There is one official Toki Pona orthography, which is the one based on the lowercase Latin alphabet. There are two others: sitelen pona, the script, and sitelen sitelen, which looks like Mayan hieroglyphs. For instance, ale li jo e tenpo (everything has a time) renders in sitelen sitelen as the rather large: 
And this is rendered in sitelen pona as ale li jo e tenpo.
Radicals in sitelen pona are an interesting idea. The color triangle forms a radical:
- kasi kasi (plant) + kule - color → laso - green/blue (plant color)
- uta uta (lip) + kule → loje - red (lip/mouth color)
- suno suno (sun) + kule → jelo - yellow (sun color)
Another radical is three lines emanating up, which seems to represent taking something and making it active somehow.
- luka (hand) → pana (give)
- lipu (document) → sona (knowledge)
- ijo (thing) → toki (speak)
There are a few more that use luka (hand) as a radical:
- luka + ilo ilo (tool) = kepeken kepeken - use
- luka + ijo ijo (thing) = pali pali - work
- luka + uta uta (mouth) = moku moku - eat/food
Most of the prepositions are formed by placing a box-like radical with a dot indicating placement:
- poki poki - container
- anpa anpa - below
- poka poka - next to
- insa insa - inside
- monsi monsi - behind
- sinpin sinpin - in front of
Sometimes the circle seems to be more like a personhood radical:
- jan jan - person
- jo jo - have
- lape lape - sleep/rest
- lawa lawa - head/leader
- mama mama
- wawa wawa - power
- mije mije - male
- meli meli - female
It also seems to have that connotation in the pronouns:
- mi mi - I, me, we
- sina sina - you
- ona ona - he/she/it/they
I also like the “nesting” composition for compound words. Several of the words (especially jan, ijo and tomo) are great for it: “the boss gave poison to his workers in the war room” might be jan-lawa li pana e ijo-moli tawa jan-pali lon tomo-utala. The nesting makes the content words darker than the syntactic words (li, e , tawa, lon) making it easier to see which concepts are together. This should make it easier to read Toki Pona in cases where two words are meant to be taken together as a compound.
Here’s a large list for this font:
linja pona compounds and roots
Many things which are unappealing about sitelen pona are addressed by this font, Linja Pona. For instance, ko ko has a pretty ambiguous definition, but looks more like a character here. Also, olin olin looks significantly better in Linja Pona than in pu (the official Toki Pona book “pu”).
I also find the cartouche idea interesting, where the first sound of each word in the cartouche tells you a letter in a name. So “jan Elena” becomes something like jan [_esun_len_en_nasa_alasa].
The above “radicals” suggest simplifications for Toki Pona, which is not something one would expect could be simplified much further.
Now I have some criticism.
Several characters seem to be intentionally unstructured. The worst offender is jaki jaki, followed by ko ko, which is at least improved in this font.
The only difference between lili lili and suli suli is the size of the glyph. Because of this, only the idea of smallness can be composed inside another glyph, bigness will always have to be written alongside. Your jan-lili (children) will not understand the sona suli (big idea).
Related to the suli / lili situation, lete lete (cold) can be embedded in other glyphs but seli seli (hot) cannot. Enjoy your telo-lete (ice water) but not your telo seli (hot water).
There are also a lot of characters that are liable to be confused with each other, especially the pronouns mi mi, sina sina and ona ona. You could say the same thing is a problem in the Latin alphabet with d b q p I suppose though.
There seems to be a relationship between sin sin (new) and namako namako (extra/spice) but I don’t get it.
kin kin follows the pattern set by a and o , except that the asterisk-shape should imply cold because of lete lete. I’m also not sure it’s a good idea to derive word characters from punctuation, especially punctuation from another language.
The prepositions seem like the kind of thing one would have trouble writing or remembering, which is compounded because many of them have senses that are different from their visual interpretation. For instance, anpa can mean defeat, and lon lon is used for a variety of purposes including “is here”, “exists” or “is true.”
Several characters seem to be taken whole from other orthographies without any real reason: nanpa for nanpa (number), esun esun, which means commerce or market. Also sewi sewi, which means high or divine seems like it should be a dot above the poki poki box for consistency with the other prepositions, although it does have this important meaning as well. ken ken (can, able to), I guess is so abstract there isn’t a more direct graphic way of conveying it.
I see some of these as playfully messing with Western-American sensibilities (the £ for money instead of $, Arabic for “Allah” as divine or above) but at least sewi misses an opportunity for more consistency while also illuminating the missed opportunity for the other prepositions, to come up with something more distinctive than dots near boxes.
I am thoroughly confused about why selo is selo yet sijelo is sijelo. The former means “surface, peel” and the latter means “body” or “physical state.” I have no idea how either of these glyphs is supposed to invoke these senses.
I kind of think a stack of lawa noka would have been good for sijelo, to represent a body as “from head to toe.” I think selo should probably have been concentric circles, which are currently the glyph for sike sike. Why is the glyph for circle two circles? Because ijo ijo is one circle. This gets reinforced by glyphs like pali pali which compound the idea of thing (pali, work, here recalling “make thing with hands”). Except it is already somewhat undermined because in many complex glyphs, the circle stands in for “person” rather than “thing” (mama mama being the best example).
Overall, I like sitelen pona a lot. Despite the shortcomings, it seems to be used quite a bit. The availability of this very nice font I think helps a lot.
Decreasing sequences
It occurred to me that I could think of two ways to generate a decreasing sequence. The built-in i. will do this:
i. _7
6 5 4 3 2 1 0But I could see a way to do it with self-reference $: or with iterate ^::
(<:^:*^:a:) 7
7 6 5 4 3 2 1 0This essentially says “iterate gathering results” ^:a: “while non-zero” ^:* “decrement” <:. This differs slightly from i. _7 because it includes the number 7, but whatever.
The self-reference $: method is a little longer:
0:`(, $:@<:) @.* 7
7 6 5 4 3 2 1 0Like any recursive function, we need a base case and an inductive case. Sentences like
f`g@.tin J give you case analysis, so a sentence like:
0:`f @.*is a strong clue that your base case maps 0 to 0 and runs all positive numbers through f, and that’s what’s happening here. So the next step is understanding , $:@<:. This is about as simple as self-reference can get: we’re making a hook (it means the same as ] , $:@<: if forks make more sense to you than hooks) basically using , to append the current value with the result of the recursive call. $:@<: says “apply myself after decrementing the argument”.
This suggests an obvious way to get the increasing list, by just flipping around the arguments to , append:
0:`($:@<: , ]) @.* 7
0 1 2 3 4 5 6 7I’m sure the self-reference version is worse in performance terms, but there isn’t as straightforward a way to flip it around like this, so this counts as an advantage here.
Detecting palindromes
This is one thing where Prolog usually has a significant advantage over other languages, because you can make the relationship between palindromes and reflection explicit:
palindrome(X) :- reverse(X, X).However, J is still able to beat this:
palindrome =: -: |.Match the value with its reflection.
We can improve slightly on the Collatz examples of Chapter 10 of Learning J by noting that, while taking a function power of infinity produces the fixed-point, taking a function power of boxed infinity (or simply the empty box) also gives us back the intermediate values. Let’s start by bringing back the function itself:
collatz =. -:`(1 + 3 * ])@.(2&|)To review briefly, we can treat f`g@.t as
false`true @. testIn other words, this is a very condensed version of what in C would look something like:
(test x) ? (true x) : (false x)So the overall expression says “if odd” (2&|) “then multiply by 3 and add one” ((1 + 3 * ])) “otherwise halve” (:-), . The @. causes the evaluation of cases and the backtick combines the cases.
As it happens there are some other J idioms that happen around this @. function, whose name is “agenda:”
<zero-case>`<non-zero case> @. *This exploits the fact that the monadic * gives you 0 for 0 and 1 for all other positive numbers. And indeed we find over a hundred instances of this in the distribution, especially in the math addons. There are several other idioms in the standard library, such as @.(*@#), which can be read:
<empty array case>`<non-empty array case> @. (*@#)or
<not length-N case>`<length N case> @. (N=#)or
<not square matrix case>`<square matrix case> @. (=/@$)The trick here being that reducing by equality against the shape will only be true if all the dimensions are the same.
The next step of Collatz is to build something that applies the function multiple times and gives us back the result. In Learning J we see that iterated application will gives 1 eventually, but we don’t see that using the ace will give us all those intermediates at once:
hailstones =. collatz^:(1&~:)^:a:So there’s basically two tricks going on here. The ^:a: is literally, to the power of empty box, which means in J, to the power of infinity, but give me all the results. The function being applied thusly is collatz^:(1&~:), which you can read as collatz, while it isn't equal to 1. This is because our definition has a stupid loop in it, from 1 to 4 to 2 to 1:
collatz 1
4
collatz 4
2
collatz 2
1
collatz 1
4With it the change, we see that it works:
hailstones 9
9 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1A note about the pattern ^:a:, it occurs pretty rarely in the library, only 9 times, mostly in dissect. ^:_ is not terribly common either. Looking through the code, I see a very large number of occurrences of ^:_1 to access inverse or obverse functions. +:^:_2 is a pattern for square root (which has its own primitive, %:) and *:^:_2 seems to be a pattern for 4th-root (why you would need this is beyond me).
One interesting thing happens if we try to apply our hailstones monad to an array:
hailstones i. 4
|rank error: collatz
| hailstones i.4This is because the rank of our functions appears to be wrong:
hailstones b. 0
_ _ _
collatz b. 0
_ _ _At rank infinity, these are hoping to apply to the whole array at once, which obviously will not work. We can improve our definition of collatz by adding an explicit rank, and then the problem with hailstones will go away, or we can just apply a rank to hailstones when we call it:
hailstones"0 i. 4
0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0
2 1 0 0 0 0 0 0
3 10 5 16 8 4 2 1
Now this is also surprising. We have a matrix with a bunch of zeros, and the answers are in the non-zero cells. This turns out to be something J and APL do to fill in when vectors of inequal length are combined to form a matrix. A better solution would probably be to box them.
(<@hailstones)"0 i. 4
┌─┬─┬───┬─────────────────┐
│0│1│2 1│3 10 5 16 8 4 2 1│
└─┴─┴───┴─────────────────┘
But, it might be more interesting to see how many iterations were necessary, rather than what those were, and just count them up:
(#@hailstones)"0 i. 4
1 1 2 8
Now we can just walk through the first hundred and find the one with the largest number of hops:
(] i. >./) ((#@hailstones)"0 i.100)
97The >./ says, “maximum” and dyadic i. finds the index of a value. So, the train ] i. >./ means, give me the index of the maximum value of this array. The answer is 97.
hailstones 97
97 292 146 73 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958...
# hailstones 97
119
There are 119 skips for #97. Wow!
Let’s talk about ΩeΩ = 1. Here’s a great blackpenredpen video about calculating this value:
This got me thinking about J, because it has some interesting “adverbs” for doing these sorts of calculations. For starters, there is a built-in numerical derivative operator D., and the power adverb, which has a note that giving an infinite power computes the limit. I think of it as a fixed-point operator: it repeatedly feeds the output back in as an input until the input and output are equal, which is a fixed point. The power adverb turns out to be a hugely useful control construct in several ways—you can use it to describe various kinds of conditions as well as loops.
The first problem in J is figuring out how to express the function ΩeΩ - 1 = 0. A little help from 13 : produced this: 1 -~ ] * ^. As usual, you read J from right to left. Start with the fork ] * ^. ] is effectively id for functional programmers. ^ is exponentiation; the dyadic form, such as 2^3 calculates 23, for instance, and the monadic form ^x computes ex. The fork trick being that the result of applying the left and the right are fed in as the left and right arguments to the center verb, ] * ^ is exactly xex. 1 -~ exploits a little trick about J, that constants can occur in certain positions of a fork or hook and act as values instead of functions, and because ~ flips the arguments of a verb, 1 -~ ... at the start of a train is a great way to signify “… - 1” in a formula.
xex = 1 -~ ] * ^.
There turns out to be no need to determine the derivative, because we can use the D. adverb. In fact, there is an essay about Newton’s method on the J software site; I wound up having to change d. to D. for reasons I don’t understand. In the end, we wind up with this adverb definition: N =. 1 : '- u % u D. 1'. Applying this once looks like:
(1 -~ ] * ^) N ] 1
0.68394Applying it two more times looks like:
(1 -~ ] * ^) N ] 0.68394
0.577455
(1 -~ ] * ^) N ] 0.57745
0.56723But, we can just let the power adverb iterate it for us until we converge:
(1 -~ ] * ^) N^:_ ] 1
0.567143Not enough precision? We can always ask for more:
0j50 ": (1 -~ ] * ^) N^:_ ] 1
0.56714329040978384011140178699861280620098114013672In the end the whole program is these two lines:
N =. 1 : '- u % u D. 1
0j50 ": (1 -~ ] * ^) N^:_ ] 1
0.56714329040978384011140178699861280620098114013672Unbelievable.
Curious how many iterations it took? If you give a boxed value to ^:, it will give you all the intermediates. So we can use # to count them up and <_ to produce an infinity in a box and find out:
# 0j50 ": (1x -~ ] * ^) N^:(<_) ] 1x
317For six places, it only takes 6 tries:
# (1x -~ ] * ^) N^:(<_) ] 1x
6
(1x -~ ] * ^) N^:(<_) ] 1x
1 0.68394 0.577454 0.56723 0.567143 0.567143Update on D. and d.
There are a few differences between D. and d. in modern J. The version of Newton’s method on the wiki page actually does work for this definition of ΩeΩ = 1: <:@(] * ^). There is not a huge difference between this and 1 -~ ] * ^, just that in the original case we are performing an argument-swapped subtraction with 1. In the new case we are composing a decrement function. The derivative operator d. is able to symbolically differentiate this definition, probably by simply discarding increment and decrement in composition since such things would fall off in general according to the power rule:
<:@(] * ^) d. 1
^ + ] * ^
(] * ^) d. 1
^ + ] * ^This is just the fact that d/dx(xex - 1) = d/dx(xex) = xex + ex.
In short, the differences between D. and d. are:
d.performs symbolic differentiationD.performs numeric approximation of a derivativeD.has different rankD.can be used to produce partial derivatives as well
The following books have made an impression on me and my beliefs.
Biblical Literacy by Rabbi Joseph Telushkin. This book gives you a synopsis of the bible, and Telushkin draws your attention to the moments and ideas that are important in Judaism. In a similar vein, How to Read the Jewish Bible by Marc Brettler, also surveys the content of the Bible and helps to put it into a modern Jewish perspective. Robert Alter’s translation of the Hebrew bible The Five Books of Moses, as well as its continuation in several more volumes, is also a vital resource to me. Alter brings an incredible amount of knowledge of Hebrew and related languages to bear on his translation and has copious notes about the decisions to be made, as well as point out puns or inside jokes that would not be apparent in the English translation. Bringing this edition to Bible study is worth a lot. Etz Hayim is the Conservative movement’s official chumash; the translation is bland, but you get 2:1 notes to text, which is wonderful, including a lot of very interesting tangential material. I found the combination of these two books to be very effective for bible study.
In a different vein, Chuang Tzu, translated by Burton Watson. The inner chapters in particular are both powerful and beautiful, but there are lots of gems in the remaining chapters as well, if you can ignore some repetition. I find a lot of compelling ideas in Taoism, especially Chuang Tzu’s version of it, but there is beauty in Tao Te Ching, the Addiss/Lombardo translation being the one I have.
The Rise of Christianity by Rodney Stark. This book shines a light on the darkness between 70 CE and the moment Christianity became the religion of the Roman Empire. Where did it come from, how did it grow so quickly? This book gave me a deeper appreciation of what it is about Christianity that made it change the world, and gave me more compassion for my Christian friends. Similarly but for Islam, Introduction to Islam for Jews by Reuven Firestone clarified things greatly, by showing ways that Judaism and Islam are similar and different. I think this book would work with a non-Jewish audience.
The Other God by Yuri Stoyanov is a fascinating deep-dive into the history of dualist thought, from ancient Egypt, through Zoroastrianism to defunct and mostly lost religions like Manichaeism and Catharism. Similarly, Ancient Mystery Cults is a deep dive into Mithraism and the Eleusian mysteries, what is known anyway, and the book was an effective antidote to tropes like “Christianity is just Mithraism dressed-up.” The Indo-European ideas that reappeared in Mithraism were also the bedrock of Iranian religion, where the dualist religion of Zoroastrianism was born and many other religions underwent change: the topic of the book Religions of Iran by Richard Foltz. Although not so much about religion, Genghis Khan and the Making of the Modern World by Jack Weatherford illustrates how many modern ideas were born by the Mongols and the fruit of their conquest, in the neighborhood.
In the Dust of This Planet and volume 2 of the same series, Starry Speculative Corpse are excellent overviews of a lot of areas of inquiry. I hesitate to come down hard as a pessimist but negative theology conceptually is very appealing to me and my understanding of it comes from these two books, which are short and approachable. I also got a lot out of Emerson, especially “Self-Reliance” and “Circles.”
Two other philosophers made deep impressions on me: Henri Bergson, whose Creative Evolution kept me struggling in college but whose ideas about time, duration, evolution and intuition have stuck with me in some bastard form, and Jiddu Krishnamurti, who really only had one thing to say (paraphrased “you don’t need a teacher, which is handy because you can’t have one anyway”) but said it so audaciously and powerfully that he wound up attracting a following and having to say it repeatedly. Try Freedom from the Known. (He deserves bonus points for dissolving the cult he was brought up to lead.)
In more depth with Judaism, we must discuss Heschel, whose books are so powerful I haven’t finished any of them. God in Search of Man is the one I most want to finish, The Sabbath is one I actually have finished, I Asked for Wonder is to my recollection, quotes, but even his quotes are great.
Some dimensions of Jewish practice that are worth discussion: Everyday Holiness teaches the practice of mussar, which is a form of Jewish-religious self-help; an interesting topic for someday when I’m bored. Jewish Meditation is what it says on the tin, and Rabbi Kaplan also did translations of other important Kabbalistic works, especially the purported manual for making golems Sefer Yetzirah and proto-Zohar Bahir, both of which are only approachable thanks to his copious notes. Notes outweigh source matter by about 10:1 in each of those.
Some more comparative religion, The Sikhs by Patwant Singh is a nice overview introduction to the religion I read before Wikipedia. Ofudesaki is the holy text of a fairly obscure Japanese religion, Tenrikyo; I never made it further than about 10 pages.
More crap—I mean, stuff—in the Western esoteric traditions: The Secret Doctrine of the Rosicrucians explains their “philosophy” of vibrations and magnetism and whatever. Similarly, Alchemy Rediscovered and Restored gives you more of the wider story of “spiritual alchemy” rather than just the Rosicrucian “version” of it. Feel free to go full stupid with Practical Qabalah and The Mystical Qabalah, but be sure to pick up Aleister Crowley’s books at some point.
I’ve been investigating radio networking a bit lately for a side project I’m thinking about. This summarizes what I’ve learned.
Different radio networking technologies in the hobbyist space have a fundamental tradeoff between range, bandwidth and power usage. Increasing range or bandwidth tends to increase power usage. So one has to ask questions like, how much data do you want to exchange on your network, at what rate, how far apart are they, and will your devices be powered.
- WiFi is a high-bandwidth, high-power-use option with medium range
- LTE is a medium-bandwidth, high-power-use option with long range (if you have coverage) that is pay-to-use.
- Bluetooth Low Energy is medium-high bandwidth, medium-low energy usage with very short range.
You’ve probably run into these already at some point, so it will be a relief to learn that it’s fairly easy to build out hobby projects using these technologies. You may be surprised to learn that none of these are what Phillips Hue, Smart Things, Nest or any other home automation system uses. Why is that?
- Connecting to WiFi (as you know) is not fast, but if your device enters a sleep state, it will have to rejoin when it wakes up. If you have a 20-byte packet to send every minute, the vast majority of your energy use is going to be wasted on WiFi associating. Most residential IoT things would rather have longer battery life.
- Who wants to spend $5/month per LTE device in your house? And what’s going to happen if you exceed a few MB of data?
- BLE is explicitly a one-to-one network with low range. It’s intended to be a cable replacement. Everything you want to coordinate has to be within the same short distance of your controller.
Now, there are bleeding-edge solutions to many of these problems. There is a low-power WiFi standard and Bluetooth 5 Mesh. But, there are other technologies that might be interesting to a hobbyist. If we were making a chart of bandwidth, power, distance with the options above you’ll notice we don’t have any medium-long distance, low-bandwidth, low energy use options. Those are:
- ISM-band packet radio
- 802.15.4/Zigbee/Thread
- LoRa
These options are all medium-low bandwidth, medium to long range, low power use. ISM band packet radio is what you get using a BBC micro:bit radio. The lowest-level option is the packet radio, which is essentially the most straightforward spray of a packet of bits on a particular frequency. This is low power use, but also not very reliable. The distance will depend on the power level and the frequency, with lower frequencies having lower bandwidth but longer range. Your choices are going to be 433 MHz, 915 MHz or 2.4 GHz, at least in the US. The BBC micro:bit is essentially doing this using its Bluetooth radio when you use the packet radio.
Zigbee and Thread essentially add addressing and mesh networking on top of the packet radio. The range is tens of feet, so somewhat longer than BLE but not quite WiFi. The main difference between the two is that Zigbee has a complex suite of protocols for different types of appliance and it’s own simple addressing scheme, where Thread just lets you use IPv6 addresses to talk to devices and leaves it at that.
LoRa doubles down on distance, having a range measured in multiple miles or kilometers. However, the packet size is very small, around 50 bytes, and you really can’t send more than 1% of the time. LoRa devices listen only directly after a broadcast for a tiny amount of time. I’m not sure what this is for. Perhaps farm automation? It’s very cool technology though.
Anyway, this is basically what I’ve learned.