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I will be showing my ignorance with this post.

I am reading the book "The Martians of Science: Five Physicists Who Changed the Twentieth Century" by Istvan Hargittai. I am currently reading about the early upbringing of Theodore von Karman. As I was reading the following caught my attention:

"As an adult, even though he could add and subtract in several languages, he could multiply only in Hungarian."

I have never thought of numbers, addition, subtraction and multiplication as being "done in a particular language."

I know there is a wide cross section of nationalities and languages here and that many of you are mathematicians.

So my question is - do you do mathematics in a particular language or is mathematics just universal - independent of any particular language.

Like I said, I am exposing my total ignorance on this.

Thanks,

Bill
Smithville, NJ
I always thought that mathematics *is* a language. I suppose that there are different dialects of mathematics -- certainly there are over history -- but there's no need for it to be translated into a natural language to solve a problem (unless it's a so-called "word problem").
Multiplication in English :
eight times seven equals fifty-six

In French :
huit fois sept égal cinquante six

When I was a child I learned the multiplication tables in French, later on I learned English. Now as an adult it's faster for me to think to numbers and to calculate in French than in English.
Multiplication in English :
8 x 7 = 56

In French :
8 x 7 = 56

In German :
8 x 7 = 56

In Arabic :
٧ = ٥٦ x ٨

Cheers
Thomas
(11-19-2015 05:15 AM)Thomas Klemm Wrote: [ -> ]Multiplication in English :
8 x 7 = 56

In French :
8 x 7 = 56

In German :
8 x 7 = 56

In Arabic :
٧ = ٥٦ x ٨

Cheers
Thomas

Well, you're not using the listed languages, just a graphical representation of the numbers. But when you talk about them you have to use names in one specific language.
Over the phone I cannot say 8, I have to say eight or huit or acht depending on who I am talking to.
And the way I learned the multiplication tables is deeply tied to the French names of the numbers. Other people may have their brain setup differently.
Based on reading directions, it looks like two-digit numbers are "spoken" in Arabic like in German, sequence-wise. Compare fifty-six and sechsundfünfzig, for instance. Is anybody on this forum who can confirm or deny that?

d:-)
Hi,

For calcuations I thing all of us think in their mother language. I speak very well polish, but if I have to calcul, I calcul in french.
(11-19-2015 10:31 AM)walter b Wrote: [ -> ]Is anybody on this forum who can confirm or deny that?

Can confirm:
ستة وخمسو
sitah wa khamsun: sechs und fünfzig

But it's similar to German for bigger numbers:
tausend und eine Nacht
ألف ليلة وليلة
alf lailat wa laila: tausend Nächte und eine Nacht

Cheers
Thomas
It is different:

1 + 1 = 2

1 1 +
2

There is also the cryptography called higher mathematics where everything is discuised with odd hieroglypth based on where the writer have found his education. Universal and exact .. nope.

(11-19-2015 10:49 AM)Thomas Klemm Wrote: [ -> ]But it's similar to German for bigger numbers:
tausend und eine Nacht
ألف ليلة وليلة
alf lailat wa laila: tausend Nächte und eine Nacht

Why "but"? It applies for smaller numbers as well AFAICS.

d:-?

P.S.: Quoting without proper filing is also an interesting experience. Chaos rules ...
(11-19-2015 11:33 AM)walter b Wrote: [ -> ]Why "but"?

I referred to "sequence-wise": you cold have the idea that the digits are just read from right to left. The example 1001 shows that this is not the case.

HTH
Thomas
It is interesting that not only I must add in Spanish, but even arithmetical operations have a different "feeling" in different languages. Multiplication in Spanish "feels' like a 2-dimensional object, as if measuring area: 7 x 9 is a rectangle of size 7 by 9 in Spanish (7 por 9), but it is a linear object resulting from placing a length of 9 seven times (7 times 9, which would be "7 veces 9" in Spanish). So the commutative law for multiplication is implicit in Spanish, but requires a proof in English. I wonder if this is just an idiosyncrasy.
It would be interesting if someone with a mother tonge which is written from right to left like arabic or hebrew could explain how they write a technical paper with formulas. You are writting right to left, switch to left to right for formulas and continue right to left?
For the original post of this thread I agree with Didier or ggauny, we calculate in our mother tongue. I remember when I started studying English, reading simple sentences with numbers in it, like an address, was a problem because I read the numbers in spanish. It took an aditional effort to "translate" numbers, as Didier said, 8 was "ocho" (in Spanish) for me. The additional effort was to convert 8 in eight.
Very interesting also the "feeling" Alberto explains in the previous post.
(11-20-2015 06:39 PM)Julián Miranda (Spain) Wrote: [ -> ]You are writting right to left, switch to left to right for formulas and continue right to left?

Modern Arabic mathematical notation

Quote:The most remarkable of those features is the fact that it is written from right to left following the normal direction of the Arabic script.

Cheers
Thomas
(11-19-2015 04:18 AM)Bill (Smithville NJ) Wrote: [ -> ]So my question is - do you do mathematics in a particular language or is mathematics just universal - independent of any particular language.

Yet another seemingly obvious concept leads to another fascinating thread - thanks for asking this Bill; like you, it never occurred to me...
While we mentally resolve maths using our mother language, mathematics is an example of a universal language, if you accept Latin characters as being "universal" (well, it is universal at least in the Occident anyway).

But, unfortunately for us occidentals, Latin alphabet is not the universal world standard, as there are other strong competitors like Cyrillic, Greek, Arabic, Hebrew and Chinese among others, and this creates a barrier when trying to read a book written in those alphabets and languages.

There are other universal languages in different fields, be it pure science or technological ones.
As I see it, the essence behind all things is pure logic. Logic thinking is common among all human cultures, independently of the mother language or alphabet, and this lead us to tell that mathematics is a universal language.

For instance, in electrical engineering a schematics diagram is instantaneously recognized and more or less understood by anyone in the field, independently of the used language or alphabet.

Again, the used alphabet and language will create obstacles to fully understand the message.

I remember too well my first contact with a Russian professional navigation system´s service guide more than 35 years ago.
At the time I knew nothing about Russian language or Cyrillic, but I could understood most of the schematics contents to be able to do my job, only needing assistance to translate some text parts.
Later on, after learning the Cyrillic alphabet, I was much more confident when consulting the Russian technical guides, as the electrical and physic units are basically the same in Latin and in Cyrillic, but written on a different alphabet.

Just my 2 Cents anyway.
Is there btw. a study made (and written) of the history of mathematical notation used along the years?

I must add to above example that there is still a lot of variation, while normally people in field knows what some diagram or drawing means, it is a lot based to the knowledge that there is variation. We can take example of logic gates which are different in different "standard" regions, same goes with ie. resistor markings. Then there is whole lot of style draw relays and how the wiring logics goes. If the reader knows enough the subject he can fill the voids.

Same in the maths different people use different notation of symbols for same stuff, ie. how something like voltage or current is written ie. is it peak or rms and how are the super or subscripts used etc. etc. Same goes with pure mathematics, there is different styles to write ie. derivative f'(x) or d/dx which makes reading even relative simple mathematics bizarre until you get enough knowledge in notation and get knowledge to regognice patterns in mathematical sentences, oh this is Eulers formula and the next line looks like it does because he did this and that trick to get there. So basicly the maths is as much pattern recognition as ie. reading a wiring diagram and there is also variation of writing what you are saying, like how complex numbers are written.

Then there is the so called basic math vs. so called higher maths language differences, which are total sidetrack. Ie. the classic square root with negative numbers is there a solution or not. For person of knowledge of only basic math there is no solution of square root of negative number in his/her world, while for person who have knowledge of more advanced math there is solution(s) on complex domain for that mathematical operation.

Logics and rules are pretty universal I would assume.
(11-20-2015 07:53 PM)rprosperi Wrote: [ -> ]
(11-19-2015 04:18 AM)Bill (Smithville NJ) Wrote: [ -> ]So my question is - do you do mathematics in a particular language or is mathematics just universal - independent of any particular language.

Yet another seemingly obvious concept leads to another fascinating thread - thanks for asking this Bill; like you, it never occurred to me...

Hi Bob,

I almost didn't start this thread - I was afraid I had missed the obvious.

But from what I have read here, how people think about math can be affected by the particular languages they may know.

Fascinating. Thanks to everyone for posting.

Bill
Smithville, NJ
(11-21-2015 12:57 AM)Vtile Wrote: [ -> ]Is there btw. a study made (and written) of the history of mathematical notation used along the years?

Following is list of a few books on Math Notation.
NOTE: I have not read or reviewed any of these, but some do look interesting:

A History of Mathematical Notations: Vol I
by Florian Cajori

A History of Mathematical Notations, Volume II
by Florian Cajori

Enlightening Symbols: A Short History of Mathematical Notation and Its Hidden Powers
by Joseph Mazur

Writing the History of Mathematical Notations: 1483-1700
by Sr. Mary Leontius Schulte and Albrecht Heeffer

Numerical Notation: A Comparative History
by Stephen Chrisomalis

Maybe some of the members here have seen some of these and may want to comment.

Bill
Smithville, NJ
(11-20-2015 06:39 PM)Julián Miranda (Spain) Wrote: [ -> ]It would be interesting if someone with a mother tonge which is written from right to left like arabic or hebrew could explain how they write a technical paper with formulas. You are writting right to left, switch to left to right for formulas and continue right to left?
For the original post of this thread I agree with Didier or ggauny, we calculate in our mother tongue. I remember when I started studying English, reading simple sentences with numbers in it, like an address, was a problem because I read the numbers in spanish. It took an aditional effort to "translate" numbers, as Didier said, 8 was "ocho" (in Spanish) for me. The additional effort was to convert 8 in eight.
Very interesting also the "feeling" Alberto explains in the previous post.

The feeling may be the same as a Spaniard adding two multidigit numbers starting from the right & proceeding leftwards who then has to divide two multidigit numbers & starts from the left proceeding rightwards?
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