Tech Comm & Number Theory

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As I’ve written previously, mathematics and technical communication (tech comm) both model reality. In math, numbers do not “exist” in the literal sense of the word. You can have 3 coins, but the concept of 3 does not occupy a physical point in time or space; it transcends it. Numbers, therefore, describe the quantities or properties of a person, place or thing but are not actual people, places or things.

Similarly, tech comm is a description of reality but is not reality itself. A guide explaining how to use a smartphone is not an smartphone but a representation of it. The ideas, lesson and concepts in the guide must be interpreted and understood by a human reader; therefore these things exist only in the reader’s mind.

Now, if mathematics and tech comm are attempts to describe reality, it follows that some of the basic principles of math should apply to tech comm.

Numbers are the building blocks of all mathematics. The 10 digits which form all numbers are math’s “alphabet”, however, not all numbers are equal; they fall into various groups.

Natural numbers are all whole positive numbers: 1, 2, 3 and so on. These are the practical, real-world numbers that we use each day when counting, ordering, adding, and so on. They are precise and complete because they exclude fractions or decimals. Any simple, clear and complete positively stated information corresponds to a natural number, for example: Sales increased 7% over last year.

Negative numbers are numbers less than 0. They were first envisioned by the Chinese over 2,000 years ago. There is a theory that the idea of duality in Chinese philosophy made it easier for this culture to develop the idea of a number less than zero.

Any negative statement corresponds to a negative number, for example:

Do not turn off your computer during the installation.

Fractions have at least two parts: the top number of the fraction or numerator and the lower portion or denominator. However, fractions can have more than two parts in the form of a complex fraction, for example (2/3)/( 5/7).

Complex modern content management systems (CMS) are actually composed of fractional pieces of information which are reused as required. For example, there may be many procedures which all refer to a specific part number. If you are using are using a typical Word processor to document these procedures and the part number changes, you’d have to manually search and replace every occurrence of this number. However, in a CMS, the part number is stored once in a database as a variable, and therefore only has to be changed once. All references to that part number are then automatically updated. Any piece of information can be a “informational fraction”, from a word, to a sentence, a paragraph, and even a page.

Irrational numbers have an infinitely long series of non-repeating digits after the decimal place. You can’t write them as a fraction or ratio. Examples include the square root of 2 (1.4142135…) and pi (π) which is equal to 3.14159265…. As you continue down the line of infinite digits, you get incrementally closer and closer to the true value of the number. However, when calculating values, you have to stop a certain point; you can’t simply go on forever. NASA scientists are able to keep the space station running using only 16 digits of pi. For calculating the fundamental constants of the universe, they need 32 digits.

Irrational communication is comprised of pieces of information which each add ever-decreasing value to the information. For example, let’s say you need to write a step that instructs users how to connect to a wi-fi network. The statement you develop is:

To connect to the wi-fi network, select the ABC_Network, then enter the following password: Pass1532.

For most people, this would suffice. However, what about novice users who don’t even know how to select a wi-fi network? We’d have to add another piece of information, underlined below:

To connect to the wi-fi network, on your device, under Settings, select Wi-Fi connections, select the ABC_Network, then enter the following password: Pass1532.

This seems complete, right? But what about people who are not sure what you mean by “device”? To address this, we add even more information:

To connect to the wi-fi network, on your SmartPhone, tablet, laptop or desktop, under Settings, select Wi-Fi connections, select the ABC_Network, then enter the following password: Pass1532.

But what about people who don’t know what a wi-fi network is? We add:

You can use our wi-fi network to connect to the Internet. To connect to the wi-fi network, on your SmartPhone, tablet, laptop or desktop, under Settings, select Wi-Fi connections, select the ABC_Network, then enter the following password: Pass1532.

And what about those poor souls who don’t know what the Internet is?

The internet is the world’s largest information network. It used to send and receive information, view news items, images, videos and sound, and to connect with others. You can use our wi-fi network to connect to the Internet. To connect to the wi-fi network, on your SmartPhone, tablet, laptop or desktop, under Settings, select Wi-Fi connections, select the ABC_Network, then enter the following password: Pass1532.

One could go adding information forever but I think you get the point. Each piece of new information, just like each additional digit in an irrational number, adds a bit more value to the original piece of information. How many “decimals” of information are required depends on the knowledge level of the average user. Too much information is as bad as not enough.

Now we come to one the most challenging types of numbers: imaginary. At some point, mathematicians asked: what is the square root of a negative number? There is no clear answer, because no number multiplied by itself produces a negative number. Two negative numbers multiplied together produce a positive number. To resolve this, mathematicians invented imaginary numbers, written with the letter i. For example, the square root of -9 is 3i.

The essence of imaginary numbers is:

  • two numbers are combined together
  • combining numbers normally creates a larger number but in this case actually creates a smaller one, therefore,
  • an inherent contradiction is created

The informational equivalent of an imaginary number is a statement added to another statement that creates a conflict and therefore lowers the value of both statements.

For example:

  1. If you over 18 years old, complete Form A.
  2. If you are less than 25 years old, complete Form B.

The second statement contradicts the first, and thereby negatively impacts both statements. It is the equivalent of the mathematical i, in this case, the i standing for incomprehensible, impossible, inexcusable and, quite possibly, insane. This is actually a common problem, especially with complex policies, procedures and regulations that are riddled with contradictions.

Finally, an exponent is a number that dramatically increases the value of another number, for example, 3³ which equals 3 x 3 x 3 or 27. Conversely, a square root is a number that when multiplied by itself creates a larger number, for example, 10 is the square root of 100. In either case, we are changing a small number very rapidly to much larger one, or vice versa.

If there’s one thing that information experts agree on, it’s that the amount of information in the world has grown exponentially. How much? A quick math lesson is in order. An exabyte is one quintillion (1018) bytes, which is one billion gigabytes or one thousand million billion bytes, a byte being equivalent to about one letter. One exabyte is up to 3,000 times the size of all the content in the Library of Congress. Between the start of history and 2003, five exabytes of information in total were created. We now create five exabytes every two days. Big data, indeed.

The single informational device that has contributed to the ability to access this near-infinite amount of information is a textual object that is absurdly simple yet staggeringly complex: the hyperlink. For with a single hyperlink, a tiny piece of information directly connects to something much larger. (This small link, for example, links to something vast.) The destination of the hyperlink is the exponent of the hyperlink itself; the hyperlink, therefore, is the root of the much larger piece of information that it points to.

It’s no coincidence that the word mathematics literally means “to learn”. The primary goal of tech comm is that the user learns something, whether it is a concept or a task. The connections between mathematics and tech comm are, as with math itself, measured, complex, and infinite.