# How fast can a species communicate using only tapping?

Most members of my species are fairly human-like and can communicate using speech, but many of them possess mutations that make normal speech impossible. These mutations can also significantly change their limbs and digits, so a shared sign language won't work either. So that everyone can talk to each other, they have invented a way to communicate by tapping or clicking, but I'm not sure if it would be too slow to be practical for everyday use.

Some information:

• Members of the species are about as intelligent as humans.
• They have not evolved to communicate using taps- it's a modern invention.
• They tap on small, simple devices they carry with them, personalised to the individual so that their taps sound unique. For this reason there is no standard on how the taps sound, except they are approximately the same length.
• They can produce two different-sounding taps with the devices. Of course, the absence of a tap can be used for communication too.
• I'll assume they can make up to 12 taps per second, and a listener can distinguish different taps at the same speed. Humans can tap 10-11 times per second, but because the species communicates this way constantly they're a little faster.
• The tapping language doesn't necessarily need to be similar to any spoken language.
• The tapping language must be able to communicate concepts just as complex as in English or another spoken language.

The obvious real-world parallel is morse code, but it's pretty slow to tap out each individual letter. Instead, my idea was to have each series of taps represent a different word, where each word's meaning is highly context-dependent (somewhat like the way Chinese characters work). However, I'm unsure of how fast communicating this way could be, and I feel that it might be easy to miscommunicate. Is there a better way? How fast could they communicate compared to real-world languages?

• Considering your morse example. Taking 13 words-per-minute as an average metric we can achieve about 10-11 taps per second when morsing. Now imagining that tapping has evolved as the main mean of communication instead of talking, that speed would very likely be wayyyyyyyyy higher :) – dot_Sp0T Sep 23 '16 at 10:14
• @dot_Sp0T, I didn't know humans can tap so fast! However tapping is not an evolved form of communication for this species. I'll add more information to the question to clear this up. – K-T Sep 23 '16 at 10:24
• So I think your concept of tapping is intuitive enough, but I love pushing against intuitions to open up new options. Cicada make their noise by creating a series of clicks so close together that they sound like a continuous sound. If you think in those ways, then you could actually produce speech with tapping. All you have to do is tap fast enough and modify the tone of the taps with a vocal tract. – Cort Ammon Sep 23 '16 at 15:01
• Can they produce both types of taps simultaneously? – rek Sep 23 '16 at 19:56
• @rek I don't see why not. – K-T Sep 24 '16 at 0:26

## 11 Answers

Use Huffman coding like language. If a word is used more often, it has a shorter tap duration. For instance, if I do a low tap (l), it would be "be" most used essential word in English. If I do a high tap (h), this means it will be followed by another say hhl would be "to" and hll would be "of" and continues like this. I tried to find the relation to regular human speech. At 2 levels, a document containing 50000 words could be spoken by your species would take 19 hours while it would take around 8 hours for a regular human. If you include silence and double tap it would take half of it, 9.5 hours. With small changes to the language you could easily get it down to regular speech. Note that this document contains many names, numbers and the like.

• Huffman coding of words is the answer to this. Making the language context-dependent, as the OP suggests, doesn't actually help all that much, because you have to have escape codes from the context, or you can only speak in clichés. Context-dependency also makes it almost impossible to recover from a missed or misheard tap. – John Dallman Sep 23 '16 at 18:11
• Note that with "no tap" being included it would become difficult to distinguish one word from another. It would necessarily include a standard wait time between words greater than the greatest "no tap" period, which could be difficult to work. Not impossible, but I'm not sure you would improve the efficiency of the language by a full 50%. Maybe 20-30%? Mind, 20-30% on top can still be a big difference. – GrinningX Sep 28 '16 at 14:59
• You don't need spaces with huffmann coding. You should know when a word ends. Doubling number of symbols would exactly double the efficiency as it is simple math, 2^(2x) = 4^(x). But using spacing between words have its own merit and can be incorporated as a special symbol. Even then that would help to improve the efficiency. With spaces you could use LL, LH, HH and HL at the same time instead of only two symbols with length two. Without spaces each tier can contain 2^n - 2 symbols, with space that is 2^n. It looks a little but that means more shorter taps and since shorter taps are used ... – Cem Kalyoncu Sep 28 '16 at 15:23
• ... more frequently, it will definitely reduce the average word length. Additionally, using spaces will help people to synchronize easier to the speech. – Cem Kalyoncu Sep 28 '16 at 15:24

Well, let's see.

Edit: my post was written when the Op still went with 6 taps per second. It was now changed to 12, so you can half all times and double the amount of sentences per minute... which makes this a VERY fast language in comparison.

But arguably... 12 per second is SUPER fast, that's almost the rate of fire of a machine gun... back to original answer:

There are three possible stati for each "tap": no tap, low tap, high tap. You said each individual can make two different sounds. Can they make both at once, like a double tap?

So, my first tap has 3 different possibilities. My second tap also has that many, making it 9 possible tap-combinations. (3²). The third tap has 27 different ones (3³). After 1 second, and 6 taps, i have 729 possible combinations. After 2 seconds, i reach 531441 possible combinations.

Edit: to put that into relation: UTF8 can code 1.048.576 characters, which we can reach with just one tap more.... and most of UTF8 characters aren't even used.

According to several sites, there are 50,000 chinese kanji characters, of which there are 2136 commonly used. So 2 seconds are MORE than enough to code all known characters and more.

But how effective is communication this way?!

Using taps, we could reach the usual 2136 after roughly 1,17 seconds. (3^7=2187). That's nice.

Let's assume the double-tap is possible. That will increase the number of possible combinations per second to: 4^6=4096. Sadly, that only reduces the amount of time we require for the minimum set to 1,0 seconds, as 0,83 seconds only give us 1024 characters.

Wow, that was a lot of math. As we can see, the double-tap would be nice to reduce "talking times", but is not necessary, so i will not further investigate here. Let's assume everything without doubletapping from here on.

So, we can communicate 1 word per 1,17 seconds. An average sentence length in english is 15-20 words. In asian languages, as i speak a bit japanese (weeb alert), i assume the word count is a bit less, as at least japanese has a fairly easy grammar, and allows to omit words, if the context is clear to the listener.

So, our tapping aliens would need 1,17 * sentence length in seconds for each sentence... lets say the average is 12-15. So it takes them 14-18 seconds to tap an average sentence. That makes 3-4 sentences per minute. in english, you can speak roughly 5 per minute, 8-10 maximum. So it sounds like it can actually enter the competition.

overall, it sounds not like the fastest way to communicate, as i can probably type much faster, but it still sounds feasible and possible. Especially if the language offers a very simple grammar.

But how about those extra chinese characters? The ones above our 2000? Well, maybe the aliens have two ways of tapping: fast-tapping, and long tapping. If they want to tap a word that is not one of the usual characters (that are all the same length!), they start off with a special sequence, and then they tap the word for 12 taps (2 full seconds), giving them enough room to tap everything they want, all known chinese, japanese, greek, latin and farsi characters and some smileys, too.

That't it for my answer, and here are some links i used for sources:

http://www.sljfaq.org/afaq/how-many-kanji.html

https://strainindex.wordpress.com/2008/07/28/the-average-sentence-length/

http://www.urch.com/forums/tse/16887-how-many-sentences-do-you-speak-one-minute.html

https://de.wikipedia.org/wiki/UTF-8

• You've figured out how long it takes to tap out a Chinese character, but then multiplied that by the number of words in a sentence in English. I don't think they can be equated that way. Wouldn't it make more sense to find the average number of Chinese characters in a Chinese sentence? – K-T Sep 23 '16 at 11:08
• @K-T i tried, but a quick google search offered no usable result. So i went with an estimate. If you have a good number, i'd be happy to edit my answer with more precise numbers. – Andreas Heese Sep 23 '16 at 11:46
• Chinese words tend to be only a couple of characters anyway, so it's an okay estimate. Might be off by a factor of two. – Reese Sep 23 '16 at 11:52
• Keep in mind that more common characters can be given less taps. – PyRulez Sep 24 '16 at 1:58
• I think you meant Unicode, not UTF8. Encoding bytes as UTF8 will increase the number of bits needed, and you didn't consider the variable number of bytes. A better encoding would use Huffman trees or the like, giving shorter sequences to common symbols. – JDługosz Sep 24 '16 at 8:13

In pure information content, as Andreas Heese noted above, tapping 12 times a second is more than fast enough to code data considerably faster than English. But remember - at a very conservative estimate, English has 7 different vowel sounds (a/e/i/o/u plus diphthongs) and 15 different consonants (p/t/k/b/d/g/s/z/sh/zh/th/l/r/n/m plus some more that can only be written in IPA), and packs upwards of eight separate sounds into a second. In pure information content, if we have to alternate between consonants and vowels, that should put us in the neighborhood of $7^4 \cdot 15^4 = 121,550,625$ possibilities per second. The English language only has about a million words (according to a quick Google search). If we're speaking at a rate of about one word per second, why are we leaving one hundred and twenty million possibilities open?

The best answer I'm aware of is redundancy - a language that relies on using every one of its possibilities is too vulnerable to getting misheard or misunderstood. Let's assume that English is about as efficient as it gets in that respect (not an entirely unrealistic assumption, after ten thousand years of linguistic evolution) but that the artificially designed language these tap-people will speak can do a bit better. So let's say we have to waste about $50$ times as many options as we use. Three options per tap, twelve taps per second, gives us $3^{12} = 531441$ options per second. That gives us about ten thousand usable options per second, comparing with English's million. Looks bad, right? But in two seconds that gives us a hundred million options, more than enough to handle English. In fact, we should be able to express one English word in $1.5$ seconds. So this tap-language should take about $50$ percent longer than English, which puts it neatly in the "workable" category.

• Great point about redundancy! However, I'm not sure that they would waste less words than English- if anything, I think they'd waste more because with only 3 different sounds to distinguish, it'd be very easy to confuse one word with another. – K-T Sep 23 '16 at 11:23
• Agreed - I'm being generous. But it's reasonable to expect that a designed language would be more efficient than a natural one, so it should balance out at least a little. In any case, it would take a lot more inefficiency to take more than two seconds to express a second of English. – Reese Sep 23 '16 at 11:51
• English has 20 or more vowel phones depending on your dialect. – rek Sep 28 '16 at 16:02

The beings in question can tap 12 times per second and have a vocabulary of 2 sounds for this purpose. Let's call one . and one - for the simplicity of notification. There is also not tapping as a way to split information chunks. To efficiently transport information, the message should be short. So the best method of packing the information is to use an algorithm, that sorts the characters of the alphabet in a way, that makes often used characters very short but has the downside of making seldom used characters longer. The method of storing is a tree diagram, and the result for the English language is pretty much Morse Code - the most common 2 letters are . (E) and - (T). The sentence "to be" could be transferred as "- --- -... .", which would be exactly 12 taps, bringing it to the same speed of spoken language. It would be even faster than spoken language when telling numbers: the Morse encoding uses 5-tap chunks for each number, meaning 2 numerals per second. However, the encoding is still not the fastest:

Let's assume any character is 1 byte of information. So that makes at best (a message only made from T and E, maybe it was teetet) 6 byte per second and at worst (2 numerals) a 2 byte per second. If the tappers would use the average speed of the current world record holder, conversations would be held at 230 bytes per minute, so 3.83 bytes per second. That is ok for a somewhat slowed down conversation in English (which has an average word length of 5.1 letters).

It could be sped up if there would be no vowels in the alphabet used (because it would cut the average word length and the character length - 5 less!) so the information tree is only 21 characters tall. If we cut out close homophones, the information tree could be trimmed to as small as 16 characters + 10 numerals. 16 characters encoded as . - and combinations means one needs 2+4+8+16=40 possible combination of at worst 4 taps - that would pack the language better than current more, but it would read more like the transcript of ancient Egypt.

Now, they could also speak ASCII encoded. Of the 255 characters that the system allows, only 2x 26 are letters. Let's cut the 31 control taps from the front and just tap continuously with 26 characters + 10 letters encoded in same-length chunks. Each letter would need a chunk of 5 taps so we get all of them encoded, that would put us at exactly 2 byte per second... better use morse tree encoding with the gap than this. But if we use non-sound as an encoding method, our alphabet is down to combinations of 3 taps for 39 possibilities - that speeds us up to 4 characters per second, a bit better than our morse!

Now, one could ALSO encode the text in something like Katakana, which uses 73 syllables - while the average Japanese word uses something between 2 or 3 of these per word. Not using the no-sound as a possibility but only . and -, the 73 characters need a tree of depth 6, while only 11 characters (+ the 10 numerals) are in the 6th layer. So the standard tap length for a word is probably below the 12 taps. That would give us a speed of slightly over 1 word per second!

You say that "[m]embers of the species are about as intelligent as humans." All the other answers have only addressed the possible maximum speed of sending information through tapping, but none have addressed the question of how much information can be mentally processed by a being of average human intelligence.

Many people can speak pretty fast, if they say the same word over and over again. But if they have to actually form meaningful sentences that are relevant to the context, they usually have to slow down.

And many people can hear words coming in very fast, but they won't understand what is being said unless you speak slow enough for them to process the words.

So what you need to determine is maximum verbal processing speed, both for the production and the understanding of language.

There is a lot of literature on this, but you can find out yourself. To measure the maximum speed with which an average human (i.e. you) can understand language, simply use an audiobook that you are unfamiliar with and play it on your computer using a software such as VLC that allows you to change playback speed. Speed it up until it is as fast you can follow mentally for longer than a minute. Now use a printed version of that book and count the number of words you have heard in that minute. That's the maximum amount of verbal input processing.

To measure the maximum speed with which an average human can produce language, use your computer's built-in microphone to record you talking. Now do any speaking task your like (e.g. "Explain to me what you do at your job.") and then count the words. That's the maximum amount of verbal output processing.

• 110-150 is the number of words per minute for an average human (some can reach to 400+) that can talk. Without reasoning, a human can understand up to 600 words per minute (if you are a fast reader, regular reader can read around 300). Reasoning depends on the context and difficulty of the subject but sometimes won't be even necessary. – Cem Kalyoncu Sep 23 '16 at 19:42

comparing this to morse code, experts can read/hear at 140 words per minute and transmit at around 40-45 words per minute.

That's using morse code, whilst a language entirely made up of taps including slang could be even quicker.

• Just for reference: 40-45 is one third of a regular speaker. – Cem Kalyoncu Sep 23 '16 at 11:17

You did not specify a tech level, so i will assume it comparable to our moderrn day.

Your species will quickly discover that the tapping device is the limiting factor.
If you replace it with something resembling a smartphone, you do not only gain a lot more tappable surfaces, you might also get autocomplete-features, "smart" layout of tappable surfaces and whatnot. This will multiply the information density per tap.

Obviously, you also gain the possibility to overcome range limits, since you could display the result either on the device for your partner to read, or send it over a network to a remote partner.

Broadcasting, locally or remotely, will also be simple.

A side effect is that audio signals are easier misunderstood or obscured by noise than written signals, so they may even communicate with a lower loss rate.

As you've said they are capable of making both types of taps (High and Low, they've been called) simultaneously, and the lack of a tap can also communicate information, this means there are four possible taps:

High
Low
High + Low
No Tap

You've specified they are capable of making and distinguishing 12 taps per second, which means every second there are 16,777,216 ($4^{12}$) potential combinations (including repeating the same tap 12 times) per second. This is essentially a quaternary system. In comparison, binary (tap or no tap) communication at 12 taps per second would produce only 4,096 potential taps per second.

The smallest unit of information is a single tap lasting 1/12th of a second, but the largest would last multiple seconds maxing out at the limit of the human attention span. Since we're prizing speed above all other qualities, let's assume the longest tap-word is three seconds long. That's over 50 million potentially valid word formations (4$^{12}$ x 3 = 50,331,648).

With over 50 million twelfths-of-a-second slots to be filled, it's entirely possible for this language to compress more meaning into a three-second word (or shorter) than most natural languages manage in complex sentences. Consider that English has roughly a tenth the number of words that your tap-lang could contain.

For an example of a constructed language pursuing higher info density, look at Ithkuil. It is a constructed language designed to convey complex meaning without ambiguity.

The many examples from the original grammar book show that a message, like a meaningful phrase or a sentence, can usually be expressed in Ithkuil with fewer sounds, or lexically distinct speech-elements, than in natural human languages. For example, the two-word Ithkuil sentence "Tram-mļöi hhâsmařpţuktôx" can be translated into English as "On the contrary, I think it may turn out that this rugged mountain range trails off at some point".

So it's entirely possible that in a span of a few seconds your tappers could have conversations that would take us a minute or more. The difference of a few taps (each a twelfth of a second long) could completely change the meaning of a tap-word or phrase, meaning this would be a synthetic language if not polysynthetic:

Polysynthetic languages typically have long "sentence-words" such as the Yupik word tuntussuqatarniksaitengqiggtuq which means "He had not yet said again that he was going to hunt reindeer." The word consists of the morphemes tuntu-ssur-qatar-ni-ksaite-ngqiggte-uq with the meanings, reindeer-hunt-future-say-negation-again-third.person.singular.indicative; and except for the morpheme tuntu "reindeer", none of the other morphemes can appear in isolation.

In conclusion your tappers would "speak" faster than the general population, and in short bursts, in my opinion.

Why tapping?

There are quite a few humans in the world today who cannot communicate by speaking. The problem is usually not with their vocal apparatus, but with their ears. They are profoundly deaf.

They have solved the problem of "speaking" between themselves, and with normal humans willing to learn how to "talk" with them, many times over. Many sign languages. A simultaneous translation from speech to sign language is perfectly possible, so there is clearly no bandwidth problem.

So why use a click language which is likely four times slower? Unless this species has some strange anatomy or neurology which makes them unable to sign. A click language might briefly be of use during the technological era of sound-only telephony. But once video phones become widely available I'd anticipate signing would take over.

• The mutations that prevent them from speaking result in somewhat unpredictable physiology. They always have limbs of some sort, but not always digits- they might have something like tentacles or pincers instead. I don't think a sign language would be practical in this case. – K-T Sep 24 '16 at 0:38

Have you read about Tap Code? I remember hearing a radio interview of a former Vietnam POW who claimed they could send 25 to 30 words per minute using it.

Just to throw some simple math in here, you basically have a language with 3 units (High, low, and none)

Assuming that everything in the language is just long hyper-overloaded words, this means that you can express 3^n different ideas with n taps.

So a 1 second word (12 taps) is 3^12 = 531,441 And a 2 second word (24 taps) is 3^24 = 282,429,536,481

So assuming they have some form of edict memory, They can easily communicate a lot of information quickly. And if you want to reserve no sound as a word-break, than it just becomes 2^n (and for sum x^y for y= 0 to z, (x^z)*2 is roughly close enough)

And similar any other language, the most commonly used words/phrases would make up the shorter tap portion of the language.

On another note, Humans can only remember roughly 7 things at a time, but can artificially increase that with grouping (say remembering 4 clicks as a 'syllable'. So you max word length would probably be about 3^(7*4)

Hopefully this should give you some numbers/formulas to play with (and adding a wider verity of clicks, like scratching, rolling tap (with bumps on the device), or increasing the recognizable volume range; would greatly improve the language's communication)

Also a note, people who use languages with subtle pronunciation differences are better at picking up those subtle differences, so even with personalized devices, they could easily learn to recognize a wider verity of clicks. ^w^

And for the language itself, morose code would be a good starting reference with Huffman encoding (Which pretty much was the practice of using code words that have little meaning alone, like book, to mean whole phrases like "come ASAP")