23 February 2015

How a mutually retweeting network can make a hashtag trend in Twitter

A. Problem

If you have a Twitter team who mutually retweet each other's posts, and each member posts the same number of original tweets per day, how large must the team be in order to send one tweet per second, one tweet per minute, or one tweet per hour in your chosen hashtag?

B. Solution

Suppose you have two groups of people that shall implement your Twitter campaign to promote a particular hashtag:
  • Influencers--Their task is to write original tweets using the hashtag.
  • Retweeters--These are the Tweet amplifiers.  Their job is to share the tweets of the Twitter influencers. They may be a pure retweeter, i.e. he doesn't write his own tweet, or he may also be an influencer, too.
One way to think of this is to think in terms of a Twitter army. Your influencers are your standard bearers. Your retweeters are your foot soldiers. Once an influencer raises his standard by posting a tweet, the retweeters flock to his banner and retweet his post. After the all the retweeters have done their duties, another influencer raises his standard by making another tweet and the process repeats itself. This may not be a good strategy in real war, because foot soldiers take time to assemble under one banner. But in Twitter, retweeters can repost a tweet in less than one minute. And if the influencers and retweeters can post a significant number of tweets per day, then the can make a hashtag trend in Twitter, i.e. its number of tweets per day is greater than those of other hashtags.
Let $n_I$ be the number of Influencers and let $n_R$ to be the number of pure Retweeters. If $n_{T/I}$ is the average number of original tweets per influencer per day, then the total number of tweets that your influencers can write is $n_{T/I}n_I$ and the total number of retweets is $n_{T/I}n_I n_R$. Thus, the total number of tweets that your marketing team can produce per day is \begin{equation} N = n_{T/I}n_I n_R + n_{T/I}n_I = n_{T/I}n_I (n_R + 1). \end{equation} For example, if you have 5 influencers tweeting 6 times a day and you have 10 pure retweeters, then the number of tweets you can produce per day is $6(5)(10+1) = 330$.

If you include your influencers as part of your retweeter team, provided that they cannot retweet their own posts, then we need to modify our formula to \begin{equation} N = n_{T/I}n_I n_R + n_{T/I}n_I + n_{T/I}n_I(n_I - 1) = n_{T/I}n_I(n_R + n_I). \end{equation} For example, if you have 5 influencers tweeting 6 times a day and you have 10 pure retweeters, with your influencers allowed to retweet posts of other influencers, then the number of tweets that your marketing team can produce per day is $6(5)(10+5)= 450$.

One special case is when you have no pure retweeters, $n_R=0$, so that your influencers become a mutually retweeting network. Then the number of tweets your team can produce per day reduces to \begin{equation} N = n_{T/I}n_I^2. \end{equation} That is, the number $N$ of your tweets per day is proportional to the number $n_I$ of your influencers and the number $n_{T/I}$ of tweets per influencer per day. For example, if you have 5 mutually retweeting influencers with each influencer posting 6 original tweets per day, then the total number of tweets your team can produce per day is $6(5^2)=150$.

Now, let us assume that your team consists of $n_I$ mutually retweeting influencers who can produce a total of $N$ combined tweets and retweets. The time interval $\Delta t$ between tweets that your team produced for a particular hashtag for one day would then be \begin{align} \Delta t &= \frac{t_D}{N} = \frac{t_D}{n_{T/I}n_I^2},\\ \end{align} where $t_D = 24\ hr = 1,440\ min = 86,400\ s$. Solving for $n_I$, we get \begin{equation} n_I = \sqrt{\frac{t_D/\Delta t}{n_{T/I}}}. \end{equation} That is, the number $n_I$ of mutually retweeting influencers to produce one tweet every time interval $\Delta t$ is inversely proportional to the square root of the the number $n_{T/I}$ of tweets per influencer. For example, if you want to produce a tweet every hour at a rate of 6 tweets per influencer, then $t_D/\Delta t = 24$ and the number of mutually retweeting influencers needed is $n_I = \sqrt{24/6} = 2$. If you want to produce a tweet every hour, then $t_D/\Delta t = 1,400$ and $n_I = \sqrt{1,400/6} = 15.5$ influencers. And if you want to produce a tweet every second, then $t_D/\Delta t = 86,400$ and $n_I = \sqrt{86,400/6} = 120$ influencers. In other words, you can build a mutually retweeting army of 120 men, each tweeting 6 times per day, to produce one tweet per second for the hashtag of your choice.

15 February 2015

4 media quadrants according to traditional-modern and unsocial-social classifications

Many believed that Traditional Media and Social Media are distinct and opposite media forms.  Traditional media is said to be TV, radio, and newspapers, while social media are Facebook, Google+, Twitter, Linkedin, etc.  But I think this is a mistaken distinction.

Traditional and social are not opposite adjectives.

Traditional is a temporal adjective, which is associated with a time dimension, e.g. the past. Thus, the opposite of traditional is modern or new, e.g. the opposite of Traditional Catholicism is Modernism (includes New Age teachings) and the opposite of Traditional (Classical) Physics is Modern Physics.

On the other hand, social is a spatial adjective which describes the connections between pairs of points (persons).  Thus, the opposite of social (many connections) is anti-social or unsocial (no connections).  Antisocial may be the right word, since antiproton has all the properties of a proton, except for a charge, in the same way an antisocial is repelled by engagement with others.  Or perhaps unsocial may sound better: the "un" or "not" does not have the violence of "anti", as shown, for example, in St. Paul's description of love (happy Valentine's day!):
Love is patient, love is kind. It is not jealous, [love] is not pompous, it is not inflated,d it is not rude, it does not seek its own interests, it is not quick-tempered, it does not brood over injury,e it does not rejoice over wrongdoing but rejoices with the truth. It bears all things, believes all things, hopes all things, endures all things.(1 Cor 13:4)
In summary, the opposite of traditional is modern or new, while the opposite of social is antisocial. If we define traditional-modern as the temporal $t-$axis and the antisocial-social as the spatial $x-$axis, then we see that there are four spacetime quadrants where a particular media can fall:
  • Traditional Unsocial Media (TUM)
  • Traditional Social Media (TSM)
  • Modern Unsocial Media (MUM)
  • Modern Social Media (MSM)
Let's discuss these media quadrants one by one.

1. Traditional Unsocial Media

This is the media of autocratic states, such as those under Communist and Socialist rule during the Cold War before the Internet era.  That is, the government blasts the message in traditional media (TV, radio, and newspapers) and the people are expected to follow them or at least show no resistance. 

Many TV, radio, and newspaper also operate as traditional antisocial media.  They just blast off the message without allowing the audience to use their platform to send a feedback.  At most, the only feedback that traditional antisocial companies get is binary: whether a particular group of people listened to them or not at a particular time of the day, i.e., whether the people either turned the TV or radio on or off, such as done by ACNielsen ratings.

2. Traditional Social Media

This is the media of companies that allow their audience some feedback in media's owned platform.  The image that we can use is a concert singer.  If the concert singer just sings and delivers his piece, he is fulfilling a traditional antisocial media role.  But if he engages with his audience by letting them sing parts of the song or even invite one person to sing with him on the stage, this is social media.
  • Some traditional TV companies have adapted to the ubiquity of text messages and smartphones, while still retaining their traditional media platform, e.g. the audience votes for the person who shall win or lose using text messages. 
  • Some FM radio show hosts reads messages from their Twitter and Facebook audience; they also allow some of them to talk live over the phone to ask questions about love, for example.
3. Modern Unsocial Media

According to Wikipedia:
Web 2.0 describes World Wide Web sites that use technology beyond the static pages of earlier Web sites.... A Web 2.0 site may allow users to interact and collaborate with each other in a social media dialogue as creators of user-generated content in a virtual community, in contrast to Web sites where people are limited to the passive viewing of content. Examples of Web 2.0 include social networking sites, blogs, wikis, folksonomies, video sharing sites, hosted services, Web applications, and mashups.
But even with the advent of Web 2.0, some websites still operate as Web 1.0, by not allowing comments on their articles or worse, deliberately filtering out non-spammy negative opinions of the website's articles. Wordpress, for example, allows you to turn off comments on posts and pages.  You'll only hear about comments on your articles from another blog or by word of mouth.

4. Modern Social Media

This is what Social Media as it should be: a democratic marketplace of ideas where people can comment or reply to other people's statements.  Here's a list of social media platforms and their real world equivalents:
  • Facebook: This is a gathering of friends.  You talk in one table; other groups talk in other tables, but you can barely hear them, for Facebook's News Feed algorithm ensures that you only see the posts of people you like most and comment on.
  • Google+: This is a gathering of geeks.  You join communities and talk about specific topics from content marketing to Python programming to Lord of the Rings.
  • LinkedIn: This is a business or scientific conference. You meet people and describe who you are, where you're from, what you did, etc.
  • Twitter: This is the agora or marketplace of the Ancient Greeks where the democracy of ideas is at work.  No one can stop you from sending a public message to another person or brand.  There is no Twitter algorithm to filter out what it thinks are relevant to you or not.  Tweets are received in your news feed in real-time with time stamps.  You say or write your speech in 140 characters or make signboards.
  • Pinterest: This is the collector's paradise. In the olden days, collecting just the domain of stamp, coin, and rock collectors.  Now with Pinterest, you can collect anything through their pictures, such as recipes, gowns, and crafts. You can love the pin, comment on it, or repin it on your boards.   
Ideally all posts are set public and comments are allowed unfiltered. But this is not generally true: there is still selective filtering by friends or circles.  But at least, some persons are allowed to interact with the website, in contrast to Web 1.0 where no interaction is allowed on the platform. Perhaps we can define a metric for the degree of openness or socialness of a website, but we shall reserve this another post.


There are four types of mass media according to their classifications as traditional vs modern or antisocial vs social.  Traditional media are TV, radio, and newspapers, while modern media are Web 2.0 technologies. Social media allows conversations with the audience, while antisocial media restricts or forbids this conversation.  Thus, the four types of mass media are (1) traditional antisocial media, (2) traditional social media, (3) modern antisocial media, and (4) modern social media.

 Media quadrant classification: (1) Traditional Social Media, (2) Modern Social Media,
(3) Traditional Unsocial Media, and (4) Modern Unsocial Media

07 February 2015

Social media discovery models via topical hashtags and social proofs

I have been active in Facebook, Twitter, and Google+ these past weeks, so I'll comment on their discovery models. (I am not yet a power user of Pinterest and Linkedin, so I'll comment on them when the right time comes.) A discovery model is an algorithm that suggests related posts to the user.  This algorithm can take different input variables such as likes, favorites, shares, comments, etc, and outputs several posts in the user feed.

A. Facebook

Facebook's discovery model is primarily on the number of engagements you have on a particular user.  If you like or comment on the post of a particular person, then Facebook will put that person's post on the upper fold of your news feed.  Even the posts that he or she commented or liked will also appear on your news feed. Before, Facebook also provides related posts to articles that you read.  But today I haven't seen any. I don't know how Facebook does this.  Probably Facebook uses the title and the abstract of the articles, then finds a good match. Some of the related articles that Facebook suggests comes outside Facebook, e.g. websites and blogs.  If several of your friends shared the same article, you'll see the same article with attached comments of your friends when they shared the article.  As you can see, Facebook relies much on social proof for its content discovery model.  Of course, you can create hashtags.  But I don't click on hashtags in Facebook and I don't bother creating one.

B. Google+

Aside from your usual news feed from your friends and communities, Google+ has what's hot and recommended.  By hot, Google+ means that it's liked, shared, and commented a lot. By recommended, Google+ means that it's topic of interest is related to what you posted on your timeline. Google + can extract the topic of interest of each blog post from the title and the first paragraph.  This is seen, for example, when you connect your Blogger blog to your Google+ account and set your blog to post directly to Google+. If you do this, then Google+ will extract the paragraph and image snippets, then post the topical hashtags for you.  With this ability to extract the hashtag topic automatically, Google+ can compare different posts with the same hashtag, and use the post with more engagement as the one to show to the user in its discovery model.

C. Twitter

Twitter relies primarily on what user accounts your friends followed or favorited.  It is surprising that Twitter do not use the hashtags much in its discovery model, even though hashtags are organic in Twitter. I think the reason for this is that the Twitter hashtags are too random, such as #howaboutthiscrazyhashtag, so that the number persons using a particular hashtag are sparse and few. But I think Twitter can determine if a user used a trending hashtag, so that the trendingness of the hashtag can be used as a parameter in the discovery model.  For this to work, Twitter may like to adopt the multi-column Pinterest layout for desktop users, so that the eye can scan left to right as it gazes from top to bottom. But perhaps, this may not anymore be necessary, since Twitter has Tweetdeck which has columns on which you can monitor the hashtag of your choice.


No discovery model is perfect, because it depends on the nature of the platform's user base. What may work in one platform, may not work in another.  Topical discovery works well with Google+, while social proof from friends works well with Facebook. But for Twitter, social proof from friends seems not to work. You need to manually click on the Twitter hashtags to see what others wrote about it and participate in the global conversation. You may also use Tweetdeck to monitor the tweets using that hashtag.

01 February 2015

Should you display the publication date of your blog post?

Do you display the date of publication on your content?  And will people in the future dismiss it as old and out of date before even reading it?--M. Ward (Linkedin)

 To answer the question properly, we need to divide it into four sub-questions:

A. Can you remove the displayed date in your content?

I shall only speak for Blogger.  In Blogger, you can remove the date stamp of your blog post by going to Layout, then to Blog Post.  Uncheck the date stamp and save your configuration.  You won't see the date stamp after this.  But the url will still have the date stamp, at least the year and the month numbers.

The other option is to use Pages.  You won't have a date stamp in the url, but you'll just have an ordinary website--a catalog of sorts or a wiki.

B. What are the advantages and disadvantages of having a date stamp on your content?

1. With a time stamp

The advantage of a date stamp is that you to have a sense of history: you see how your writing progressed from seven years ago until today.   Did your style of writing change? How about your topical categories and tagging system? You see your blog as a living organism, with its own persona and mood.

The disadvantage of a date stamp is that your content becomes ephemeral like a flower that blooms today and is thrown to the oven tomorrow.  And if your content is a news report or an opinion piece about a news report, you are morally compelled to provide the date stamps.  If your readers are looking for news, then they would shun your old article at a first glance at the date stamp.  But if your reader is looking for historical facts in order to reconstruct events, the date stamp would help piece together what happened.

2. Without a time stamp

The advantage of having no time stamp is that your blog becomes arranged according to topics, either in alphabetical or logical or networked order, which corresponds to a dictionary, a book, or a wiki, respectively.

The disadvantage of having no time stamp is that you can't call your website a blog.  It's a catalog or wiki, but it can never be a blog, because a blog needs a date stamp, with the newest blog article posted on top followed by the older articles as you scroll down the bottom.

C. How does one make a content evergreen even with a time stamp?

There are four ways:

1. Write excellent prose.  A well-written content transcends time and space, because people would read it again and again for sheer beauty, such as Hamlet's monologue or Saruman's declamation.  And who can forget the simple stories of Christ in the Gospels, such as the Prodigal Son and the Good Samaritan?

2. Write about eternal truths. This can be Euclid's Fifth Postulate regarding parallel lines, Maxwell's Equations in Classical Electrodynamics, the Catechism of the Catholic Church, the Rules of Latin Grammar, or How to Make Readers Love Your Blog.

3. Write about perennial practical questions. This can be how to cook an adobo dish, how to make a clove hitch, or how to go to Mars.  Or maybe how to find a good date, how to find a wife or husband, how to raise good kids, and how to die a good death.

4. Use Twitter to promote your old posts. Reposting old content in Twitter is one content marketing method.  Check out my blog post on this topic: 3 types of Twitter posting methods. Are you a police, sniper, or soldier?

D. Will people dismiss your content as old or out of date even before reading it?

There are many reasons why a person may dismiss your content, and most likely it's not the date but the headline.  Some headlines can pull readers to read the entire article.  Other headlines are equally good, but with a weak article, the readers immediately click away.

It is really difficult to measure "dismissal of your content as old" outside of literally asking each reader in a survey whether they dismissed your article or not because it is old. One metric that you may like to look at is the length of time for the readers to read the article.  If the reader spent several minutes to read your 1,500 word essay, then you can be sure that he did not dismiss your article. But if he spends only 2 seconds before clicking away, you can be sure that he dismissed your article.  I think Wordpress stats has average duration per article stat, but not in Blogger.  But I think Google Analytics would be an excellent supplement to Blogger stats and it would show you this particular statistic.

If you want to know whether your articles were dismissed as old or not, you can group all your articles that have an engagement length of less than 5 seconds.  Classify them according to new or old, e.g. one year ago is old.  Choose only articles with comparable length, e.g. 1,500 articles and with similar topics.  Randomly select 20 old articles and 20 new articles.  Is the average rejection rate of the old articles higher than those of new articles? You may need to apply some statistical techniques to determine whether this difference in average is significant or not.  As you can see, testing hypothesis in reader behavior is not an easy job but hard work.


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