February 7, 2014 at 19:55About the prospects of using AutoCorrect when typing
In a previous article, I examined the issues of creating alternative keyboard layouts, including problems that arise when building optimization models for these layouts.
Here we will go in a slightly different way and consider the possibility of reducing the total number of keystrokes (except for using chord dialing methods and stenotypes , as this is another big topic).
Immediately make a reservation that the use of stenotype together with knowledge of shorthand, of course, will give a much greater effect in terms of productivity growth. But the method discussed below is easy to implement (there is no need for special equipment, complex software) and requires orders of magnitude less time to learn (remembering a few dozen abbreviations is usually not difficult).
AutoCorrect (AZ) will be called such a method of printing a combination of letters / words / phrases, in which the source text is programmatically reassigned to other keyboard shortcuts. In order to increase productivity, the typed key combination (let's call it key or abbreviation) should have a minimum length with respect to the original sequence of letters. The difference in the number of keys pressed when typing a combination in its original form and when typing with abbreviations will be a gain on this combination due to AZ.
For example, you need to type such a frequently used word as "because." If the abbreviation looks like "n", then the gain in typing only one word will be 5 characters.
Note that in the world such a practice has long existed. Even competitions are held in various offsets - using the abbreviation system and without it. In the first case, the world record in the 30-minute interval is 955 bpm , in the second - 821 bpm . Both records were set by the notorious Helena Matushkova.
The most developed abbreviation system for the Czech language, called Zavavis (ZAVpis). There is even a training site , and there is information that the development of the abbreviation system begins only after acquiring a fairly high level of blind typing skill.
As we can see from the ratio of the numbers 955 and 821, the gain when using AZ is not so high (~ 16%). However, in this case, the AZ system is adapted to the average structure of the language, and does not take into account specific words, features that are characteristic of various fields of knowledge. Also, the user's vocabulary used in communication, everyday correspondence is not taken into account. In everyday life or in a narrow practical area, the vocabulary is much smaller in volume, and the effectiveness of the AZ system, compiled for specific needs, can significantly increase.
First you need to decide for what purpose the AutoCorrect system is created. If a AZ system is required to reduce the time needed to recruit an average sentence in Russian, then the structure of the language as a whole must be taken into account. Here you can go in two ways.
One of them is to collect with your own hand a large sample of texts that adequately represents the language (usually the size of such a sample is from several hundred megabytes) and analyze them statistically - to identify the most common words, combinations of letters, characters. Then, based on the analysis, build statistical tables.
Note that this method is more suitable for the case when the AZ system is created for yourself, under your most frequently used words - in articles, in business correspondence, when chatting, on a forum, etc.
The second is to use ready-made tables. Of course, such tables are already in a suitable form for use. This implies the use of the National Corps of the Russian language and frequency dictionaries of the Russian language (one of the most famous is Sharov’s frequency dictionary: [1] ; [2] ).
A list of the 100 most common word forms can be viewed here .
It seems logical that the most frequent words should be subjected to AutoCorrect in the first place, and among them the longest ones. In general, all language statisticians obey Zipf's law. This is a generalized hyperbolic distribution of ranked statistics, no matter at what level - whether it is the level of individual letters, symbols; level of letter combinations (n-gram); word level; phraseological level.
Such statistics, along with the Gaussian ones, very often appear in the world around us, and have been found in various fields of knowledge. For example, the distribution of people by income (Pareto), the distribution of scientists by productivity (Lotka), the distribution of articles by journals (Bradford), the distribution of settlements by number, the distribution of earthquakes by intensity, etc. In general, such statistics arise due to the strong interdependence of events in the system (analogue of positive feedback), according to the type of chain reaction, as a result of which both extreme amplification and strong weakening can occur.
It is important for us that the peaks, positive deviations from the hyperbolic trend will just point to those words that should first enter the AZ system. At the same time, the first several hundred of the most frequent words will make the greatest contribution to the total efficiency of the system.
Consider other features of the construction of the AZ system:
1. Keys must be unique (do not match words and other keys), minimal in length, and easy to remember. Such keys should consist of either the first few letters of the word, or the first and last.
2.The purpose of the keys (their length, letters, symbols used) will also depend on the size of the AZ system itself. Consider the simplest example. Suppose we want to create a system for a single word “later”, it is obvious that the best option is the abbreviation “p”. If the system will consist of two of more words (the real option), then you need to take into account the occurrence, as well as paragraph 1. Let the word “later” occur 10,000 times, and the word “therefore” 100,000 times. Obviously, the word with maximum occurrence must be assigned the reduction of the minimum length "p", and the word "later" - the abbreviation "pm". Of course, in the case of only two abbreviations, the second word can also be attributed to a single letter. But this case is still far from practical application, and therefore we applied the abbreviation "pm", which is more plausible.
It should also be taken into account that there are a maximum of 33 single-letter keys (without using numbers and symbols as keys), two-letter keys 33 2 = 1089. And then, with an overestimated estimate. It is unlikely that there will be keys of the form "b" or "yu."
3. Some keys may be in hierarchical form. For example, “h” -> “what” -> “anything”. In this case, the key can “unfold” as immediately after dialing, and after pressing the activator key.
4. The size of the AZ system should be a compromise between the theoretical gain and the time required to study the system. I did not use AZ extensively, but for a deployed system, a decent ceiling is estimated at about 1,000 cuts. For the system used in everyday life - 100 abbreviations is quite enough for the most frequently used words, phrases, turns.
AutoCorrect reduces the number of typed characters. Those. the word length is reduced by L SL -L AZ . Suppose, if we replace the word “what” with “h”, then on one word the gain will be L (what) -L (h) = 3-1 = 2 characters. Further, each word has its own specific frequency, expressed as a percentage. Or, if we use the corpus , then it usually provides data on the occurrence of the word - i.e. In general, the number of such words in the corpus.
For example, the word “what” is found in the corpus 2210373 times. Then the total gain from the set of all the words “what” in the case will be
characters.
To calculate the relative gain as a percentage of the total number of typed characters, we need to know the characteristics of the Russian language on average. The total body size is 1.93 ∙ 10 8 words. It would be logical to divide the number of words “what” into the total number of words, but the words have different lengths, which also need to be taken into account. The average word length in Russian, according to the corpus, is 5.28 characters.
Now we can now calculate the volume of the case in characters. But the corpus is not the whole text. In reality, there are many service signs in the text, such as a space, a period, a comma, a semicolon, quotation marks, various signs, numbers, etc. And to find the volume of the entire text in the corpus, we need to multiply the number of characters found by a certain coefficient, which reflects the share of service signs in the Russian-language text. According to our own calculations, approximately, the proportion of service signs is ~ 20%, with slight deviations in one direction or another.
Then the expression for calculating the relative gain on the constant auto-replacement of one word takes the form:
where
is the total number of words in the corpus,
is the average word length in Russian,
k- the proportion of service signs, numbers and other characters that are not included in the words.
The remaining designations were deciphered earlier.
Thus, for a single autocorrect on the word “what” we get a relative gain equal to.
As we can see, for a single word the gain is quite large, and many might think that for a developed AZ system, a gain of the order of tens of percent can be expected. But we used one of the most frequent words. And since the statistics of word occurrence obeys a hyperbolic law, the contribution (frequency) of each subsequent word will decrease significantly. Accordingly, the gain from AZ on such less frequent words will also not be very noticeable.
Lines are sorted by the total gain received from all AZs of the specified word throughout the corpus.
When choosing the number of words subjected to AZ, it is necessary to take into account the fact that the time to study the AZ system in a first approximation is proportional to the number of abbreviations. Those. the list of AZs must be of a reasonable size, where a compromise is found between the number of AZs and the gain they give. For this, it is necessary to construct an approximate graph of the dependence of the relative gain on the number of AZ.
A priori, we can assume that at first the gain will be significant, and the slope of the curve will be maximum (because the words are more frequent). With a decrease in the frequency of words, the gain from each subsequent word will decrease, the slope of the curve will also decrease. An interesting question is, will saturation be observed? Each AZ will give some gain, but will the word frequency not fall so much that each next relative increase will tend to zero.
In this paragraph, the main task is to find out to what number of AZs it is necessary to increase the list in order to maintain a compromise between the relative gain and time for training. Those. it is necessary to identify the transition region where the slope of the payoff curve becomes relatively small, in order to exclude ineffective AZs.
The graph was built on the basis of some simplifications for the general analysis. First, the lengths of all abbreviations AZ were assumed to be equal to two characters. Accordingly, words with a length of less than 3 characters were excluded from the list of the most frequent words. there will be no gain from them on such a AZ system. Further, it was assumed that the number of 2-character abbreviations would be no more than 700. This should be close to the truth, even with a somewhat overestimated estimate, as it is obvious that absolutely all 1089 digrams cannot be used as abbreviations for obvious reasons (for example, combinations of letters that are not associated with anything, as mentioned above). Three-character abbreviations were not considered at this stage.
The abscissa axis represents the total number of words with AZ, the ordinate axis represents the relative reduction in the number of keystrokes.
As expected, at the very beginning of the chart, for the first 100 cuts, the gain growth rate is maximum.
Here are some data on the schedule:
for the first 10 cuts, the gain is 0.82%,
for the first 20 - 1.24%,
for the first 50 - 2.23%,
for the first 100 - 3.50%,
for the first 200 - 5, 37%,
for the first 300 - 6.63%,
for the first 400 - 7.52%,
for the first 500 - 8.33%,
for the first 600 - 9.04%,
for the first 700 - 9.76%.
We calculate the winnings for the 1st, 2nd, 3rd, etc. hundreds of AZ.
For the first hundred, as already mentioned, 3.50%,
for the second - 1.87%,
for the third - 1.26%,
for the fourth - 0.89,
5th - 0.81%,
6th - 0 , 72%,
7th - 0.72%.
As we see, the growth rate drops, but then stabilizes. This is a rather unexpected result, which does not coincide with the a priori assumption. There is not even a hint of satiation of dependence. Apparently, with a sufficient number of cuts, you can ensure a big win. For example, with 700 AZs, the schedule gain will be 9.76%. This is already an acceptable value.
In reality, the gain will be even greater (by about 0.2-0.3%), because not only 2-character AZs are used, but also 1-character ones for the most common words. But in the future it will be necessary to use already 3-character abbreviations, therefore, the gain growth rate will drop a little, abruptly, relative to that observed in the 6th and 7th hundreds of AZs.
Based on the gain in gain, you can limit yourself to a list of AZs, consisting of 500 reductions, which will give a gain of 8.33%. It is also necessary to mention that in everyday life a person uses a limited set of words for correspondence, communication, writing texts, which is not at all equivalent in structure to the corpus of the Russian language. Every day, the words that are among the most common are used. Thus, for everyday tasks that do not include writing scientific articles, the gain will be even more significant, possibly even at times.
One can speculate why the gain rate of gain does not slow down constantly. Apparently, the decrease in the word frequency is compensated by the fact that less frequency words are also longer, and the gain is proportional to the product of the difference between the word lengths and the AZ by the word frequency.
For visual analysis, it is necessary to plot the dependence of the product of the word length by its frequency on the rank of the word in the frequency list. The most effective will be AZ words forming peaks relative to the average trend (of course, with some reservations - for example, the word should be quite long).
AutoCorrect will not be equally effective for different languages due to the varying complexity of the languages themselves. Printing in those languages that are considered “richer” (in the sense of a larger number of word forms) will be more difficult to reduce with the help of AZ.
For example, for a number of European languages, apparently, AZs will be more effective than for Russian. In turn, the English language will probably be more adapted to AZ than German.
Let's take an example: in Russian there are cases, numbers, in English there are no cases, but there is a number. For example, the word lamp is lamp.
Perhaps the given example is not true in all cases (for example, the situation will be different for verbs). However, it shows several salient features.
The table shows that for all cases the word "lamp" in the singular and plural for the Russian language will need 12-3 = 9 auto-replace, and for the English language - only 2 auto-replace (singular and plural). Those. with a highly developed, more redundant, with a large number of wordforms language, the task of assigning autocorrect is greatly complicated.
Also in English there are fewer letters themselves (26 versus 33 in Russian), and therefore, there are much fewer combinations of these symbols. The highest possible top score is 26 2 for English and 33 2for Russian. In reality, of course, even less is used. For the Russian total, there are about ~ 700 semantic digrams (two-letter combinations). The aforementioned circumstances once again indicate that languages whose entropy (redundancy) is higher are worse suited to autocorrect.
Finally, the list of the most frequent words in English should also be much shorter than for Russian. Those. if, for example, you take 10%, 20% coverage (the most common words that make up 10%, 20% of all words), then for English such a list should also be shorter.
It can already be seen from the above examples that the task of constructing a flexible system of automatic substitution for the Russian language is a rather complicated non-trivial task, and it is even more difficult to provide a good performance boost. In our case, the overall performance gain, starting from 10%, in the average sense, will be considered good. This is the minimum to which we must strive.
In addition to words, a tangible fraction of the characters are so-called. service, syntactic characters: white space, punctuation, etc. They account for about 20% of the total number of characters.
Let us turn to the list of the most frequent 2-character combinations (for all characters there are usually no such tables, so you need to do them yourself, analyzing large amounts of text information). The most common 2-character combination is “,”, i.e. comma + space. According to its own data, it accounts for 1.64% of the total number of digrams (two-character combinations).
Let’s evaluate the winnings during the auto replacement of this combination with one character (or with one click). You can assign such a combination to the CapsLock key, since it is rarely used in everyday work (of course, you can use other options that are convenient for a particular user).
In the standard YTsUKEN layout, to type a comma, you need to press 2 keys - “Shift” and “.”. Thus, the combination, for the set of which required 3 clicks, will be typed with one click. Which is equivalent to a reduction of 2 clicks.
In this case, the gain is calculated as follows: if the digram were completely excluded from the set, then the gain was equal to its frequency. But in our case, there is simply a reduction in the combination. Those. the gain will be proportional to the relative reduction of the combination and its frequency:
where
is the length of the combination before reduction,
is the length of the combination after reduction (taking into account AZ),
is the frequency of the combination among combinations of the same length.
Thus, we get a gain from reducing “,” to one click.
In reality, taking this one digram into account will not give a big picture, because it is necessary to take into account the fact that commas are excluded in digrams, where they are in the second position.
To calculate the gain in this case, it is convenient to use unary (single-character) statistics if it was calculated in the process of preparing the tables. In our case, such a table was calculated. Despite some variability of statistical characteristics for texts of different genres, their considerable stability is nevertheless observed, which allows us to talk about a certain statistical structure of the Russian language on average.
In texts more or less widely encountered in practice, the fraction of a dot and a comma are generally equal and amount to approximately 1.5% each. For indicative calculations, the gain from replacing “,” with CapsLock is quite sufficient.
In order to understand how to consider the effectiveness of AZ in this case, we can give an example. Consider a piece of text consisting of three sentences, each of which has 70 characters. Let each sentence have one capital letter (beginning) and 2 commas. Then the total number of strokes will be 219. We use the replacement “,” with CapsLock. Further, the gain can be defined as follows: since instead of three taps for the “,” set, we only make one (CapsLock), this is equivalent to excluding the comma from the set, because it needs 2 clicks. Total remains 207 clicks. The gain will be 12 / 219≈5.5%, which is a lot for one combination with AZ. Of course, this is a purely hypothetical example in which the frequency of commas is overstated.
From this, incidentally, another aspect of the use of AZ arises - competitive, because in a short light text, with frequency words, you can quite significantly increase the result - up to 20-25% (and even higher). As already mentioned at the very beginning of the article, when using AZ, a separate offset should be made.
In general, in order to evaluate the real gain, it is necessary to recalculate the statistics of symbols in the statistics of clicks, i.e. Symbols do not take into account such a frequently pressed key as “Shift”. We should also mention “Enter,” but in the usual analysis of arrays of textual data, this key (equivalent to a paragraph or a line break) is usually not taken into account. And this article does not cover this issue.
To count the number of presses of the “Shift” key while typing on the standard layout, you need to know the percentage of capital letters, as well as the percentage of characters “,” and “!”, “” ”,“ “”, “No.”, “;”, “ % ",": ","? "," * "," (",") "," _ "," + ", I.e. all dialed in the fourth row (digital) using Shift. For the first approximation (which, however, should be fairly accurate), we assume that the fractions of the characters typed in the fourth row are approximately equal to zero (to a sufficient extent this corresponds to reality).
Capital letters in the vast majority of cases are typed only at the beginning of sentences. You can add one capital in the middle of the sentence to account for the proper name, if one is used. To simplify, let’s say that there are 2 capital letters per sentence. The total length of the sentence in characters, according to the statistics of the Russian language corpus, will be
where
is the average number of words in the sentence.
If we take into account that the fraction of the comma is 1.5%, then this corresponds to approximately one comma per sentence: 65.8 ∙ 0.015≈0.9. In addition, there are an average of 2 capital letters. That is, it turns out that there are 3 more clicks than characters or 68.8 clicks per 1 sentence on average. Of these 68.8 clicks, 2 clicks are per comma. As mentioned earlier, the AZ, on CapsLock is equivalent to excluding a comma from the set, so the gain from such AZ in clicks will be:
Compared to the gain that was obtained in words, this is a very tangible increase from only one combination. In principle, this was to be expected, because the more often the combination, the greater the gain from reducing such a combination (with a sufficient length or number of clicks). Of course, the minimum that can still be reduced is two-character combinations. And individual letters are no longer abbreviated. Here you can consider different levels of aggregation: 2-character, 3-character, etc. After the 4-character, it is more reasonable to consider the level of words, and then the phraseological level. Of course, there are some frequency combinations of letters, symbols, words, other than those that we have already considered.
What other common syntax characters can improve performance? For example, you can notice that in the vast majority of cases, a space is followed by a dot (except for the ellipsis, which is rare, and it can also be assigned to a separate key, at least in an additional layer). Also, a space always comes after a dash (but not after a hyphen). In principle, in most editors, dashes and hyphens are typed with the same “- / _” key, but, for example, in Word, a dash is set if there were spaces before and after it.
It is proposed to set the auto-space after the dash, i.e. the combination “-” puts an additional space. This will also save a little on the set of service signs. You can also set auto-spaces after such frequently occurring characters as the colon “:” and the semicolon “;”. You can put a space after other signs of the end of the sentence - interrogative and exclamation "?" and "!".
There are cases, but very rarely, when you need to type several identical characters in a row. For this case, you can provide the following AZ. Suppose you need to type five exclamation points: "!!!!!", for this an AZ of the form "5!" Will be used. For rarely encountered dots, you can also provide a separate key, for example, “ё”, since the letters “e” and “ё” are often not distinguished and “ё” remains unused (I ask you not to throw stones at me for the ubiquitous use of the letter “ё”, since AZ can be assigned to any other key). In principle, everyone can determine for themselves unused keys and assign them the most effective AZ.
Consider the auto-space after the point, and the gain from such a function. As mentioned, the probability of a dot in the text is 1.5%. Each sentence has approximately one point, followed by a space. Except in cases where the dots "..." are used, which are very rare. The dot and the space after it make up about 1.5% ∙ 2 = 3% of all characters. Using automated space after the period, we exclude half of these 3%, i.e. we get another 1.5% gain. This is a good result for one function. Considering auto-spaces after other signs - interrogative and exclamatory, you can still increase the gain. But, as a rule, the proportion of such signs is very small compared to the point and you can not consider it as significant.
Достаточно частой комбинацией является « –» (пробел и тире), после нее идет еще один пробел. Если ставить автопробел после этой комбинации, то выигрыш в символах будет равен числу таких комбинаций, соответственно, выигрыш в процентах будет равен доле таких комбинаций в % от общего числа комбинаций заданной длины.
Можно записать общую формулу для расчета выигрыша от сокращения любой комбинации, зная ее долю (частоту) в общей структуре языка, включая синтаксические символы:
где kк — доля данной комбинации среди всех комбинаций такой же длины; это может быть диграмма (2 символа), триграмма (3 символа), n-грамма (длина n символов); в нашем случае имеем дело с диграммами;
n- the number of characters by which you can reduce the text after meeting this combination; this wording takes into account both the possibility of AZ, as well as auto space and similar functions;
V add - additional gain from the reduction of all other combinations, which include the excluded characters; in each case should be calculated separately.
As already mentioned, AZ can be used not only at the level of words, but also at the level of phrases, phraseological level. There are stable phrases, for example, some of them: “how are you”, “like life”, “good afternoon”, “because”, “despite”, “at all costs”, etc .; less frequent - "in any case", "based on the foregoing," "from what follows."
Each has his most frequent phrases, which he uses in conversation and business communication, in correspondence. Based on these stable phrases, you can develop an addition to the AZ system specifically for them. In each case, one should take into account the consistency with the existing AZ system and calculate the winnings provided by the auto-replacement of each new combination.
But much more frequent than words or phrases are n-grams (n-character combinations with a small n, n <5). For example, one can distinguish such frequently encountered combinations at the end of words as “ny”, “nn”, “tys”, “tys”. You can provide AZ for them.
For example, if the key with the letter “ё” is not used (forgive me for its use), then assign one of the AZ to this key. A combination of this key with Shift will give another combination, i.e. Shitf + ё = tsya; ё = tsya. Again, each of these combinations needs to be considered separately, in accordance with their frequency and consistency with the already made reduction system. It is important that there is no confusion and no abbreviations similar in writing to words that are written in completely completely different ways.
Next, you can connect the AZ system and the layout optimization procedure.
The optimization procedure described in the previous article has a fine system and digram statistics as input parameters. The system of fines / incentives will remain the same, and due to the application of the AZ system, the statistics of digrams will somehow change.
Accordingly, the optimal layout for some AZ system will differ from the optimal layout used without AZ. It is necessary to recalculate the changes in statistics for each position of the auto-replacement - for each word with AZ, combinations, combinations of syntactic characters.
To calculate the change in the frequency of the combination, you need to consider a specific example, from which then you can derive general patterns. Take the word "more." The frequency of occurrence of a word in a corpus is 124201 times. The total number of words in the corpus= 1.93 ∙ 10 8 . The average word length is ≈5.28 characters. The proportion of syntactic symbols k ≈20%. Now we have all the data to calculate the number of characters in the case. Such a recount is needed to bring the statistics of words to the statistics of digrams (and the number of digrams in the text is equal to the number of characters in it minus 1). The total number of characters in the case:
Knowing the number of occurrences of a particular word in the corpus, we automatically know the number of occurrences of each digram from this word in the corpus. Those. for the word “more” it will not be the total frequency of the digrams “bo”, “ol”, “eh”, etc., but only the frequency of the digrams “bo”, “ol”, “eh”, ... of that particular word. This frequency will be written:
where
is the frequency of any digram of the word in question;
- frequency of occurrence of the word in the corpus;
- The total number of shell characters found above.
For example, we calculate the frequencies of the digrams introduced into the case with the word “more”:
When using AZ, these frequencies will be subtracted from the total number of corresponding digrams, and some new ones introduced by reduction will be added.
For concretization, suppose that the word "more" will be reduced when typing to "bo." Then the found frequencies of the digrams "ol", "eh", "hh", "sheh", "e" will be subtracted from the general table of frequencies of the digrams. The combination of "bo" remains unchanged, and it is not necessary to recount it. But a new digram will be added, previously not existing in the word - “o”.
Its frequency will be the same as that of the rest (i.e., the number of its occurrences in the corpus is equal to the frequency of occurrences of the word) - 0.01%. The value of this frequency will be added to the general table of frequencies of the digrams. To complete the analysis, we calculate the resulting frequencies obtained only for the AZ "bo" = "more".
If strictly, it is also necessary to take into account the fact that the volume of the typed text will decrease with an increase in the number of AZ. Those. the effect is better calculated in absolute terms per text of a certain volume. Thus, it will be more accurate if we consider not relative changes (percent), but absolute values: how many digrams of this type were in the text and how many became. The conversion to relative values is needed only at the final stage of the calculation, before starting the optimization procedure.
Since the amount of data is quite large, this stage (however, like all) requires partial or complete automation.
The described procedure should be repeated for each AutoCorrect. As a result, we get recalculated statistics of digrams, which can be used as an input variable for the layout optimization procedure.
When using a layout optimized for AZ, and the corresponding AZ system, in the aggregate, one can achieve a noticeable improvement in the dialing parameters both in terms of convenience and speed.
For practical use of AutoCorrect, you can use the popular AutoHotKey or PuntoSwitcher programs .
AutoHotKey documentation can be viewed here , some of the features are here .
Making individual lines of a common script with AZ:
the word “time” will appear after pressing “in” and the activation key, usually a space.
in this case, the word “time” will appear immediately after typing “in”.
; - an optional character, separates comments.
As an afterword, I note that this article, like the previous one, has a mainly academic focus. Practical application is limited only by professional or semi-professional typesetters, which are extremely few in the total mass of PC users. Nevertheless, I hope that some of the most convenient replacements are already used or can be used by almost everyone. Constructive criticism on the issues of calculations and logic of presentation is welcome.
Here we will go in a slightly different way and consider the possibility of reducing the total number of keystrokes (except for using chord dialing methods and stenotypes , as this is another big topic).
Immediately make a reservation that the use of stenotype together with knowledge of shorthand, of course, will give a much greater effect in terms of productivity growth. But the method discussed below is easy to implement (there is no need for special equipment, complex software) and requires orders of magnitude less time to learn (remembering a few dozen abbreviations is usually not difficult).
What are AutoCorrect?
AutoCorrect (AZ) will be called such a method of printing a combination of letters / words / phrases, in which the source text is programmatically reassigned to other keyboard shortcuts. In order to increase productivity, the typed key combination (let's call it key or abbreviation) should have a minimum length with respect to the original sequence of letters. The difference in the number of keys pressed when typing a combination in its original form and when typing with abbreviations will be a gain on this combination due to AZ.
For example, you need to type such a frequently used word as "because." If the abbreviation looks like "n", then the gain in typing only one word will be 5 characters.
Note that in the world such a practice has long existed. Even competitions are held in various offsets - using the abbreviation system and without it. In the first case, the world record in the 30-minute interval is 955 bpm , in the second - 821 bpm . Both records were set by the notorious Helena Matushkova.
The most developed abbreviation system for the Czech language, called Zavavis (ZAVpis). There is even a training site , and there is information that the development of the abbreviation system begins only after acquiring a fairly high level of blind typing skill.
As we can see from the ratio of the numbers 955 and 821, the gain when using AZ is not so high (~ 16%). However, in this case, the AZ system is adapted to the average structure of the language, and does not take into account specific words, features that are characteristic of various fields of knowledge. Also, the user's vocabulary used in communication, everyday correspondence is not taken into account. In everyday life or in a narrow practical area, the vocabulary is much smaller in volume, and the effectiveness of the AZ system, compiled for specific needs, can significantly increase.
The choice of words and other issues of creating a system of autocorrect
First you need to decide for what purpose the AutoCorrect system is created. If a AZ system is required to reduce the time needed to recruit an average sentence in Russian, then the structure of the language as a whole must be taken into account. Here you can go in two ways.
One of them is to collect with your own hand a large sample of texts that adequately represents the language (usually the size of such a sample is from several hundred megabytes) and analyze them statistically - to identify the most common words, combinations of letters, characters. Then, based on the analysis, build statistical tables.
Note that this method is more suitable for the case when the AZ system is created for yourself, under your most frequently used words - in articles, in business correspondence, when chatting, on a forum, etc.
The second is to use ready-made tables. Of course, such tables are already in a suitable form for use. This implies the use of the National Corps of the Russian language and frequency dictionaries of the Russian language (one of the most famous is Sharov’s frequency dictionary: [1] ; [2] ).
A list of the 100 most common word forms can be viewed here .
It seems logical that the most frequent words should be subjected to AutoCorrect in the first place, and among them the longest ones. In general, all language statisticians obey Zipf's law. This is a generalized hyperbolic distribution of ranked statistics, no matter at what level - whether it is the level of individual letters, symbols; level of letter combinations (n-gram); word level; phraseological level.
Such statistics, along with the Gaussian ones, very often appear in the world around us, and have been found in various fields of knowledge. For example, the distribution of people by income (Pareto), the distribution of scientists by productivity (Lotka), the distribution of articles by journals (Bradford), the distribution of settlements by number, the distribution of earthquakes by intensity, etc. In general, such statistics arise due to the strong interdependence of events in the system (analogue of positive feedback), according to the type of chain reaction, as a result of which both extreme amplification and strong weakening can occur.
It is important for us that the peaks, positive deviations from the hyperbolic trend will just point to those words that should first enter the AZ system. At the same time, the first several hundred of the most frequent words will make the greatest contribution to the total efficiency of the system.
Consider other features of the construction of the AZ system:
1. Keys must be unique (do not match words and other keys), minimal in length, and easy to remember. Such keys should consist of either the first few letters of the word, or the first and last.
2.The purpose of the keys (their length, letters, symbols used) will also depend on the size of the AZ system itself. Consider the simplest example. Suppose we want to create a system for a single word “later”, it is obvious that the best option is the abbreviation “p”. If the system will consist of two of more words (the real option), then you need to take into account the occurrence, as well as paragraph 1. Let the word “later” occur 10,000 times, and the word “therefore” 100,000 times. Obviously, the word with maximum occurrence must be assigned the reduction of the minimum length "p", and the word "later" - the abbreviation "pm". Of course, in the case of only two abbreviations, the second word can also be attributed to a single letter. But this case is still far from practical application, and therefore we applied the abbreviation "pm", which is more plausible.
It should also be taken into account that there are a maximum of 33 single-letter keys (without using numbers and symbols as keys), two-letter keys 33 2 = 1089. And then, with an overestimated estimate. It is unlikely that there will be keys of the form "b" or "yu."
3. Some keys may be in hierarchical form. For example, “h” -> “what” -> “anything”. In this case, the key can “unfold” as immediately after dialing, and after pressing the activator key.
4. The size of the AZ system should be a compromise between the theoretical gain and the time required to study the system. I did not use AZ extensively, but for a deployed system, a decent ceiling is estimated at about 1,000 cuts. For the system used in everyday life - 100 abbreviations is quite enough for the most frequently used words, phrases, turns.
Calculating winnings from using AutoCorrect
AutoCorrect reduces the number of typed characters. Those. the word length is reduced by L SL -L AZ . Suppose, if we replace the word “what” with “h”, then on one word the gain will be L (what) -L (h) = 3-1 = 2 characters. Further, each word has its own specific frequency, expressed as a percentage. Or, if we use the corpus , then it usually provides data on the occurrence of the word - i.e. In general, the number of such words in the corpus.
For example, the word “what” is found in the corpus 2210373 times. Then the total gain from the set of all the words “what” in the case will be
characters.
To calculate the relative gain as a percentage of the total number of typed characters, we need to know the characteristics of the Russian language on average. The total body size is 1.93 ∙ 10 8 words. It would be logical to divide the number of words “what” into the total number of words, but the words have different lengths, which also need to be taken into account. The average word length in Russian, according to the corpus, is 5.28 characters.
Now we can now calculate the volume of the case in characters. But the corpus is not the whole text. In reality, there are many service signs in the text, such as a space, a period, a comma, a semicolon, quotation marks, various signs, numbers, etc. And to find the volume of the entire text in the corpus, we need to multiply the number of characters found by a certain coefficient, which reflects the share of service signs in the Russian-language text. According to our own calculations, approximately, the proportion of service signs is ~ 20%, with slight deviations in one direction or another.
Then the expression for calculating the relative gain on the constant auto-replacement of one word takes the form:
where
is the total number of words in the corpus, is the average word length in Russian, k- the proportion of service signs, numbers and other characters that are not included in the words.
The remaining designations were deciphered earlier.
Thus, for a single autocorrect on the word “what” we get a relative gain equal to.
As we can see, for a single word the gain is quite large, and many might think that for a developed AZ system, a gain of the order of tens of percent can be expected. But we used one of the most frequent words. And since the statistics of word occurrence obeys a hyperbolic law, the contribution (frequency) of each subsequent word will decrease significantly. Accordingly, the gain from AZ on such less frequent words will also not be very noticeable.
Begin Abbreviation Table
Lines are sorted by the total gain received from all AZs of the specified word throughout the corpus.
Effect of AutoCorrect system volume on its effectiveness
When choosing the number of words subjected to AZ, it is necessary to take into account the fact that the time to study the AZ system in a first approximation is proportional to the number of abbreviations. Those. the list of AZs must be of a reasonable size, where a compromise is found between the number of AZs and the gain they give. For this, it is necessary to construct an approximate graph of the dependence of the relative gain on the number of AZ.
A priori, we can assume that at first the gain will be significant, and the slope of the curve will be maximum (because the words are more frequent). With a decrease in the frequency of words, the gain from each subsequent word will decrease, the slope of the curve will also decrease. An interesting question is, will saturation be observed? Each AZ will give some gain, but will the word frequency not fall so much that each next relative increase will tend to zero.
In this paragraph, the main task is to find out to what number of AZs it is necessary to increase the list in order to maintain a compromise between the relative gain and time for training. Those. it is necessary to identify the transition region where the slope of the payoff curve becomes relatively small, in order to exclude ineffective AZs.
The graph was built on the basis of some simplifications for the general analysis. First, the lengths of all abbreviations AZ were assumed to be equal to two characters. Accordingly, words with a length of less than 3 characters were excluded from the list of the most frequent words. there will be no gain from them on such a AZ system. Further, it was assumed that the number of 2-character abbreviations would be no more than 700. This should be close to the truth, even with a somewhat overestimated estimate, as it is obvious that absolutely all 1089 digrams cannot be used as abbreviations for obvious reasons (for example, combinations of letters that are not associated with anything, as mentioned above). Three-character abbreviations were not considered at this stage.
The abscissa axis represents the total number of words with AZ, the ordinate axis represents the relative reduction in the number of keystrokes.
As expected, at the very beginning of the chart, for the first 100 cuts, the gain growth rate is maximum.
Here are some data on the schedule:
for the first 10 cuts, the gain is 0.82%,
for the first 20 - 1.24%,
for the first 50 - 2.23%,
for the first 100 - 3.50%,
for the first 200 - 5, 37%,
for the first 300 - 6.63%,
for the first 400 - 7.52%,
for the first 500 - 8.33%,
for the first 600 - 9.04%,
for the first 700 - 9.76%.
We calculate the winnings for the 1st, 2nd, 3rd, etc. hundreds of AZ.
For the first hundred, as already mentioned, 3.50%,
for the second - 1.87%,
for the third - 1.26%,
for the fourth - 0.89,
5th - 0.81%,
6th - 0 , 72%,
7th - 0.72%.
As we see, the growth rate drops, but then stabilizes. This is a rather unexpected result, which does not coincide with the a priori assumption. There is not even a hint of satiation of dependence. Apparently, with a sufficient number of cuts, you can ensure a big win. For example, with 700 AZs, the schedule gain will be 9.76%. This is already an acceptable value.
In reality, the gain will be even greater (by about 0.2-0.3%), because not only 2-character AZs are used, but also 1-character ones for the most common words. But in the future it will be necessary to use already 3-character abbreviations, therefore, the gain growth rate will drop a little, abruptly, relative to that observed in the 6th and 7th hundreds of AZs.
Based on the gain in gain, you can limit yourself to a list of AZs, consisting of 500 reductions, which will give a gain of 8.33%. It is also necessary to mention that in everyday life a person uses a limited set of words for correspondence, communication, writing texts, which is not at all equivalent in structure to the corpus of the Russian language. Every day, the words that are among the most common are used. Thus, for everyday tasks that do not include writing scientific articles, the gain will be even more significant, possibly even at times.
One can speculate why the gain rate of gain does not slow down constantly. Apparently, the decrease in the word frequency is compensated by the fact that less frequency words are also longer, and the gain is proportional to the product of the difference between the word lengths and the AZ by the word frequency.
For visual analysis, it is necessary to plot the dependence of the product of the word length by its frequency on the rank of the word in the frequency list. The most effective will be AZ words forming peaks relative to the average trend (of course, with some reservations - for example, the word should be quite long).
On the comparative effectiveness of AutoCorrect for Russian and English
AutoCorrect will not be equally effective for different languages due to the varying complexity of the languages themselves. Printing in those languages that are considered “richer” (in the sense of a larger number of word forms) will be more difficult to reduce with the help of AZ.
For example, for a number of European languages, apparently, AZs will be more effective than for Russian. In turn, the English language will probably be more adapted to AZ than German.
Let's take an example: in Russian there are cases, numbers, in English there are no cases, but there is a number. For example, the word lamp is lamp.
Perhaps the given example is not true in all cases (for example, the situation will be different for verbs). However, it shows several salient features.
The table shows that for all cases the word "lamp" in the singular and plural for the Russian language will need 12-3 = 9 auto-replace, and for the English language - only 2 auto-replace (singular and plural). Those. with a highly developed, more redundant, with a large number of wordforms language, the task of assigning autocorrect is greatly complicated.
Also in English there are fewer letters themselves (26 versus 33 in Russian), and therefore, there are much fewer combinations of these symbols. The highest possible top score is 26 2 for English and 33 2for Russian. In reality, of course, even less is used. For the Russian total, there are about ~ 700 semantic digrams (two-letter combinations). The aforementioned circumstances once again indicate that languages whose entropy (redundancy) is higher are worse suited to autocorrect.
Finally, the list of the most frequent words in English should also be much shorter than for Russian. Those. if, for example, you take 10%, 20% coverage (the most common words that make up 10%, 20% of all words), then for English such a list should also be shorter.
It can already be seen from the above examples that the task of constructing a flexible system of automatic substitution for the Russian language is a rather complicated non-trivial task, and it is even more difficult to provide a good performance boost. In our case, the overall performance gain, starting from 10%, in the average sense, will be considered good. This is the minimum to which we must strive.
Using AutoCorrect for Service Symbols
In addition to words, a tangible fraction of the characters are so-called. service, syntactic characters: white space, punctuation, etc. They account for about 20% of the total number of characters.
Let us turn to the list of the most frequent 2-character combinations (for all characters there are usually no such tables, so you need to do them yourself, analyzing large amounts of text information). The most common 2-character combination is “,”, i.e. comma + space. According to its own data, it accounts for 1.64% of the total number of digrams (two-character combinations).
Let’s evaluate the winnings during the auto replacement of this combination with one character (or with one click). You can assign such a combination to the CapsLock key, since it is rarely used in everyday work (of course, you can use other options that are convenient for a particular user).
In the standard YTsUKEN layout, to type a comma, you need to press 2 keys - “Shift” and “.”. Thus, the combination, for the set of which required 3 clicks, will be typed with one click. Which is equivalent to a reduction of 2 clicks.
In this case, the gain is calculated as follows: if the digram were completely excluded from the set, then the gain was equal to its frequency. But in our case, there is simply a reduction in the combination. Those. the gain will be proportional to the relative reduction of the combination and its frequency:
where
is the length of the combination before reduction, is the length of the combination after reduction (taking into account AZ), is the frequency of the combination among combinations of the same length. Thus, we get a gain from reducing “,” to one click.
In reality, taking this one digram into account will not give a big picture, because it is necessary to take into account the fact that commas are excluded in digrams, where they are in the second position.
To calculate the gain in this case, it is convenient to use unary (single-character) statistics if it was calculated in the process of preparing the tables. In our case, such a table was calculated. Despite some variability of statistical characteristics for texts of different genres, their considerable stability is nevertheless observed, which allows us to talk about a certain statistical structure of the Russian language on average.
In texts more or less widely encountered in practice, the fraction of a dot and a comma are generally equal and amount to approximately 1.5% each. For indicative calculations, the gain from replacing “,” with CapsLock is quite sufficient.
In order to understand how to consider the effectiveness of AZ in this case, we can give an example. Consider a piece of text consisting of three sentences, each of which has 70 characters. Let each sentence have one capital letter (beginning) and 2 commas. Then the total number of strokes will be 219. We use the replacement “,” with CapsLock. Further, the gain can be defined as follows: since instead of three taps for the “,” set, we only make one (CapsLock), this is equivalent to excluding the comma from the set, because it needs 2 clicks. Total remains 207 clicks. The gain will be 12 / 219≈5.5%, which is a lot for one combination with AZ. Of course, this is a purely hypothetical example in which the frequency of commas is overstated.
From this, incidentally, another aspect of the use of AZ arises - competitive, because in a short light text, with frequency words, you can quite significantly increase the result - up to 20-25% (and even higher). As already mentioned at the very beginning of the article, when using AZ, a separate offset should be made.
In general, in order to evaluate the real gain, it is necessary to recalculate the statistics of symbols in the statistics of clicks, i.e. Symbols do not take into account such a frequently pressed key as “Shift”. We should also mention “Enter,” but in the usual analysis of arrays of textual data, this key (equivalent to a paragraph or a line break) is usually not taken into account. And this article does not cover this issue.
To count the number of presses of the “Shift” key while typing on the standard layout, you need to know the percentage of capital letters, as well as the percentage of characters “,” and “!”, “” ”,“ “”, “No.”, “;”, “ % ",": ","? "," * "," (",") "," _ "," + ", I.e. all dialed in the fourth row (digital) using Shift. For the first approximation (which, however, should be fairly accurate), we assume that the fractions of the characters typed in the fourth row are approximately equal to zero (to a sufficient extent this corresponds to reality).
Capital letters in the vast majority of cases are typed only at the beginning of sentences. You can add one capital in the middle of the sentence to account for the proper name, if one is used. To simplify, let’s say that there are 2 capital letters per sentence. The total length of the sentence in characters, according to the statistics of the Russian language corpus, will be
where
is the average number of words in the sentence.If we take into account that the fraction of the comma is 1.5%, then this corresponds to approximately one comma per sentence: 65.8 ∙ 0.015≈0.9. In addition, there are an average of 2 capital letters. That is, it turns out that there are 3 more clicks than characters or 68.8 clicks per 1 sentence on average. Of these 68.8 clicks, 2 clicks are per comma. As mentioned earlier, the AZ, on CapsLock is equivalent to excluding a comma from the set, so the gain from such AZ in clicks will be:
Compared to the gain that was obtained in words, this is a very tangible increase from only one combination. In principle, this was to be expected, because the more often the combination, the greater the gain from reducing such a combination (with a sufficient length or number of clicks). Of course, the minimum that can still be reduced is two-character combinations. And individual letters are no longer abbreviated. Here you can consider different levels of aggregation: 2-character, 3-character, etc. After the 4-character, it is more reasonable to consider the level of words, and then the phraseological level. Of course, there are some frequency combinations of letters, symbols, words, other than those that we have already considered.
What other common syntax characters can improve performance? For example, you can notice that in the vast majority of cases, a space is followed by a dot (except for the ellipsis, which is rare, and it can also be assigned to a separate key, at least in an additional layer). Also, a space always comes after a dash (but not after a hyphen). In principle, in most editors, dashes and hyphens are typed with the same “- / _” key, but, for example, in Word, a dash is set if there were spaces before and after it.
It is proposed to set the auto-space after the dash, i.e. the combination “-” puts an additional space. This will also save a little on the set of service signs. You can also set auto-spaces after such frequently occurring characters as the colon “:” and the semicolon “;”. You can put a space after other signs of the end of the sentence - interrogative and exclamation "?" and "!".
There are cases, but very rarely, when you need to type several identical characters in a row. For this case, you can provide the following AZ. Suppose you need to type five exclamation points: "!!!!!", for this an AZ of the form "5!" Will be used. For rarely encountered dots, you can also provide a separate key, for example, “ё”, since the letters “e” and “ё” are often not distinguished and “ё” remains unused (I ask you not to throw stones at me for the ubiquitous use of the letter “ё”, since AZ can be assigned to any other key). In principle, everyone can determine for themselves unused keys and assign them the most effective AZ.
Consider the auto-space after the point, and the gain from such a function. As mentioned, the probability of a dot in the text is 1.5%. Each sentence has approximately one point, followed by a space. Except in cases where the dots "..." are used, which are very rare. The dot and the space after it make up about 1.5% ∙ 2 = 3% of all characters. Using automated space after the period, we exclude half of these 3%, i.e. we get another 1.5% gain. This is a good result for one function. Considering auto-spaces after other signs - interrogative and exclamatory, you can still increase the gain. But, as a rule, the proportion of such signs is very small compared to the point and you can not consider it as significant.
Достаточно частой комбинацией является « –» (пробел и тире), после нее идет еще один пробел. Если ставить автопробел после этой комбинации, то выигрыш в символах будет равен числу таких комбинаций, соответственно, выигрыш в процентах будет равен доле таких комбинаций в % от общего числа комбинаций заданной длины.
Можно записать общую формулу для расчета выигрыша от сокращения любой комбинации, зная ее долю (частоту) в общей структуре языка, включая синтаксические символы:
где kк — доля данной комбинации среди всех комбинаций такой же длины; это может быть диграмма (2 символа), триграмма (3 символа), n-грамма (длина n символов); в нашем случае имеем дело с диграммами;
n- the number of characters by which you can reduce the text after meeting this combination; this wording takes into account both the possibility of AZ, as well as auto space and similar functions;
V add - additional gain from the reduction of all other combinations, which include the excluded characters; in each case should be calculated separately.
AutoCorrect at the level of individual letter and word combinations
As already mentioned, AZ can be used not only at the level of words, but also at the level of phrases, phraseological level. There are stable phrases, for example, some of them: “how are you”, “like life”, “good afternoon”, “because”, “despite”, “at all costs”, etc .; less frequent - "in any case", "based on the foregoing," "from what follows."
Each has his most frequent phrases, which he uses in conversation and business communication, in correspondence. Based on these stable phrases, you can develop an addition to the AZ system specifically for them. In each case, one should take into account the consistency with the existing AZ system and calculate the winnings provided by the auto-replacement of each new combination.
But much more frequent than words or phrases are n-grams (n-character combinations with a small n, n <5). For example, one can distinguish such frequently encountered combinations at the end of words as “ny”, “nn”, “tys”, “tys”. You can provide AZ for them.
For example, if the key with the letter “ё” is not used (forgive me for its use), then assign one of the AZ to this key. A combination of this key with Shift will give another combination, i.e. Shitf + ё = tsya; ё = tsya. Again, each of these combinations needs to be considered separately, in accordance with their frequency and consistency with the already made reduction system. It is important that there is no confusion and no abbreviations similar in writing to words that are written in completely completely different ways.
AutoCorrect layout optimization
Next, you can connect the AZ system and the layout optimization procedure.
The optimization procedure described in the previous article has a fine system and digram statistics as input parameters. The system of fines / incentives will remain the same, and due to the application of the AZ system, the statistics of digrams will somehow change.
Accordingly, the optimal layout for some AZ system will differ from the optimal layout used without AZ. It is necessary to recalculate the changes in statistics for each position of the auto-replacement - for each word with AZ, combinations, combinations of syntactic characters.
To calculate the change in the frequency of the combination, you need to consider a specific example, from which then you can derive general patterns. Take the word "more." The frequency of occurrence of a word in a corpus is 124201 times. The total number of words in the corpus
= 1.93 ∙ 10 8 . The average word length is ≈5.28 characters. The proportion of syntactic symbols k ≈20%. Now we have all the data to calculate the number of characters in the case. Such a recount is needed to bring the statistics of words to the statistics of digrams (and the number of digrams in the text is equal to the number of characters in it minus 1). The total number of characters in the case:Knowing the number of occurrences of a particular word in the corpus, we automatically know the number of occurrences of each digram from this word in the corpus. Those. for the word “more” it will not be the total frequency of the digrams “bo”, “ol”, “eh”, etc., but only the frequency of the digrams “bo”, “ol”, “eh”, ... of that particular word. This frequency will be written:
where
is the frequency of any digram of the word in question; - frequency of occurrence of the word in the corpus; - The total number of shell characters found above. For example, we calculate the frequencies of the digrams introduced into the case with the word “more”:
When using AZ, these frequencies will be subtracted from the total number of corresponding digrams, and some new ones introduced by reduction will be added.
For concretization, suppose that the word "more" will be reduced when typing to "bo." Then the found frequencies of the digrams "ol", "eh", "hh", "sheh", "e" will be subtracted from the general table of frequencies of the digrams. The combination of "bo" remains unchanged, and it is not necessary to recount it. But a new digram will be added, previously not existing in the word - “o”.
Its frequency will be the same as that of the rest (i.e., the number of its occurrences in the corpus is equal to the frequency of occurrences of the word) - 0.01%. The value of this frequency will be added to the general table of frequencies of the digrams. To complete the analysis, we calculate the resulting frequencies obtained only for the AZ "bo" = "more".
If strictly, it is also necessary to take into account the fact that the volume of the typed text will decrease with an increase in the number of AZ. Those. the effect is better calculated in absolute terms per text of a certain volume. Thus, it will be more accurate if we consider not relative changes (percent), but absolute values: how many digrams of this type were in the text and how many became. The conversion to relative values is needed only at the final stage of the calculation, before starting the optimization procedure.
Since the amount of data is quite large, this stage (however, like all) requires partial or complete automation.
The described procedure should be repeated for each AutoCorrect. As a result, we get recalculated statistics of digrams, which can be used as an input variable for the layout optimization procedure.
When using a layout optimized for AZ, and the corresponding AZ system, in the aggregate, one can achieve a noticeable improvement in the dialing parameters both in terms of convenience and speed.
Implement AutoCorrect
For practical use of AutoCorrect, you can use the popular AutoHotKey or PuntoSwitcher programs .
AutoHotKey documentation can be viewed here , some of the features are here .
Making individual lines of a common script with AZ:
::в::время;
the word “time” will appear after pressing “in” and the activation key, usually a space.
в::время;
in this case, the word “time” will appear immediately after typing “in”.
:*:в::время; - то же самое, что и в предыдущем случае.
; - an optional character, separates comments.
As an afterword, I note that this article, like the previous one, has a mainly academic focus. Practical application is limited only by professional or semi-professional typesetters, which are extremely few in the total mass of PC users. Nevertheless, I hope that some of the most convenient replacements are already used or can be used by almost everyone. Constructive criticism on the issues of calculations and logic of presentation is welcome.