What's the minimum number of words you'd need to define all other words? (2012)

The Oxford Advanced Learner’s Dictionary has a “Defining vocabulary” that they claim is used to write almost all definitions (I used the Fifth edition, where it is appendix 10). It’s about 8½ pages, with 5 columns of about 63 lines, so about 2,700 words.<p>It doesn’t list inflections, proper names, adjectives for colors such as yellowish and words used in an entry that derive from that entry (the dictionary mentions <i>blearily</i> and <i>bleary-eyed</i> being used in the definition of <i>bleary</i>)<p>They also say they <i>occassionally</i> had to use a word not in the list, but don’t say how often they had to. Those words _are_ defined in the dictionary, so it is possible that the reference graph does not have any cycles.<p>So, I guess 3,000 is a good first guess.

The work of Ana Wierzbicka and Cliff Goddard studied &#x27;Semantic Primes&#x27;, &#x27;the set of semantic concepts that are innately understood but cannot be expressed in simpler terms&#x27;.<p><a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Semantic_primes" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Semantic_primes</a><p>The combination of a set of semantic primes and the rules of combining them forms a &#x27;Natural Semantic Metalanguage&#x27; , which is the core from which all the words in a given language would be built up.<p><a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Natural_semantic_metalanguage" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Natural_semantic_metalanguage</a><p>The current agreed-upon number of semantic primes is 65 (see list at wikipedia links above).<p>That means that any English word can be defined using a lexicon of about 65 concepts in the English natural semantic metalanguage.

I am a little suprised that toki pona (&quot;language of good&quot;, <a href="https:&#x2F;&#x2F;en.m.wikipedia.org&#x2F;wiki&#x2F;Toki_Pona" rel="nofollow">https:&#x2F;&#x2F;en.m.wikipedia.org&#x2F;wiki&#x2F;Toki_Pona</a>) is not mentioned. It is a language that consists of about 125 words, which aims to make you think about describing complicated subjects. To give an example: The concept &quot;friend&quot; could both be described as &quot;good man&quot; or &quot;man good to me&quot; depending on whether you think your friend is intrinsically good.<p>Admittedly, the original question is specifically about the English language, but toki pona is a nice experiment related to this.

An interesting related talk, touching on the minimality and expressiveness of both natural and computer languages, is Guy Steele&#x27;s 1998 talk &quot;Growing a Language&quot;:<p>Video: <a href="https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=_ahvzDzKdB0" rel="nofollow">https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=_ahvzDzKdB0</a><p>PDF: <a href="https:&#x2F;&#x2F;www.cs.virginia.edu&#x2F;~evans&#x2F;cs655&#x2F;readings&#x2F;steele.pdf" rel="nofollow">https:&#x2F;&#x2F;www.cs.virginia.edu&#x2F;~evans&#x2F;cs655&#x2F;readings&#x2F;steele.pdf</a><p>Prior HN discussion: <a href="https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=16847691" rel="nofollow">https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=16847691</a>, <a href="https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=2359174" rel="nofollow">https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=2359174</a>, &amp; others

I think the approach I would use is as follows:<p>0. Get a dictionary.<p>1. Form a directed graph, with an edge from each word to every word that uses that word in its definition.<p>2. Remove all words that have no outgoing edges.<p>3. If you removed some words, go to step 1. Otherwise, all words left in the dictionary are minimal.<p>EDIT: If anyone knows of a machine-readable dictionary, I&#x27;d love to actually do this.

Definitions are not enough to fully capture the meaning of a word. In order to do that you need full language modelling and to ground words into other sensory modalities, plus the word in relation to actions taken in various situations when the word was used.<p>GPT-2 (of recent OpenAI fame) uses 1.5 billion parameters and, though capable of interesting results, is far from human level. It also uses just text so it&#x27;s incomplete.<p><a href="https:&#x2F;&#x2F;blog.openai.com&#x2F;better-language-models&#x2F;" rel="nofollow">https:&#x2F;&#x2F;blog.openai.com&#x2F;better-language-models&#x2F;</a><p>Another interesting metric is Bits Per Character - BPC. The state of the art is around 1.06 on English Wikipedia. This measures the average achievable compression on character sequences and doesn&#x27;t include the size of the model, just the size of the compressed sequence.<p><a href="https:&#x2F;&#x2F;arxiv.org&#x2F;pdf&#x2F;1808.04444.pdf" rel="nofollow">https:&#x2F;&#x2F;arxiv.org&#x2F;pdf&#x2F;1808.04444.pdf</a>

I used to work for Pearson Longman, and one of their USPs was that their defining vocabulary was significantly smaller than the main competitors, namely OUP and CUP. Longman&#x27;s was just over 2000 (about 2100 IIRC), whereas OUP&#x27;s was approx 3000.<p>Even then, one is rather constrained and definitions frequently cross-referenced other words to bootstrap the definition.

Words in the English language are not the same as computer code. I&#x27;m not sure you can fully define most words in terms of other words -- hence the variety. Dictionaries generally only provide rough sketches of the meaning of a word. Even synonyms can have slightly different subtexts, connotations, and histories. Hell, individual words have wildly different meanings depending on context.

Besides Basic English, I&#x27;ve run into a neat French dictionary for children, <a href="https:&#x2F;&#x2F;www.amazon.com&#x2F;Mon-premier-dictionnaire-Roger-Pillet&#x2F;dp&#x2F;B0007DU07S" rel="nofollow">https:&#x2F;&#x2F;www.amazon.com&#x2F;Mon-premier-dictionnaire-Roger-Pillet...</a><p>It sticks to a basic vocabulary, has an entry for every word it uses, and goes heavy on examples and pictures in preference to formal definitions. (And it&#x27;s monolingual even though written mainly for learners in North America.)<p>I don&#x27;t have it to check, but estimating from memory: around 2000 to 4000 words. I found it useful while bootstrapping up from Duolingo.

It depends on what is meant by &quot;define&quot;. If we are allowed to use existing words in a language, L, to create a new language, L&#x27;, then use expressions in L&#x27; to define each word in L, a single word w, originally in L, suffices.<p>The idea is to first index each word v in the lexicon of L (including w), starting at 1 and ending at n, whatever is the number of distinct words in the language. Alternatively, you can index _meanings_. Then (should be obvious where I&#x27;m going with this by this point) you map a sequence S_k of repetitions of w of length k in [1,n] to each k&#x27;th word, v_k, in L. So now L&#x27; is the language of n sequences S_1,...,S_n of w each of which maps to a word (or meaning) in L. And you have &quot;defined&quot; L in terms of a single word, the word w.<p>But that&#x27;s probably not at all what the reddit poster had in mind.<p>However, it should be noted that natural language is such that there&#x27;s really no reason that we have many words- it&#x27;s just convenient and helps us create new utterances without having to create long sequences of one word, as above. The important ability in human language is that we can combine words to create new utterances, forever- which we can do with one word just as well as with a few thousand.<p>Finally, I suspect that if there <i>was</i> a minimal set of (more than one!) words sufficient to define all other words (meanings) in a language, all natural languages would converge to about that number of words- which I really don&#x27;t think is the case.

I once found (plausibly from another HN commenter) a text based adventure where (almost?) all the words used were replaced with alternative English-sounding nonsense words, but have never rediscovered the link.<p>I feel this would be of interest to the thread, if anyone knows what I&#x27;m talking about or knows how to successfully Google for such a thing.

I looked at this question a while back, and wrote this: <a href="https:&#x2F;&#x2F;kybernetikos.com&#x2F;2007&#x2F;12&#x2F;03&#x2F;atoms-of-english&#x2F;" rel="nofollow">https:&#x2F;&#x2F;kybernetikos.com&#x2F;2007&#x2F;12&#x2F;03&#x2F;atoms-of-english&#x2F;</a> (blog is only up some of the time sadly, I&#x27;ll fix it eventually).<p>I took Websters dictionary from the project Gutenberg site. I started with 95712 words. After the initial throwing away of words that weren’t in any definitions, I was down to 4489 words. After expanding them, and throwing away words that weren’t in the expanded definitions, I was down to 3601 words. Setting recursive definitions as atoms and continuing got me down to 2565 words.

Reminds me of Randall Munroe&#x27;s Thing Explainer:<p>&quot;In Thing Explainer: Complicated Stuff in Simple Words, things are explained in the style of Up Goer Five, using only drawings and a vocabulary of the 1,000 (or &quot;ten hundred&quot;) most common words.&quot;<p><a href="https:&#x2F;&#x2F;xkcd.com&#x2F;thing-explainer&#x2F;" rel="nofollow">https:&#x2F;&#x2F;xkcd.com&#x2F;thing-explainer&#x2F;</a>

I&#x27;d say most nouns need to be seen.<p>To understand duck you must see a duck (Eat a duck, pet a duck, smell a duck, hear a duck)<p>Perhaps you could cheat and uses pixels and coordinates to use English to draw photos and videos to explain ducks.

this reminds me of <a href="https:&#x2F;&#x2F;youtu.be&#x2F;_ahvzDzKdB0" rel="nofollow">https:&#x2F;&#x2F;youtu.be&#x2F;_ahvzDzKdB0</a> awesome talk!

Just one: &quot;nor&quot;<p><a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Functional_completeness" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Functional_completeness</a><p>Hope you are one of the 10000 lucky ones whose mind is blown for the first time.<p>Or another one: &quot;1&quot;<p><a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Unary_coding" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Unary_coding</a>

The words needed to define a universal turing machine (and a program to simulate a human brain, but that doesn&#x27;t require additional words).<p>We could extend it to cover words not conceivable by humans, and any universe, by using a program to simulate those, but (1) I assume the question implicitly assumes <i>human</i> words, though (2) it wouldn&#x27;t require more words anyway.

0 obviously. Babies start with no definitions of words, but here we all are.<p>The baby learns the words via example, not by definitions.

How does this make any sense?<p>You could have 100 synonyms with the same &quot;definition&quot; but 100 different shades of meaning, implied degree of strength, or connotations.<p>You don&#x27;t necessarily simplify anything by making people add additional words get across those subtleties.<p>Of course of some are useless equivalents, but many aren&#x27;t.

Wow, I had no idea there was such a thing as simple.wikipedia.com! It apparently tries to follow &#x27;Basic English&#x27;[0] that&#x27;s comprised of only 850 words. The difference between the simple version[1] of artificial neural networks is a lot more approachable than the normal version[2]!<p>0: <a href="https:&#x2F;&#x2F;simple.wikipedia.org&#x2F;wiki&#x2F;Basic_English" rel="nofollow">https:&#x2F;&#x2F;simple.wikipedia.org&#x2F;wiki&#x2F;Basic_English</a><p>1: <a href="https:&#x2F;&#x2F;simple.wikipedia.org&#x2F;wiki&#x2F;Artificial_neural_network" rel="nofollow">https:&#x2F;&#x2F;simple.wikipedia.org&#x2F;wiki&#x2F;Artificial_neural_network</a><p>2: <a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Artificial_neural_network" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Artificial_neural_network</a>

The answer is 2: zero and one. What you need is to describe second-order logic. Just define &quot;every&quot; quantifier to be 0 0 0, NAND [1] - 0 0 1, and all other words as other sequences of 0s and 1s, for clarity, that look like 1 *. There might need to be some trick to ensure unambiguity of splitting a &quot;sentence&quot; into &quot;words&quot;, but that should be trivial.<p>1: <a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Sheffer_stroke" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Sheffer_stroke</a>

Taken to the logical extreme, the question is: &quot;how many intrinsic symbols do we need to convey any meaning when presented to a fully logical being&quot;, to which, in my opininon, the answer is 1 (or 2, really, since 1 is only &quot;possible&quot;).<p>You might not have words for it, but a fully logical being can decipher any bitstream given enough interactivity.<p>So start from 1 and 0, form basis of mathematics and symbols, then start with physics from all the way bottom.

0) Initialize set X to contain every word.<p>1) Y = set of words in every definition of the words in set X<p>2) X = Y - X (all words in Y that are not in X)<p>3) Repeat from 1 if the set of words in X has changed<p>Does that reduce all words down to the actual minimal set of words required to define other ones? Since you can build upwards from the resulting set X to get the original set of words.<p>Also, this reminds me of the knapsack problem a little bit (for example what is the minimum set of coins required to be able to make $X).

Isn&#x27;t the answer &quot;two&quot; ? &quot;One&quot; and &quot;None&quot; (or on and off) ?<p>Of course I see the obvious bootstrapping problem where you relate the encoding starting with just those two words but ... somehow I think that&#x27;s easier to overcome than it seems ... as in, I think it must be possible.<p>If Helen Keller can write a book, surely I can relate digital encoding to a toddler over the course of a year or three, right ?

I&#x27;ve seen a dictionary that defined 120 words using those same 120 words (morphemes really), though some of the definitions were a bit ... weak. Toki Pona also has about 120 words but it&#x27;s a very different set of words: Toki Pona&#x27;s vocabulary is concrete and everyday, while the dictionary&#x27;s was very abstract. So probably it&#x27;s just a cute coincidence that both numbers were about 120.

It depends on the context assumed about the audience that is supposed to understand the definitions.<p>Do they have the experiences relevant to the word being defined? If not, what experiences do they have in common with the person providing the definition?<p>How intelligent are they? Can they understand complex concepts through logic, through examples or both?<p>How much do they know about English (besides the few words assumed known)?

So, once the human race had discovered roughly this number of words (give or take a few for whatever language existed at the time, and minus the useless words demanded by grammar) then humans had a Turing Complete language? That must have been a crucial point for the evolution of human culture.

I am reminded of <a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Natural_semantic_metalanguage" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Natural_semantic_metalanguage</a>

I bet this heavily depends on what you consider an accurate definition.

There are lots of ways it&#x27;s not at all the same, but it&#x27;s at least sort of interesting to compare this question to the number of dimensions needed for effective word embeddings.

Reminds me of Toki Pona — with about 120 words it seems to work.

What&#x27;s the minimum number of words you&#x27;d need to define the word &quot;left&quot;, as in &quot;left hand&quot;?

a, b, c, d, e, f, g, j, k, l, m, n, p, r, s, v, x, y, (, ), and, concatenate.<p>Some hints:<p>- &quot;backwards j&quot;<p>- &quot;a circle&quot;<p>- &quot;a cross&quot;<p>- &quot;n, but rotated ninety degrees&quot;<p>- &quot;mirror of p&quot;<p>- &quot;vv, except no gap&quot;<p>- &quot;pixel-wise union n and l&quot;<p>- &quot;mirror of s, and make the lines straight&quot;<p>Semantics are impossible anyways, I challenge you to define the word &quot;dog&quot;.<p>Challenge: Do better, make sure you don&#x27;t have circular dependencies.

Can go from 1 word: Entity, to every word.<p>The tradeoff being density of information, understandability to the readers, and conciseness.

This feels intuitively like it&#x27;s closely associated with some measure of the Komolgorov complexity of a passage.

Two words. &quot;1&quot; and &quot;0&quot;

&quot;a&quot; and &quot;i&quot; since its binary you could define all others.

Good to see this silly question off r&#x2F;lisp for once. :)

Reminds me of Toki Pona

I&#x27;m guessing but I can&#x27;t really explain why, my gut feel is 42.

Randall Munroe of XKCD experimented with this in his book Thing Explainer:<p><a href="https:&#x2F;&#x2F;xkcd.com&#x2F;thing-explainer&#x2F;" rel="nofollow">https:&#x2F;&#x2F;xkcd.com&#x2F;thing-explainer&#x2F;</a>

One.

and kernel is one of them

I&#x27;ve actually been wondering about this a lot myself recently, though I have been thinking of it in terms of &quot;axiomatic English&quot; i.e. the set of words and grammar&#x2F;syntax rules from which all other meanings expressible in English can be represented, and cannot be explained themselves except through tautology? It&#x27;s a really, really interesting question, and answering it would explain a lot about how we actually think.

I can actually answer this question. Back in the day I was going through Oxford Dictionary and it mentioned that all the meaning use words from a like of about 3,000 words. The list, IIRC, was also at the back of the dictionary. And it also mentioned that on rare occasions they have to use words outside of those 3,000.<p>Source: My memory of something I read at British Council Library 17 years ago.

Finally, something thought-provoking! Everybody, ready your Internets, this gentleman deserves an answer!

Finally, something thought-provoking! Everybody, ready your Internets, this gentleman deserves an answer!

Doesn&#x27;t Goedel&#x27;s incompleteness theorems imply that it is impossible to define all words using words, unless you have some axiomatic words that are not defined within the system?