Posts Tagged‘exponential growth’

Let’s Get Moore’s Law Straight, Ok?

Anyone who’s had a passing interest in computers has likely run up against the notion of Moore’s Law, even if they don’t know the exact name for it. Moore’s Law is a simple idea, approximately every 2 years the amount of computing power than can be bought cheaply doubles. This often takes the more common forms of “computer power doubles every 18 months” (thanks to Intel executive David House) or, for those uninitiated with the law, computers get obsoleted faster than any other product in the world. Since Gordon E. Moore first stated the idea back in 1970 it’s held on extremely well and for the most part we’ve beaten the predictions pretty handily.

Of course there’s been a lot of research into the upper limits of Moore’s Law as with anything exponential it seems impossible for it to continue on for an extended period of time. Indeed current generation processors built on the standard 22nm lithography process were originally thought to be one such barrier, because the gate leakage at that point was going to be unable to be overcome. Of course new technologies enabled this process to be used and indeed we’ve still got another 2 generations of lithography processes ahead of us before current technology suggests another barrier.

More recently however researches believe they’ve found the real upper limit after creating a transistor that consists only of a single atom:

Transistors — the basic building block of the complex electronic devices around you. Literally billions of them make up that Core i7 in your gaming rig and Moore’s law says that number will double every 18 months as they get smaller and smaller. Researchers at the University of New South Wales may have found the limit of this basic computational rule however, by creating the world’s first single atom transistor. A single phosphorus atom was placed into a silicon lattice and read with a pair of extremely tiny silicon leads that allowed them to observe both its transistor behavior and its quantum state. Presumably this spells the end of the road for Moore’s Law, as it would seem all but impossible to shrink transistors any farther. But, it could also points to a future featuring miniaturized solid-state quantum computers.

It’s true that this seems to suggest an upper limit to Moore’s Law, I mean if the transistors can’t get any smaller than how can the law be upheld? The answer is simple, the size of transistors isn’t actually a limitation of Moore’s Law, the cost of their production is.

You see most people are only familiar with the basic “computing power doubles every 18 months” version of Moore’s Law and many draw a link between that idea and the size of transistors. Indeed the size is definitely a factor as that means we can squeeze more transistors into the same space, but what this negates is the fact that modern CPU dies haven’t really increased in size at all in the past decade. Additionally new techniques like 3D CPUs (currently all the transistors on a CPU are in a single plane) have the potential to exponentially grow the number of transistors without needing the die shrinks that we currently rely on.

So whilst the fundamental limit of how small a transistor is might be a factor that affects Moore’s Law it by no means determines the upper limit; the cost of adding in those extra transistors does. Indeed every time we believe we’ve discovered yet another limit another technology gets developed or improved to the point where Moore’s Law becomes applicable again. This doesn’t negate work like that in the linked article above as discovering potential limitations like that better equips us for dealing with them. For the next decade or so though I’m very confident that Moore’s Law will hold up, and I see no reason why it won’t continue on for decades afterward.

Population Sustainability.

There comes a time in every bloggers life when the people who comment on topics provide the inspiration for future posts. For me this day has come from an interesting tangent brought about by one my more recent posts on Australia’s property market. The underlying ideal behind a lot of property investors is that people will always need a place to live and that we’re always going to have more and more people in the world so it becomes a very secure investment. This then begs the question, how long can continued population growth continue before we can’t sustain it?

What we should first look at is the historic population trend for us humans:


It’s an interesting graph mathematically as it combines several different behaviours. The first is for all intents and purposes a steady state function. All the way up to approximately 1000BC the human population did not undergo much growth at all and for the most part was steady. Around 1000BC to 900AD we can see a typical steady, linear growth function where the population increases basically at a set rate every year. After 1000AD it starts to get really interesting and demonstrates an exponential growth function that rockets up unimaginably high. Generating a line of best fit for this data (mathematical note: I’m using data from 0 to 2000 so the equation is simpler) gives something along the lines of y = 110.53e0.1048x where y is the population, x is the year and e is the mathematical constant. Using this to map future populations is a tad scary, take a look in the Wolfram Alpha for a taste.

The graph shows what happens when technology significantly improves life and thus allows people to live longer and have more children. Things like the invention of agriculture, the industrial revolution and the baby boom following world war 2 represent those significant changes in the population. It’s also interesting to note that they also correlate succintly with the change in mathematical behaviour of the graph from constant to linear to exponential. As anyone with a scientific bent will tell you exponential growth can’t last and will eventually end once a limitation in resources is reached.

Now before I go into a bit of philosophical hand waving about the world’s population I want to get a definition clear that is wildly misrepresented. Third world countries refers to a political affiliation, not a level of development. The term is used today to describe countries that are more aptly described as developing nations and is often used as a call to sympathy for them.

The world as it stands today could easily support the current population with a decent standard of living. Predominately the issue seems to stem from our inability to provide life’s essentials to certain countries, namely those ones who are still developing.  There will come a time when even the western world won’t be able to provide enough food for its people and this is when the populations will have to plateau. Current thinking is this will happen sometime around 2050 with the world’s population hitting a staggering 9 billion. However this idea is rooted in today’s ideals and technology and as we’ve seen in the past revolutions in technology enabled the human race to expand at rates that no one thought was possible before. A classic example of this was the horse manure crisis of 1984, where planning authorities predicted that all the streets of London would be buried in 9 feet of manure. Of course this did not happen thanks to a technological breakthrough and the potential is there for this to happen with us humans.

My personal view on the matter is that whilst exponential growth is unsustainable the human race as a whole has a lot of potential to overcome these issues. Unfortunately history has shown that until the problem becomes critical not much will be done to avoid it, as we’ve seen with things like alternatives to fossil fuels. The good news is that a lot of the framework is already in place and proven to be able to cope with a much larger population, we will just have to encourage our governments to bolster sustainable practices and put pressure on other governments who don’t.

I’ve tried to steer clear of squarely blaming political issues as the cause of all the problems that third world countries face as it is only my opinion and I haven’t been able to find substantial evidence to back it up. So instead I want to put it to you my readers: what are the causes of the issues that developing nations face? Is it their tyrannical governments? Or does it stem from inherit environmental problems?

We as a species are quite capable of sustaining our current population with a good standard of living. What is stopping us from accomplishing this?

Update: Slight rephrasing of the question. As my intrepid fellow blogger Andrew Carr points out this issue isn’t as simple as I might have first thought.