December 10, 2019

How cells grow

Cells in a culture grow every day

We want to know the number of cells every day: ncell[t]

Here t is the time in days.

We start with an initial number of cells, that we call initial

Each day, the number of cells increases by a factor rate

\[\texttt{ncell[t]} = \texttt{initial} \cdot \texttt{rate}^\texttt{t}\]


plot(t, ncell)

We cannot see what happens when values are small

Logarithmic scale (“semi-log”)

plot(ncell ~ t, log="y")

We can see better using a logarithmic vertical scale

Size of the culture

When the cells grow in a petri dish, then the culture will form a circle

The area of the circle is proportional to the number of cells.

Thus, the circle radius changes with time following this equation \[\texttt{ncell[t]}=K \texttt{r}^2\] in other words \[\texttt{r}=\sqrt{\frac{\texttt{ncell[t]}}{K}}\]

Log-log scale

plot(radius ~ ncell)
plot(radius ~ ncell, log="xy")

Kleiber’s Law

(Physiological Reviews 1947 27:4, 511-541)

Relation of Body size v/s metabolic rate

Same in log-log scale

We saw the same in Homework 5

plot(income~population, world)

Using log-log scale

plot(income~population, world, log="xy")

Same, with colors and point size

plot(income~population, world, log="xy", pch=16,
     col=region, cex = 3*sqrt(area/max(area))+0.1)

Exponential growth in Science and Technology

Moore’s Law

A idea from ~1970, by George Moore (Intel)

The simple version of this law states that processor speeds will double every two years

More specifically, “the number of transistors on a CPU would double every two years”

(see paper)

Intel says

Real data: Number of transistors in chips v/s year

plot(count~Date, data=trans)

Semilog scale: Number of transistors v/s year

plot(count ~ Date, data=trans, log="y")

Same happens with DNA

Cost of sequencing human genome

Cost of sequencing human genome

Months since Sept 2000

What does this mean for you?

The Robots Are Coming

John Lanchester

  • 1992 Russo-American moratorium on nuclear testing
  • 1996 Computer simulations to design new weapons
  • Needed more computing power than could be delivered by any existing machine

The Robots Are Coming

John Lanchester

  • USA designed ASCI Red, the first supercomputer doing over one teraflop
    • ‘flop’ is a floating point operation (multiplication) per second
    • teraflop is \(10^{12}\) flops
  • In 1997, ASCI Red did 1.8 teraflops
  • The most powerful supercomputer in the world until about the end of 2000.

The Robots Are Coming

In his book, John Lanchester says

"I was playing on Red only yesterday – I wasn’t really, but I did have a go on a machine that can process 1.8 teraflops.

"This Red equivalent is called the PS3: it was launched by Sony in 2005 and went on sale in 2006.

The Robots Are Coming

"Red was [the size of] a tennis court, used as much electricity as 800 houses, and cost US$55 million. The PS3 fits under the TV, runs off a normal power socket, and you can buy one for £200.

"[In 10 years], a computer able to process 1.8 teraflops went from being something that could only be made by the world’s richest government […], to something a teenager could expect [as a gift].

The Robots Are Coming