faster and faster, obeying an exponential curve. But of course this growth can’t go on forever. Eventually the entire population that might possibly choose to adopt the gadget is reached. The growth slows down as it reaches this carrying capacity, obeying its logistic shape.
These curves are also often referred to as S-curves, due to their stretched S-like shapes. This is the term that’s commonly used when discussing innovation adoption. Clayton Christensen, a professor at Harvard Business School, argues that a series of tightly coupled and successive S-curves—each describing the progression and lifetime of a single technology—can be combined sequentially when looking at what each consecutive technology is actually doing (such as transforming information) and together yield a steady and smooth exponential curve, exactly as Magee and Koh found. This is known as linked S-curve theory, and it explains how multiple technologies have been combined to explain the shapes ofchange we see over time.
Figure 4. Schematic of linked S-curves (or linked logistic curves). When combined, they can yield a smooth curve over time.
But Magee and Koh didn’t simply expand Moore’s Law and examine information transformation. They looked at a whole host of technological functions to see how they have changed over the years. From information storage and information transportation to how we deal with energy, in each case they found mathematical regularities.
This ongoing doubling of technological capabilities has even been found in robots. Rodney Brooks is a professor emeritus at MIT who has lived through much of the current growth in robotics and is himself a pioneer in the field. He even cofounded the company that created the Roomba. Brooks looked at how robots have improved over the years and found that their movement abilities—how far and how fast a robot can move—have gone through about thirteen doublings in twenty-six years. That means that we have had a doubling about every two years: right on schedule and similar to Moore’s Law.
Kevin Kelly, in his book
What Technology Wants
, has cataloged a wide collection of technological growth rates that fit an exponential curve. The doubling time of each kind of technology, as shown in the following table, acts as a sort of half-life for it and is indicative of exponential growth: It’s the amount of time before what you have is out-of-date and you’re itching to upgrade.
Technology
Doubling Time (in months)
Wireless, bits per second
10
Digital cameras, pixels per dollar
12
Pixels, per array
19
Hard-drive storage, gigabytes per dollar
20
DNA sequencing, base pairs per dollar
22
Bandwidth, kilobits per second per dollar
30
Notably, this table bears a strikingly similarity to the chart seen in chapter 2 , from Price’s research. Technological knowledge exhibits rapid growth just like scientific knowledge.
But the relationship between the progression of technological facts and that of science is even more tightly intertwined. One of the simplest ways to begin seeing this is by looking at scientific prefixes.
. . .
IN chapter 8 , I explore how advances in measurement enable the creation of new facts and new knowledge. But one fundamental way that measurement is affected is through the tools that we have to understand our surroundings. And we can see the effects of technological advances in measurement by looking at it in one small and simple area: the scientific prefix.
The International Bureau of Weights and Measures, which is responsible for defining the length of a meter, and for a long time maintained in a special vault the quintessential and canonical kilogram, is also in charge of providing the officially sanctioned metric prefixes. We are all aware of
centi
- (one hundredth), from the world of length, and
giga
- (one billion), from measuring hard disk space. But there are other, more exotic, prefixes. For example,
femto
- is one quadrillionth and
zeta
- is a
These curves are also often referred to as S-curves, due to their stretched S-like shapes. This is the term that’s commonly used when discussing innovation adoption. Clayton Christensen, a professor at Harvard Business School, argues that a series of tightly coupled and successive S-curves—each describing the progression and lifetime of a single technology—can be combined sequentially when looking at what each consecutive technology is actually doing (such as transforming information) and together yield a steady and smooth exponential curve, exactly as Magee and Koh found. This is known as linked S-curve theory, and it explains how multiple technologies have been combined to explain the shapes ofchange we see over time.
Figure 4. Schematic of linked S-curves (or linked logistic curves). When combined, they can yield a smooth curve over time.
But Magee and Koh didn’t simply expand Moore’s Law and examine information transformation. They looked at a whole host of technological functions to see how they have changed over the years. From information storage and information transportation to how we deal with energy, in each case they found mathematical regularities.
This ongoing doubling of technological capabilities has even been found in robots. Rodney Brooks is a professor emeritus at MIT who has lived through much of the current growth in robotics and is himself a pioneer in the field. He even cofounded the company that created the Roomba. Brooks looked at how robots have improved over the years and found that their movement abilities—how far and how fast a robot can move—have gone through about thirteen doublings in twenty-six years. That means that we have had a doubling about every two years: right on schedule and similar to Moore’s Law.
Kevin Kelly, in his book
What Technology Wants
, has cataloged a wide collection of technological growth rates that fit an exponential curve. The doubling time of each kind of technology, as shown in the following table, acts as a sort of half-life for it and is indicative of exponential growth: It’s the amount of time before what you have is out-of-date and you’re itching to upgrade.
Technology
Doubling Time (in months)
Wireless, bits per second
10
Digital cameras, pixels per dollar
12
Pixels, per array
19
Hard-drive storage, gigabytes per dollar
20
DNA sequencing, base pairs per dollar
22
Bandwidth, kilobits per second per dollar
30
Notably, this table bears a strikingly similarity to the chart seen in chapter 2 , from Price’s research. Technological knowledge exhibits rapid growth just like scientific knowledge.
But the relationship between the progression of technological facts and that of science is even more tightly intertwined. One of the simplest ways to begin seeing this is by looking at scientific prefixes.
. . .
IN chapter 8 , I explore how advances in measurement enable the creation of new facts and new knowledge. But one fundamental way that measurement is affected is through the tools that we have to understand our surroundings. And we can see the effects of technological advances in measurement by looking at it in one small and simple area: the scientific prefix.
The International Bureau of Weights and Measures, which is responsible for defining the length of a meter, and for a long time maintained in a special vault the quintessential and canonical kilogram, is also in charge of providing the officially sanctioned metric prefixes. We are all aware of
centi
- (one hundredth), from the world of length, and
giga
- (one billion), from measuring hard disk space. But there are other, more exotic, prefixes. For example,
femto
- is one quadrillionth and
zeta
- is a
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