## Inventions = population x (time)^{2}

The technology equation has linear and exponential components. By studying 2000 inventions, some powerful relationships become apparent:

## 1) inventions increase directly as the population increases.

That is, inventions have a linear relationship to population. This linear relationship, or direct proportion, is similar to Isaac Newton’s famous equation – Force = mass x acceleration. In graphing 2000 inventions versus population, a clear linear relationship is seen. Common sense suggests a linear relationship between population and inventions. More people means more brains with ideas which leads to more inventions.

## 2) inventions increase exponentially with time.

That is, inventions have a logarithmic relationship to time. This exponential relationship similar to Albert Einstein’s famous equation – Energy = mass x (speed of light)^{2}. In graphing 2000 inventions versus time, an exponential relationship is seen. At first, common sense does NOT immediately suggest the exponential relationship inventions and time. That inventions increase in proportion to (time)^{2} is not intuitively obvious. It is not until we see than data is proportional to(time)^{2} that the accuracy of the technology equation becomes apparent.

## In the technology equation, why do inventions increase with (time)^{2 }?

Without a doubt, data is increasing exponentially. In my blog, “5 Dimensions Of Data”, the growth of data with each new dimension of data is striking. The first dimension of data which began in 250.000 BCE, oral or spoken language, produced little data. Oral stories passed between generations of hunter-gatherer peoples limit information content. The second dimension of data, hand written language, created a huge explosion data in 3500 BCE. Over 500,000 ancient cuneiform clay tablets originate from Mesopotamia documenting this era of history. With written language, cities and civilizations were born. I have called this explosion of inventions and civilizations of 3500 BCE as the Big Bang of Technology (see blog).

The third dimension of data, mechanical printing press with movable type on paper in 1450, created another powerful wave of data and inventions. I have called this next wave in data and technology as the Big Surge of Technology (see blog). Millions of books published in this era created another logarithmic expansion of data. The fourth dimension of data, electronic language, began in 1837 with the telegraph and Morse code. The era progressed with the telephone, radio, television, and ultimately computers. By 1989, billions of documents published creating another exponential increase in data. The World Wide Web and internet created in 1989, launched the fifth dimension of data, hypertext language. Hypertext allows interconnection or links between the billions of documents and videos creating another exponential expansion of data.

## Above all, data and inventions link closely.

Intuitively, common sense suggests as data increases, inventions increase. That is: inventions = population x data. If data is increasing exponentially as it obviously is, then data is proportional to (time)^{2}.

So logic or deduction allows us to conclude with the technology equation: