I
will try to compare natural human languages and mathematical language
in order to try to answer the question '''Is Maths really a
language?' This is a very big question which will require a lot of
writing and my purpose is not to make you feel bored but to fire your
curiosity about the topic, and after that you will carry on exploring
by yourself. That's why I will do this comparison briefly.
Maths
is really very often called a language and it is true that Maths is
used in many other areas of human knowledge as a tool. Remember
engineering, science, geography and almost every other area, they use
something from Maths. It looks like the Maths language exists to
serve others by offering them a lot – arithmetic,
statistical graphical ways to represent certain knowledge,
probability, which is part of a risk assessment, geometry is
everywhere in building business and algebra is just sometimes so
annoying with her constant effort to find ‘X’ in our lives. But
this is what we are doing very often in our lives – we are
detectives who are trying to solve our own little mysteries. So, we
agree, Maths is present in every aspect in our personal and
professional lives.
What
is a natural human language then? By 'natural' I mean languages which
are spoken by people and which develop through the centuries.
They could be official state languages or a dialect, which is a
language which is spoken locally and it doesn't have official state
status. There are more than 6000 languages in the world and most of
them are disappearing, mainly due to migration. Some of the languages
are big – many people use them, such English, Arabic, Russian,
Spanish and some others. Some are little and some of them are
micro-languages. I spent some time of my university career doing
research about one very little Slavic micro-language – the Upper
Sorbian language and I even wrote two books about this language. It
is spoken in Eastern Germany and it is a disappearing language (only
around 50 000 people are speaking it), people are bilingual – they
know German as well. Their main cultural place is called
Bautzen. It is 60 km from Dresden. They have a Sorbian institute
there in Bautzen and I have been there many times to do research
about my books.
What
is the definition of a natural human language? We want to compare
Maths language with human languages so we need to have a starting
point and we need to know that the things we are comparing are
comparable.
Let's
take this definition as a working one: ' Natural human languages have
a structure which consists of many systems of symbols and signs.
There is a great hierarchy between the systems. The main function of
human languages is communicative, people use them to
communicate between themselves.' It is not a perfect definition but
it gives us main features of the language and we will try to find the
same features in the Maths language. So, we are looking for
similarities and differences.
Human
languages have systems of symbols and there is a hierarchy between
these systems. That means that the structure of the languages is like
a pyramid and if we miss learning one stage we won't be able to build
the next one. We start with the alphabet that gives us the letters,
but behind the letters there are sounds. So we have letters, sounds,
we connect them and we build words, we connect the words following
the rules of the Grammar, Semantics, Syntax and we create the
sentences. We connect the sentences together and we build a text. The
text is the highest floor of the language and the definition for the
text is – ‘The text exists when we have at least two sentences
connected together semantically and syntactically.’ Let's sum up
that the hierarchy of the language includes floors for letters,
sounds, words, sentences, text. They connect by the rules of the
Grammar, the Semantics and the Syntax. This is the most simple
understanding but we don't need it to be complicated. To say that you
know a language you need to know the speaking part – listening and
understanding, reading, understanding and writing. The teacher
should know all of these levels of a certain language if he teaches
it, otherwise it is not fair to the students.
One
more thing – the definition in the beginning included –
'communicative function'. This is the main function of human
languages – they developed because of the need of people to
communicate using their symbolic nature. There are other functions
like creative and some others, but we are not interested in that now.
Languages are very complex organisms, which develop by their own
rules. Most of the time linguists only register the changes
they cannot influence the change to happen.
What
about the Mathematical language? Does it look the same as human
languages? There are different opinions but we can see for sure some
similarities and some differences.
Similarities:
Mathematics uses symbols and signs as well, there is a hierarchy
between the systems as well. Like in the languages if you miss one
system you cannot build the other, the upper one. You have digits,
numbers that connect with operation symbols (signs for add, subtract,
multiply, divide), then they connect to create expressions, formulas,
identities, inequalities, and there is a story behind this, so they
express certain meanings and intentions.
In
human languages and in Maths language we have parts of speech.
Remember the parts of speech in English for example? Actually, in
every language they are the same (with some differences): Noun, Verb,
Adjective, Pronoun, Adverb, Preposition, Conjunctions, Particles
and Interjection.
We
can talk about parts of Mathematical speech as well, which have
the same functions like in human languages, and they are:
- Digits and numbers are like equivalents of Nouns in human languages.
- Operation symbols are actions, like verbs in the languages.
- Relation symbols - ‘equal to’, ‘greater than’, ‘less than’, they are statesman of comparison, of relationships. In a human language this is equivalent to adjectives and adverbs.
- Grouping symbols (like brackets) and they show the associations. In a human language this is equivalent to punctuation.
- Variables or Place holders and they are the unknowns. In the human language they are equivalent to pronouns.
The
Mathematical language is specific and exact but at the same time it
is highly abstract – when we say ‘4’ we don't mean any object
behind, it could apply to anything - to a very tiny object but to the
whole universe as well. Problem solving is like the text – it
expresses the application of the skills (the sentences).
What
are mathematical functions? Can we use it to communicate? Yes, we can
communicate certain knowledge and intentions, certain more
complex thoughts, ideas and concepts. Many fields of knowledge use
the mathematical language to communicate their ideas.
Differences:
It is a matter of convention that the mathematical language is not
used for everyday communication. If people agree what kind of syntax
will express certain meaning, maybe we can even write poetry.
This will be tricky because the poetic language is full of metaphors
and comparisons. It is not Maths’ fault that it didn't develop in
the same direction as natural languages. We can say that the Maths
language exists more in a written form.
So,
both natural human languages and the mathematical language,
together they allow people to express all possible intentions, highly
logical, using mathematical language, and highly poetic, using
natural human languages.
I
hope that this brief comparison made you think about some problems
you never spent time thinking about before. If this will happen even
only to some of you, I will be happy to be able to open your
eyes for some unusual sides
of
Maths knowledge. Thinking (together with Love) is one of the biggest
joys we can experience.
I
have one activity for you:
Use
your own native/first language and compare it with Maths language.
Choose some features to compare, make a list and put them in a Venn
diagram. For example: if you speak French, your Venn diagram should
be about comparing French language and Maths language. It will be
interesting to see your Venn diagrams. In the intersection part there
will be the features which are common for both.
In
our lives we are like walking human Venn diagrams. Relationships
could sometimes be complicated, especially if there is no
intersection area between the two human Venn diagrams. This is a sad
case when people just don't go well together because they are two
circles, two parts of a Venn diagram without intersection between. We
can improve this by making an effort of building the
intersection area in our relationships with other people – the
things that connect us, the things that unites us. Peace in the world
depends on the intersection area between us.
Let's
hope you learnt something more about Maths and you love Maths and
the languages even more.
(E.
S. Lyubenova; LoveMathsStory for my students)
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