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Your motivation and enthusiasm for a subject may have more impact on your ability than IQ. A recent study measured math ability and improvement in a group of students from 5th to 10th grade. Not surprisingly, at the start of the study students with the highest IQs performed best on math tests. However, by the 10th grade the greatest improvement was shown by average students who were most interested in math and showed the most motivation to do well. Share this post with friends and let us know your favorite subject to learn about in the comments. 

Read about the research here: http://bit.ly/Z07akv
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A Mathematical Modeling on Turkish


"Victor Hugo" wrote his poems by using 40,000 words. Yet, it is a common view that novels of Yasar Kemal, who uses Turkish profusely, don't have more than 3,500 words. This view is correct because it is true that Turkish contains fewer words than French does. Moreover, it should have fewer words compared to English, German, or Spanish. However, this doesn't mean that Turkish is a poor language because it can tell a lot with fewer words. Having more words is harmless, but it isn't necessary.

When those who translate from other languages to Turkish check a dictionary,they see the same Turkish word for the corresponding foreign words that have small differences in meaning. At first, this may seem as aninadequacy. However, it is not, because the languages afore mentioned are based on learning the static meanings of the words, while Turkish is based on finding out these meanings, that is to say, based on dynamic explanation. In Turkish, positions of the words in a sentence define the meanings, not their meanings in a dictionary. At this point, one can even argue that dictionaries contain only necessary Turkish words as a reference and Turkish contain countless number of words.

In an English-Turkish dictionary, the word "hasta" corresponds to"sick," "ill," and "patient." So, it would be correct to say that English contained thrice more words than Turkish. However, it isn't correct to say Turkish cannot emphasize the differences in meaning of these words.Anybody who speaks Turkish immediately understands the differences between "doktor falanca beyin hastasi olmak (to be a patient of Dr.so-and-so)," "böbrek hastasi olmak (to be a kidney patient),""Internet hastasi olmak (to be addicted to internet)," and "filanca sarkinin hastasi olmak (to be fond of a song so-and-so.)" It isn't that hard to see how this happens. We can write the following equations and numbers and then, sum them up.

3 + 5 =

12 + 5 =

38 + 5 =

Although all equations contain "+ 5", the results are different. Then, the same is true for Turkish as well: Although all sentences mentioned above contain the verb "hastasi olmak", the results (i.e., meanings)will be different. The fact that Turkish does more with less tools lies in mathematics. In mathematics, you can do infinite number of processes with 15 mathematical symbols: ten digits (0-9), four mathematical operators(plus, minus, multiply, and divide), and one decimal point. Turkish has the same characteristics. Turkish is more than a language based on mathematics; it is almost the mathematics itself in disguise.

When you learn how to make a word plural or how to change the mood/tenseofa verb in Turkish, it means that you will know plural forms of the words that were forgotten 300 years ago, or moods/tenses of the verbs yet unknown and that will enter into Turkish language in 5 years. This is the same as when you learn how to solve an equation with two unknowns: you learn to solve not only equations where x = 6 and y = 23, but all equations withthesame polynomial degree. However, for example, in English, "do" becomes"did"whereas "go" changes to "went." It is the same for the plural suffixes: "foot" becomes "feet", "boot" changes to "boots" not to"beet." There is no logic or rule behind this; you have to memorize them.

In Turkish, however, you need to learn the dynamic rules instead of memorizing the static words. There is almost no exception. There aresome minor exceptions such as the fruit name for apple turned to "elma"although it should have been "alma" because of the vowel harmony rule in Turkish. Rules are so certain and powerful that it is almost hard to believe that inventors of Turkish are Turks.

At this point, it will be helpful to formulate afore mentioned subject to concretize the relation between mathematics and Turkish. The easiest way to do is to use the binary number system, which uses only zeroes and ones to represent numbers. In the following examples, "1" means "exists"and "0" means "does not exist."

Root of Plural Word Suffix Mathematical ExpressionEv  1.0 (House)Ev -ler 1.1 (Houses)-ler 0.1 (plural suffix)

Let's assume that all of the words in Turkish consist of two bits (in the following examples, number of the bits will increase). Allsingular words are represented as 1.0 ( i.e., only the root of the word exists), and all plural words are represented as 1.1 (i.e., both root and plural suffix exist). In addition to the fact that this rule never changes, it is so powerful that you can even say plural of a non-existing word (i.e., 0.1), which you can't do in another language.When a person says only "-ler" to another in Turkish, the answer would be something like "OK, I understand '-ler', but what '-ler'?" It is obvious that something plural is beingsaid,but it isn't clear what word.

EMPHASIS ADJECTIVE ROOT DE-EMPHASIS MATHEMATICAL EXPRESSION kirmizi0.1.0 (red) kip kirmizi  1.1.0 (very red)kirmizi msi 0.1.1 (reddish)kip kirmizi msi 1.1.1 (very reddish)

The rule, which helps emphasize or de-emphasize the meaning of the adjectives, also never changes in Turkish. Furthermore, you can generate both emphasized and de-emphasized odd adjectives that complies with this rule, but don't exist in the dictionary. For instance, "Günes dogma[z]dan[sic] önce ufuk kipkirmizimsi(kip+kirmizi+msi [1.1.1]) birrenkaldi (The horizon changed to a very reddish color before the sunrise)." Everybody will understand what that adjective means, because this adjective-generated-on-the-go complies with this rulethat everybody knows very well although it doesn't exist in thedictionary.

This situation isn't so different in verb moods as well. We are constrained to use groups of 3 bits for moods and groups of 2 bits for tenses.Multi-bitgroups will express the following:

011 = I010 = you000 = s/he, it111 = we110 = you100 = them-------------00 = present tense11 = present continuous tense10 = future tense 01 = past tenseROOT ABILITY NEGATIVE TENSE PAST INFERENTIAL PERSON MATHEMATICAL EXP.oku (y)abil  di   m 1.1.0.01.0.0.011oku (y)a ma z  mis sin 1.1.1.00.0.1.010gel  me (y)ecek ti   1.0.1.10.1.0.000git  me di   k 1.0.1.01.0.0.111sasir abil  ecek ti  niz 1.1.0.10.1.0.110bil   (i)yor   lar 1.0.0.11.0.0.100

In the above table, the set related to the tense could be made 3 bits and past tense could be categorized "simple past tense (-di)" and"inferential past tense (-mis)," or you could add another bit forinterrogative suffix, or you could also add imperative and conditional moods into this combination, but the result would be the same.

The order of the elements (object, subject, verb, etc.) in a sentenceis also not random. The order in Turkish sentences gradually increases. The entire emphasis is on the verb, which is the lastelement in a sentence.Theimportance of other elements is based on the distance of theseelements to the verb. The closer the element is to the verb, the more important it is (i.e., emphasized). From the mathematical perspective,every element inthesentence has a mathematical value made of as many digit as the numberof theelements in the sentence. The sentence "Dün Ahmet cami kirdi(Yesterday, Ahmet broke the window)." has 4 elements. Therefore, everyelement willhavea 4-digit value; the first element will have the lowest value and the last element will have the highest value. SENTENCE MATHEMATICALEXPRESSION MATHEMATICAL EXPRESSION MATHEMATICAL EXPRESSIONMATHEMATICAL EXPRESSION 0001 0011 0111 11111 Dün Ahmet cami kirdi. 2 Dün cami Ahmet kirdi.3 Ahmet dün cami kirdi.4 Ahmet cami dün kirdi.5 Cami dün Ahmet kirdi.6 Cami Ahmet dün kirdi.

Now, let's examine every sentence in the table above:

1st sentence: Yesterday, Ahmet did something and that something washis breaking the window.

2nd sentence: The person who broke the window yesterday was Ahmet(guilty party is Ahmet!)

3rd sentence: The thing that Ahmet did yesterday was breaking thewindow (perhaps he had read a book the other day.)

4th sentence: Ahmet broke the window yesterday, not some other time(maybe he would break it tomorrow.)

5th sentence: The window was fine until yesterday, it is broken because of Ahmet.

6th sentence: Ahmet would probably break the window anyway. However,hedidit "yesterday."

While the elements in the sentence didn't change ('cam' was always'cami', i.e., with its direct object and definite case suffix -i; theverb was always in third person, and in simple past tense (-di), etc.), the changeintheir position changed the meaning of the corresponding sentences. Ineverysentence, 0011 had more importance than 0001, 0111 had more importancethanthose two, and 1111 had more importance than all of others. Whatdeterminedthe meaning was the mathematical value of each element.

In languages where the words have static meaning, you need to change the mood (passive mode) or put other clarifying words to give meaningsother than the two variations that can be obtained only by changingthe position of the adverb (dün = yesterday). Those who speak Turkish will immediately understand the differences between sentences.

This exchange with mathematics isn't limited to the examples givenabove. One can encounter this relation anywhere in Turkish.

I realized this characteristic of Turkish when I was seeking answersfor questions such as "How do people understand the messages conveyedtothem?";"Is this related to the spoken language?"; "If a French person, anEnglish person, and a Turkish person receive the same message in theirown languages, do they perceive it differently or in the same way?"; and "Ifthelanguage is related to perception and when you exclude the language,for example when one watches a pantomime show or when one looks aposter with nothing written on it, how do these habits affect the language?" This characteristic is very clear when one approaches tothe subject with patience and interest. Other people must have seenthese characteristicsaswell. Actually, those who say, "Turkish is very elastic language; it stretches to wherever you pull" vaguely realize it, but couldn'tcompletelyname it.

Turkish is an excellent language from the technical perspective, becauseitis blended with mathematics. Unfortunately, this is also where Turkishsetsa trap for its speakers.

Cultural clashes such as "city-dweller vs. villager," "educated vs. uneducated," and "eastern vs. western," can occur anywhere in theworld. Also, a process of "assimilation" and/or "adaptation", whichgenerallyworks everywhere in the world, synthesizes these clashes within. Turkey is alittle bit out of this generalization. This process either doesn'tworkforus or works unbelievably slow. The problem arises from the language we speakas well as other reasons. If one accepts the thinking as"talking-to-oneself-without-words," (to which I agree myself) one canarguethat native language affects how people think; people think in their nativelanguage. This is the biggest paradox for Turkish people. Turkish,whichisan excellent language from the technical perspective, is the biggestobstacle for us to perceive the outside world as is.

For instance, the first generation of workers from Turkey to foreigncountries showed exemplary resistance to learning the new language oradapting the way of life in those countries. This resistance was so powerfulthat there were developments that you could never see in any otherDiaspora.Turkish Diaspora exported its own cultural establishments to thatcountry instead of getting ghettoized and being stuck in their own circle. While Spaniards, who are the most resisting culture forassimilation, onlybroughttheir newspapers or radios to the country they migrated, Turks had allthesethings plus their own TV channels and their own fast food (lahmacun,döner,etc.) It isn't fair and realistic to conclude that those people whoachievedthese things were incompetent and couldn't achieve the adaptation becauseofincompetence. Furthermore, it is almost impossible to think that thosewho showed this much cultural resistance will ignore their ownculture, which they deeply protect, when they educate their children who were born inthatcountry. However, it is also observed that the second generationTurks,whowere born abroad, assimilated more rapidly than Spaniards. It wouldn't be misleading to think that one of the factors behind thisassimilation isthelanguage of that country, which is taught in schools and spokenoutside of the house, as well as the Turkish language spoken at home.

When we, Turks, learn to how talk, we don't learn that differentcircumstances create different concepts (like in the example of "sick,ill,and patient") and that different concepts should have different names. We start learning the rules of intuitional methods (intuitional =natural =mathematical) that help distinguishing different concepts having the samename. Brains conditioned to be intuitional are inclined to choose one method: inferring it in their own way; in other words, "perceiving astheyintuit," for they don't know how to perceive the outside world as is.

How can the codes in the messages conveyed to people, whoseperceptionshavebeen formed based on their own inference and who live in their ownsubjectively defined world, be perceived by everybody in the same way? Thisis one of the basic questions worth finding an answer. As the answertothisquestion becomes more prominent, it can also be explained why westernsystems couldn't find roots in Turkey.

This special situation, which is the result of Turkish's own dynamics,is surely valid for all verbal communication areas. Turkish is verysuccessfulin using intuitionalism to its fullest. It is this skillfulness thatwas behind to the devoted narration of "Yunus Emre" as a product oforal literature among illiterate nomad Turkic tribes from one generation to another for 700 years. We should also seek answers forwhy theintellectualsof Tanzimat and First Republic periods in Turkey couldn't reach tolarger masses. Those who learn to think like a German or French person fail, because they try to express themselves in this new way ofthinking, andtheycan't explain things like a Turkish person will do.

Messages are as effective as they are perceived. From the perspective of message's integrity, it is important how much those who producemessages know their subject. However, it is more important how peoplebeingaddressedperceive the messages conveyed to them.

<B> Written by Ahmet Okar, Translated By Pelin Bali. </B>

http://ddi.ce.itu.edu.tr/about-turkish/a-mathematical-modeling-on-turkish
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one of the best explanations that I have seen
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Is your workspace messy or organized? Two new studies show there may be advantages to both. In one study, participants were told to fill out a decoy survey in either a messy or organized office. After 10 minutes, they were offered a choice of an apple or a candy bar. Those who spent their time in the tidy office were more than twice as likely to make the healthy choice of the apple. But in a second study, participants who spent time in a messy room came up with significantly more creative solutions to a problem than those who spent time in an organized room. What do you think? Would you rather be healthy and organized, or messy and creative? Share this post with friends and let us know in the comments. 

Read more here: http://nyti.ms/1btNr7I
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