North American Computational Linguistics Open Competition (NACLO) Discussion
Go back to the Math Jam ArchivePranav Krishna will be discussing North American Computational Linguistics Open Competition (NACLO), the national competition for qualifying for the IOL (International Linguistics Olympiad). Problems require participants to decipher the structure of another language, and any central phenomena the problem writer wanted to highlight. While it is only tangentially related to mathematics, there have been those with notable accomplishments in math who have also done well in the NACLO and IOL.
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Facilitator: AoPS Staff
Hello and welcome to the North American Computational Linguistics Open Competition (NACLO) Discussion!
Yay
hello
Yay!
hi!
hi!!
yay
Yay!
Hi everyone!
Before I introduce our guests, let me briefly explain how our online classroom works.
This room is moderated, which means that all your questions and comments come to the moderators. We may share your comments with the whole room if we so choose.
We will ask you lots of questions throughout the class. You should answer them as best you can by typing in the chat.
Participate as much as you can! And feel free to shout out questions at any time.
Is this being recorded?
Yes, we will have a transcript available.
Now let me introduce our guests for the evening.
Tonight, Pranav Krishna (stronto) will be leading our discussion.
Pranav is a current undergraduate at MIT, majoring in Computer Science and Linguistics, hoping to become a Computational Linguistics researcher. He was part of the IOL team in 2018 and 2019 In his free time, he generally enjoys playing the tuba, frisbee, and a lot of card games.
(Say Hi Pranav!)
Hi
hi!
Hi Pranaaav!!
hi pranav!
HI PRANAV
Hi Pranav!!!!
HI PRANAV!!
Hello, Pranav!
heyo pranav
Hello!
He will also be joined by Daniel Lovsted (naclocanada), Mihir Singhal (msinghal), Kevin Liang (kevliang), Andy Tockman (tckmn), Aleka Blackwell (Aleka_NACLO), and Adam Hesterberg (Kamior).
Hi Daniel!
Hi Daniel!
Daniel is a graduate student in philosophy currently based in Toronto, Canada. He first competed in NACLO in 2013, won a gold medal at the IOL in 2014, and since then has been a NACLO problem writer, editor, organizer, coach, and Canadian IOL team chaperone. Daniel's interests include looking at paintings, looking at photos of paintings, and spending time with his cats
Hi Mihir!
Mihir is a current math major at MIT. He competed in the NACLO for seven years, and was on the IOL team in 2018. He enjoys puzzle hunts and card games in his free time. His favorite bird is the common hoopoe.
Yo Kevin
Hi Kevin!
Kevin is a junior majoring in Linguistics and Computer Science at the University of Pennsylvania. He first took part in NACLO in 2017 and represented Team Canada at IOL in 2017 and 2018. Since then, he has been on the organizing and problem committees of NACLO. He loves sushi, maps, and just learning about different languages.
Ello Andy!
Andy is a current undergraduate studying math at MIT, minoring in computer science and linguistics. He competed in the IOL three times, in 2017-2019. He also enjoys programming, playing piano and viola, conlangs, board games, video games, logic puzzles, and puzzle hunts.
ALEKA THE LEGEND!
Aleka is a professor of Linguistics at Middle Tennessee State University. Aleka has been serving on the NACLO organizing committee since 2008 and currently serves as co-chair of NACLO. Aleka has authored problems for the competition since 2010, and she has coached and chaperoned the team members to the IOL since 2016.
Hi Adam
Hi Adam!
Adam is the Assistant Director of Undergraduate Studies in CS at Harvard University. He competed in the NACLO in its first year, 2007, placed first in the IOL that year, and has been helping write/review problems, coach the US team, and grade the test ever since. He likes wordplay, cats, and graph theory
Cool!!
That's a lot of people. That should be all the help you guys could need.
So, tonight the general structure is:
1. They will introduce what NACLO is.
2. They will do some practice problems to show you what they are like
3. They will answer any questions you have.
This is awesome!
I'm excited to get started!
ok!
So, I'll pass you off to Pranav now.
Hello everyone!
As Deven said, I'll be leading the discussion.
First off, a bit of background about NACLO:
NACLO is a contest in which high-school students solve linguistic problems. In solving these problems, students learn about the diversity and consistency of language, while exercising logic skills. No prior knowledge of linguistics or second languages is necessary.
To learn more about this free annual competition, go to https://www.nacloweb.org/.
This year’s Open Round of NACLO is on January 28, 2021. You can compete at a university or high school site listed on the NACLO registration website, or you can compete from home (if you are homebound or homeschooled). To register for the competition, go to https://www.nacloweb.org/register_student.php.
The top 10% of participants in the Open Round of NACLO are invited to the invitational round. The top performers in the invitational round are invited to represent the US and Canada at the International Linguistics Olympiad (IOL). The 2021 IOL will be in Latvia, July 19-23, 2021. For more information, go to https://www.ioling.org/.
The IOL is one of 13 International Science Olympiads for secondary school students, and has been held annually since 2003. Each year, teams of young linguists from around the world gather and test their minds against the world’s toughest puzzles in language and linguistics.
No prior knowledge of linguistics or languages is required: even the hardest problems require only your logical ability, patient work, and willingness to think around corners.
To participate in NACLO, you must satisfy all of the following criteria:
- You have never been enrolled as a full-time college or university student.
- You must be less than 20 years old on the first day of the IOL (July 19, 2021).
- You are a citizen of the US or Canada or a student in a secondary school in the US or Canada.
- You are available to take the test at one of the times it's offered.
The Open Round is typically three hours long, whereas the Invitational Round is typically four hours long.
The judges have the authority to lengthen either competition in the event of unforeseen circumstances.
This year’s Invitational Round is on March 11, 2021.
But in order to really understand what NACLO is, it helps to showcase a few problems.
So, let's jump into some problems!
Is everyone excited?
YEAH!!!
yes!
YES!!
yes!
yes!
yep
YEs!
Yeah!
Heck yeah!
yes!
totally
yes!!
Yes
Yeah!
Ye
Yeyaaa!
Oh yeah this is like the most exciting class yet!
Yes!
Here is our first problem:
Apinayé belongs to the Ge language family of Brazil. Currently it is spoken by less than 800
people, and therefore is seriously endangered. The following are some sentences in Apinayé,
along with their English translations. You will see some letters here that do not occur in the
English or Portuguese writing systems. You do not need to know exactly how these letters are
pronounced in order to solve this problem:
Apinayé $\longrightarrow$ English
Kukrε kokoi $\longrightarrow$ The monkey eats
Ape kra $\longrightarrow$ The child works
Ape kokoi ratš $\longrightarrow$ The big monkey works
Ape mï mεtš $\longrightarrow$ The good man works
Ape mεtš kra $\longrightarrow$ The child works well
Ape punui mï piŋetš $\longrightarrow$ The old man works badly
The end goal of this problem will be to translate sentences in Apinaye to English and from English to Apinaye.
I know this looks pretty daunting, especially if this is your first time experiencing a NACLO puzzle.
But I promise all of you that once this Math Jam is over, you'll think this is a piece of cake!
First off, let's make sure we understand what we're given. What is this table telling us?
That sentence = that sentence
It is translating Apinaye to English
the translations of various sentences from Apinaye to English
haha!
Right, this table contains the English translations of several Apinaye sentences. The end goal of this problem will be to translate some new sentences in Apinaye to English and vice versa.
Of course, before we start translating new sentences, we'll need to understand the sentences we're already given better. Any ideas where to begin with that?
Ape means works
Ape = works
Good eye! It looks like 'Ape' appears in a lot of sentences.
We can guess that this word means "works" because "works" appears in all the sentences that Ape appears in, and in the one sentence where Ape doesn't appear, neither does "works"!
Some people guessed that "Ape" is "the".
That's a good guess! "The" does appear in all the sentences that have Ape, but the first sentence has the word "the", but it doesn't have Ape in its translation.
Okay, so now we have found that Ape is most probably "works". Are there any other observations, or other words that we can figure out with a similar strategy?
Look for common words
kokoi- monkey
kokoi = monkey
kokoi = monkey
kokoi = monkey
monkey = kokoi
Can kokoi = monkey?
kokoi means monkey
kokoi = monkey
kokoi is monkey
kokoi is monkey
kokoi is monkey
kokoi = monkey
Kokoi is monkey
kokoi=monkey
kokoi = monkey
kokoi - monkey
Kokoi = Monkey
kokoi is monkey
kokoi=monkey
kokoi -> monkey
Kokoi is monkey
Yup, kokoi is indeed monkey!
chid is kra
kra = child
kra means child
kra = child?
"kra" is child
kra = child
kra = child
kra = child.
kra is child
kra = child
Kra is child
kra = child
Yeah, kra is child!
You are getting this really fast!
For those who are confused - these words all appear in multiple sentences, and there are English words that also are in those corresponding sentences but no where else. This makes us think that, for example, kra is child!
mi = man
mï is man
mï = man
Yup, mi is man!
This is sort of the limit of this method. Before we continue, let's tabulate what we have so far:
Apinayé $\longrightarrow$ English
Kukrε kokoi $\longrightarrow$ The monkey eats
Ape kra $\longrightarrow$ The child works
Ape kokoi ratš $\longrightarrow$ The big monkey works
Ape mï mεtš $\longrightarrow$ The good man works
Ape mεtš kra $\longrightarrow$ The child works well
Ape punui mï piŋetš $\longrightarrow$ The old man works badly
To proceed with the problem, we'll have to dig a bit deeper. For example, I see the word mεtš in two sentences - any guesses as to what that word means?
mets = good or well?
good/well
mεtš= good/well.
good
good/well
good/well
good or well
good/well
mεtš=good, well
good/well
good or well
good/well
good or well
good or well
good/well
good / well?
good/well
good/well
good well
good or well--> a positive action
good/well
mεtš job, you all!
It means good or well. These words mean really similar things, so it's not surprising that they share the same translation in Apinaye.
What are some next steps, or other strategies to consider?
the order of the words and how that affects the sentence
consider placement of mets to discern adjective vs adverb
look at sentence order, disregard the...
discern placement of the words
find sentence structure
identify sentence structure
Look at where words with similar uses are placed.
Wow, we're already getting ahead!
Before this, let's start a bit simpler.
A common strategy is also to look for what's left to translate. For example, let's look at the sentence "Kukrε kokoi". Which word in this sentence do we know the translation of?
kokoi
kokoi
kokoi means monkey
kokoi
kokoi
And what is its translation?
monkey
monkey
monkey
monkey
monkey
So now, we're left with the word Kukrε. What is this word most likely to mean?
eats
eats
Eats
therefor Kukrε must mean eats
eats
eats
eats, 3rd Singular
That's right! We've already accounted for how "monkey" is represented in Apinaye, so we still need a word to represent the concept of eating.
eat(with conjugation)
I'm sure some of you will be wondering - well, why can't it be "the"? For this question - it's complicated. But there should be some intuitive sense that accounting for more grounded things such as "eating" is much more important than trying to account for something as abstract as the word "the".
eats
If you decide to pursue this further and do practice problems between now and January, you'll be able to hone this sense in by being exposed to a variety of languages. But for now... trust me on this.
its process of elimination, SOME word must be eats, so we assume its kukre
Yup, exactly! Couldn't have said it better!
Now, what other word can we figure out from this strategy?
rats is big
rats
rats = big
ratš = big!
ratš = big.
rats is big
rats
rats is big
(I don't like big rats...)
Me neither
But yes, that is exactly right!
Here's what we have so far:
Apinayé $\longrightarrow$ English
Kukrε kokoi $\longrightarrow$ The monkey eats
Ape kra $\longrightarrow$ The child works
Ape kokoi ratš $\longrightarrow$ The big monkey works
Ape mï mεtš $\longrightarrow$ The good man works
Ape mεtš kra $\longrightarrow$ The child works well
Ape punui mï piŋetš $\longrightarrow$ The old man works badly
Before we move on to the translation portion of the problem, we have one last sentence to fully decipher: "Ape punui mï piŋetš", which means "The old man works badly". We can remember that Ape means works, and mï means man, but between punui and piŋetš, we need to figure out which one is "old" and which one is "badly".
Any ideas on how to crack the last piece of the puzzle?
analyze sentence structur
can we use sentence structure?
look at the sentence structure
we can look at the word good
order in sentence
word order
this is where sentence structure is helpful
Probably need to look at sentence structure to figure this out.
Use the order in which the words appear?
An important part of language is that it has structure. If we want to say something, we can't just choose a random order of words and say them! Try to think about where specific kinds of words were placed.
Let's start a bit more specific - what is in common between all the first words of the Apinaye sentences?
Verb comes first.
Verb
verb
verbs
verb
they're all verbs
verbs
it's a verb
verb
verbs
They're all verbs.
All verbs
Exactly! And if there are two words, a verb and a noun, the verb always comes first.
LOOK AT SENTENCE STRUCTURE OF OTHER SENTENCES.
Verbs come first
Now, suppose we get a little more complicated, and we add an Adjective. This is a word that describes a noun. Where would this go in Apinaye?
after the noun
after subject
After the noun
Right after the noun.
adj goes after noun
after noun
last
after noun
After the noun
after the noun
after the noun
after the noun
After the noun
noun before adjective
after the noun
after noun
Exactly! We can tell this is the case by examining sentences that have just a verb, noun, and adjective.
Ape kokoi ratš. $\longrightarrow$ ‘The big monkey works.'
Ape mï mεtš. $\longrightarrow$ 'The good man works.'
Now, suppose I have an adverb that describes the verb instead of an adjective. Where would I put the adverb?
after the verb
after the verb
after the verb
after the verb
after verb
right after the verb
After verb
after the verb!!
Exactly! Apinaye puts it right after the verb, which for our purposes is the same as putting it between the verb and noun. We can actually compare the following two sentences:
Ape mï mεtš $\longrightarrow$ 'The good man works.'
Ape mεtš kra $\longrightarrow$ 'The child works well.'
And see that the meaning of mεtš (which is good/well) can change depending on if it is in the adjective position or in the adverb position.
Since Mets can be used as both as an adverb and an adjective we can look at its placement in order to determine the syntax. As we can see when used as an adverb it comes before the noun but when used as an adjective it comes after. Therefore punui is badly and piŋetš is old
verb, adverb, noun, adjective
descriptive words follow after the object of description
Good job you all!
Good job you all!Now, back to our main question - how can we distinguish which of "punui" and "piŋetš" is "old" vs "badly"?
Well, we can look at the positions of the two words. "punui" is right after the verb, so it must be the adverb "badly", while "piŋetš" is right after the noun, so it must be the adjective "old".
Here is everything that we have gathered:
Apinayé $\longrightarrow$ English
Kukrε kokoi $\longrightarrow$ The monkey eats
Ape kra $\longrightarrow$ The child works
Ape kokoi ratš $\longrightarrow$ The big monkey works
Ape mï mεtš $\longrightarrow$ The good man works
Ape mεtš kra $\longrightarrow$ The child works well
Ape punui mï piŋetš $\longrightarrow$ The old man works badly
I got it!
The order of sentences in Apinayé is Verb (Adverb) Noun (Adjective)
That's great to hear!
Now we can move on to translating those new sentences!
A1) Translate the following into English:
Ape ratš mï mεtš.
Kukrε ratš kokoi punui.
Ape piŋetš mï.
A2) Translate the following into Apinayé:
'The big child works a long time.'
'The old monkey eats a lot.'
Let's start with the first sentence of A1, and take it word by word. First, what does Ape mean?
Works
works
works
works
works
Works
works
works
works
Works
works
What does ratš mean?
big
big
big
big
big
Big
big
Big
big
big
Big
big
big
What does mï mean?
man
man
man
man
man
Man
man
Man
man
man
Man
man
man
man
man
man
man
man
Finally, what does mεtš mean?
well
well/good
good
well/good
good
good/well
good
works
good/well
good/well
Good/well
good
good/well
good
good/well
good/well
well/good
good
Putting it together, what do we get?
man
the good man works bigly (haha bigly)
the good man works a lot?
the good man works a lot
the good man works a lot.
Exactly!
A lot of students have been saying "The big man works well", which is close, but incorrect. I remember also making the same mistake when I was first trying out this puzzle (back when I was just starting on my linguistics olympiad journey). Does anyone know why it's incorrect?
adjectives come after nouns, adverbs after verbs
Sentence structure?
Correct! Here, ratš is an adverb (it comes after the verb), so it must describe the verb and mεtš is an adjective (it comes after the noun), so it must describe the noun.
But now we're sort of stuck - how does "big" become an adverb? We can't just say "The good man works bigly" (I mean, you could, but with points taken off).
Any ideas?
look at english sentences
(Hint: Look at A2)
look at A2 for ideas
you look at A2
Looks like some of you are using the secret technique of solving the test... with the test!
OH IT'S A LOT!!
Works a lot, i see
a lot
"a lot"
"a lot"
a lot
Exactly, we can translate this as "a lot". Our sentence becomes "The good man works a lot."
it provided us the idea of "a lot"
A2 omg so interesting
omg thats so cool!
LOL! I do that too if a test asks a question and it says it directly on the test!
The phrase "a long time" works better with the adjective "old".
"a lot" appears in A2 which implies you are able to say "a lot" with what you have
Yup!
Moving on, what is the translation for sentence 2?
cool!!
cool
cool
The bad monkey eats a lot
The bad monkey eats a lot.
the bad monkey eats a lot
the bad monkey eats a lot
The bad monkey eats a lot
The bad monkey eats a lot
The bad monkey eats a lot
The bad monkey eats a lot
The bad monkey eats a lot
the bad monkey eats a lot
The bad monkey eats a lot.
the bad monkey eats a lot
oh, bad not old
Exactly!
And the third sentence?
the man works a long time
The man works a long time
the man works for a long time
The man works a long time
The man works for a long time
The man works a long time
The man works a long time
The man works for a long time
the man works for a long time
the man works for a long time
the man works a long time
The man works a long time
Some people are mixing up punui and pinets - remember, we found that punui means "bad" and pinets means "old"!
"The man works a long time" is correct though!
Great job, all of you!
I think it's time to move to a different, harder problem.
Is it better to put "long" or "a long time" in situations like this?
Because A2 had "a long time", it would be safer to translate it using this phrasing.
But both should be accepted!
a long time is an adverb
i'm really enjoying this thank you!
No, thank you for coming!
How many points was this question worth?
This appeared in 2008, and it was 10 points out of 100
yes i am hyped cuz i almost solved it at first except i mixed up two words
Nowadays, it would be a 5 point problem
it's not as hard as it sounds
im so excited
Yay, that's great to hear!
Let's move on to the next problem!
YEEAAAHHHH!!!
so hyped for harder problems!
YES WE ARE HYPED
i want harder problems!!
HYPE!!
Hype!
HYPE!!!
no we are TYPED
Ahhh heck yeah!
PUZZLES!!
HYPE!
This problem appeared in the Polish Olympiad during the 2016-17 school year, and is honestly one of my all-time favorite problems that I have done. Without further ado, here it is:
In the Obolo* language, two systems of writing numbers existed. In the 1980s, the modern system replaced the older system. Below, twelve numbers between 11 and 99 are given in ascending order in the contemporary system (left column) and traditional system (right column).
$\begin{align}
\text{akɔp me iba} & = \text{akɔp me iba} \\
\text{akɔp me jeeta} & = \text{inaan iba} \\
\text{akɔp iba me go} & = \text{inaan go me etip me akɔp} \\
\text{akɔp ita me ini} & = \text{etip me akɔp me ini} \\
\text{akɔp ita me jaaba} & = \text{inaan ita me etip iba} \\
\text{akɔp ini me ge} & = \text{etip iba me ge} \\
\text{akɔp ini me jaaba} & = \text{inaan ita me etip iba me akɔp }\\
\text{akɔp go me iba} & = \text{etip iba me akɔp me iba} \\
\text{akɔp go me onaange} & = \text{inaan ge me etip ita} \\
\text{akɔp gweregwen} & = \text{etip ita} \\
\text{akɔp jaaba me jeeta} & = \text{inaan iba me etip ini }\\
\text{akɔp onaange me go} & = \text{inaan go me etip go} \\
\end{align}$
*Obolo is part of the Niger-Congo family and has over 250,000 speakers. Although Obolo is a tonal language, the tone is not recorded in this problem
oh my
I know what a lot of you might be thinking right now. "How am I supposed to solve this, we don't even have English translations to compare these numbers with. Also - two different ways to write numbers?"
ooh, interesting... no English
Maybe you're in awe that Obolo has two different systems - I know I was.
OOHH
what... even... how.. ?????
it could be that they changed bases
Languages can be really cool!
this seems a lot harder
We're going to solve this problem (and this is a general strategy) by keeping the following rule in the back of our head: all languages have some sort of structure that makes a decent amount of sense (I say decent sense here because there are some languages that are really wild).
So keeping this at the back of our head, we are going to try looking at the structure of these words to try to discern some sort of meaning from these words. First off, which system seems easier to tackle?
contemporary
left
contemporary
1
The first
the first...
left
contemporary!
left is consistent
left
left
left
left side
1st ne
Left. Less words.
The contemporary system
Contemporary.
Yeah! Let's start with this system. Everyone, focus on the numbers on the left side. What is similar between all of them?
lots of "akɔp"s
it always starts with akep
akep
akop
Akop
akop
akop
akop
akop
akop
akɔp
akɔp
Any other words that are quite commom?
me
me
me
me
"me"
me
me
me
me
Exactly!
Now, here's the hard part. Everyone, put on your "thinking like a linguist hat", and try to think about what these words might mean.
My "thinking like a linguist" hat is green, for those who are curious
akop probably denotes tens place
does akop mean "tens place" and me mean "ones place"?
akop might mean its in the tens
Akɔp is probably a base number, while me might be "and" kind of like the French "four twenties and eight" for 88?
Wow... you guys are good!
A lot of languages, especially in their number system, have words that represent digits and words that represent structure stuff. For example, in English, we may say something like "one hundred fifty" - in this case, the "one" and "five" represent digits, while the "hundred" represents the structure of the number - that the digit "one" is in the hundreds place.
Digits, in general, multiply with the values of the structure word that the digit is associated with. For example, the word "two hundred" has $2 \times 100$, with the digit being $2$.
So, because these seem like two digit numbers (they're from 11-99), we want something that sort of means the tens place. In English, this is the -ty suffix; in Obolo, this is probably one of the two words we thought were "structure words". Which one of them is most likely it?
akop
akop
akop
akop
akop
akop
akɔp
akcp
akop
Yeah, exactly - It's probably akɔp. One way to tell is to look at the line akɔp gweregwen = etip ita, and see that this is bigger than some of the other two digit numbers out there. If akɔp wasn't the tens digit, this wouldn't really make sense.
Any ideas on what "me" could possibly mean?
+
and?
and
ones place
"and" before the ones place
could mean "and"
and
and or +
to add the ones place to the tens place
Yeah, "one's digit" and "and" are both great responses.
OHHH WAIT IT KINDA MAKES SENSE NOW
That's what we're going for!
If we quickly glance at the other side (the traditional number system), we can see that there are phrases like "me etip me akɔp", which makes me lean towards a translation of "and".
and makes more sense than ones
the ones places
oh wait I see a pattern
Now, a natural step to take would be to think "well, akɔp and me are both structure words, so the other two words are likely to be digit words"
Quick question - let's take the phrase "akɔp iba me go". We can agree that iba and go are digits. Which one would be the tens digit, and which one would be the ones digit?
theres a pattern
iba is the tens digit?
iba is tens
"Iba" tens, "go" ones.
iba = tens digit, go = ones digit
iba = tens, go = ones
closer to akop
iba is tens and go is ones
Yeah, it would be iba. We already guessed that akɔp was the marker for the tens digit, so "iba" must be the tens digit because it is right next to akɔp (otherwise, the system would be linguistically unintuitive - remember from the first problem that things that describe other things are usualy next to what they describe!).
More concretely, lines 1 and 8 can't be *so far apart if iba were one's digit
Another interesting way, if you did not figure out that akɔp was the tens digit, would be to remember that the numbers are in ascending order. Then, you could notice the following section in the table:
Good observation!
\begin{align}
& \text{akɔp ini me jaaba} \\
& \text{akɔp ita me ge} \\
& \text{akɔp ita me jaaba} \\
\end{align}
If the second position was the tens digit, there would be no way for this ordering to be possible. Then, because akɔp was next to the digit that is probably the tens digit, it would be the tens place
Some of you have asked why there needs to be a set position for the tens digit and units digit. What if in one number, the first of the two digits is the tens digit, but in another number, the second of the two digits is the tens digit?
Technically, you wouldn't be able to rule this possibility out. However, having a system like that is a bit crazy and thus makes less "linguistic sense". The idea is that all language has structure that makes a decent amount of sense. In general, I would assume that the structure is clean when solving these sorts of puzzles, and if you end up getting stuck somewhere, backtrack and rethink this assumption.
what about numbers like "eleven" and "twelve"
Yes, English is weird and sometimes combines the places, or even flips them as in "thirteen" and "fourteen".
But in Obolo, we see that things are generally regular.
We'll discuss more about this soon
Does this happen with other languages on this test?
Yes, in a lot of harder problems, there are irregularities with the language that you have to figure out!
In many languages, the "teen" ending words are strange. I can't come up with any reasons. Do you have any ideas why?
NACLO is sooo fun!
Do they just not like teens?
In many languages, the teens are strange!
But let's continue with the problem.
When solving these sorts of puzzles, it's vital that we keep ourselves organized, and we also keep track of what we need to get. So, I have taken the liberty to collect all the words we see appear as digits. Here is a shortlist:
ge, go, gweregwen, iba, ita, ini, jaaba, jeeta, onaange
(Sidenote: if you see more than or less than $9$ possible digits, chances are, your language might not count in groups of $10$! This won't be discussed in this Math Jam much further, but counting in groups of $10$ is an assumption that turns out to seem to be correct in this case. If you want to know why I assumed this, it's for simplicity, and also because this is the "modern" counting system)
Right now, we have all $9$ digits in our problem, which must correspond to $1-9$. In many languages, English included, while zero is technically a possible digit, we never use it when describing other numbers. As far as I know, I don't say things like one thousand, zero hundred fify-two, but that might just be me.
What information can we gather about the values of these digits?
iba<jeeta
iba is smaller than jeeta
iba < jeeta
iba is 2 or 3
Using the ascending order and the tens place, we can figure out their values
Iba tens digit go ones digit
iba is the smallest, iba < jeeta
iba<jeeta
onaange > go?
jeeta>iba
we can order all of them except jeeta based on the ascending order of the list
Yup - from our guess about which is the tens digit and which is the ones digit, we have:
iba $<$ ita $<$ ini $<$ go $<$ gweregwen $<$ jaaba $<$ onaange
ge $<$ jaaba
iba $<$ jeeta
There's something that I hadn't really discussed in detail - that the first two numbers seem to not have a tens digit! Does anyone want to guess what this means?
it means it is a teen
The ten's digit is 1?
their tens digit is 1?
they are from 11-19
smaller than 20
it's just like saying ten, you don't have to say one ten
akop alone means "10"
Yes - it would be most likely that a tens digit of one is omitted, especially since these two are the lowest numbers. This "omission of one" is quite common across many languages, actually.
You wouldn't say, one ten and one one. You don't have to say one ten.
Exactly!
are teens like ten so 13 is like three-ten?
ten's digit is one
They are multiples of ten
10<x<20
For example, suppose I was trying to say this number: $102$. I could say "one hundred two", but sometimes you can just go for "hundred two".
What extra information does this tell us about the values of the digits?
We know that iba is really low... can it be $1$?
iba is at least 2
iba > 1
iba can't be 1
>1
at least 2
iba > 1
wait why?
why can't iba be one?
Iba cannot be $1$, as then it would be omitted. But, we know that iba is lower than seven other digits - ini, ita, go, gweregwen, jaaba, onaange, and jeeta. So, what is iba?
iba = 2 exactly
2
2
2
2
2!
Exactly! If iba was any bigger than $2$, then we would only have $6$ or less digits that were greater than it.
two!
2!
2
2!
To go back, if iba was $1$, then our assumption that having no tens digit means only $1$ ten doesn't make sense.
We can actually figure out which digit is $1$ now. Which one?
ge
ge
Ge
ge
ge
ge
more than 1 because akop iba is bigger than akop
ge?
Ge=1?
Ge
ge?
ge
ge?
ge
Exactly! ge is the only digit that we were not told in some way was greater than iba. So, this must be $1$.
OH I SEE
wow this is cool
OHH :o
Layers upon layers.
it is cool!
Cool!
this is becoming my favorite problem now xD
having so many "aha!" moments rn
Yeah, now you may understand why I love this problem
Then, we basically have a fixed order for the rest of the digits, with jeeta somewhere (we don't know exactly where though yet). This gives us that ita can be $3$ or $4$, ini can be $4$ or $5$, go can be $5$ or $6$, and so on; and jeeta can be any number from $3$ to $9$.
Unfortunately, it's hard to make any more progress just by looking at the modern system. But we made a lot of progress! So, when we're stuck, it's time to look at the part which we haven't used - the traditional system.
We'll be using a similar approach - by first assuming that this system has a structure that makes a decent amount of sense.
(Though admittedly a bit less clean than the moderm system)
inaan??
so they use etip and inaan?
We have some new words - etip and inaan. We should probably try figuring out what they mean
Let's focus on etip first. Is there a datapoint that can be really helpful in figuring out what etip is?
akop gweregwen
Ok Pranav, I can totally see why you love this problem.
etip seems to show up a lot
akop gwergewen=etip ita
akop gweregren-etip ita
akop gweregwen = etip ita
Yeah, exactly! We know what akɔp is, and we have a good idea on the meanings of both gweregwen and ita. The number akɔp gweregwen is either $60$ or $70$, while the right hand side is probably either $3 \times$ or $4 \times$ etip.
What can we conclude from this?
Does it make more sense for gweregwen to be $6$ or $7$?
6
gweregwen is most likely 6
6!
6
6
6
6
6
6
6
6
6 has more factors
I think it makes more sense for gweregwen to be 6.
Exactly, gweregwen must be $6$, because $70$ is not divisible by $3$ or $4$, and it would be very weird for a language to use fractional amounts to represent whole-numbered values.
wait, how do we know we're multiplying on the right?
why is it 3x or 4x etip?
Ah, good question!
Digits in general multiply with the place values they are associated with
For example, If I say 300, that's $3 \times 100$
we noticed the traditional system used multiplication with akop for the tens place
The pattern in the left hand side indicates that we might think that "etip ita" is ita * etip, though this is still just an educated guess
What other numbers can we conclude from this observation?
ita is 3
go 5, ini 4, ita 3
go = 5
etip is 20
ita=3?
etip is 20
etip = 20?
etip is 20 because 20 times 3 is 60
etip is 20
etip = 20
etip is 20
and etip is 20
Yeah - we get ita is $3$, ini is $4$, and go is $5$. This also means that etip is $20$. This is because we get $2 <$ ita $<$ ini $<$ go $< 6$, which forces what value these digits can be. For etip, we have $3 \cdot$ etip is $60$, meaning etip is $20$.
We're on the home stretch now! We have only four more components to take care of - the digits jaaba, jeeta, and onaange; which by process of elimination have to be $7$, $8$, and $9$ in some order; and inaan. Let's focus on figuring out the meaning of inaan, which should allow us to figure out which digit is which. I have, for the sake of time, have listed all the data where inaan is included:
$\begin{align}
\text{akɔp me jeeta} & = \text{inaan iba} \\
\text{akɔp iba me go} & = \text{inaan go me etip me akɔp} \\
\text{akɔp ita me jaaba} & = \text{inaan ita me etip iba} \\
\text{akɔp ini me jaaba} & = \text{inaan ita me etip iba me akɔp }\\
\text{akɔp go me onaange} & = \text{inaan ge me etip ita} \\
\text{akɔp jaaba me jeeta} & = \text{inaan iba me etip ini }\\
\text{akɔp onaange me go} & = \text{inaan go me etip go} \\
\end{align}$
We can now partially translate everything - basically, fill in everything we know so far:
!$\begin{align}
10 \text{ and jeeta} & = \text{inaan }2 \\
10 \cdot 2 \text{ and } 5 & = \text{inaan } 5 \text{ and } 20 \text{ and } 10 \\
10 \cdot 3 \text{ and jaaba} & = \text{inaan } 3 \text{ and } 20 \cdot 2 \\
10 \cdot 4 \text{ and jaaba} & = \text{inaan } 3 \text{ and } 20 \cdot 2 \text{ and } 10\\
10 \cdot 5 \text{ and onaange} & = \text{inaan } 1 \text{ and } 20 \cdot 3 \\
10 \cdot \text{jaaba and jeeta} & = \text{inaan } 2 \text{ and } 20 \cdot 4\\
10 \cdot \text{onaange and } 5 & = \text{inaan } 5 \text{ and } 20 \cdot 5 \\
\end{align}$
Let's clean up our translations a bit more
As our reminder, here is our progress so far:
akop: tens place
me: and
ge = 1
iba = 2
ita = 3
ini = 4
go = 5
gweregwen = 6
jaaba = 7 or 8
onaange = 8 or 9
jeeta = 7, 8, or 9
What is a good guess for what inaan is?
inaan is minus
inaan = some sort of subtraction?
minus
innan minus
subtractionm
Inaan is subtracting the number after it
minus
subtraction?
subtract
What's weird to me is that for all the numbers we know, the other side has a multiple of $10$ that is bigger than the number. For example, we have $25$ being written as (something) and $30$, $50$-something being written as (something) and $60$, and so on...
This sort of makes me thin - "well, what if inaan is some sort of subtraction"?
Well, does subtraction work?
i really like this problem
Oops, it seems like I made a typo with jaaba.
$\begin{align}
10 \text{ and jeeta} & = \text{inaan } 2 \\
25 & = \text{inaan } 5 \text{ and } 30 \\
30 \text{ and jaaba} & = \text{inaan } 3 \text{ and } 40 \\
40 \text{ and jaaba} & = \text{inaan } 3 \text{ and } 50 \\
50 \text{ and onaange} & = \text{inaan } 1 \text{ and } 60 \\
10 \cdot \text{jaaba and jeeta} & = \text{inaan } 2 \text{ and } 80\\
10 \cdot \text{onaange and } 5 & = \text{inaan } 5 \text{ and } 100 \\
\end{align}$
Now, does it work?
ok, so jaaba is 7
yes indeed
yep
yes
jaaba has to be 7
yep!
It seems like it almost works, except for $10$ and jeeta = inaan $2$. In fact, I'm going to say that it works, but I will explain how in a bit.
First, what are the values of jaaba, jeeta, and onaange that we get?
jaaba is 7!!
yeah so jaaba is 7, onaange is 9, and jeeta is 8
jaaba = 7 jeeta = 8 onaange = 9
Precisely - $7, 8, $ and $9$, respectively.
then onaange is 9
jaaba is 7, jeeta is 8, onaange is 9
jaaba -7 jeeta - 8
jaaba = 7, onaange = 8, jeeta = 8
jaaba=7 jeeta=8 oaange=9
jaaba 7, jeeta 8 and onaange 9
jaaba 7, jeeta 8, onaange 9
jaaba = 7, jeeta = 8, onaange = 9
jaba = 7, jeeta = 8, onaange = 9
does the traditional system also leave implied when the base is 1? i.e. 18 = (implied etip)-2
i love how it's all coming together!
Now, the first example currently reads $18 = -2$; we would expect the translation to be inaan iba me etip. But, we can sort of see that this etip can be implied. After all, most languages don't have negative numbers, so there wouldn't be an alternative meaning, and no confusion!
does "inaan 2" implicitly also include twenty before it?
Exactly!
*Most languages don't have negative digits
Task 1.1: Write all the expressions with numbers
What are all the numbers that were in this list?
$\begin{align}
\text{akɔp me iba} & = \text{akɔp me iba} \\
\text{akɔp me jeeta} & = \text{inaan iba} \\
\text{akɔp iba me go} & = \text{inaan go me etip me akɔp} \\
\text{akɔp ita me ini} & = \text{etip me akɔp me ini} \\
\text{akɔp ita me jaaba} & = \text{inaan ita me etip iba} \\
\text{akɔp ini me ge} & = \text{etip iba me ge} \\
\text{akɔp ini me jaaba} & = \text{inaan ita me etip iba me akɔp }\\
\text{akɔp go me iba} & = \text{etip iba me akɔp me iba} \\
\text{akɔp go me onaange} & = \text{inaan ge me etip ita} \\
\text{akɔp gweregwen} & = \text{etip ita} \\
\text{akɔp jaaba me jeeta} & = \text{inaan iba me etip ini }\\
\text{akɔp onaange me go} & = \text{inaan go me etip go} \\
\end{align}$
In this list
Let's start with the first one
12
12
12
12
12
12, 18, 25, 34, 37, 41, 47, 52, 59, 60, 78, 95
Perfect!
Task 1.2: Write the following contemporary system expressions in the traditional system:
akɔp me go
akɔp gweregwen me ita
akɔp jeeta me gweregwen
Let's start with the first one
What is this number in English?
15
15
15
15
15
15
15
15
Yup!
Now, how is this converted into the traditional system
15
it would be 5 less than 20
inaan go
inaan go
so traditional is inaan go?
inaan go
inaan go
Yup!
We have that it's 5 less than 20; but just like 18, the etip is implied
Now, let's do the others
The second one?
then why doesn't akop me iba get converted to inaan jeeta?
That's a good question!
does the subtractive system work for the teens when 15<=x<=19?
Yeah!
In general, inaan is only used when the units digit is 5-9
why is it used for 5 though
Beats me, ask the Obolo speakers.
I'm just the messenger here
wait but why can you assume that for the answer to the first one?
We can look at the examples to see what is subtractive and additive
In other numbers where there is a units digit of go, we see inaan being used.
ohhh cool!
Let's move on to the second translation, shall we?
What is the number in English?
63
63
63
63
63
63
63
63
63
63
63
63
63
63
How do we write this in the traditional system?
etip ita me ita
etip ita me ita
etip ita me ita
etip ita me ita
etip ita me ita
etip ita me ita
etip ita me ita
etip ita me ita?
etip ita me ita
Yup, it's 3 twenties and a 3
etip ita me ita
20x3+3
Precisely!
And finally, the third number.
86
86
86
86
90-4
I didn't even have to ask the question!
well we're a smart bunch what can we say
What is the translation?
inaan ini me etip ini me akop
inaan ini me etip ini me akop
inaan ini me etip ini me akɔp
86, inaan ini me etip ini me akop
inaan ini me etip ini me akop
Exactly!
Well, that's it for this problem.
Hope you had fun doing this!
this is rlly cool
Nice!
yeah!
We'll stay if people have questions about NACLO.
If you enjoyed solving today’s problems with us, you can practice solving more such problems by going to https://www.nacloweb.org/practice.php. To practice solving problems from past IOL competitions, you can go to https://ioling.org/problems/.
Now is the time to ask all your questions about NACLO.
I'll get us started: When is it?
This year’s Open Round of NACLO is on January 28, 2021. You can compete at a university or high school site listed on the NACLO registration website, or you can compete from home (if you are homebound or homeschooled). To register for the competition, go to https://www.nacloweb.org/register_student.php.
Will there be more NACLO mathjams? This was the most fun I've ever had on AOPS
We hope so!
what ages is NACLO for?
Primarily high school but we do have some younger students who participate.
Outside of doing practice problems, what are other good ways to prepare for NACLO? Should we learn linguistics?
Linguistics is not needed, but can be very helpful in terms of being exposed to what to check for.
how will the online version of the NACLO work if we are taking it from home?
When do we have to register by?
(Students under 13 need parental permission.)
January 15, 2021
approximately how many questions are given in the 3 hour open?
how many points would a question like that be worth?
There will be 8 questions
That last question would probably be worth around 10–15 points
I'd guess 15-20.
What is a normal score to advance?
Varies a lot from year to year
i feel like i'm playing 4d chess every time i solve a problem -- what do you recommend i do to organize my work>
Highlighters, and writing tables or lists
can we take naclo online?
Yes! Any student can taken it online this year
Yes, but read the handbook and reach out with questions. https://www.nacloweb.org/resources/handbook/
Would learning a language such as spanish or french put you at an advantage of understanding these linguistics concepts?
Sign up for the "at-home" sign option when you register for NACLO
site*
How will the exam be proctored if we are at home?
If we registered for an inperson site and it closed can we switch to home?
Yes! You can switch to At-Home.
MasterInTheMaking: it might, but only to the extent that it'll help you get exposed to the kinds of ways languages can be different from one another -- but specific knowledge about a certain language generally won't help
How many problems did you do to become so good?
Whats the best way to start understanding these linguistics things for competition work? Should I get any textbooks?
Learning Spanish certainly helped with my understanding of languages!
If you enjoyed solving today’s problems with us, you can practice solving more such problems by going to https://www.nacloweb.org/practice.php.
To practice solving problems from past IOL competitions, you can go to https://ioling.org/problems/.
One of our past team members has created this video that goes over another NACLO problem: https://www.youtube.com/watch?v=-4dfC9Olho0
I filled a whole 3-inch binder full of practice questions!
Will we ever be required to explain how we reached an answer?
Another good source of practice questions is https://lingclub.mycpanel.princeton.edu/challenge/puzzles.php .
Wusters: generally not in the open round, but the invitational round will ask you to write explanations for many problems
Outside of NACLO, are there any other ways for high schoolers to explore linguistics?
yeah would there be resources to learn the linguistics concepts? like would you recommend finding books?
https://calendar.stonybrook.edu/site/iacs/event/summer-youth-camp-for-computational-linguistics-syccl/ -- This is a summer event worth considering.
PBS has Crash Course Linguistics. A podcast is All Things Linguistic.
also, i personally learned a good deal about linguistics just by reading random wikipedia articles because i found it interesting
so how did u guys become inspired by linguistics?
What if someone happens to know that language?
This is a terrific online introductory textbook: https://ecampusontario.pressbooks.pub/essentialsoflinguistics/front-matter/introduction/
I got interested in linguistics through the NACLO, actually!
@nsb14 I just sort of found languages to be cool, and decided to pursue in further.
@bronzetruck20: usually the languages tend to be quite rare, so this is unlikely to happen
Have you seen a common Hoopoe in person?
I hope to someday.
nsb14: my first exposure to linguistics was through conlangs, i think, which are constructed languages people invent (like toki pona, which is a constructed language with only 120 words!)
Standards for language obscurity are higher in the NACLO second round, and even higher in the IOL. In the first round, sometimes languages are common enough that some people have seen them before.
@snb14 I grew up in Greece where I learned English and then French and finally Russian. I just love languages.
How much harder is IOL than NACLO generally speaking?
(There are ~6000 languages in the world, most spoken by only a few hundred people, so there are plenty of choices for obscure languages.)
this was really fun!
What COVID-19 precautions will be taken at the University Sites.
I found the IOL to be quite a bit harder (the questions are also a slightly different style).
Why don't test writers just make up a language?
@Joseph_Vaughn this will generally depend on the specific university site, I would suggest reaching out to the individual site hosts
@stronto I found this a really good experience and NACLO was a great find but I'm sad I found it so recently. I just applied to MIT to major in linguistics
Each site has its own NACLO website where you can read about their COVID-19 plans.
dulaman: the IOL lasts 6 hours for 5 problems, and generally only a few people get very close to a perfect score. you can see all the past problems on their website, https://ioling.org
That's great to hear amelia6grace! Good luck, and I would love to meet more fellow linguistics majors!
@bronzetruck20 We want to test what actual languages are, not what a problem-writer's idea of a language is.
can we reach out to you guys after this jam? if so, how?
Feel free to shoot Pranav (stronto) a PM on AoPS!
by the way I found this cool quiz if anyone's interested: https://www.sporcle.com/games/Scuadrado/indo-european-counting-puzzle?playlist=script-click&creator=Scuadrado&pid=1R9764e98 also, it looks like the guy's made like 30 of these; there's a playlist below the table
Also feel free to email us at naclo21org@umich.edu
One of our past team members has created this video that goes over another NACLO problem: https://www.youtube.com/watch?v=-4dfC9Olho0. Check it out, too!
do the tests get harder every year?
thank you so much for doing this!! it was so interesting and i learned a lot. will there be another mathjam soon for this?
There have been problems with constructed languages, though, but usually only well-known constructed languages like Esperanto that are interesting examples of language themselves as opposed to ones constructed for a problem.
How will the at-home site work? Are we going to be provided a portal that allows us to access the competition?
@Apollonians we will be sending more information about logistics via email in January!
Yes, we will be in touch with all At-Home participants to walk you through the process.
There are podcasts about linguistics and YouTube channels.
@bronzetruck i think conlangs are sometimes used in the NACLO (there's a problem with klingon iirc) but generally problems use natural languages. it's hard to invent a naturalistic language!
u guys are awesome, thanks for making this class fun
Looking at the NACLO website, it says that this is 1 of 12 science olympiads... what are the other 11 about! They could also be really cool!
thank you so much! i really enjoyed this
amazing but sad if the languages go extinct
Thank you, very interesting and Helpful. Have a good day!
How long is the test?
@MasterInTheMaker https://en.wikipedia.org/wiki/International_Science_Olympiad
The open round is 3 hours
4 hours for the invitational round
(which have 8 and 10 problems respectively)
@amuscorp Yes; a major project among linguists for the last few decades has been chronicling languages before they go extinct.
"Long ago the 12 science Olympiads lived in harmony"
How do we access the transcript for this thing?
The Open Round is typically three hours long, whereas the Invitational Round is typically four hours long.
The judges have the authority to lengthen either competition in the event of unforeseen circumstances.
This year’s Invitational Round is on March 11, 2021.
The transcript should be on the Math Jams page on AoPS
how hard are the test problems compared to this?
This was a super fun experience and I definitely plan on participating in as much of this as I am able! Thank you for hosting it!
Alleosonia: these are some of the previous test problems!
The second problem we did was an example of a medium-difficulty problem on the test
Thanks for the fun and the info everyone.
xD
What other types of problems are there or is it mainly finding key words and translating
what makes the hard problems hard? do you have to guess a lot?
one of the fun types of problems is what's called a "chaos and order" problem – they give you a bunch of words and their translations, but they scramble the order so that you don't know which corresponds to which
mgher: some other types of problems include problems about writing systems, how words sound, or how to make new words out of other words -- you might be able to get a sense of them by looking through some past contests at https://nacloweb.org
NACLO has a variety of problems. Check them out here: https://www.nacloweb.org/practice.php. Some are based on writing systems, others on sounds of languages, and some are computational.
@nova_says: often with hard problems, either there is less information to allow you to figure things out, or the language has a "twist" that you have to guess – think of the omission of etip in the expression for 18, but harder
what are your guys favorite language?
Food Tongue, a constructed language in which every word is a food.
Python, for the $$$
nova_says: sometimes languages can behave in unintuitive ways that you might not expect, so it can be hard to figure out how the systems work -- there can also be various processes obscuring other phenomena, like sound changes making it harder to figure out how words combine
nsb14: czech! the ř sound is the best
can you briefly discuss how you enjoy studying cs and linguistics in college?
Linguistics and cs is a great combination! There's actually a lot of overlap between the two fields
For example, any kind of problem that involves language and technology needs expertise from both linguistics and cs
mostly just taking classes that i've enjoyed -- some of my linguistics classes have been surprisingly similar to just doing naclo-style puzzles, so they were very fun
@stronto its been so long since i saw u, what up bro!
How do you get the letters from other languages on you keyboard?
copy and paste!
Copy and past from wikipedia
@nsb14 The sky is technically up
compose key on linux
\includepackage{tipa} for me
when I took a linguistics class I found software that mapped my keyboard to IPA characters
I get a lot of them by downloading Google Desktop, which is long-discontinued, and using key combinations like alt-' e in its sidebar.
What time do at-home contestants write the exam at?
This will depend on your time zone
nice talking to new people, especially older than me, I hope u guys have a great weekend!
ok thanks!
there's keyman desktop which has an ipa package
You can find more information in the handbook at the NACLO website (nacloweb.org)
What jobs can you get with a linguistics major?
Our linguistics majors move on to become researchers, teachers, editors, professors, computational linguists, translators, and so on.
Alright, I think that's a wrap everyone! Thank you for being here.
Thank you so much!
Thank you! This was so fun
thank you!
Thanks again to all our guests for spending time with us tonight to tell us all about the NACLO, and thank you all for coming to the Math Jam!
You guys are the best! AOPS is my favorite thing ever
If you joined us late (or even if you didn't), a complete transcript of the discussion will be available shortly on our Math Jam Transcripts page at: https://artofproblemsolving.com/school/mathjams-transcripts.php
And one of the NACLO people can post a link to NACLO to end the jam.
https://nacloweb.org
Great! I am closing down the session now. Thanks again everyone!
<3
This session was so valuable!! I'm feeling a lot more confident and excited about the competition! I really don't want to leave, but thank you all for the amazing experience!
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