‘Internet search engines against knowledge sharing,’ says logistic model

The internet is changing. Everybody knows that, especially mathematicians and advanced users…and so do pigs. Specifically the way users interact with search engines has been changing in the last decade.
When Internet search engines used unbiased algorithms every user who searched with the same keywords, received the same result. This should be the way of searching for something. Knowledge is an absolute concept, or at least it should be.
Today, most search engines are using algorithms designed around the user who searches a  customized way. Thus, different people get different results when they search for the same thing.
As Eli Pariser said in a recent talk “people receive things they want to see, not what they need to see”.
I was very impressed when I used two different accounts, my flatmate’s and mine, to carry out searches about distinct topics he regularly searches but I don’t. Google produced two lists of results for the two accounts which were quite different. Those differences were generated by re-positioning some websites in the first indexes for his search but not for mine.
I found this to be alarming and I had to have a break with some Panini before starting again.
Basically, this means that there is much less knowledge sharing and if we push this concept to the limit, people on the Internet will end up sharing their knowledge and searching in their own buckets in the long term.
Ok! Piggy has to explain this very deep concept (oo)

Imagine this scenario:

  • x(t) represents the number of people who know something new (for example they publish websites that Google can crawl and make them available for potential searches made by other users)
  • t is time of course

My assumptions are that

  • If someone knows something, they don’t simply “forget” that thing (true, unless these users have serious problems that I will not discuss here)
  • Someone can learn something she doesn’t know from someone else

One of the most commonly used models to explain this kind of dynamic (and many others like population dynamics) is the logistic curve proposed by Belgian mathematician and demographer Pierre-François Verhulst in 1825.
The differential equation that regulates the model is


Let’s rethink this in Internet terms.

  • x(t) is the number of people who know something new a.k.a. those who contribute to the Google database by posting/creating new content
  • R is the learning rate (for our purposes, I left it 1)
  • k is the overall Internet population who makes use of this search engine (I can leave it as a parameter)

The maximum of x'(t) occurs when x(t) = k/2, i.e. the number of people who contribute is half the Internet population (this keeps knowledge sharing at the maximum rate).

But filtering the search and using an algorithm that gives results based on other factors such as the user’s private interests, one’s  search history or the interests of one’s friends, irrespective of x(t), will most certainly reduce the number of contributors x(t).
That is, it will most certainly decrease the rate of knowledge sharing.

Personalized search might be useful if and only if the majority of the results come from an unbiased algorithm.
But is this really the case?

Dynamical l(oo)ve

My dear flatmate broke up a while ago with his girlfriend and of course he had his sad period to deal with, crying his pants off and drying his tears. He didn’t even eat that much. So I had to eat a bit more than usual, not to throw things away, of course.
When I was thinking about how to dress my 42nd sandwich I remembered about a mathematical way to explain the situation to my poor flatmate.

What is love?
Love can be thought as a dynamical system that, exactly like any dynamical system starts from some conditions, evolves, enters a regime or dies.
So, for instance, a couple who starts dating, may evolve by going to the cinema, having some coffee together and some dinners.
Since I am a shy pig I will not go further and will stop at dinners, although I can barely imagine how differently this couple may evolve…

If there is a dual interest the couple will end up in a regime in which things will happen and they could love each other, let’s say, indefinitely. This is a successful couple.
If there is no interest or something bad happens (like falling in love with someone else, or not having a nice feedback from each other) the couple dies and they split. This is an unsuccessful couple.
In dynamical systems these situations are called equilibria which attract or reject the trajectories of the system based on the type of the point. A stable point attracts. An unstable point rejects. A saddle point attracts and rejects making the trajectory pass very close to the point but not exactly through it.
I was thinking about a simple way to explain all of this and ended up to a system of differential equations.
I first want to call the couple of my explanation with two fictitious names like… I don’t know… Laura and Frank.
The system used to explain what’s going on looks like this:

 Here is a picture of me while I am explaining to my flatmate.

No panic! I can explain.

 represents how much Laura loves Frank (actually loved (oo) and
represents how much Frank loves Laura
 are the forgetting coefficients of Laura and Frank. This is the oblivion, a feeling that humans have against each other and which make them forget.
Pigs don’t have that. That’s why we are considered the most pleasant animals in the world :) Ok, we eat a lot and we don’t wash. But we never forget (oo)

Here comes the best part.

  are two functions which regulate the reaction of Laura to the love of Frank and the other way round, the reaction of Frank to the love of Laura. This is important because it is the main component to explain a kind of mutual love.
Finally  are two quantities which represent the appeal for Laura and Frank respectively.
Objectively, they are very pretty although Frank is not exactly my type and Laura is a bit too much white.
The reaction function can be a very simple thing like a straight line (the most linear system ever). But I decided to complicate things a bit more and choose a function which is closer to human behaviour and goes like this

This function is cool because it says that if Frank loves a lot, Laura reacts positively but below a constant value R+ (instead of an infinite reaction which means dying of too much happiness). If Frank doesn’t love Laura, she reacts bad (up to R-) without killing herself.
The same is for Frank when Laura loves or doesn’t. If I used a straight line for this function their reaction would have been proportional to the love received. Which is not generally true for humans. It’s true for pigs. Actually, we can love also more than the love we receive.
That’s why they say we are lovely (oo)

Analytically, this function may look a bit difficult. But just skip this if you get bored. It’s really not important.

With this said I solved this system with the aid of my flatmate’s computer to draw some c(oo)l graphs about his love.

Since I know Frank and Laura I could fill all the parameters needed to graph the system. Basically, I set the parameters to represent a specific couple.
Laura loves to be loved and hates to be hated. In mathematical terms she is a secure individual.
Frank reduces his reaction when he receives too much pressure. He is a non-secure individual.
The system has two stable equilibria, one negative and one positive, and a saddle equilibrium.

What this means?

Until they love each other enough their story is successful because they are going toward the positive stable equilibrium.
But if they react bad to the love of the other they are directed towards the negative stable equilibrium which means they split.
I want to give you some numbers.
Laura loved him with a positive amount of love and everything was just fine. She could also have loved him with a negative amount (which means not loving him), as she did. Humans have these periods…
She could have loved negatively up to a certain amount. But not too negative!!
In numerical terms she loved -1.8. Everything was still fine. But when she loved -2.3 (just a bit less), B(oo)m! They started driving towards the negative equilibrium.
This change of behaviour is called fold bifurcation.
But for what matters they broke up and I have nobody who cuddle me anym(oo)re!

Sad Piggy (who needs some sweets to recover)

Live from the geekest of places (so far)

Dear public, at the moment I am very busy working on this project about Operating System Virtualization my flatmate wants to deliver before going on holiday. Since I wanna go on vacation as s(oo)n as possible I decided to help him.

Plus, the eng. was pushing me hard to publish a picture… and here you can see me while I am trying to write some C code. Me @work
I find this mouse  very heavy for me! Ok! Blogging is over and I go back to work.  I promise to publish a nice conclusion about l(oo)ve in my next post.

Creativity-enhanced sandwiches

sandwichesI just came back from the PhD defence of my flatmate’s collegue… It was not that interesting to be honest. But I think it was because of the subject (which was not related to math).
The reception was good. I had a lot of super fat and piggy sandwiches (○○). But haven’t drunk alcohol because I am studying a way to convince my flatmate about some love affairs, I will post soon.
My flatmate – who is an engineer – says I better post a picture of me. But I am a very shy pig and have to get comfortable with computers and cameras.
Moreover, I don’t trust engineers that much. They’re always so pragmatic… I think they should relax a bit and think more creatively… like I did when I was thinking about those super fat piggy sandwiches which were actually only healthy appetizers :(


Hello dear.
I just finished setting up the appearance of this blog. Will work on the content from tonight… although I already have cool stuff in mind.
I will use this space to write about my adventures in the human world, my travels, hobbies and several curiosities about math and computers.
As a pig I am easily distracted by food. Indeed now it’s dinner time.

Groo Groo!