90's or 90s?

[meatyochre]

Statistically everything will happen given infinite time, so you might as well pay up now.

No. If you flip a coin an infinite number of times, it will never come up pancakes...

Depends on the universe in which the flipping is done.

Interestingly - if you flip a coin an infinite number of times, it is possible that it will never come up tails.

Wouldn't the chance of that happening be c/infinity, where c is any constant, which simplifies to zero? Been a while since my calculus days so I could be wrong, but it sounds about right.

[gmalivuk]

Yeah, but probability on uncountable spaces gets tricky. Probability 1 doesn't mean "definitely will happen" any more, and probability 0 doesn't mean "is impossible".

[brakos82]

Statistically everything will happen given infinite time, so you might as well pay up now.

No. If you flip a coin an infinite number of times, it will never come up pancakes...

Depends on the universe in which the flipping is done.

Or if you happen to be flipping a coin that says "PANCAKES!" on one side.

mmm... pancakes.....

[Promac]

Statistically everything will happen given infinite time, so you might as well pay up now.

No. If you flip a coin an infinite number of times, it will never come up pancakes...

Depends on the universe in which the flipping is done.

Interestingly - if you flip a coin an infinite number of times, it is possible that it will never come up tails.

Wouldn't the chance of that happening be c/infinity, where c is any constant, which simplifies to zero? Been a while since my calculus days so I could be wrong, but it sounds about right.

The chances of it coming up heads or tails is always 50/50 (for a perfectly balanced coin in ideal circumstances) regardless of previous coin tosses so it's completely feasible that it will always come up heads, even if you flip it for all of eternity.

[PM 2Ring]

Yeah, we have a thread or two about this probability of infinite coin tossing stuff, but they're over on the Mathematics forum, for some crazy reason.

[Promac]

Yeah, sorry. Slight derailment there

Although, mathematics is a language...

[gmalivuk]

If it's a language, then you should be able to convey the proposition, "I watched a cat chase a dog" in mathematics.

Can you?

[Rilian]

'90's.
Heh.

I saw on this website once 90ies, 80ies, 70ies, and I said to the person sitting at the computer, "What idiot typed that?" Obvious conclusion is obvious.

[Promac]

If it's a language, then you should be able to convey the proposition, "I watched a cat chase a dog" in mathematics.

Can you?

Can you do the same in cantonese?

Maths is a written form of communication for the purposes of exchanging ideas. Those ideas may or may not describe the real world. In your example you could use maths to describe how fast the cat and dog were moving, in which direction, when, for how long, etc.

In fact, your statement is actually just a different way of saying that light bounced off both the cat and the dog and struck your eye. That can easily be described by some basic mathematics.

[gmalivuk]

If it's a language, then you should be able to convey the proposition, "I watched a cat chase a dog" in mathematics.

Can you?

Can you do the same in cantonese?

As someone who's never studied Cantonese? No, of course not. But Cantonese at least has the ability to do this. Math doesn't.

Maths is a written form of communication for the purposes of exchanging ideas.

That doesn't make it a language in itself.

In your example you could use maths to describe how fast the cat and dog were moving, in which direction, when, for how long, etc.

Sure, *after* using a real language to tell you what all the symbols I was using referred to in the cat and dog example.

[Promac]

Interesting derailment!

A language is a set of symbols that its users agree to apply to specific objects or concepts for the purpose of exchanging information. How does that apply to english and not mathematics? What criteria does english, or cantonese, meet that mathematics doesn't?

Sure, *after* using a real language to tell you what all the symbols I was using referred to in the cat and dog example.

At some point, someone used "real" language to explain to you what the symbols "cat", "dog" and "chased" mean. That's just translation. If you learn french, someone will explain to you what the french words for cat and dog are. The only reason you see french as a language and not mathematics is that the grammar of french is a lot closer to that of english.

Take japanese for an example - they drop a lot of words that we consider necessary for a "proper" sentence. "Go shop" isn't a sentence in english but it would be in japanese as they can infer the subject of the verb from who says it and when. Similarly, anyone looking at a mathematical description of "the cat chases the dog" would be able to infer what they needed to in order to understand what is going on.

This should be a lot more detailed but it's just an example to illustrate a point:
θ_cat = θ_dog
V_cat < V_dog

That tells a mathematician that something called "cat" is going in the same direction as something called "dog" but it's not going as fast. Add a couple more bits and pieces and you'd have a cat chasing a dog.

[Bobber]

But you are still using the English words "cat" and "dog" in your "math-sentence". This proves that you can't, with mathematics by itself, convey gmal's example. There is no word in math that means "cat", so you have to use the English word.

[Promac]

But you are still using the English words "cat" and "dog" in your "math-sentence". This proves that you can't, with mathematics by itself, convey gmal's example. There is no word in math that means "cat", so you have to use the English word.

I'm using the label "cat" but I could easily have used the label "flibbertigibbets" and the math would be exactly the same. Labels like that in math are like proper nouns in other languages. They are independant of the language itself. I suppose my example is more analogous to "Felix is chasing Fido" than "the cat is chasing the dog".

How's this instead?

θ_Felix = θ_Fido
V_Felix < V_Fido

[goofy]

A language is a set of symbols that its users agree to apply to specific objects or concepts for the purpose of exchanging information. How does that apply to english and not mathematics? What criteria does english, or cantonese, meet that mathematics doesn't?

Mathematics is not acquired by children as a first language.

[Promac]

A language is a set of symbols that its users agree to apply to specific objects or concepts for the purpose of exchanging information. How does that apply to english and not mathematics? What criteria does english, or cantonese, meet that mathematics doesn't?

Mathematics is not acquired by children as a first language.

What about lojban? Or any other constructed language?

[gmalivuk]

Math might be a language in the sense that a programming language is, but not in the sense that natural (or constructed) human languages are.

No matter how much mathematics I study, I can never get the concept "cat" without resorting to some real language vocabulary at some point. There's a mathematical symbol that translates to the word "plus", but there isn't any purely mathematical symbol or set of symbols that translate to the word "cat".

[Promac]

There are words in many languages for which there are no direct equivalent in English but that doesn't mean that English isn't a language.

We can't extend the definition of "language" to only include examples that have a representative symbol for everything. And if you've no objections to that then it's logical to assume that some languages are better at others in describing the world. Some have more words than others so some are logically missing words for concepts or things that are covered in others. In this case, English has a word for "cat" while maths doesn't.

I'll be honest here though, I've never even thought out an argument for the inclusion of Mathematics as a language so I'm totally winging this but I don't see why it shouldn't be.

[gmalivuk]

There are words in many languages for which there are no direct equivalent in English but that doesn't mean that English isn't a language.

You can explain any concept from one natural language in another natural language, even if it takes more than one word. This is why I included "or set of symbols" above.

[goofy]

What about lojban? Or any other constructed language?

OK, how about this. A constructed language can in theory be acquired by children. It will probably change a lot when it is nativized, but in theory it could be acquired. But can mathematics be acquired?

[gmalivuk]

And remember, we mean acquired as the child's only means of communicating with others, because of course children can learn math but that's not the point.

[Promac]

There are words in many languages for which there are no direct equivalent in English but that doesn't mean that English isn't a language.

You can explain any concept from one natural language in another natural language, even if it takes more than one word. This is why I included "or set of symbols" above.

Take it far enough and you can describe any physical object with mathematics. In a basic sense, I can give you a set of co-ordinates that, when plotted on a graph, will look like a cat. It's non-verbal but it still qualifies as a language component. Sign language is non-verbal, so is heiroglyphics.

And I'm not trying to be a twat here by they way - I'm enjoying the topic. Well the derailment of it

[Promac]

What about lojban? Or any other constructed language?

OK, how about this. A constructed language can in theory be acquired by children. It will probably change a lot when it is nativized, but in theory it could be acquired. But can mathematics be acquired?

Short answer = I don't see why not.

Explanation = The child would be horribly handicapped by only being able to refer to things using mathematical symbols but I don't see why it would be impossible for it to only have maths as its language.

[goofy]

Short answer = I don't see why not.

Explanation = The child would be horribly handicapped by only being able to refer to things using mathematical symbols but I don't see why it would be impossible for it to only have maths as its language.

So how does a child acquire math as a language? What sort of input does he get from his parents and peers? How does a two-year old express his wants and needs using math?

[Promac]

Short answer = I don't see why not.

Explanation = The child would be horribly handicapped by only being able to refer to things using mathematical symbols but I don't see why it would be impossible for it to only have maths as its language.

So how does a child acquire math as a language? What sort of input does he get from his parents and peers? How does a two-year old express his wants and needs using math?

No idea! Like I said, I've never considered this before but I find it really interesting. I suppose it's somewhat similar to how a parrot will learn a few dozen words - it understands the very limited vocabulary it might have and can use it to interact with the world to some degree but it's not gonna have any kind of conversation any time soon.

[goofy]

No idea! Like I said, I've never considered this before but I find it really interesting. I suppose it's somewhat similar to how a parrot will learn a few dozen words - it understands the very limited vocabulary it might have and can use it to interact with the world to some degree but it's not gonna have any kind of conversation any time soon.

Parrots mimic. They don't understand or use language the way humans do.

[gmalivuk]

How does a two-year old express his wants and needs using math?

Good point. If you ignore the additional connotation of "chase" that suggests something about intent, you perhaps can, at great length, get across the meaning of the cat chasing the dog. But I don't know how you're going to do that with things like desires and beliefs, which no real language has particular difficulties with. "I believe the cat chased the dog" or "I want food".

Take it far enough and you can describe any physical object with mathematics.

Fine. That gives you concrete nouns. Add information about position and velocity and you've got a tiny list of verbs on top of that. How would you go about describing abstract nouns, though? Or verbs that contain a component of purpose or intent?

[Makri]

Wait a moment, in what sense is mathematics a language?

[Alx_xlA]

I've always used "90's" because it prevents confusion with "905," especially when it's written by hand.

[Promac]

No idea! Like I said, I've never considered this before but I find it really interesting. I suppose it's somewhat similar to how a parrot will learn a few dozen words - it understands the very limited vocabulary it might have and can use it to interact with the world to some degree but it's not gonna have any kind of conversation any time soon.

Parrots mimic. They don't understand or use language the way humans do.

Try this one:
http://www.youtube.com/watch?v=7yGOgs_U ... re=related

That's a bird displaying understanding of concepts like counting and identifying the solutions to problems with multiple steps. "What colour is the bigger object" for example.

Makri - you're being awkward again. I think I'll ignore you from now on.

gmalivuk - I've no idea. As I said, I'm just exploring an idea. It might well be a load of crap.

[gmalivuk]

Wait a moment, in what sense is mathematics a language?

In the sense that

A language is a set of symbols that its users agree to apply to specific objects or concepts for the purpose of exchanging information.

Which, yes, is something that mathematics does. But that's not what linguists understand "language" to mean.

[Promac]

The underlying and obvious question here then is how do you define a language?

There are lots of different definitions and some exclude maths but most don't and some even specifically include it:
http://dictionary.reference.com/browse/language

any system of formalized symbols, signs, sounds, gestures, or the like used or conceived as a means of communicating thought, emotion, etc.: the language of mathematics; sign language.

en.wikipedia.org/wiki/Language

A language is a particular kind of system for encoding and decoding information. Since language and languages became an object of study (logos) by the ancient grammarians, the term has had many definitions. ...

[gmalivuk]

The underlying and obvious question here then is how do you define a language?

There are lots of different definitions and some exclude maths but most don't and some even specifically include it:

Which is why I helpfully specified that I was talking about how linguists generally use the word "language".

Mathematics might be described as (or more properly can be said to make use of) a formal language, and is involved in studying the logically resulting structures, but as such does not itself include semantics. And so if a communication system cannot actually say things about the external world, I don't see how you can consider it a language in the sense that we talk about languages in this forum.

And when someone uses expressions like "the language of mathematics", they are typically referring to a combination of this formal language and mathematical jargon that is part of the actual human language being used to discuss the math in question.

[goofy]

Try this one:
http://www.youtube.com/watch?v=7yGOgs_U ... re=related

That's a bird displaying understanding of concepts like counting and identifying the solutions to problems with multiple steps. "What colour is the bigger object" for example.

The parrot might be able to say the appropriate word when in the presence of an object - but that's not language. As for answering questions like "What colour is the bigger object", I need more than some short video clips to convince me. How many times did he give the wrong answer?

[Promac]

And so if a communication system cannot actually say things about the external world, I don't see how you can consider it a language in the sense that we talk about languages in this forum.

I thought I'd already demonstrated that it can say things about the external world. In fact, I don't know of any system that describes the external world in any greater detail.

Goofy - I'm not going to go and research the parrot for you. If you're interested it shouldn't be hard to find. I've shown you a video that demonstrates what seems to be a parrot understanding and using language, I'm not going to go and find evidence to disprove that hyphothesis when I've no interest in doing so.

[PM 2Ring]

Also see page 2 of the Toki Pona thread for a few recent posts about parrots & their vocal skills, eg:

Many parrot species have a way with words, especially the larger ones. I have a couple of friends that live with Eclectus parrots that are quite vocal. I'm not claiming that they fully understand what they are saying, but they don't just imitate words. Halley (the Comet Parrot), who is in his early 20s will tell you what he wants to eat. Parrots like seeds & grains, but their diet should be mainly fresh greens. Unfortunately, Halley developed an attachment for icecream with his previous owner (parrots are lactose intolerant), and he often asks for it.

One day, my friend took Halley to show off to friends at an arts & crafts workshop. The other students though he was great, and offered him various rich treats like cookies. Later, when somone offered him something healthier, he said "You've got to be joking!".

I showed the above to Halley's companion, Ms Spockatiel, and she replied:

He also will say "Shower" so I take him for a shower or the bath. I made him cupcakes just the once and he occasionally asks for "Cupcakes!"

When the other parrots make noise he says "Be quiet!"

On one occasion when I was sleeping. He got on to my feet, ran up me and said "Wake up! Wake up!"

[goofy]

I've shown you a video that demonstrates what seems to be a parrot understanding and using language

but there's nothing in that video that demonstrates that a parrot can understand language. I haven't been able to find any controlled experiments that suggest that animals can use language the way humans do. Even Alex's trainer doesn't claim that Alex can use language.

I'm not going to go and find evidence to disprove that hyphothesis when I've no interest in doing so.

That's ok, I don't expect you to

[gmalivuk]

I thought I'd already demonstrated that it can say things about the external world.

No, you've demonstrated that it can produce a detailed graph of a cat-looking thing.

[Makri]

And when someone uses expressions like "the language of mathematics", they are typically referring to a combination of this formal language and mathematical jargon that is part of the actual human language being used to discuss the math in question.

This formulation suggests that you can rather easily talk about the world in that language. Because the "formal language" involved is, if I'm not mistaken, just first or second order logic (depending on what you want to do). And the "language of second order logic" doesn't contain a fixed lexicon, so you're free to just introduce constants that refer to things in the world.

Or you're forced to give a definitional restriction of what terms in the language are allowed to refer to...

I'm bringing this up because I'm not convinced that the question of whether it's possible to talk about the world in the language of mathematics makes much sense.

[gmalivuk]

This formulation suggests that you can rather easily talk about the world in that language.

Well, yeah, because of the natural language you use on top of the formalism. The formal language itself doesn't have much semantics, if any, so you use English or Cantonese or whatever for that.

[PM 2Ring]

I thought I'd already demonstrated that it can say things about the external world.

No, you've demonstrated that it can produce a detailed graph of a cat-looking thing.

Give me enough maths to build a decent cellular automation, and enough time, and I'll simulate a planetful of cats for you.

But I certainly agree that using maths is a very unwieldy way to try & communicate real-world stuff, and my cellular automaton gizmo is definitely a whole different ballgame to what we normally do when we communicate in natural languages.


The new Gemini pattern (the first true self-reproducing pattern in Conway's Life) occupies over 16 trillion pixels. And it's very simple compared to a real biological cell. Building a cat would not be easy, by any means! Trying to understand the resulting critter from the maths would be absurd. Yes, the math would be, in one sense, a description of the cat, but it would not be not in a form suitable for the human mind to digest.