November 30, 2007 5:14 PM Subscribe

My son asked me how many trees there are in the world. I know there are a finite number, yet I also know that it is not practical to count them. Same with grains of sand. When the set cannot be measured because it goes on forever we say the set is infinite. Is there a single word to express the concept of a countable, finite number too large to actually count?

I was able to convey the thought that the number of trees is a definite number unlike the concept of infinity (which I understand in theory there is no infinite number because you could always add 1). I think he understands the concept as I dumped out a cup of sugar on the counter and asked him to count them. He saw right away that there were clearly a definite number, but for this purpose too many to count. (Smart boy that he is, he licked his finger, put it in the sugar and ate it pronouncing, "there are now less grains of sugar Dad!"

Knowing that there is a term like google to express a certain large number, he asked "what do we call it when there is a number that stops really large, but it is too big to count."

I googled "too large to count" and got a few good definitions of infinity and the concept of large finite sets, but no one word to describe it. Does the word exist? (Not looking for a phrase such as "uncountable finite number") If no one word exists, any suggestions for a word my family can use? Shitload came to mind, but I think it could be argued that shitload is a countable number.

I was able to convey the thought that the number of trees is a definite number unlike the concept of infinity (which I understand in theory there is no infinite number because you could always add 1). I think he understands the concept as I dumped out a cup of sugar on the counter and asked him to count them. He saw right away that there were clearly a definite number, but for this purpose too many to count. (Smart boy that he is, he licked his finger, put it in the sugar and ate it pronouncing, "there are now less grains of sugar Dad!"

Knowing that there is a term like google to express a certain large number, he asked "what do we call it when there is a number that stops really large, but it is too big to count."

I googled "too large to count" and got a few good definitions of infinity and the concept of large finite sets, but no one word to describe it. Does the word exist? (Not looking for a phrase such as "uncountable finite number") If no one word exists, any suggestions for a word my family can use? Shitload came to mind, but I think it could be argued that shitload is a countable number.

Ah yes, mhum has it. It is most certainly innumerable.

posted by numinous at 5:22 PM on November 30, 2007

posted by numinous at 5:22 PM on November 30, 2007

Innumerable is probably your best bet.

("uncountable finite number" is not only clumsy, but it will cause mathematicians to get their underthings in a knot, as a finite number is, in math-speak, countable.)

posted by ssg at 5:23 PM on November 30, 2007

("uncountable finite number" is not only clumsy, but it will cause mathematicians to get their underthings in a knot, as a finite number is, in math-speak, countable.)

posted by ssg at 5:23 PM on November 30, 2007

Also, I'm not sure that the number is necessarily 'finite' per se, as it is utterly fluid so never exact.

The rate that trees are dying and seeding at any one time leaves a massive, ebbing and flowing, grey area. So it is perhaps a slightly different definition required - a number that is extremely large and impractical to count, yet also changes in value at a rate impossible to track.

But, back to the original point, I can't think of a better word than 'shitload', and certainly use it as 'a lot of something that requires too much effort to nail down further', so it qualifies in that regard.

posted by Brockles at 5:24 PM on November 30, 2007 [1 favorite]

The rate that trees are dying and seeding at any one time leaves a massive, ebbing and flowing, grey area. So it is perhaps a slightly different definition required - a number that is extremely large and impractical to count, yet also changes in value at a rate impossible to track.

But, back to the original point, I can't think of a better word than 'shitload', and certainly use it as 'a lot of something that requires too much effort to nail down further', so it qualifies in that regard.

posted by Brockles at 5:24 PM on November 30, 2007 [1 favorite]

In microbiology, a petri dish with too many bacterial colonies to count is described as Too Numerous To Count, or TNTC.

posted by Brian James at 5:24 PM on November 30, 2007 [1 favorite]

posted by Brian James at 5:24 PM on November 30, 2007 [1 favorite]

Traditionally, if there are too many gibbons to count you would refer to them as "innumerable." As in "the shrieking of innumerable gibbons."

posted by wemayfreeze at 5:28 PM on November 30, 2007 [2 favorites]

posted by wemayfreeze at 5:28 PM on November 30, 2007 [2 favorites]

You may be interested in the class of questions known as Fermi problems (see also).

posted by Wolfdog at 5:29 PM on November 30, 2007

posted by Wolfdog at 5:29 PM on November 30, 2007

I do agree that "innumerable" is close. But the definition seems to me to imply that it is not a finite set. Countless is too many to be counted, but that doesn't mean that it is finite. It could be infinite. Also, is there a mathematical term for this concept?

posted by JohnnyGunn at 5:32 PM on November 30, 2007

posted by JohnnyGunn at 5:32 PM on November 30, 2007

Wolfdog - thank you for the Fermi links and concept.

posted by JohnnyGunn at 5:35 PM on November 30, 2007

posted by JohnnyGunn at 5:35 PM on November 30, 2007

Innumerable really is what you want. It is *not* synonymous with "infinitely many", and despite *sounding* similar to the technical term *nondenumerable*, it is not synonymous with that, either. In fact, innumerable is not a technical term, and would never be used in mathematical writing as if it had a technical definition.

There isn't any technical mathematical term for what you're describing because it isn't a precise concept that would be amenable to definition.

posted by Wolfdog at 5:38 PM on November 30, 2007 [1 favorite]

There isn't any technical mathematical term for what you're describing because it isn't a precise concept that would be amenable to definition.

posted by Wolfdog at 5:38 PM on November 30, 2007 [1 favorite]

I think you might want to convey the idea that, while we can't know the number of trees precisely, we can certainly *name a number which is larger than that*. That's why the Fermi stuff is kind of relevant. "There certainly aren't as many as 2,000,000,000,000,000 - and that's a pretty big number, but not so big you can't write it down."

posted by Wolfdog at 5:42 PM on November 30, 2007

posted by Wolfdog at 5:42 PM on November 30, 2007

Thank you Wolfdog.

posted by JohnnyGunn at 5:43 PM on November 30, 2007

posted by JohnnyGunn at 5:43 PM on November 30, 2007

What about "myriad"? Or, if you are looking for something more vernacular, I think that a "metric fuckton" is considerably more than a "shitload."

posted by mrmojoflying at 5:44 PM on November 30, 2007

posted by mrmojoflying at 5:44 PM on November 30, 2007

Mrmojoflying, I struggled with the metric system for some reason, but I certainly understand your definition.

posted by JohnnyGunn at 5:47 PM on November 30, 2007

posted by JohnnyGunn at 5:47 PM on November 30, 2007

I can see your point if you interpret Merriam-Webster's definition of "too many to be numbered" to be something like "too many to be put into correspondence with the set of positive integers", in which case you get the mathematical definition of "uncountable" or "nondenumerable". On the other hand, if you interpret "numbered" to mean something more like "counted by a human", then you get closer to what you were looking for.

Keep in mind that you need not get too tangled up in the exact wording of dictionary definitions. There are many dictionaries out there, each with their own particular definitions. See, for example, this page. It gives the

Generally speaking, mathematics isn't really concerned with actually, practically counting things. There are terms in complexity theory regarding the computational difficulty of classes of counting problems, but this is almost certainly not what you're looking for.

posted by mhum at 5:52 PM on November 30, 2007

Derail: I know you didn't actually ask the question about how many trees there are in the world, but I'm easily sucked in by an estimation problem. Using data from the UN, there are 3 billion hectares of forest in the world and (using my wild-ass guess) there are about 1000 trees per hectare (this would depend very heavily on your definition of trees versus shrubs, etc.), I'd estimate that there are 3 trillion trees in the world.

posted by ssg at 6:02 PM on November 30, 2007 [3 favorites]

posted by ssg at 6:02 PM on November 30, 2007 [3 favorites]

Funny related linguistic anecdote: when I asked things like that to my dad as a kid, he would reply: they are fifty, because in Spanish "fifty" (cincuenta) sounds the same as "countless" (sin cuenta). He would say "son cincuenta, porque no tienen cuenta" (literally translated as: they are fifty because they are countless.)

The translation obviously doesn't work and it doesn't mean anything in English, I only included it to better explain the pun. So there it is, a little father-and-son related story.

posted by micayetoca at 6:11 PM on November 30, 2007 [5 favorites]

The translation obviously doesn't work and it doesn't mean anything in English, I only included it to better explain the pun. So there it is, a little father-and-son related story.

posted by micayetoca at 6:11 PM on November 30, 2007 [5 favorites]

These used to be popular questions at Microsoft interviews (though things have apparently changed a bit). The actual answer isn't the point, it's the method you use to get to the answer. Usually most people will use some form of scaling to get to their answer. For example (from Wolfdog's first link): *"How many hairs are on your head?"* Count how many are in a small patch, divide the total area by the size of the small section, then multiply with your original tally.

The problem with this approach is that it assumes uniformity. If I asked you how many*Smith*s are in the phone book, the answer for New York City would be completely different than, say, Beijing. With the "hair" question, you need to account for different densities of hair growth distributed across the head. What if the subject is balding? A woman vs. a man? Black vs. Native American? There are an infinite number of variables that could factor into the answer, so the only way to *really* know is to go and count them.

I hate these questions, and my favorite way of answering them was to answer only what I could personally account for. So if someone asked me*"How many Smiths in New York?"* I'd respond "two," because I could personally attest to knowing two people who's last name was Smith.

The traditional story that illustrates this problem is the old*"How long is the Emperor of China's nose?"* The emperor of China lives in the Forbidden City and no common person has ever laid eyes on him. So to figure out how long his nose is, this guy sets out and measures the length of *everyone else's nose* and averages the results. Of course, the answer means *nothing* because the method is fundamentally flawed.

posted by Civil_Disobedient at 6:12 PM on November 30, 2007

The problem with this approach is that it assumes uniformity. If I asked you how many

I hate these questions, and my favorite way of answering them was to answer only what I could personally account for. So if someone asked me

The traditional story that illustrates this problem is the old

posted by Civil_Disobedient at 6:12 PM on November 30, 2007

I would turn this in to a lesson on orders of magnitude and estimation thereof. Powers of Ten is a classic (~10 minute long!) film that really drives the point home.

You could definitely come up with an order of magnitude estimation of the number of trees on earth. I have homework to do, otherwise I'd be all over it.

posted by phrontist at 6:13 PM on November 30, 2007

You could definitely come up with an order of magnitude estimation of the number of trees on earth. I have homework to do, otherwise I'd be all over it.

posted by phrontist at 6:13 PM on November 30, 2007

myriad - innumerable, countless. It's a much prettier word, it's literary or something.

posted by bluejayk at 6:23 PM on November 30, 2007

posted by bluejayk at 6:23 PM on November 30, 2007

I think there's something to be said for "a lot".

It is frequently used as a stand in for "large number that I can't be bothered to ennumerate". That is, while it doesn't imply a number so large it can't be counted, it does imply a number so large that it won't be counted.

posted by tkolar at 6:35 PM on November 30, 2007

It is frequently used as a stand in for "large number that I can't be bothered to ennumerate". That is, while it doesn't imply a number so large it can't be counted, it does imply a number so large that it won't be counted.

posted by tkolar at 6:35 PM on November 30, 2007

phrontist, excellent video that Powers of Ten.

My son and I appreciate all the answers given so far. Getting comfortable with numbers, especially large one and the relationship between numbers is very interesting to me and my son.

posted by JohnnyGunn at 6:36 PM on November 30, 2007

My son and I appreciate all the answers given so far. Getting comfortable with numbers, especially large one and the relationship between numbers is very interesting to me and my son.

posted by JohnnyGunn at 6:36 PM on November 30, 2007

It is frequently used as a stand in for "large number that I can't be bothered to ennumerate". That is, while it doesn't imply a number so large it can't be counted, it does imply a number so large that it won't be counted.

I think it is a matter of personal experience, but while I agree that "a lot" implies it won't be counted, from my experience the reason it won't be counted is more out of convenience or laziness than it is not practical to actually count them. It has too many modifiers. Some people would say "a real lot". Is that more than "a lot"?

posted by JohnnyGunn at 6:40 PM on November 30, 2007

Actually math has some pretty darn interesting things to say about counting. For example, the set of irrational numbers is "larger" than the set of rational numbers, even though both contain an infinite number of numbers! The set of rational numbers can be counted [in order] (even though you'll never get to the end) while the irrational numbers can't be counted (no matter how carefully you count in order, I can prove that you've missed one).

Anyway, back on topic, my vote is for "lots". As in one, two, many, many many, lots.

posted by anaelith at 6:47 PM on November 30, 2007

Anyway, back on topic, my vote is for "lots". As in one, two, many, many many, lots.

posted by anaelith at 6:47 PM on November 30, 2007

How about: "The number is so large that by the time you got done counting each of them, it would have changed significantly - some would have been cut down, burned, died, grown, etc. " And of course, you'd have to define "tree". Is a pine sapling a tree? Or only plants over 4 feet tall?

So yeah, innumerable is probably the best term.

posted by blaneyphoto at 6:50 PM on November 30, 2007

So yeah, innumerable is probably the best term.

posted by blaneyphoto at 6:50 PM on November 30, 2007

Interesting, Civil_Disobediant. Two Smith's in New York is certainly a good lower bound. It got me thinking of confidence intervals. When asked such an estimation question, you might wildly throw out a number; the asker could gauge for how certain you are by asking for upper and lower bounds that you are 95% confident could not be exceeded. For Smith's, my 100% confidence bounds are zero and eight billion. I will up the 95% bounds to 100 and one million. For a more useful estimate, I don't think I could be too confident about the bounds (without doing some research first).

Now the interesting thing about confidence intervals is that if you give an estimate first and then bound it afterwards, your initial guess influences the bounds a lot. If I had made a reasoned guess that there were 5,000 Smith's in New York, I might say my confidence bounds are 1,000 and 10,000. In fact I could be way way off. See here for an interesting read.

posted by PercussivePaul at 7:00 PM on November 30, 2007

Now the interesting thing about confidence intervals is that if you give an estimate first and then bound it afterwards, your initial guess influences the bounds a lot. If I had made a reasoned guess that there were 5,000 Smith's in New York, I might say my confidence bounds are 1,000 and 10,000. In fact I could be way way off. See here for an interesting read.

posted by PercussivePaul at 7:00 PM on November 30, 2007

One problem with the original question is that it's a moving target. Trees are being created and destroyed all the time.

Another problem is fuzzy boundaries. When is something a tree, and when is it not? Is laurel a tree? Is a stump with a tiny branch growing out of it a tree?

The problem isn't just that there's no way to make a count. It's that those making the count would run into cases where they couldn't be sure whether to include or exclude.

posted by Steven C. Den Beste at 7:07 PM on November 30, 2007

Another problem is fuzzy boundaries. When is something a tree, and when is it not? Is laurel a tree? Is a stump with a tiny branch growing out of it a tree?

The problem isn't just that there's no way to make a count. It's that those making the count would run into cases where they couldn't be sure whether to include or exclude.

posted by Steven C. Den Beste at 7:07 PM on November 30, 2007

PercussivePaul, if I follow what you said, my bounds are influenced by my estimate. But, when I (me personally) make an estimate I first come up with a range I think would be appropriate. I see it as a chicken and egg issue. Do you make an estimate and then come up with bounds or a bounds and then place the estimate inside it? What do most people do?

Why are humans prone to underestimating tail risks as the article notes? Is it a hard wiring, our education or relying too much on personal experience like the two smiths answer?

posted by JohnnyGunn at 7:16 PM on November 30, 2007

Why are humans prone to underestimating tail risks as the article notes? Is it a hard wiring, our education or relying too much on personal experience like the two smiths answer?

posted by JohnnyGunn at 7:16 PM on November 30, 2007

SCDB, you are correct in the fact that it is not a static number and it needs to be better defined, but the point could be made with some other item that is static or at least static at a specific point in time. In my quick attempt to make the question a finite knowable answer, what if he asked how many trees had been cut down by a saw since the beginning of time that were at least one year old and 4" in diameter?

posted by JohnnyGunn at 7:20 PM on November 30, 2007

posted by JohnnyGunn at 7:20 PM on November 30, 2007

a fuckload

posted by fumbducker at 8:43 PM on November 30, 2007

posted by fumbducker at 8:43 PM on November 30, 2007

JG, most of my knowledge on the topic comes from the article I linked. (If you read the page, you'll notice they link to a much larger article that the page is quoting. It's a great read, I recommend it.)

posted by PercussivePaul at 8:53 PM on November 30, 2007

posted by PercussivePaul at 8:53 PM on November 30, 2007

what?

By the way, according to Everything2 there are about 1.9 trillion trees in the world.

posted by delmoi at 9:34 PM on November 30, 2007

Also, for this type of question you may want to try the reverse dictionary. Typing "too many to count" gives some good answers.

posted by kepano at 4:01 AM on December 1, 2007

posted by kepano at 4:01 AM on December 1, 2007

If this were written in a math textbook, they would just say it's "large."

posted by spiderskull at 4:09 AM on December 1, 2007

posted by spiderskull at 4:09 AM on December 1, 2007

micayetoca's answer made me think of this:

"Seventy times seven" is the amount of times Jesus said to forgive someone in the Bible. My childhood religion class taught me that in that time, they wouldn't multiply it out and would just take that to mean "as many times as you're asked." That result is still a finite number, though, just unnamed.

I think a similar concept in modern American English, at least for young people, is something like a "trillion." Does the English language have the words for counting that high? Yes. Is it a finite number? Yes. Could one actually multiply or add large sums up to get to a trillion? Yes. Would one actually want to attempt counting that high, one by one? No. So, same concept as Jesus'.

posted by RobotHeart at 5:01 AM on December 1, 2007

"Seventy times seven" is the amount of times Jesus said to forgive someone in the Bible. My childhood religion class taught me that in that time, they wouldn't multiply it out and would just take that to mean "as many times as you're asked." That result is still a finite number, though, just unnamed.

I think a similar concept in modern American English, at least for young people, is something like a "trillion." Does the English language have the words for counting that high? Yes. Is it a finite number? Yes. Could one actually multiply or add large sums up to get to a trillion? Yes. Would one actually want to attempt counting that high, one by one? No. So, same concept as Jesus'.

posted by RobotHeart at 5:01 AM on December 1, 2007

It's not just that one would not

posted by mdn at 6:40 AM on December 1, 2007

I am *n*thing "shitload". The "metric shitload" is slightly larger, so I would say there are a metric shitload of trees in the world.

posted by Meatbomb at 8:32 AM on December 1, 2007

posted by Meatbomb at 8:32 AM on December 1, 2007

I want to thank everyone for help. I really appreciate the introduction to concepts and the links as well as the resources like the reverse dictionary I did not know existed.

And more amazingly, my son cleaned up the cup of sugar I dumped on the counter to demonstrate!!

posted by JohnnyGunn at 9:44 AM on December 1, 2007

And more amazingly, my son cleaned up the cup of sugar I dumped on the counter to demonstrate!!

posted by JohnnyGunn at 9:44 AM on December 1, 2007

Neat question and cool thread!!

posted by Salamandrous at 10:04 AM on December 1, 2007

posted by Salamandrous at 10:04 AM on December 1, 2007

It

posted by Civil_Disobedient at 10:08 PM on December 1, 2007

This thread is closed to new comments.

You may want to avoid "uncountable" or "nondenumerable" since they also have a technical, mathematical meaning in addition to their lay meanings.

posted by mhum at 5:19 PM on November 30, 2007