While the article says there are only aout 200 Piraha tribe members, I believe others were located four years ago working for the Dade, Broward and Palm Beach County boards of elections.

Another explaination is that they are just really, really stupid.

It would seems to me that mathematical logic remains true everywhere despite the fact that a culture may have no use for that truth in their life context. If we agree on the definitions of mathematical quantities and their derivatives then we and the aliens would agree on mathematical truths.

Yes, that is the news item I referred to here a couple of days ago :-)

What irks me is this line, "raises questions about how language may affect thinking."

Language is a tool! I heard an interview with the researcher on NPR's Science Friday, and he said that the tribespeople's innumeracy means they get ripped off in their dealings with traders.

The day they get tired of getting ripped off is the day they start counting -- and they will either make up new words or "borrow" words from Portuguese.

I find nothing to support the assumption that the Piraha language is a prison that prevents them from counting.

Pilgrim:

"If we agree on the definitions of mathematical quantities and their derivatives" kind of gives away the game.

This tribe doesn't hold a radically different concept of number. They have not developed the concept of number. That says nothing about objective truth. Find a better example, if you can.

"This tribe doesn't hold a radically different concept of number. They have not developed the concept of number."

Belief in faeries and absence of belief in faeries are radically different concepts of faeriedom.

Before I could count in five languages. Does this mean that now I can automatically add a sixth?

No doubt the aliens would consider us ignorant and backwards people, but that doesn't seem to prove that mathematics is false. If it was only some social construct, then we couldn't use it to predict the motion of the planets or send a rocket into space. 2+2 does equal 4 everywhere, but it may not simply be evident. Much like most people probably don't see calculus as evident even though it does exist.

Despite all these protestations of objective knowledge, we are no different in kind (rather than size) in our arithmetic ignorance. While we believe we can calculate anything, of any magnitude, we have theorems in set theory that aleph-null + aleph-null = aleph null with infinite sets (i.e., many + many = many, just like these so-called primitives). Yet we maintain that these (aleph-nulls) are cardinal numbers, just like the ordinary 2+2=4. We have only increased the limits of our ignorance, not its substance.

This is hardly a new concept. C.G. Jung and Hajime Nakamura have had a lot to say about it.
But let us fast forward to our own time and lose the fantasy science fiction thinking for a moment. What does this concept mean for multicultural education. Do we prepare children for life in a modern civilization by weaning them away from dead, white male concepts such as person, number, causation, and linear time?
There are other ways to think, other than the way we think. They may be equally valid to a space alien; they may be more valid to their practitioners. But the world they would structure would not support a tiny fraction of its present population. Western civilization in not a tiger that mankind may dismount.

Chris:

Just keep saying that to yourself.

More on the Pirahã and their inability/refusal to count:

A treatise by Prof. Dan Everett, the foremost authority on the Piraha: Cultural Constraints on Grammar and Cognition in Pirahã:
Another Look at the Design Features of Human Language (.pdf file).

And Mark Liberman at Language Log weighs in to correct some misperceptions.

I am a bit puzzled by the tangent that Orrin Judd is pursuing here; I fail to see a parallel between the situation of the Pirahã vs. the rest of mankind on the one hand, and the situation of the rest of mankind versus space aliens on the other.

Nothing suggests that our "reality-tested" knowledge would crumble upon the arrival of a spaceship; after all, the Pirahã body of knowledge (where animals live, what their habits are and how to hunt them) surely has withstood the arrival of outsiders largely intact, having already been tested by reality.

Hmmm... What I should have written:

"I am a bit puzzled by the tangent that Orrin Judd is pursuing here; there may be parallels between the situation of the Pirahã vs. the rest of mankind on the one hand, and the hypothetical situation of the rest of mankind versus space aliens on the other.

"However, nothing suggests that etc.."

OJ, is the law of gravity also a social construct?

The "law" of gravity? Absolutely.

>One of the central claims for the possibility
>of objective truth has always been the
>irrefutable "logic" of 2 + 2 = 4, which must be
>true everywhere.

"We know that two and two make four,
'Til Demos votes them three or naught..."
-- Rudyard Kipling, "Bonfires on the Ice"

"How much are two and two?"
"Four."
"And if The Party says it is Not Four But Five?"
-- Comrade O'Brian, Inner Party, Airstrip One, Oceania, 1984

"social construct"?

Eh? Have I come through the Looking-glass into a dream version of reality, where 2 plus 2 does not equal four?

Let us not forget, 2+2=4 is axiomatic. Axioms are not theorems, you cannot disprove them. Not even a hyper-dominant race of space aliens could impose such a change on us. So 2+2=4 is safe, forevermore. Is there an "alternative" math in which 2+2 does not (always) equal four? It sounds crazy ... but maybe the answer is yes: for two millenniae we believed Euclid who said that parallel straight lines never meet... until non-Euclidian geometries came along!

In school we all learned that 2 times 3 gives the same result as 3 times 2: the principle of commutativity.

And yet there are non-commutative algebras!

BUT, neither Euclidian geometry nor commutative algebra have been "disproven" or "superseded" by the more recent "alternatives".

So, even if some future genius comes up with a math that postulates "Two plus two equals [something other than four]", our accustomed math will not be invalidated.

A separate issue is the real-world applicability of mathematics. This may be a gift from God, for how else to explain the Unreasonable Effectiveness of Mathematics in the Natural Sciences?

Ah, I see. The mistake you're making is in thinking that numbers exist. Numbers do not exist, they are a human construct. You are failing to distinguish between the world as it exists (assuming, for the moment, that it does exist) and the model of the world you carry around in your brain (assuming, for the moment, that you exist).

Change "social constructs" to "useful mathematical models that seem to work well when applied to the real world."

A mathematical system where 2+2=5 is innocuous. Whereas some "social constructs" can be demonstrably harmful when applied (nilihism, communism, wahhabism, etc).

I don't think anyone has been killed over Godel's Incompleteness Theory or Cantor's transfinite number system.

"Numbers do not exist, they are a human construct."

DC:
That is exactly my point, but I'm having trouble getting it across :-(

May be my own fault because I'm not totally clear yet in my own mind.

Okay, how about this: Orrin's hypothesis is that the super-advanced space aliens are going to smile condescendingly at our "parochial notions of mathematics". However, I believe that all -- or nearly all -- of our mathematics will be just as valid then as they are today.

In part, that is because to the extent that mathematics is "constructed" and not "discovered", the construction takes place in the realm of the mind, which means that different rules apply than to a theory about what we find in physical nature. Prime numbers are something that strikes our fancy because they "stick out" from the rest and serve as a pathway to learning more about numbers. But nature does not single out prime numbers of entities for special treatment. That already makes mathematics partway immune to wholesale discreditation.

The phrase "social construct" says, arbitrary! it could turn out to be totally wrong! Can the mathematical accomplishments of the great thinkers ever be overturned? The Binomial Theorem has been proven, can that ever be reversed?

Moreover, apart from the pure world of thought, the correlation between mathematics and hard, physical reality is great. This tells us that while the human invention called mathematics is not a matter of discovery alone but also of construction, and while of course there is a "sociology of mathematics, or of mathematicians"... it is not an arbitrary social construct ... nor subject to a change in fashion ... but something fairly close to the bedrock of reality.

If you disagree with me here, doesn't that imply that you consider the parody by Alain Sokal in "Social Text" a failure, and the post-modernist "constructivists" to be right?!

In his autobiography, Isaac Asimov told this story about his father or grandfather (I forget) .

He was a grain dealer who would visit farms. The peasant would bring out his sacks of grain, and as a counter, Asimov would elaborately place a shiny silver 10-kopeck piece in a bowl.

He made it a point to be distracted. Seldom would the peasant be able to resist filching a few coins.

Then they'd settle up. The sacks were worth rubles, of course.

There is, by the way, a whole literature about peoples who have restricted counting systems, though I'm not familiar with it.

Here, the confusion is between counting systems and mathematics. They are not the same thing.

tictoc:

Of course you believe that, we all believe it. Belief being the point.

Harry:

Yes, advanced people think they have math and the savages only counting systems. If we're the most advanced beings going than you're safe on that count, though we're back to a geocentric Universe.

Infinite sets are not cardinal numbers.

Offhand I can't think of any form of arithmetic where 2+2=5 (1 or 0, yes), but there may be one. That's not the same as a social concept, though.

Was there some point?

Orrin would probably like the Incompleteness Theorum, though... people were all but driven out of the field by it, but I don't think there were any deaths per se.

Is the idea of "social construct" a social contruct?

Will this claim last any longer than Margaret Mead's claims about Samoans?

How reliable are anthropologists anyway?

Here is proof that 64=65.

As far as counting goes, we and the Indians have the same failing -- although we can count to an arbitrarily large number, and they can't, we cannot count to the highest number.

It's just a question of where each chooses to stop.

And, yes, our stopping point is more advanced than theirs. But counting systems, in themselves, are not mathematics. Just a tool to think about math.

Or, as a friend of mine who was a missionary in Bolivia told me, before the Conquest the Incas knew how to count to the millions. (I don't know how high they could go.) After Catholicism took over, the Indians got ignorant, and there was an American missionary priest in the altiplano that they named "Mr. Million" because he knew the Quechua word for million and they didn't.

The largest (or smallest) number anyone except a mathematician uses in daily life is probably the reciprocal of 2 to the 60th power, which is the dilution of homeopathic medicines.

Of course, this dilution is nonsense physically, but they can count that high.

Don't results count?

What results?

Well according to Prof. Everett, it isn't even accurate to say that the Piraha can count only up to two.

They refuse to count at all! And the reason is not that they are stupid or that their language imprisons them, but that their culture constrains them in this way (see the hyperlink a few posts up).

Incidentally, Prof. Everett got his early training from the Summer Institute of Linguistics. A fellow translator also shares that background: he told me once of being sent to the Peruvian rainforest to spread the Gospel to the natives in their own language(s), living with them, and experiencing the "pre-historic" culture in all its harshness, up to and including the killing of a tribe member with psychological abnormalities, based on a decision by the tribal council.

Tragically, most of the natives he trained are now dead, murdered by the communist guerilla of Peru for being a threat to their dominance.

To Joseph H: Today's researchers are a great deal more thorough and careful than Margaret Mead was.

tictoc:

You just lurched into an epiphany: "their culture constrains them"

About the opinions of space aliens: There is a negative correlation between UFO sightings and abortion rates. Clearly, the space people are preventing abortions.

Orrin, you are the one who argues, strenuously, that gasoline taxes should be raised by an amount per gallon, so that driverrs can choose to correlate the distance they travel v. the cost of traveling.

Those are the results I'm talking about.

If you pay money and get a random amount of gasoline back, your scheme would not work.

This coy pretense of yours is tiresome. You believe in counting as much as any of us.

I bet you know how many children you have. In some sense, so do those Indians, I'd bet.

Harry:

I agree with the results. We are all believers. You just think you can switch from calling it belief to calling it fact at some arbitrary point.

Orrin,

What do you call your position here?

Radical skepticism?

No, just universal skepticism. There's nothing less becoming than a skepticism applied only to that which you oppose.

Here is where you go from belief to fact:

Would you live in a house where the builders concluded 2+2=5?

Would you fly in an airplane whose designers figured KE=1/2mv^2 was a mere social construct, and, that, all things considered, KE=2mv^2 was much more compatible with the zeitgeist?

" There's nothing less becoming than a skepticism applied only to that which you oppose."

This, from the lead practicioner.

Jeff:

If the house stands and the plane flies no one will question the math.

But if the math is wrong, it won't stand or fly.

Facts are things that can be tested up to whatever limit you are clever enough to devise. Beliefs are, by their nature, untested.

This history of bridge-building demonstrates conclusively enough what happens when you don't do the math.

Harry:

We've discovered all kinds of mathematical stuff that we had wrong but stuff has worked well enough. These Indians couldn't count but their huts stood up fine.

Wait a minute... How can anything be socially constructed when society doesn't really exist?

Actually, it hasn't. You should read Petroski on the desirability of having a few bridges fail.

Operative term: huts.

Harry:

A few logs over water works fine. It's those ones folks who know math build that are untrustworthy.