When 10-3 = 13

Lynne McTaggart

Recently, an American researcher from the University of California  was conducting research on the Suya Indians of Mato Grosso, Brazil, attempting to determine how they count.  This group of Amazonian Indians are largely famous for their music; Anthony Seeger, a Professor of Ethnomusicology at the University of California, Los Angeles, who has produced a book called Why Suya Sing, says that their singing is used to create community, establish relationships and social identity and also formulate ideas about time and space. 
Singing, to a Suya, is hard and soft science.
Math lesson
This particular researcher was investigating the level of sophistication of the Suya concerning mathematics.  Many scientists examining cultural differences over number systems operate on the assumption that many native cultures basically don’t have language to describe quantities of things; for instance, the Piraha people use the same word ‘hoi’ to describe ‘about one’ and ‘about two’; the only difference is a subtle alteration in inflection of pronunciation.  The much-studied Munduruku in the Amazon have words for numbers only up to 5.
This has led many scientists to examine whether human beings have innate numerical skills or whether it is simply a part of cultural conditioning.  Is it possible to operate entirely without numbers?
So this particular researcher asked a member of the Suya tribe what was the correct answer to the following numerical problems:  If you had 10 fish and gave away three fish, how many would you have?
The Suya answered without hesitation and as though the researcher were a bit dull-witted to have even asked the question. 
As anybody in the village could tell you, the answer, of course, is 13. 
Minus equals plus
This was how he worked it out.  In the Suya tradition, whenever you give something away to someone else, the recipient pays you back double.  So if he gave three fish to his brother, he said, his brother would have to give him back two times three fish, or six.  So added to his 10 original fish he would first have 16 fish.
Once he deducted the three fish he originally gave his brother, he would have a net increase of three, or 13. 
So, 10-3 = 7 in Western mathematics transforms into 10 + (2x3) - 3 = 13 in Suya mathematics.
In fact, the native was dismayed at the American version of the equation.  He does not view giving away as equivalent to subtraction.  He finds the entire notion of it abhorrent. 
“Why is it that ‘giving’ is always seen as a ‘minus’ for white people?’ another member of the tribe asked.  “I know that you want me to use the minus sign instead of the plus sign, but I don’t understand why.”
This was a little shocking to Alex Bellos, the author of the recently published Alex’s Adventures in Numberland (Bloomsbury, 2010), a study of cultural differences in mathematics.  He began the study of his fascinating book with the belief that numbers are a universal language – the way in which we could, say, communicate with extra terrestrials — only to find that our basic understanding of arithmetical relationships depends upon cultural context.
Relationships in the numbers
I find the story delightful for several reasons. 
It reveals something very profound not simply about mathematics but about how different cultures view relationships in general, particularly how we view ourselves in relation to other things.
Our sense of mathematics very much depends upon how we define our world, and whether we view ourselves and all the things around us as individual entities separate from each other or inherently intertwined.
Many non-Western societies — pre-literate cultures such as the Aborigines, the ancient Greeks and the Egyptians, the adherents of Eastern religions such as Buddhism, Zen and Taoism, and a number of modern indigenous cultures  —  conceive of the universe as inseparable, connected by some universal energy ‘life force’. The beliefs of many tribal societies about this central energy force have many similarities, suggesting that an intuitive understanding of the interconnectedness of all things is fundamental to human experience.
This central belief breeds an extraordinarily different way of seeing and interacting with the world.  These traditional cultures believe that we are in relationship with all of life – even with the earth itself.  They hold a very different notion of time and space as one vast continuum of ‘now’ and ‘here’.
They even perceive the world out there very differently.  We see the thing; they see the totality, the relationship between the things.  To an indigenous native, math and the song are equivalent —  all about the plus sign, the connection, in this instance, between the man with the fish and his brother. 
We would do well to take a few math lessons from the Amazon.

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Lynne McTaggart


37 comments on “When 10-3 = 13”

  1. Wow, this was fascinating! Once again we're reminded of how assumptions color what we think and see. Especially assumptions that are "so obvious" that we don't have to question them. In this case we have math that is determined by connectedness and reciprocity in relationships. Thanks for the post, and the reminder.

  2. The difference has nothing to do with their mathematical concepts but with their concept of giving. I'm sure if you asked them "If there were ten birds sitting on a branch and three of them flew away, how many birds would there be on the branch?" they would not answer "thirteen."

  3. You have to love it when the teacher becomes the student. It's an important lesson for a society that often views their way as the 'right' way. Thanks for this wonderful story!

  4. This is a great story. To realize that our reality is just one of may perceptions of the world is a great awareness. Western science still has a hard time understanding how such things as acupuncture, distant healing etc. work, but one should not think that there is only one reality. Good stuff Lynn.

  5. So does this mean that all the detailed mathematics a professor writes on the blackboard only exist in the mind of the beholder?

  6. I wonder what the Suya indian would say if asked a non-personal math question? For instance : If there were 10 trees on an Island and a storm washed away 3- how many would be left? Or if there were 10 coconuts in a tree and the wind blew 3 down, how many would be left in the tree? Maybe the author came to a general conclusion- from a too specific question! I love your work. W. Cridge

  7. I wish you wouldput a link to share on facebook !
    This kind of math ---needs to be shared ;0)

  8. As others have said, it strikes me that this really isn't about math. I don't think you have to leave our own country to find that cultural differences will influence how someone interprets story problems, whether they be in math or some other subject. That's why it can be challenging for many who belong to groups other than the dominant one when they are attempting to learn through a curriculum designed by and for the dominant group.

  9. dear lynn,
    there is a deeper message in what you have written.
    it is about CULTURE.
    there can be NO peace on this planet , unless culture is understood.
    to read more punch in --
    in google search.
    -- for long culture has been about survival.
    capt ajit vadakayil

  10. What a wondrful message! Does this however add to the evidence that an objective world (in the way Plato and Kant understood it) cannot exist?

  11. "The difference has nothing to do with their mathematical concepts but with their concept of giving" R. Turner
    Neither one. The reason is that they see the universe as nonlinear, nonlocal. We localize things due to our limitations. A tree never loses her 3 coconuts. It just changed location in our perception of time and space. A bird from a distance would never see as a loss of the 3 coconuts. If there were 10 birds in a tree branch and 3 flew away to a near by tree, what difference does it make if you see the episode from a birds eye view? None. Giving is never a minus, because giving is receiving. The Universe is a constant exchange, never a 'take it and run'.

  12. Its a blessing to read this kind of perspective, because it help us realize how powerfull is the act of giving...
    The multiplying effect of giving is the prove of our true god nature !

  13. Mixed concepts. We use math to measure; to establish quantity. We localize things, not due to our 'limitations', but due to the requirements of specificity. To accurately define what is being measured, the parameters must be specific. Thus if in the last example the 3 birds had not flown to a nearby tree (thus maintaining the local population of birds) but had been consumed and digested by a predator, the answer would likely be different. If you asked a economist to put a 'value' on the giving away of 3 of your 10 fish, you would likely get a credit in the 'goodwill' column that could well amount to 6 for a total of 13. Merchants use this concept all the time; giving away freebies in the expectation of earning goodwill and getting more customers.

  14. Western mind believes in separation, which is non existent. Native and awakened people know separation from the all is an illusion only.
    By the way, wealth begins with giving. (Just imagine everyone was giving, how rich we all would be).
    We are all manifestation of the same. All one.

  15. Jose and Richard, I like your ideas on this article...the problem we face as a “modern society” is we are not self-sufficient any more.
    We don’t view life as an exchange, we perceive it as ‘give and take’...so 10 – 3 must = 7...these native societies are self-sufficient, so they understand how the exchange of energy works.
    All most of us do is consume...very few of us could survive (myself included) if we found ourselves in that situation...I bet we would all quickly come to appreciate anything that was given to us, especially food, if we suddenly had to live off the land!
    I imagine we would also quickly learn the power of working together as a group, sharing the workload and the supplies...it requires mutual support....an exchange of energies...
    This story is a fascinating example of a totally different philosophy of life.
    Why can’t 10 – 3 = 13? Their just numbers...
    Write On!

  16. I feel that they would regard a situation whereby the amount of coconuts left on a tree after a storm would be what-ever is on the tree at that moment in time - not what is no longer there!!!

  17. "So does this mean that all the detailed mathematics a professor writes on the blackboard only exist in the mind of the beholder?" JAN
    I liked the question. What if everything only exists in our minds? We don't assume this because this construct is not individualized but colective. We're always assuming someone out there with greater power created all this. We are explorers of our own creation. Illusions can be intricate, complex constructs and be measured by mathematical concepts, why not? Perhaps in the greater context of things, there is really nothing to be measured, subtracted, added, only exchanged, giving the illusion of gain and loss. We do what we do because we are accustomed to focus on content rather context. The Universe is context, we are its contents dealing with contents.

  18. Music and math are found to be mutually interesting to those with a gift in either one. That Lynne begins this blog with a dual study of the Suya approach to both music and counting is worth considering. Counting has to do with rhythm and in dance rhythm has to do with both time (and timing) and space (and spacing) in the working out of social relationships. And as people dance or rhythmically interact they enrich each other. X and Y might be in superposition until the dance begins and precision timing and spacing says step here then disappear here and land there. If Descartes and Newton spearheaded separation and atomization leading to the development of vast schemes of counting, perhaps non-local intimately present healing and group intention reunification approaches will integrate the dance of the human family, the sentient family, the music of the spheres.

  19. It is the concept of the differance between giving and adding. 1 + 1=2 mathematically as we as human created it, but in nature 1+1 could be 3 or even 4. Maths can’t solve al aspects of nature; nature has got its own mathematical concepts.

  20. It is good that the researcher, although showing his bias by using words such as "sophistication" and "only" when approaching this research, was open to learning with and from the Suya. Kudos to him for trying on another perspective and values. Kudoes to the Suya for not taking on the researcher's ways and sharing their knowledge with him!

  21. I love this article and would enjoy reading more about this subject...native cultures and math. Math and music are linked in the Western societies, are they linked in these native cultures, also?

  22. So, how do the Suya relate "math and the song"? They may have some knowledge of the universal Law of Octaves [Music, Math, DNA, periodic table, etc]

  23. Thanks, Lyn...we've had a breakthrouigh in this house as another of our tribe is reading The Field after enjoying The Lost Symbol.
    We all tread our own paths, looking for the same Peace.

  24. This is an amazing article!!! I love math and numbers, and this has blown my mind, about how something we think in our society is so "set", and is a correct system, is totally blown out of the water...Nothing in this universe is set, and the possibilities are infinite. Thank you!

  25. If you look closely, when the Greeks developed what would become modern advanced mathematics, it was mainly about inclusion as well. Even when subtracting and dividing, the eventual answers always require the use of addition and multiplication - and when one wants to check one's answers to any math problem, its opposite action is required to do so.
    Pythagoras might disagree, but the Chaldeans would love these people -
    Negatives were never meant to stand separately from positives - in numbers or in any other way!
    The balance is not in "righting wrongs" or in "taking away" but in the synthesis of the whole.
    Lynne - thank you for a wonderful article, and the book suggestion, too!!

  26. Thanks! Love hearing of stories about how the western world does not know everything, and that reality can be vastly different based on your orientation to the world and to others.

  27. Thank you, Lynne, for sharing this story. It is all about remembering. And how lucky we are to still have these people on earth from whom we can (re-)learn these lessons in unity and interconnectedness. They lift us out of our boxed minds. I'll pass it on!

  28. Sorry to be the downer, but first to those that speak about the equilibrium of energy (when it leaves one place it goes to another). Read about the second law of thermo dynamics.
    Additionally, the mathematical systems (base 5 or base 10 logarithmic systems) developed by every society in history provides evidences that humans are by nature ego centric. Even with Suya, her equation has the expectation of a return on investment (Double in return), which to me seems worse. A truly altruistic being would say 10 - 3 = 10. As
    Interesting article but, unfortunately, it has nothing to do with mathematics or the universe or Suya's conceptualization of mathematics. It has to do with social interpretation of language. What the author does do, is provide evidence that there is no such thing as a valid standardized test (there are substantial cultural disadvantages in standardized testing).
    In the case of Suya, the differential concept is "ownership" or "giving". This concept would make a simple math question on a standardized exam invalid. Many Native Americans don't understand ownership, so of course they don't understand giving. Obviously if you asked her, "If there are 10 apples on the table and then you eat 3, how many are left on the table?" She would answer 7. Unless their is a social difference in how she interpret food that has been eaten. That is, she returns it to the earth, but is still there. Even so, she has take the entropy out of the apple. Therefore, she has still taken from the earth.
    Also, the famous Mundurucu tribe does have words for numbers larger than 5, they just don't have more than 5 numeric symbols (base 5 system), and they represent numbers on a logarithmic scale much like scientific numbers (the Latin system does too through repetition of number sequences [i.e. 1=10^0, 10=10^2, 100=10^3, etc.]).
    The Mundurucu are one of the few societies in history that didn't settle on a base 10 system (there are others, the Romans used a base 5 & 10 hybrid system logarithmic system). Saying that the Munduruku don't have words for numbers larger than five is like saying that Americans don't have words for numbers larger than ten. The Munduruku had no problem conceptualizing very large numbers (and most interestingly very small numbers, they were arguably one of the first to use continued fractions). Actually, numbers smaller than 1 don't really exist in the universe. That is a concept that the human mind created, and is why representations of numbers smaller than 1 differ greatly in different societies.
    Though the Mundurucu settled on 5 instead of 10 as a number base, it is more interesting that all societies settled on a base 10 or base 5 logarithmic structure. Clearly, all societies use either base 5 or base 10 number systems (Romans used both, but still logarithmic) because we have 10 fingers, 5 on each hand. This implies the opposite of what the author postulated. It shows that when societies develop independently, they still end up with very similar mathematical systems. It implies that our mathematical thinking [and everything else for that matter] is far from autonomous, and is determined by our environment and genetic makeup. We are far less "free willed" than assumed.
    Also, the fact that all societies developed a logarithmic way of representing numbers implies that there is something consistent about the mathematics of the universe (it's not just in our minds), or at the very least, the universe always yields a similar mathematical human interpretation.
    Lastly, using numbers to describe humans as non egocentric beings heavily breaks down in the face of the base 5 / base 10 social/psychological bottleneck. Given that we based our entire number systems, which determines much of how we interpret the universe, on how many fingers we have on our hands is an indication that we are extremely ego centric. We view and interpret the world based on the most basic characteristics of ourselves ("I have as many apples as I have fingers"). Me, Me, Me

  29. Suya's equation 10 - 3 = 13 doesn't seem very altruistic. Her reasoning is based on the expectation of a return on investment. It is based on the reasoning that she will get back double what she gives. Though this may encourage her to give (and it is unlikely that she will really receive twice as much back), the giving nature is not based on altruistic reasoning if she expects a return of double. Does the ends justify the means?
    Her selfish reasoning is a bit like the intentions of those who sensor information from the public. It seems your hypocrisy knows no bounds. You know who I talking about.
    It took a tremendous amount of time to write that response and you can't even grant the courtesy of a response? I'll take that as a fold.


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