Moore's Constant

There is an idea in computer engineering called Moore's Law. The basic idea is that every two years the number of transistors on a given piece of silicon will double. It's implications are a little staggering because it's an exponential law. If you were paying attention in 1990, when computers had around 1MB of RAM, then anyone who knew Moore's law would have predicted that computers in 2010 would have 1GB of RAM. But actually imagining a world where budget laptops have 1GB of RAM was beyond most of us, even if we knew the law.

There are some challenges for Moore's law. Gordon Moore himself was specifically talking about transistors on silicon. People are quick to point out that existing silicon techniques do have theoretical limits and that we are in fact bumping against these right now. Some say that this means Moore's law is about to end.

I think that this formulation of Moore's law is unduly limited. Moore made his money building silicon chips, so of course that was where his focus was. But the idea applies to almost every element of computer engineering, and the icing is that it usually applies to derived properties.

For example, you may predict that bandwidth over copper conductor will increase according to a variation of Moore's law. You may talk to a physicist and learn of a fundamental limitation of copper, and say therefore that this expansion has a cap. This is especially comforting to those of us who worry about The Singularity, as it is much less ominous if all of these exponential growth patterns we see have an obvious near-term cap.

But the derived property we should really be paying attention to is bandwidth -- drop the closed-minded dependence on copper. When we exhaust the capabilities of copper, it is not unreasonable to suspect that a new technology (such as optical fiber) may take its place and carry Moore's law forward a few generations beyond what copper is capable of. There may still be a cap but it is much further in the future.

[update 2017/05/02] CPU speed is a notable departure from even this framing of Moore's law. From my 12MHz 80286 (1990) to my 1.83GHz Athlon XP (2003), it held true. But there was no point upgrading that until it failed in 2010, when I bought a Core 2 Duo E5200 2.5GHz, which I have to this day. If I were to buy a new CPU, it would be only about twice as fast at single-threaded computation, even though 7 years have passed. Some marginal improvements in purchase cost, number of cores, and power consumption. But none of these compare to the biennial doubling of speed that we saw for so long. Even the dramatic speed improvements in cellphone CPUs is just a consequence of consumer resignation to abysmal battery life.

Anyways, enough preamble. I believe that for most fields of technology there is something I call a Moore's constant: the number of years required for that quantity to double. More often than not, this figure is between 1.5 and 2. I occasionally find myself computing it, for example to find out how long I'm going to have to wait for a cellphone wristwatch. I've done this enough times that I'm starting to repeat myself, so I figured I would throw together this page as a handy reference.

My methodology for most of these is to simply examine my own personal history. So to some small extent these numbers are distorted by the fact that I have more spending money in 2010 than I did in 1990. However, from my own subjective experience I have generally found that things have been getting cheaper even as they have been getting faster/better. For example the 4MB that I cite for 1993 cost $200 whereas the 4GB that I cite for 2010 cost $100. And the amount of money I am willing to spend on a desktop PC has been continuously decreasing (even if I do not adjust for inflation!).

You should be warned that these are all essentially back-of-the-envelope computations using datapoints from personal experience, and are correct to approximately one significant figure.

RAM

Let's start with some easy ones.

19901MB
19934MB
199716MB
1998128MB
2003512MB
20071GB
20104GB

Moore's constant for RAM is about 1.7 years, so I'll probably have 1TB of RAM in 2024.

[update 2015/11/10] I actually have bought several laptops with only 2GB of memory since 2010, and I have felt no urge to upgrade my PC since then. I simply don't have interest in much more RAM than 4GB. My laptops keep getting better -- lighter and more inexpensive and more delightful to use -- but I no longer seem to care about the biennial doubling in capacity.

Hard Disk

199020MB
1993170MB
1996540MB
19973.2GB
200140GB
2003200GB
2007500GB
20091TB
20122TB
20163TB

[OLD]Until recently, Moore's constant for HDD space is about 1.2 years, so I'll probably have a petabyte in some fashion by 2024.

[update 2016/11/18] It seems we've fallen off of the original chart. That's a disappointment. Fitting the curve again gets a constant of 1.5 years, but obviously for the past few years this is still too low. An optimist might still expect a petabyte by 2029, but I do not. Cause would appear to be fundamental limits of spinning disk technology. The breakthroughs recently have all been in making flash (SSD) cheaper, not in making significantly higher density. So I guess the lack of market demand for very high capacity single units might be relevant.

On that lack of demand...I've always bought the HDD that has the best MB/$ ratio. Except today, I just bought a 3TB drive without even looking. In hindsight, the 4TB drive seems to be a slightly better MB/$. So I, at least, have had a measurable decrease in interest in bigger storage.

Flash memory

This shows how a paradigm shift really influences the picture. Really, flash shares characteristics with both RAM and hard disks, and something which seems more like flash could well replace both of them, causing their growth curves to look like they converge at flash. But for the moment, let's pretend flash has its own curve:

2003256MB
20098GB
2012128GB

If you'll ignore the paltry number of data points (I just haven't bought much flash in my life), you'll see a Moore's constant of 1.0, showing that over time Flash will grow at least as well as hard disks have. 1TB of flash by 2018. Then, truly, who will want a spinning disk at all? 1PB of flash around 2025...

Long-distance network speed

19902400bps
199414.4kb/s
2003256kb/s
20051Mb/s
200910Mb/s
201015Mb/s
201325Mb/s
201784Mb/s

Moore's constant of 1.8, so I'll likely have 1Gb/s to my doorstep by 2023. So when you see Google making headlines with a limited deployment of an experimental gigabit network, just keep in mind that the steady march of progress was going to bring that to all of us in only a decade anyways. Seem like a long ways off? Just remember how pipe-dreamy megabit home internet seemed to you in 1995. As I recall, mass-market broadband wasn't so much as a rumor until 1997 or so.

[update 2017/04/13] My bandwidth stayed at 25Mbps for so long that I began to think I had fallen off of Moore's curve, but it turns out Comcast is just playing games with my bill - 15 minutes on the phone and I'm right back on the curve. Now that my cablemodem is effectively as fast as my wired ethernet, I find it easy to believe that in a few years I'll have gigabit service if I want it.

Cellphone size

This is a little harder because they're still making phones as large as the typical phone in 2003, and there are limitations such as user interface that are preventing them from making a truly small phone today (it has artificially bottomed out until we have good voice interfaces).

199520 in^3
20036 in^3
20083 in^3

So a Moore's constant for cellphone sizes around 4.6 years (note this is halving rather than doubling). Or a wristwatch cellphone (less than 1 in^3) around 2017.

[update 2015/11/10] It's informative that the market thinks it has beaten my predictions with Apple Watch and Google Wear taking off this year, but it hasn't -- these smart watches suck because it won't be possible to make one until 2017.

Battery density

This is a little harder because battery technologies are so much older. I don't have the patience to find out at what point nickel cadmium batteries reached modern levels of efficiency, for example. But let's give it a try anyways.

Note that I'm only interested in rechargables.

186030 Wh/kgapproximate invention of lead-acid
191040 Wh/kgapproximate invention of ni-cad
1997100 Wh/kgapproximate invention of modern lithium ion design
2010150 Wh/kgbest modern lithium ion battery

Which gives a Moore's constant of around 70 years! That's pretty pathetic. There is a convergence now of knowledge about the fine-scale atomic structure of the universe as well as demand for battery technology that may cause a considerable acceleration in the near future. However, this shows a potent hurdle as cellphones shrink.

[update 2016/09/21] The Tesla Model S 85kWh battery in June 2012 supposdely weighs 600 kg (142 Wh/kg), so that 150 Wh/kg has been shown to scale.

e-book Reader Price

Let's actually do a few analyses. See, I've had a lot of trouble explaining to people how e-books will work in the future. I keep running into this statement, "I want a book to be something that I can take to the beach and scratch up in the sand or drop in the ocean without crying about losing some expensive newfangled toy."

So first, let's examine the price trends in eInk-based e-book readers:

Nov 2007$400Kindle
Jul 2009$300Kindle 2
Oct 2009$260Kindle 2 price cut
Jun 2010$150Nook - real competition
April 2011$100Kobo
Nov 2011$100Nook Touch Simple
Apr 2014$69Kindle 6" (with special offers)

A Moore's constant around 2.3 years. (was 2.6 years before 2014/04/23 update)

So let's look at the MP3 player market as an example of a similar niche-matures-into-mass-market phenomenon. I don't consider size or capacity to be relevant for this, though I know it is how companies compete with eachother now. I'm just looking at roughly the cheapest available.

1998$200Diamond Rio PMP300 (32MB)
2003$47D-link DMP 100 (32MB)
2007$26cheapest player I could find (1GB)
2010$15iPod Nano ripoffs (2GB flash)

Again we get 2.6 years to halve the price. But I should apologize for the sparseness of the data. Historical price research is difficult! If I hadn't purchased "the cheapest I could find" in 2007, I wouldn't have been confident enough to even throw this table together. You'll note that at some point the price basically bottomed out and the capacity kept increasing dramatically (see the section on Flash). That's why I didn't bother considering capacity in my ranking.

But that kind of shows that these sorts of price patterns are roughly valid -- there reaches a point where Chinese factories can turn 'em out by the million count for a low per-unit price, and they become essentially disposable.

But we're missing one more piece to the puzzle. Books! I am considering the long-popular and priced-to-sell mass-market paperback fiction format. Most are priced roughly equivalently (when I was a kid, I remember, a paperback cost about $4). Luckily they are printed with their price on the binding, so I'll simply peruse my collection. Also, this is a little handicapped because I apparently don't own hardly any books printed after 1990. And most of the books I have from before 1980 give only the date of first printing. Caveat. Caveat. *sigh*

1978$2.25Frank Herbert - The Dosadi Experiment
1984$2.95Arthur C. Clarke - Imperial Earth
1988$4.95Greg Bear - The Forge of God
1991$5.99Arthur C. Clarke - Rama II
2004$7.99Brian Herbet & Kevin Anderson - Dune: The Machine Crusade
2009$7.99Orson Scott Card - Hidden Empire

As you can see, unlike tech toys, paperback books are getting more expensive over time, doubling approximately every 15.9 years. Of course, you'll note that really they're barely keeping up with inflation (they may even be falling behind). So? e-readers are decreasing faster than inflation. It's a controlled variable, so I can just ignore it.

So let's assume these numbers are approximately right, and they will continue to follow their exponential curves. In 2020, books are at $12 and ebook readers at $37. 2030 and books will cost around $18 and e-book readers will cost around $9. By that point, the market will have fundamentally transformed. The price-conscious literature consumers will leave paper behind, the publishers will stop pandering to them, and before you know it only novelty and collector's editions will be published in paper. You know, for luddites.

And don't get onto me about battery life or eye strain or any of that garbage. You didn't want to use an MP3 player in 1999, right? They sucked. But you own an iPod today, right? As technology improves the usability of the digital readers will improve substantially even as the price continues to drop.

So, on the outside, paper books have about 20 years left. Realistically I think the market will flip over in about 10-15 years. Enjoy them while you can.

Then enjoy something else.

[update 2014/04/23] With my purchase of a Nexus 4 ("smartphone"), I have already made the switch in 2014! The Nexus is as light as a 300 page paperback, so small it's always on me, never loses my place, and (most importantly) it is comfortable to read in the dark. Without even meaning to, I have almost completely lost interest in reading dead trees.

And...?

Feel free to suggest other domains for me to examine, especially if you have a convenient dataset.