Mathematics, only a language? (Part 1)
[Last update: 22nd July 2017]
There are mathematicians who would not want to see and accept mathematics as a language or a formal language. The reduction of mathematics to a formal language is important to understand the math behind the mathematics and perhaps to be able to internalize the underlying philosophy – especially for non-mathematicians.
Regardless of the point of view, mathematics is mostly used as a tool / instrument in natural sciences and other disciplines.
Sometimes the reality of mathematics is often deformed* by persons or group of interests, mostly with statistics and its related statements. This is not a fault of mathematics or intended by mathematics, it’s only the cognition or the suggestion intended by the initiator.
Back to our assumption: Mathematics is just a formal language! To understand this, one should internalize what is a formal language. A formal language is a construct over a given alphabet and production rules. One can also regard the rules of production as axioms or grammars. Attention, I’m using the terms here as synonyms, although they are well-defined and circumscribable – but as synonyms it’ll help you to understand it better!
Now back to mathematics. Mathematics also has well-defined signs and axioms. Based on this, the whole mathematics is built up. The axioms are non-contradictory. If they should contradict each other, then the whole mathematics would collapse like a house of cards.
Appeal to the linguistic genes who feel that they can’t do anything with mathematics. It is also just a language 😊.
* This is not only the case in mathematics, it is also in many other disciplines too – from simple test reports to scientific reports. Here is a case that has lasted for almost a century:
- Falsches Komma → Spinat ist gesund, weil er besonders viel Eisen enthält. Stimmt’s?
[Translation of the Headline: Wrong comma? Spinach is healthy because it contains a lot of iron. Is it true?] – unfortunately, this article is only in German language available
(article from October 1997, Die Zeit)
This can have happened accidentally, but it has been swept under the carpet, so that one does not sit on the overproduction. Another example is the works of Shakespeare. What if the works are not from Shakespeare, everyone can make his or her own picture. There was even a good show. I think it was on ZDF, but I’m not sure about it at this juncture. Please note: Just because I recommend a tv program or show, one should not conclude that all parts of this program must always fulfill the consensus of the truth. I have noticed in the last ten years that some TV shows or channels (no matter which channel or show), after I have classified it as good, are no longer good or only partial good. Coincidence? My criticism or statement here does not refer to the TV show: TerraX or the channel ZDF. Please do not misinterpret it, but – for current cause – this applies generally to all my links. All channels of the Germany’s public broadcasting are recommendable, regardless of whose hands they were or are still now (partially).
I have completely switched to the Germany‘s public broadcasting channels as I was a teenager. The quality of the content is unbeatable in those channels. The few channels, which I possibly look besides the public broadcasting channels, are sometimes the news channels.
Some of the elder generations still knows the difference of the first-row channels and the second-row channels, as well as day and week newspapers like FAZ or ZEIT, magazines like Spiegel or the Stern, at least the parent houses of my German friends knew that, how these channels, newspapers and magazines mentioned here were politically oriented – of course, it was not talked officially about that. The interests were associated with political parties. Maybe you can understand it better today that the association with political parties will not bring the absolute truth into the daylight. This dualism can also be found in foreign news channels, magazines, etc.
Because I overstrain the freedom granted by the definition for the footnote, I will proceed the continuation in the future under a separate heading.
Another example from everyday life. I’m buying already over several years a special cheese for my pizza and other dishes. I could see that the cheese was not as good as before. After optical examination, I could conclude that the color was lighter – this can only be attributed to the fact that the ripening process has not been properly observed. Whether they leave a product ripening for four weeks or ripening for only two weeks is reflected in the profits of the company. This is one of the way to increase the prices without the customer noticing this. To hell with them. There are some cheeses which are defined in the cheese regulation (Käseverordnung). The German Lebensmittelbuch (Food Book & Labelling) has a similar function, which is not necessarily legally binding.
It is important to know that many competing theories exist in science, which may even contradict one another. An example from the astrophysics of the beginnings of the last century is that one has thought that the universe is static. It has been proven that the universe is not static. It is expanding constantly and the universe has an end, in the sense of existing. The entire science, of course, build on each other. If a theory has been disproved, it has consequences for the whole theories which have been built from it.
If certain theories and things are the result of conscious or unconscious actions, that is not the subject here. My primary goal is to enlighten, not only the science.
The most important message at all – God given sign in the science of nature and other disciplines (cover or overlap the sign, so that people thing that the signs are coincidence or unnatural):