The Internet began with equations

It’s really amusing when some members of the younger generation scoff at mathematics and its importance in their world. I usually ask them to do a search on their smartphone for “Leonard Kleinrock internet equations”—Afterwards they ask, “Who is Leonard Kleinrock?” they are astounded at what they find.

I go on to tell them that they would never be able to search the web for answers, send a Tweet, use Facebook or look at a YouTube video without mathematical equations and Leonard Kleinrock, the Father of the Internet.

It all started with Claude Shannon’s equation says Kleinrock. Shannon had a great influence on Kleinrock who commented that he had a very complex problem and the answer turned out to be very simple. He walked into Shannon's office as soon as he got the result and asked him, “Why does it turn out so easy?” In two minutes Shannon had it and he never seen the problem before.

Kleinrock’s Independence Approximation was the next mathematical key to the Internet. See Figure 1 and Equation 1 and Reference 6.

Kleinrock commented on the 1969 big events, “For one thing we put a man on the moon. Second thing is the Woodstock Festival took place up in New York State–A bunch of crazy people running around doing different kinds of things. An Event with probability of zero occurred: the Mets Won the World Series In baseball. Charles Manson went on a murderous killing spree in Los Angeles. Oh, And by the way, the Internet was born. Nobody noticed. Even those of us who were putting it together didn't notice in some sense.”

Kleinrock says that the key to the success of the Internet was not really in the technology but the environment in which it was developed. Advanced Research Projects Agency (ARPA) managers’ interests in the so-called Internet was primarily concerned with long-range funding, high-risk/high-payoff, and their brilliant program managers had a limited term so they had no real agendas that could affect the long term and they did not interfere with the studies.

There was a very relaxed attitude by the principle investigators in the research, so graduate students were allowed to blossom and show off their creativity in cross-university cooperation. No one was really in charge, but they trusted each other and put the best ideas into action. That was the big contribution to the success of the Internet in the early days.

I highly recommend that you check out this film: Lo and Behold–That's Leonard Kleinrock pounding on that Interface Message Processor!


1 Leonard Kleinrock Opening Keynote Global INET, April 23, 2012, Geneva, Switzerland

2 Oral History: Leonard Kleinrock

3 Principles from the Past

4 Leonard Kleinrock: Charting the Course of the Internet (This is on IEEE XPlore which will require a purchase of a membership)

5 The Guardian—Claude Shannon equation

6 The Kleinrock Independence Approximation

7 Leonard Kleinrock: Imagining the Internet

8 comments on “The Internet began with equations

  1. DrJeff1
    September 21, 2016

    Please don't forget Donald Davies

  2. jimfordbroadcom
    September 21, 2016

    Not really a Reply, but Comment doesn't work.  Well, that queueing theory is a bit too high level for my Phy taste.  That is, I'd be more interested in stuff closer to the physics of moving information from one place to another.  But that's just me.  Good reminder that the Internet did indeed begin with equations.  I'll have to remember that to pass on to my sons.  Math is indeed underneath it all, whether it's Maxwell's equations, the Friis transmission formula, etc.  BTW, I was fortunate enough to hear Len Kleinrock and other engineering luminaries speak about 4 years ago when Henry Samueli was presented with the Marconi Award.  Ah, the good old days…

  3. Mathew12
    September 22, 2016

    Thank you for that reminder

  4. Steve Taranovich
    September 22, 2016

    @jimfordbroadcom—thanks for sharing

  5. sandrine25
    September 25, 2016

    all starts with an equation, the mathematics is the basis of everything and besides, the attraction is also the result of equation

  6. Mboux
    September 25, 2016

    We need maths to reasoning. In discoveries, technology and daily life, we need mathematics

  7. kristen.villemez
    September 26, 2016

    I have to fight this battle daily with my high school robotics students! Sure, we have these great powerful computers to do all of the work for us, but you also have to be able to understand the answer a computer gives you and determine whether or not that answer makes sense. So yes, even though computers do the heavy lifting, you still need to understand the result!

    This was a lesson one of the best professors I ever had taught me.


  8. Steve Taranovich
    September 26, 2016

    Thanks for your excellent experience with high school students Kristen. Mathematics is really not always portrayed in a positive light to the younger generation

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