Miscellanea Archive

Reflecting on Breath of the Wild

I’ve been enjoying The Legend of Zelda: Breath of the Wild recently, and reflected some on what makes it interesting to me from a non-gameplay perspective. This document is a version of those musings organized for publication, though perhaps less well organized than my usual writings- I am by no means a skilled critic, but spending longer in composing this would likely just delay its completion to little benefit.

Note that at the time of this writing I have not yet completed the game, but there are still some minor spoilers for the early portions of the game and general premise.


The player climbing a long ladder in an otherwise featureless shaft
A bit of a callout to Metal Gear Solid 3, here.

I haven’t really played any Zelda games before Breath of the Wild. Once (long ago) I played a little bit of A Link to the Past but didn’t find it interesting (and was bad at it). Similarly, some time later I tried Ocarina of Time and failed to find anything compelling about it. Claiming that those games are simply not fun would be disingenuous, given both of them appear in multiple lists of “greatest video games ever” compiled by various parties. The correct question to answer here is then which of the differences between those earlier games and Breath of the Wild make the latter interesting to me, but the former not.

Having had extremely limited exposure to earlier Zelda games, I am in a poor position to comment on gameplay differences. In principle I appreciate the open design of Breath of the Wild that allows the player to go anywhere and do just about anything following the completion of a short tutorial section, but it seems to me that I have not been taking much advantage of that freedom. My general impression of the older Zelda style is that there is usually only one way to progress and that may be a frustrating factor that is not highly ranked in my mind however, whereas Breath of the Wild has given me as a player a sufficiently precise goal and the freedom to go after it at any time, but also hints as to things I may do to make success in that quest more probable.

It’s possible that merely offering more freedom to the player and applying contemporary popular game design principles (and resources) to the general Zelda formula is enough to capture the interest of the Present Me. Certainly when I tried the other above-described games they would have been relatively old so I may have been accustomed to games simply built with different style.

On the other hand, I have opinions about how Zelda has previously approached storytelling and how it does in Breath of the Wild which make for rather more interesting thoughts, so I will turn to those considerations instead.

The Big Bad

My general impression of the typical Zelda plot is “oh no stop the evil man from doing the evil thing.” As far as it goes, that’s fine but I find it uninteresting. Breath of the Wild takes a somewhat different approach to the general concept that I find much more compelling.

Malevolent light silhouettes a castle under the gaze of an elemental monster
Elemental evil infests the seat of power.

Ganon, the usual Big Bad, is depicted as an elemental evil in Breath of the Wild, rather than some kind of dark wizard. If a mere dark wizard could be the source of an existential threat of the sort that requires a Great Hero (the player) to protect the world, it seems that there would be more frequent existential threats. Given the presentation suggesting that the player is a unique and noteworthy hero (for instance, collecting artifacts that are implied to be unique and offer powerful abilities to a chosen wielder), putting them in a world where the threat demanding heroism is as mundane as a dark wizard of some kind is rather unconvincing.

The ability of the player character to defeat this elemental evil is not (at least from the start) taken as self-evident, in comparison to how I see other Zelda games, which from the beginning seem to take it as given that the player character is destined to become a great hero and save the world.

Towers rise from the ground in a verdant but desolate landscape
A wild landscape with aspects of decaying grandeur.

Breath of the Wild starts with the player as the only sentient being in a wild landscape with traces of former glory, quickly introducing a guide sort of character who acts as a gently-guided tutorial before giving fuzzy backstory about how the player character is essentialy one in a long line of heroes. The details of this are revealed over hours of gameplay, largely leaving the player alone in a vast world scattered with suggestions of a long history.

I previously found the official canon for Zelda to be rather silly, because every new game is basically the same structurally (Link the hero must do hero things to assist/rescue Zelda the princess-heroine from the Big Bad). This has been justified as that they are these recurring characters over very long periods of time, but it struck me mostly as a convenient excuse for recycling characters that are well-liked.

A world with history

In Breath of the Wild the history of the world is used to good effect, including the recurring nature of the major characters. Lore-keeping NPCs allude to the distant past and what are effectively past incarnations of the main characters, while side characters are more defined by their roles so it is plausible to reuse them.

Two figures stand near a monster surrounded by an army in the style of a hand-woven tapestry
The elemental evil is eternally opposed by the guardian souls.

The world itself acts as a testament to the long history of the land, with ruined structures dotting the landscape (often large stone constructions that are impressive even as ruins) and even older structures (shrines) that serve as a kind of waypoints in what might otherwise be aimless wandering for the player. While the shrines are largely ignored by NPCs, they are not invisible- NPCs seem aware of their presence, but because they are not useful go largely ignored. If there is a weak point in this bit of world-building, the lack of interest or elaboration around shrines seems to be it- but this seems fair when these shrines are meant to be orders of magnitude older than any other relevant features of the landscape.

The art style might earn some credit for informing the feel of the world, but I don’t feel qualified to comment on that. I’ll leave comments on the art of the game to commentators better informed about art, leaving my thoughts at how it seems to be a good use of the limited computing power available to the game’s developers, recognizing that the Wii U and Switch are underpowered systems by the standards of other contemporary gaming platforms.

Characterization

I noted earlier that Breath of the Wild does not seem to take it as given that the player’s character is destined to become a great hero and save the world, but an alternate interpretation might be that the player already has hero credentials. It is shown early on that Link was some kind of royally appointed champion, and it is then implied that those selfsame credentials derive to some extent from Link being an embodiment of a spirit that protects the world through time immemorial.

Link holding the Master Sword aloft triumphantly.
Only the Chosen Hero can wield the Sword that Seals the Darkness!

Despite these heroic credentials, the player at the beginning of the game is effectively powerless, having been idle (unconscious) for a century, following a disastrous defeat at the hands of an encroaching Ganon.

Much of the characterization is done through flashbacks, which I find pretty effective. Putting this kind of backstory in-line might have been distracting and taken away from the feel of a desolate and ruined world, which makes for some of the most intriguing parts of the setting.

It is a bit unusual among games (those with this kind of budget available at least) that this one largely does without voice acting- most characters (the player included) “speak” in what amounts to grunts, except in flashbacks and with a few major characters who are fully voiced. This works well I find; they are not particularly wordy, and suggest some kind of connection between Link and the world’s past, making the player’s task something more resembling a quest to regain the glory of the land, rather than just preventing a cataclysm (which has already happened!).

I appreciate the gravitas of the voiced instances in general as appropriate to the events surrounding a kingdom under mortal threat. Despite that, there are welcome comedic and otherwise lighthearted instances that seem appropriate when considering that Link and Zelda are supposed to be relatively young. In particular, Zelda as a character does not come across to me as a nearly-omniscient plot device (“go here and do this, you must!”), but instead as a typical person thrust into a position of power as royalty doing what they feel is right in a difficult situation.

A chipped and rusted Master Sword
Zelda accepts a difficult role when the best efforts of the people have failed.

Other characters help the game illustrate that in the past Link is coming from, there were organized attempts to resist the impending doom embodied in Ganon. Compare this to my impression of other Zeldas, where if anybody else is aware of the existential hazard that must be defeated by the player they foolishly choose to put their trust in the abilities of the player who begins with no credentials to speak of.

The most guidance any person gives to the player regarding how best to achieve their ultimate goal of defeating the Great Evil hanging over the land amounts to general information, stating what happened in the past and suggesting what might be helpful. Not only does this support the feeling that nobody knows a magical secret that will defeat Ganon, but it also meshes nicely with the feeling that the player is responsible for restoring the former glory of the land (and themselves), leaving it up to the player what level of achievement is appropriate.

If desired, a sufficiently skilled player can go directly from the game’s introduction to defeating the Big Bad, in some fashion asserting that there is nothing that need be reclaimed.

Concluding

With a largely ruined and wild world in the grip of an elemental evil, Breath of the Wild suggests that there is a long and glorious forgotten history to be rediscovered and reclaimed. Whereas the feeling I get from the narrative setup of other Zelda games is “become a hero and save the land!”, this one is closer to “reclaim the forgotten glory of the land by rediscovering your own heroic nature.” Less a story of self-actualization, the player is fighting the universe itself to build a better world for themselves and every other character in it- but they are granted great freedom to decide what must be done and how.

Link stands in the midst of some ruins facing away from the viewer, looking at Hyrule Castle in the distance surrounded by a malevolent aura.
Nice framing of a highly visible goal.

Recognizing my preferences in fiction, it is hardly surprising that I find Breath of the Wild’s approach to storytelling compelling. For instance, I quite enjoy the works of Alastair Reynolds, which often have themes relating to inhumanly long timescales and the inability of humans to comprehend all relevant aspects. Taken slightly differently, I greatly appreciate Lovecraftian horror with its bleak outlook and Breath of the Wild hits some similar notes (albeit in a much more positive fashion).

So, yeah. I like Breath of the Wild and really appreciate how it diverges from other Zelda games in presentation (though I lack the perspective to objectively judge how much it actually differs!). Even if you, dear reader, have found other Zelda iterations uninteresting, this one might be worth looking at.

The player character looking contemplatively at snow-capped mountains from a wooden platform
At this point I'm just appreciating the scenery.

Matrioshka brains and IPv6: a thought experiment

Nich (one of my roommates) mentioned recently that discussion in his computer networking course this semester turned to IPv6 in a recent session, and we spent a short while coming up with interesting ways to consider the size of the IPv6 address pool.

Assuming 2^128 available addresses (an overestimate since some number of them are reserved for certain uses and are not publicly routable), for example, there are more IPv6 addresses than there are (estimated) grains of sand on Earth by a factor of approximately 3 × 10^14 (Wolfram|Alpha says there are between 10^20 and 10^24 grains of sand on Earth).

A Matrioshka brain?

While Nich quickly lost interest in this diversion into math, I started venturing into cosmic scales to find numbers that compare to that very large address space. I eventually started attempting to do things with the total mass of the Solar System, at which point I made the connection to a Matrioshka brain.

“A what?” you might say. A Matrioshka brain is a megastructure composed of multiple nested Dyson spheres, themselves megastructures of orbiting solar-power satellites in density sufficient to capture most of a star’s energy output. A Matrioshka brain uses the captured energy to power computation at an incredible scale, probably to run an uploaded version of something evolved from contemporary civilization (compared to a more classical use of powering a laser death ray or something). Random note: a civilization capable of building a Dyson sphere would be at least Type II on the Kardashev scale. I find Charlie Stross’ novel Accelerando to be a particularly vivid example, beginning in a recognizable near-future sort of setting and eventually progressing into a Matrioshka brain-based civilization.

While the typical depiction of a Dyson sphere is a solid shell, it’s much more practical to build a swam of individual devices that together form a sort of soft shell, and this is how it’s approached in Accelerando, where the Solar System’s non-Solar mass is converted into “computronium”, effectively a Dyson swarm of processors with integrated thermal generators. By receiving energy from the sunward side and radiating waste heat to the next layer out, computation may be performed.

Let’s calculate

Okay, we’ve gotten definitions out of the way. Now, what I was actually pondering: how does the number of routable IPv6 addresses compare to an estimate of the number of computing devices there might be in a Matrioshka brain? That is, would IPv6 be sufficient as a routing protocol for such a network, and how many devices might that be?

A silicon wafer used for manufacturing electronics, looking into the near future, has a diameter of 450 millimeters and thickness of 925 micrometers (450mm wafers are not yet common, but mass-production processes for this size are being developed as the next standard). These wafers are effectively pure crystals of elemental (that is, monocrystalline) silicon, which are processed to become semiconductor integrated circuits. Our first target, then, will be to determine the mass of an ideal 450mm wafer.

First, we’ll need the volume of that wafer (since I was unable to find a precise number for a typical wafer’s mass):

$$ \pi \times \left( \frac{450 \; \mathrm{mm}}{2} \right)^2 \times 925 \;\mathrm{\mu m} = 147115 \;\mathrm{mm^3} $$

Given the wafer’s volume, we then need to find its density in order to calculate its mass. I’m no chemist, but I know enough to be dangerous in this instance. A little bit of research reveals that silicon crystals have the same structure as diamond, which is known as diamond cubic. It looks something like this:

Silicon crystal structure

Now, this diagram is rather difficult to make sense of, and I struggled with a way to estimate the number of atoms in a given volume from that. A little more searching revealed a handy reference in a materials science textbook, however. The example I’ve linked here notes that there are 8 atoms per unit cell, which puts us in a useful position for further computation. Given that, the only remaining question is how large each unit cell is. That turns out to be provided by the crystal’s lattice constant. According to the above reference, and supported by the same information from the ever-useful HyperPhysics, the lattice constant of silicon is 0.543 nanometers. With this knowledge in hand, we can compute the average volume per atom in a silicon crystal, since the crystal structure fits 8 atoms into a cube with sides 0.543 nanometers long.

$$ \frac{0.543^3 \mathrm{\frac{nm^3}{cell}}}{8 \mathrm{\frac{atoms}{cell}}} = .02001 \mathrm{\frac{nm^3}{atom}} $$

Now that we know the amount of space each atom (on average) takes up in this crystal, we can use the atomic mass of silicon to compute the density. Silicon’s atomic mass is 28.0855 atomic mass units, or about 4.66371 × 10^-23 grams.

$$ \frac{4.66371 \times 10^{-23} \mathrm{\frac{g}{atom}}}{.02001 \mathrm{\frac{nm^3}{atom}}} = 2.3307 \mathrm{\frac{g}{cm^3}} $$

Thus, we can easily compute the mass of a single wafer, given the volume we computed earlier.

$$ \frac{147115 \;\mathrm{mm}^3}{1000 \mathrm{\frac{mm^3}{cm^3}}} \times 2.3307 \mathrm{\frac{g}{cm^3}} = 342.881 \;\mathrm{g} $$

Aside: impurities are negligible

We’re going to ignore impurities in the crystal, both the undesired and desired ones. Silicon is doped to control its semiconductor properties when manufacturing integrated circuits, and these intentional impurities will affect the crystal’s density. For illustrative examples, we might refer to materials published by Chipworks, a company that specializes in reverse-engineering of integrated circuits. Below I’ve included one example from Chipworks with doped regions of the substrate annotated:

Left: plan view of a small part of a doped semiconductor substrate. Right: cross-sectional view of same. Images by Chipworks.

There’s also a question of the undesired impurities, but those concentrations should be even less important to our case. If we refer to some (slightly old) figures on the tolerances of a commercial wafer, well.. I’m not entirely sure how to make sense of those numbers. We can consider that the magnitude of undesired impurities in the wafer must be significantly less than that of the intentional ones (since that would affect the semiconductor properties in a hard-to-control fashion), however, and decide it’s not worth worrying about. If you look around that tolerance sheet though, you can get a good idea of how exact the mechanical specifications are. For example, local deviations in the surface must be less than 0.25 micrometers (although it doesn’t appear to include a definition for “local flatness”, rather disappointingly).

More importantly than impurities in the silicon, additional metal and insulator layers are deposited on top of the wafer for interconnection. Using material from Chipworks again, a complex integrated circuit is quite tall when considered in cross-section, mainly due to the numerous interconnects necessary:

Interconnect stacks of metal and insulator layers on two common types of integrated circuits.

How does this metal stack compare to the wafer’s thickness? Chipworks don’t publish many cross-sectional images like the one above, but here’s one of the same Intel 22 nanometer process featured on the left side of the above image, this time with scale bars (and much higher magnification).

A PMOS FET on Intel's 22 nanometer process.

From that, we can estimate a bit from the image we have of the metal layers. It looks like the 1x-pitch metal layers are each about 40 nanometers tall, since I know that the smallest serrated-looking bits at the bottom of the stack are the FETs. Working from that, the entire interconnect stack is about (1 + 1.4 + 2 + 3 + 4) × 40 = 456 nanometers tall, assuming the metal pitch is proportional to its thickness. That’s a small fraction of the wafer’s overall thickness, which is 925000 nanometers.1

But enough of things that don’t enter into our computations. Back to the real work!

A real-world reference CPU

To this point, we’ve computed the density of monocrystalline silicon and determined the volume of a 450mm silicon wafer. Next, we should determine how many useful computing devices can be obtained from a single wafer.

As a possible model for a hypothetical processor to drive a computronium Dyson swarm, I’ll refer to Texas Instruments’ MSP430 microcontrollers. These devices include an efficient CPU core with a number of analog peripherals on-chip. The analog consideration is important, because some way for the members of our Dyson swarm to communicate is required. In this situation, I’ll assume some sort of radio is on the same die (the piece of a silicon wafer that makes up a single chip) as the CPU, allowing two-way communication with nearby processors. In addition, power generation components (since these devices must gather energy from the sun independently) will likely be at least partially analog.

This assumption of radio communication is perhaps not accurate, since optical communication may be much easier to control in such a dense network, with optical emitters (LEDs or laser diodes, probably) and receivers (photodiodes) constructed directly on the wafer. For this case, however, it’s not terribly important, since space taken by unneeded analog parts on the real-world MSP430 could easily be reused, for example to provide additional on-chip memory.

With a model chip to refer to, we must now determine the size of an MSP430’s die. The smallest package (integrated circuits are usually sold encased in epoxy packages with exposed metal pads to make electrical connections to) any MSP430 is available in (that I can quickly find) appears to be a chip-scale BGA, on the MSP430F2370 (I’m providing a copy of the datasheet here, as well). This is perfect for die size estimation, since we can assume that the chip-scale BGA package (YFF in TI’s parlance) is essentially the same size as the die. This estimate is supported by a note on the package drawing (note D) that the exact package size of a device is specified in the device-specific datasheet.

TI's YFF (R-XBGA-N49) 49-pin chip-scale BGA package, planar drawing.

Since the note indicates actual package dimensions are determined by the device contained therein, I believe it is safe to assume that the device package is approximately the same size as the die. Referring to the Device Pinout section of our datasheet, Table 2 (on page 4) provides the overall package dimensions: 3.2 ± 0.05 millimeters on each side.

Now we must determine the number of dies that can be made from a single wafer. This turns into a geometric packing problem where we want to fit as many squares (dies) as possible into a circle (the wafer), which is surprisingly hard. I found an interesting collection of records for some number of squares packed into the smallest circle, but, there’s no simple way to determine an optimal packing. Wolfram|Alpha has some capability to estimate properties of such an optimal packing, and it says we could get 15279 dies out of a 450mm wafer, with 98.37% efficiency.

But wait! We’re assuming somewhat more advanced manufacturing than is currently available. Certainly, I’d expect a computronium manufacturing effort with intent to convert the entire Solar System to recycle waste materials whenever possible, so per-wafer waste isn’t really a concern, since the portions of the wafer that cannot be made into usable dies can simply be recycled into new wafers. Thus, a simple area calculation can be used to determine the amortized number of dies yielded from each wafer.

$$ \frac{\pi \times \left( \frac{450 \;\mathrm{mm}}{2} \right) ^2}{3.2^2 \frac{\mathrm{mm^2}}{\mathrm{die}}} = 15531.6 \;\mathrm{dies} $$

A silicon Solar System

Now it’s time to determine how many processors we could get by converting the entire non-Solar mass of the Solar System into integrated circuits. We will assume a way exists to efficiently form the requisite materials out of what may be available, likely via nuclear fusion (particularly for converting the mostly-hydrogen gas giants into silicon).

Our first order of business, since we’re assuming all mass may be converted to be whatever elements are required, is to determine the Solar System’s mass, excluding that of the Sun itself. Wikipedia notes the following:

The mass of the Solar System excluding the Sun, Jupiter and Saturn can be determined by adding together all the calculated masses for its largest objects and using rough calculations for the masses of the Oort cloud (estimated at roughly 3 Earth masses), the Kuiper belt (estimated at roughly 0.1 Earth mass) and the asteroid belt (estimated to be 0.0005 Earth mass) for a total, rounded upwards, of ~37 Earth masses, or 8.1 percent the mass in orbit around the Sun. With the combined masses of Uranus and Neptune (~31 Earth masses) subtracted, the remaining ~6 Earth masses of material comprise 1.3 percent of the total.

Well, we could manually compute these figures, but such numbers are fairly well-known, so we’ll just ask Wolfram|Alpha what they are. It responds that the Solar System’s mass (including the Sun) is 1.9911 × 10^30 kilograms, and the Sun’s mass is 1.988435 × 10^30 kilograms. Thus the non-Solar mass is trivial to compute:

$$ 1.9911 \times 10^{30} \; \mathrm{kg} - 1.988435 \times 10^{30} \; \mathrm{kg} = 2.7 \times 10^{27} \; \mathrm{kg} $$

Now determine the number of dies we can make from that mass:

$$ \frac{2.7 \times 10^{27} \; \mathrm{kg}}{342.881 \mathrm{\frac{g}{wafer}}} \times 15531.6\mathrm{\frac{dies}{wafer}} = 1.223 \times 10^{32} \;\mathrm{dies} $$

Final quantitative analysis

Having done all the physical computations, we finally have a sense of how a Matrioshka brain could use IPv6. We can make about 10^32 processors out of the Solar System, compared to about 10^38 (theoretically) available IPv6 addresses. That is, it would take approximately one million Matrioshka brains to completely exhaust the IPv6 address pool.

In practice, such a dense network would not be desirable, since the very large IPv6 address space allows a lot of slack in address allocation to make routing easier. For example, clearly-defined hierarchical address allocations allow routers to efficiently determine destinations for traffic via route aggregation or other methods.

Basically: once networks shift to IPv6, address exhaustion is not a concern for any forseeable future. The IPv6 address pool could support Matrioshka brains around about 1% of the stars in our galaxy (extimating about 2 × 10^11 stars in the galaxy) all in a single network. Without superluminal communication, such a network would pose its own challenges (mainly in message latency), to the point where I believe it would make more sense to have interstellar communications running on a different network that happens to be bridged with a local IP network.

I had a bit of difficulty remembering which novels I was thinking of, but Charlie Stross’ “Singularity Sky” and “Iron Sunrise” and Vernor Vinge’s “A Fire Upon the Deep” involve interesting cases where sublight shipping of information remains relevant in galactic civilizations, representing cases where (non-transcended) civilizations maintain local networks with dedicated (comparatively high-cost) links for long-range communication. I think that is a logical way to approach the problem of networking a galactic civilization, given any expected means of interstellar communication will have limited bandwidth, high latency, or both.

So what’s my conclusion? Don’t worry about IPv6 exhaustion. Even if address allocation seems extremely inefficient, since they can (in theory) be reallocated if necessary, and even extremely inefficient allocation still allows a transcended Solar civilization to function comfortably on top of an IP network.

Epilogue

Wow, that was a lot of writing. Over about a week, I spent four evenings actively writing this post, for a total of approximately 10 hours.

I wrote the math markup in this post with the Interactive LaTeX Editor, which is a really slick tool and allows me to ensure MathJax (which I use to render math markup on the site and is itself magical) will handle the expressions as expected. Highly recommended!

Anybody who finds the very lowest level of technology to be interesting (as I do) would probably do well to follow the Chipworks blogs. They also publish teardowns of consumer goods, if that’s more your thing.


  1. As a more informed estimate, somebody who works in the semiconductor industry estimates in a talk from HoPE in 2012 that the total stackup on Intel’s 22nm process is about 100 microns, still only about a tenth of the wafer thickness. [return]

"Four"ier transform

Today’s Saturday Morning Breakfast Cereal:

SMBC for February 1, 2013

I liked the joke and am familiar enough with the math of working in unusual bases that I felt a need to implement a quick version of this in Python. Code follows.

#!/usr/bin/env python

def fourier(x, b):
    """Attempts to find a fourier version of x, working down from base b.

    Returns the fouriest base."""
    mostFours = 0
    bestBase = -1

    for base in range(b, 1, -1):
        fours = 0
        t = x
        while t != 0:
            if (t % base) == 4:
                fours += 1
            t //= base

        # Prefer lower bases
        if fours >= mostFours:
            print(baseconvert(x, base) + "_{0}".format(base))
            mostFours = fours
            bestBase = base

    return bestBase

BASE_CHARS = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"
def baseconvert(x, base):
    s = ""
    while x != 0:
        s += BASE_CHARS[x % base]
        x //= base
    return ''.join(reversed(s))

if __name__ == '__main__':
    from sys import argv, exit
    if len(argv) < 2:
        print("""Usage: {0} <number>

Computes the "four"ier transform of <number>, printing the optimizations to
reach the "fouriest" form.""".format(argv[0]))
        exit(1)

    x = int(argv[1])
    # Base 36 is the largest sensible base to use
    base = fourier(x, 36)

    if base == -1:
        print("{0} is four-prime!".format(x))

This is Python 3.x code, using explicit integer division. It should work under the 2.x series if you change line 34 to use “/=” rather than “//=”. It can only go up to base 36, because I didn’t want to deal with bases that are hard to represent in reasonable ways. Up to base 64 is an option, but in that case I would have wanted to use MIME base 64, which puts digits at positions 52 through 61, which would be confusing to read. Thus it only supports up to base 36, but could be adjusted with relative east to do larger bases.

Running a few examples:

$ python fourier.py 624
HC_36
HT_35
IC_34
IU_33
JG_32
K4_31
143_23
1B4_20
440_12
4444_5

$ python fourier.py 65535
1EKF_36
1IHF_35
1MNH_34
1R5U_33
1VVV_32
2661_31
2COF_30
2JQO_29
2RGF_28
38O6_27
3IOF_26
44LA_25
B44F_18
14640_15
4044120_5

$ python fourier.py 3
3 is four-prime!

A few quirks: it prefers lower bases, so bases that match earlier attempts in fouriness will be printed, despite having equal fouriness. I’ve decided to call values that have no representations containing a ‘4’ character “four-prime”, which is probably going to be a rare occurrence, but the program handles it okay.

Generalization of the algorithm is certainly possible, and basically requires changing the condition on line 14 to match different digit values. For example, a hypothetical “Three”ier transform would replace the ‘4’ on line 14 with a ‘3’.

Further reading

There’s a rather interesting discussion of the topic over on Reddit, as well as a few other implementations. (Thanks to Merth for pointing those out to me.)

Of Cable Modems and the Dumb Solution

I was studying in Japan last semester (which explains somewhat why I haven’t posted anything interesting here in a while). That’s a whole different set of things to blog about, which I’ll get to at some point with any luck (maybe I’ll just force myself to write one post per day for a bit, even though these things tend to take at least a few hours to write..).

Background

At any rate, back in Houghton I live with a few roommates in an apartment served by Charter internet service (which I believe is currently DOCSIS2). The performance tends to be quite good (it seems that the numbers that they quote for service speeds are guaranteed minimums, unlike most other ISPs), but I like to have complete control over my firewall and routing.

In the past, such freedom has been achieved through my trusty WRT54GL, but the 4-megabyte Flash chip in that device makes it hard to fit in a configuration that includes IPv6 support, which is increasingly important to me. As I had an Intel Atom-based board sitting around some time ago, I decided to turn that into a full-time router/firewall running pfSense. The power available with pfSense is probably overkill for my needs, but it ensures I’ll be able to stay up to date and potentially do fancy things with my network configuration at some future date.

Returning to the matter at hand: the whole system was working just fine for a while, but I got a report from my roommates that the internet connection had stopped working, but came up okay with a bargain-basement consumer router (a Linksys/Cisco E900). From what information I was able to get from my roommates, it sounded like a hardware failure in the secondary network card, which is used for the WAN uplink (not exactly surprising, since it’s a 100-megabit PCI Ethernet card I pulled out of something else some time ago).

Debugging

On my recent return to the apartment, one of my priorities was getting the pfSense system up and running again as the main router/firewall. While the E900 was performing fine, pfSense allows me to get a few additional things out of the connection. Most notably, Charter provide a 6rd relay for ISP-provided IPv6 (compared to something like the public IPv6 tunnel service available from Hurricane Electric), which is quite desirable to me.

After performing a basic test, the pfSense box did indeed fail to get a public IP address from Charter when put in place as the primary gateway. At that point, I decided to break out a network analyzer (Wireshark in this case) and see how the DHCP solicitations on the WAN interface differed between the E900 and my pfSense configuration. What follows is Wireshark’s dissection of a single DHCP Discover message from each system.

Linksys E900:

Ethernet II, Src: Micro-St_60:86:0c (8c:89:a5:60:86:0c), Dst: Broadcast (ff:ff:ff:ff:ff:ff)
    Destination: Broadcast (ff:ff:ff:ff:ff:ff)
    Source: Micro-St_60:86:0c (8c:89:a5:60:86:0c)
    Type: IP (0x0800)
Internet Protocol Version 4, Src: 0.0.0.0 (0.0.0.0), Dst: 255.255.255.255 (255.255.255.255)
    Version: 4
    Header length: 20 bytes
    Differentiated Services Field: 0x10 (DSCP 0x04: Unknown DSCP; ECN: 0x00: Not-ECT (Not ECN-Capable Transport))
        0001 00.. = Differentiated Services Codepoint: Unknown (0x04)
        .... ..00 = Explicit Congestion Notification: Not-ECT (Not ECN-Capable Transport) (0x00)
    Total Length: 328
    Identification: 0x0000 (0)
    Flags: 0x00
    Fragment offset: 0
    Time to live: 128
    Protocol: UDP (17)
    Header checksum: 0x3996 [correct]
    Source: 0.0.0.0 (0.0.0.0)
    Destination: 255.255.255.255 (255.255.255.255)
User Datagram Protocol, Src Port: bootpc (68), Dst Port: bootps (67)
    Source port: bootpc (68)
    Destination port: bootps (67)
    Length: 308
    Checksum: 0x9918 [validation disabled]
Bootstrap Protocol
    Message type: Boot Request (1)
    Hardware type: Ethernet
    Hardware address length: 6
    Hops: 0
    Transaction ID: 0x1a5f4329
    Seconds elapsed: 0
    Bootp flags: 0x8000 (Broadcast)
        1... .... .... .... = Broadcast flag: Broadcast
        .000 0000 0000 0000 = Reserved flags: 0x0000
    Client IP address: 0.0.0.0 (0.0.0.0)
    Your (client) IP address: 0.0.0.0 (0.0.0.0)
    Next server IP address: 0.0.0.0 (0.0.0.0)
    Relay agent IP address: 0.0.0.0 (0.0.0.0)
    Client MAC address: Micro-St_60:86:0c (8c:89:a5:60:86:0c)
    Client hardware address padding: 00000000000000000000
    Server host name not given
    Boot file name not given
    Magic cookie: DHCP
    Option: (53) DHCP Message Type
        Length: 1
        DHCP: Discover (1)
    Option: (12) Host Name
        Length: 10
        Host Name: Needlecast
    Option: (55) Parameter Request List
        Length: 4
        Parameter Request List Item: (1) Subnet Mask
        Parameter Request List Item: (3) Router
        Parameter Request List Item: (15) Domain Name
        Parameter Request List Item: (6) Domain Name Server
    Option: (61) Client identifier
        Length: 7
        Hardware type: Ethernet
        Client MAC address: Micro-St_60:86:0c (8c:89:a5:60:86:0c)
    Option: (255) End
        Option End: 255
    Padding

pfSense 2.0.2:

Ethernet II, Src: 3com_8a:b9:6b (00:50:da:8a:b9:6b), Dst: Broadcast (ff:ff:ff:ff:ff:ff)
    Destination: Broadcast (ff:ff:ff:ff:ff:ff)
    Source: 3com_8a:b9:6b (00:50:da:8a:b9:6b)
    Type: IP (0x0800)
Internet Protocol Version 4, Src: 0.0.0.0 (0.0.0.0), Dst: 255.255.255.255 (255.255.255.255)
    Version: 4
    Header length: 20 bytes
    Differentiated Services Field: 0x10 (DSCP 0x04: Unknown DSCP; ECN: 0x00: Not-ECT (Not ECN-Capable Transport))
        0001 00.. = Differentiated Services Codepoint: Unknown (0x04)
        .... ..00 = Explicit Congestion Notification: Not-ECT (Not ECN-Capable Transport) (0x00)
    Total Length: 328
    Identification: 0x0000 (0)
    Flags: 0x00
    Fragment offset: 0
    Time to live: 16
    Protocol: UDP (17)
    Header checksum: 0xa996 [correct]
    Source: 0.0.0.0 (0.0.0.0)
    Destination: 255.255.255.255 (255.255.255.255)
User Datagram Protocol, Src Port: bootpc (68), Dst Port: bootps (67)
    Source port: bootpc (68)
    Destination port: bootps (67)
    Length: 308
    Checksum: 0x3a68 [validation disabled]
Bootstrap Protocol
    Message type: Boot Request (1)
    Hardware type: Ethernet
    Hardware address length: 6
    Hops: 0
    Transaction ID: 0x06303c2b
    Seconds elapsed: 0
    Bootp flags: 0x0000 (Unicast)
        0... .... .... .... = Broadcast flag: Unicast
        .000 0000 0000 0000 = Reserved flags: 0x0000
    Client IP address: 0.0.0.0 (0.0.0.0)
    Your (client) IP address: 0.0.0.0 (0.0.0.0)
    Next server IP address: 0.0.0.0 (0.0.0.0)
    Relay agent IP address: 0.0.0.0 (0.0.0.0)
    Client MAC address: 3com_8a:b9:6b (00:50:da:8a:b9:6b)
    Client hardware address padding: 00000000000000000000
    Server host name not given
    Boot file name not given
    Magic cookie: DHCP
    Option: (53) DHCP Message Type
        Length: 1
        DHCP: Discover (1)
    Option: (61) Client identifier
        Length: 7
        Hardware type: Ethernet
        Client MAC address: 3com_8a:b9:6b (00:50:da:8a:b9:6b)
    Option: (12) Host Name
        Length: 7
        Host Name: pfSense
    Option: (55) Parameter Request List
        Length: 8
        Parameter Request List Item: (1) Subnet Mask
        Parameter Request List Item: (28) Broadcast Address
        Parameter Request List Item: (2) Time Offset
        Parameter Request List Item: (121) Classless Static Route
        Parameter Request List Item: (3) Router
        Parameter Request List Item: (15) Domain Name
        Parameter Request List Item: (6) Domain Name Server
        Parameter Request List Item: (12) Host Name
    Option: (255) End
        Option End: 255
    Padding

(Apologies to anybody who finds the above ugly, but I only have so much patience for CSS while blogging.)

There are a few differences there, none of which seem really harmful. Given it was working without incident before, however, I guessed that maybe some upstream configuration had changed and become buggy. In particular, I thought that either the BOOTP broadcast flag (line 32 of both packet dissections) needed to be set for some reason, or the upstream DHCP server was choking on some of the parameters pfSense was requesting.

In an effort to pin down the problem, I manually made some DHCP requests with dhclient configured to match what I was seeing from the E900. The configuration I used with dhclient looked like this (where xl0 is the identifier BSD assigns to my WAN interface):

interface "xl0" {
    send host-name "Needlecast";
    request subnet-mask, routers, domain-name, domain-name-server;
    send dhcp-client-identifier 1:8c:89:a5:60:86:0c;
}

This yielded packets that, when examined in Wireshark, only differed by some of the hardware addresses and the BOOTP broadcast flag. At that point I was rather stuck. Newer releases of dhclient support an option to force the broadcast flag in requests, but FreeBSD (which pfSense is derived from) does not provide a new enough version to have that option, and I didn’t want to try building it myself. In addition, I know that my ISP doesn’t lock connections to MAC addresses, so I shouldn’t have to spoof the MAC address of the E900 (indeed, nothing needed to be changed when switching from pfSense to the E900, so the other direction shouldn’t need anything special).

Since I was stuck, it was time to start doing things that seemed increasingly unlikely. One comment on the pfSense forum related to a similar issue mentioned that cable modems tend to be simple DOCSIS-to-Ethernet bridges, so there’s some sort of binding to the client MAC address in the upstream DOCSIS machinery, which rebooting the modem should reset. So I hooked everything up normally, cycled power to the modem and booted up pfSense, and…

…it worked.

I had spent a few evenings working on the problem, and the fix was that simple. I was glad it was finally working so I could reconfigure internet-y goodness (QoS, DDNS updating, 6rd tunneling, VPN) on it, but there was certainly also frustration mixed in there.

Lessons

So what’s the lesson? I suppose we might say that “you’re never too knowledgeable to try rebooting it”. It’s common advice to less savvy users to “try rebooting it”, but I think that’s an oft-neglected solution when more technically-inclined individuals are working on a problem. On the other hand, maybe I’ve just learned some details about DOCSIS systems and the solution in this case happened to be rebooting.

<witty and relevant image goes here>

Better SSL

I updated the site’s SSL certificate to no longer be self-signed. This means that if you use the site over HTTPS, you won’t need to manually accept the certificate, since it is now signed by StartSSL. If you’re interested in doing similar, Ars Technica have a decent walk through the process (though they target nginx for configuration, which may not be useful to those running other web servers).

Copyright is broken

I got a.. “fun” e-mail from mediafire a few weeks ago, saying that one of my files had been suspended due to suspected copyright infringement.

Use of a file in your account has been suspended

fb-hitler? Oh, that’s some Free Software I wrote. I disputed the claim, simply stating that fb-hitler.tar.bz2 is a piece of software that I created (and thus own the copyright to). As of tonight, I’ve heard nothing back about it, and the file is still inaccessible. Here’s the link to it, for future reference:

http://www.mediafire.com/?mhnmnjztyn3 (.tar.bz2, 477 KB)

And here’s the complete message I got. Notice it somehow got pulled in by somebody looking to get links to Dragonball Z downloads removed, and that the link to fb-hitler itself isn’t even in the (absurdly long) list of URLs given.

Dear MediaFire User:

MediaFire has received notification under the provisions of the Digital Millennium Copyright Act ("DMCA") that your usage of a file is allegedly infringing on the file creator's copyright protection.

The file named fb-hitler.tar.bz2 is identified by the key (mhnmnjztyn3).

As a result of this notice, pursuant to Section 512(c)(1)(C) of the DMCA, we have suspended access to the file.

The reason for suspension was:

BDM user "lachandra" says: Demand for Immediate Take-Down: Notice of Infringing Activity Dear Sir or Madam, Toei Animation has received information that the domain listed above, which appears to be on servers under your control, is offering unlicensed copies of, or is engaged in other unauthorized activities relating to copyrighted works published by Toei animation. 1. Identification of copyrighted works: Copyrighted work(s): see below Copyright owner: TOEI ANIMATION CO., LTD. 2. Copyright infringing material or activity found at the following location(s): See below The above TV animated series and / or animated movies is being made available for copying, through downloading and / or for streaming viewing, at the above location without authorization of the copyright owner. 3. Statement of authority: The information in this notice is accurate, and I hereby certify under penalty of perjury that I am authorized to act on behalf of Toei Animation , the owner of the copyright(s) in the work(s) identified above. I have a good faith belief that none of the materials or activities listed above have been authorized by Toei Animation, its agents, or the law. We hereby give notice of these activities to you and request that you take expeditious action to remove or disable access to the material described above, and thereby prevent the illegal reproduction and distribution of these copyrighted works via your company's network. ??We appreciate your cooperation in this matter. Please advise us regarding what actions you take.? Yours sincerely, Hervé lemaire Internet Investigator E-mail: herve.lemaire@leakid.com Dragon Ball http://www.mediafire.com/?v9ju2pbujak2i (http://www.gratispeliculas.org/descargar/dragon-ball-z-remasterizado-mkv-espanol-latino-mf/) http://www.mediafire.com/?7ba7yb7y313lyvm (http://rapidlibrary.com/index.php?q=dragon+ball+z+de+fr) http://www.mediafire.com/?8yhkhkax4r0ib5y (http://rapidlibrary.com/index.php?q=dragon+ball+z+de+fr) http://www.mediafire.com/?ndc5ccadnujcjfg (http://rapidlibrary.com/index.php?q=dragon+ball+z+de+fr) http://www.mediafire.com/?mx1dmrjtn5k (http://rapidlibrary.com/index.php?q=dragon+ball+z+de+fr) http://www.mediafire.com/?3ad5uw08uxhnn5n (http://rapidlibrary.com/index.php?q=dragon+ball+z+de+fr) http://www.mediafire.com/?gwmcwnotg2i (http://www.4shared.net/look_for.html?q=dragon+ball+z+mp4&page=11) http://www.mediafire.com/?2f5317t91hceo02 (http://www.4shared.net/look_for.html?q=dragon+ball+z+mp4&page=11) http://www.mediafire.com/?jld1i21c1lu 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(http://rapidlibrary.com/index.php?q=dbz+kai) http://www.mediafire.com/?ljy0t3mnnok (http://rapidlibrary.com/index.php?q=dbz+kai) http://www.mediafire.com/?0kgnmhqhmhi (http://rapidlibrary.com/index.php?q=dbz+kai) http://www.mediafire.com/?ica56r1lq7cuaa3 (http://rapidlibrary.com/index.php?q=dragon+ball+z+123) http://www.mediafire.com/?7yhtwaa0bjkfaws (http://rapidlibrary.com/index.php?q=dragon+ball+z+123) http://www.mediafire.com/?799xz2ztnto (http://rapidlibrary.com/index.php?q=dragon+ball+z+3) http://www.mediafire.com/?foyow2vyfzl (http://rapidlibrary.com/index.php?q=dragon+ball+z+3) http://www.mediafire.com/?ylzxtzrbynk (http://rapidlibrary.com/index.php?q=dragon+ball+z+3) http://www.mediafire.com/?kmjm2mdmegd (http://rapidlibrary.com/index.php?q=dragon+ball+z+3) http://www.mediafire.com/?n3t1mtnnczw (http://rapidlibrary.com/index.php?q=dragon+ball+z+3) http://www.mediafire.com/?navozmgdndj (http://rapidlibrary.com/index.php?q=dragon+ball+z+3) http://www.mediafire.com/?ynxoiysmgyn 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Information about the party that filed the report:

Company Name: LeakID Contact Address: 15 bis rue de chateaudun, 02250 La garenne colombes, France Contact Name: Hervé Lemaire Contact Phone: Contact Email: herve.lemaire@leakid.com

Copyright infringement violates MediaFire's Terms of Service. MediaFire accounts that experience multiple incidents of alleged copyright infringement without viable counterclaims may be terminated.

If you feel this suspension was in error, please submit a counterclaim by following the process below.

Step 1. Click on the following link to open the counterclaim webpage.

http://www.mediafire.com/myaccount/suspension_claim.php?u=4a073e30ad74998332f012514ce955f5b6b521b8123171aa

Step 2. Use this PIN on the counterclaim webpage to begin the process:

[removed by Tari]

Step 3. Fill in the fields on the counterclaim form with as much detail as possible.

This is a post-only mailing. Replies to this message are not monitored or answered.

So, what of it? In theory, the DMCA is pretty reasonable (discounting the criminalization of DRM circumvention). The safe harbor provisions for hosts are worthwhile, and the takedown process (that is, sending a request to the host) is reasonable. Problem is, it’s been twisted- there’s supposed to be a penalty for requesting the takedown of items that the requestor does not own copyright to, in order to deter trolls. In practice, there is no penalty and content creators go around freely demanding the removal of just about anything, with no repercussions. The automated systems on most service providers now just worsen the problem (though understandably, because the hosts have little ability to fight against the underlying policy that results in these things), because rightsholders can spew all kinds of takedown demands with minimal effort.

For those subject to these takedown demands, it’s unfair because many hosts will deactivate users’ accounts when they receive too many demands for removal of items uploaded by a given user, even if the user proves they have the right to upload the content. For example, YouTube suspends accounts after three copyright-related incidents, no matter the outcome.

To my mind, this situation is unacceptable, and it reeks of the “old media” clutching at straws to prop up an outdated business model, to the detriment of everyone else. As recent history has shown, legal force has little effect on the economic problem of media piracy, and utterly fails to address the economics that lead to this phenomenon (sounds a bit like the US government’s war on drugs, actually..).

Going forward, I would support greatly reducing the length of copyright terms (to somewhere around 20 years, perhaps). While I can’t comment much on what exactly that means to rightsholders and their profits (though I have little sympathy for them, whatever the situation is, due to such things as seen in this post), it would be hugely useful to anybody concerned with preserving history (whom I count myself among), because the time required before something can legally be reproduced without the creator’s consent is greatly reduced. With shorter time spans, it is much less likely that any given piece of content will be lost forever, which is the ultimate result that should be avoided.

Enough of a rant regarding my position on copyright, though. The real point here is that I was annoyed by a spurious copyright claim on something I created, and I will be avoiding mediafire for my future file storage needs (not that I ever used them for much).

SSL enabled

I just enabled SSL on this site in a fit of paranoia. It shouldn’t cause any problems, but please let me know if you notice something that’s broken. Normal browsing shouldn’t be affected, but site login is forced to SSL. My (self-signed) certificate has SHA1 fingerprint 6c:e4:77:91:e8:59:f8:d1:fd:ea:cf:87:6b:af:ce:3b:19:be:fa:b5.

Divergence meter progress

One project which I’ve been working on since about October and just got around to creating a project page for is the divergence meter.

There’s not a lot to see there yet, but I’ve recorded my notes on what the design needs and the outline for the control and power supply module.  I ordered the PCB in early December in the hopes that they would be available for me to work on while in Wauwatosa during the semester break.  That didn’t pan out, so unfortunately the whole project won’t move until next week, when I return to Houghton and can get my boards from the mailbox.

My batch of nixie tubes arrived earlier than expected, however, and I got the components to populate the board in mid-November.  All I need is the boards and some time to solder, while hoping I don’t completely botch the job of soldering a 38-TSOP package, especially since that chip (the MSP430F2272) cost me $5.  Photos follow.

Nixie tube closeup
A lone tube, freshly unpacked

One I find the time to assemble the control board, the software should come together pretty quickly.  Just a matter of time now..

Of Names and Localization

When I’m not thinking in or of computer languages, one of the things that I find consistently interesting is natural languages. As such, I’ll occasionally spend some time simply puzzling over bits of language (for which purpose Language Log is an excellent feed of topics).

As it happened, I spent some time today informing myself more on the fairly well-known conlangs Esperanto and Lojban. I find each of them interesting, although my usual pragmatic approach to things probably means I’ll never do any serious study or either.

The point of this rambling, however, is that an exercise in Lojban For Beginners challenges the reader to spell their name using the lojban orthography. Jumping off from there, I endeavoured to see how my name might be translated to other languages.

Beginning with Lojban, I believe my name might be written as pitir.mar’aini (using the Latin orthography). For the uninitiated, the ‘.’ is a full stop, since Lojban doesn’t routinely capitalize (it mainly serves to denote unusual emphasis in pronounciation) nor is spacing a strictly enforced part of notation. Beyond that, the apostrophe is actually pronounced as an ‘h’ would be in English, and is considered a letter rather than a piece of punctuation. Everything else is fairly straightforward, just using rather different spelling conventions than might be seen in English.

Overall, I find that the Lojban orthography is pretty easy to get a hold of as a native English speaker. But what about some other languages? I have a bit of experience with Japanese, so I gave that one a try.

Coming up with a proper equivalent of my name with Japanese orthography is a bit of a kludge, since Japanese names are traditionally written with kanji, and so may also be considered to encode literal meanings[citation needed]. Choosing appropriate kanji for a translation of my name is far outside my expertise and it would sound completely different (and thus diverges from the point of this exercise), so I’ll settle with a katakana approximation: ピーター・マルハイニ. I use katakana here because it is traditionally used for words of foreign origin, which indeed my name is.

It’s an interesting challenge to transliterate from a European language (English here) into Japanese, since the Japanese syllabary is almost exclusively open (that is, the sounds end with vowels). In this case, I had to fudge my given name (Peter), since Japanese completely lacks the sound that ‘r’ provides in English- it becomes ‘PeTa’ instead, which I find to be acceptably close (the ーs denote long vowels).

In ‘Marheine’, the ‘rh’ construct is difficult, since it’s a consonant cluster which doesn’t fit into the aforementioned open syllables. For that, I fudged it with ‘ru’, which is (as far as I can deduce) a fairly common trick.

While I’m considering Japanese pronounciation, it’s worth mentioning the characters in the header on this web site (タリ). That’s a representation of my usual alias, Tari, in katakana.

Raptor Speech

In a fit of boredom this evening, I tried to see what the speech recognition in Windows 7 would give back when I made raptor noises into it. The result.. speaks pretty well for itself:

F and has and has a Hack it has A hack who know Her house Just how hot enough And who know how It has had To add up data at data to go out and It’s all of all Go ahead goal happened: how has a Staff headed to a

And if his own booth for th FFI have had for the hand-held her and who often have no