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.

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.

[update 2020/06/14] Buying 16GB of RAM last year was so uneventful for me. If I think about it, I can barely detect the improvement in my PC even though 4GB seemed like a pointless limitation. The silicon technology itself has fallen somewhat significantly below the old curve, but I have fallen even further than that because I simply don't care. I will not have 1TB in 2024. I simply won't care. I'm on a cycle where I upgrade my PC about once a decade, and my laptop today has the same specs as in 2012 and I have no interest in upgrading.

Hard Disk

[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:

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...

[update 2021/05/21] I've completely fallen off this chart. In 2018 and 2020, I happened to buy 256GB flash devices. But one was just "the cheapest SATA SSD" because I wanted to put one in my PC as an experiment (I haven't noticed it one way or the other). And the other was just "the largest USB flash stick" for a specific archival need. My personal experience simply isn't enough to go on for flash, but from a glance it looks like flash has slowed down some. I can't find a 32TB SSD at any price today, and even the 4TB ones are pretty expensive compared to spinning drives. No one I know is likely to have a PB of flash in 2025!

[update 2023/06/06] A surprising update...just buying cheapest giant microSD at the store for leaving permanently installed in consumer devices, I bought 128GB for $32 16 months ago and 256GB for $25 just now. So there is still some significant movement, of a kind. FWIW, I don't expect either of those to ever hold more than 32GB of data.

Long-distance network speed

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.

[update 2020/06/14] I tested today and my speed isn't really any better than in 2017. There's fiber to my street but I haven't bothered to sign up for it. I think I could get gigabit (at a high price), but it just doesn't interest me. Most of my devices support gigabit ethernet but only one of them even has the 4-pair wiring to support it. Sometimes I'm reminded that my connection is asymmetric (upload is still slow), but it doesn't bother me even when I notice it and I haven't bothered to even benchmark upstream.

[update 2021/05/11] I signed up for nominally 300Mbit fiber because Comcast kept going down for 5 minutes at a time most days. I did not look forward to having change in my life but the downtime was really getting on my nerves and didn't seem to be a resolvable problem with Comcast. For a couple clicks and bucks, I could change my plan to gigabit. As an aside, I happened to upgrade my home ethernet to gigabit at the end of last year because my old switch died, so at least I can "take advantage" of it. (BTW, more than 60Mb/s upstream)

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).

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.

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:

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

[update 2021/05/21] Looks like this price trend met its limit already in 2014. E-ink is still just a niche. Mostly people are just using LCD/OLED tablets and phones to read these things. The cheapest usable tablet, like the cheapest usable phone, has bottomed out consistently around $100-$150. You can, of course, beat that price with a particularly out-dated device. The incredibly large functionality of these devices is valuable enough that *everyone* has one even though the price remains (barely) significant.

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.

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*

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, and I will 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.

[update 2017/08/20] I have switched back to primarily dead trees. There is a used book store here with haphazard curation which carries books you won't find at the library (not popular enough), or pirated (not nerdy enough). I pretty much only read books between 1850 and 1990 now. In addition, publisher collusion has prevented commercial ebooks from being priced competitively. It is astonishing and bad. If publishers continue to overprice ebooks, my predictions won't pan out. Also, because of merging product categories (mp3 players, ereaders are both now just smartphones or tablets), the price curve I predicted will become increasingly irrelevant.

[update 2019/03/05] In my purchases, I've nudged a little further along some of these curves, but they simply aren't interesting to me anymore. They ran fiber to my house and I shrugged. For the most part, the specifications that used to weigh so heavily on us are now irrelevant compared to other product details. Even price has fallen away for most of these product categories, as they've reached basic commodity-scale pricing (eg, newer Kindles are actually slightly more expensive than older ones).

[update 2021/05/21] A brief glance found that a new/recent mass-market paperback book is trending around $14.99 now?? And is the same price for the Kindle version! And on top of that, no one writes novels anymore, they're all trilogies. I can't even...

And...?

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