability is used to define the liquid nature of new media.  While old media could be fixed and could be multiplied off of its master.  New media is different in that it gives rise to many different versions.  It builds on itself as it progresses.  Variability would not be possible without modularity where these digitally stored elements can be assembled into many different sequences and can be created and customized easily.  This makes me think about the website we used in class the other day where we could see a screen shot for old websites.  They are updated and made better as they move along.  Pepper even said some images will not be shown because they were not stored correctly, so this shows the variability of these new media websites.

Transcoding gives a great summary of all we've discussed.  New media consists of two layers, the cultural layer and computer layer.  The cultural layer and computer layer influence each other and result in a new computer culture.  "A blend of human and computer meanings, of traditional ways in which human culture modeled the world and the computer's own means of representing it.

I do not pretend to even slightly understand what in the world this chapter is talking about.  Yes, I have written this blog post, but no, it still doesn't make great sense to me.  I hope you all can help me understand better through your posts.  Sorry, that I am of no help!