Sunday, August 08, 2010

Drawing Inferences about a Tree

When I visited Scott Brewer's home recently, I discovered a magnificent tree in his yard.

I asked if it was a Sycamore tree. Scott and his mother said it was a beech tree. I said the massive tree must be at least 200 years old. Scott said it was 100 years old.

I had recently purchased a lovely book, John Laird Farrar, Trees of the Northern United States and Canada (Blackwell, 1995). I was determined to confirm that the tree was a beech tree. I turned to pp. 268-269 and I saw:

I then snatched a leaf from the tree and the leaf looks like this:

The leaf looks very much like the leaf of the American beech tree shown in the book.
But then I noticed:

1. The book entry states that there are 9-14 lateral veins on each side. The leaf snatched from the tree appeared to me to have 8 lateral veins on each side. Scott said he saw 9 lateral veins.

2. The book entry said that American beeches are as much as 25 meters high. The beech in Scott's yard, it seemed to me, was taller.

3. An entry in the book states that "[b]ark remains smooth even on mature trees." The bark at the bottom of the tree was gnarled and contorted. But Scott's mother later noted that the tree had become infested with a fungus.

5. An entry in the book states the veins of the American beech trees end in a tooth. I wondered if those were or were not "teeth" I saw on the leaf.

Then I looked over at an entry on the lower part of page 269. That entry deals with the European Beech. I had ignored that entry because the European Beech is a non-native species and I thought it unlikely that the tree in the back yard had been planted there 200 years ago. But then I looked at the picture of a leaf of the European Beech and it looked less serrated than the pictured leaf for the America Beech. Moreover, the entry for the European Beech said that its leaves have 5-9 veins on each side.

So is the tree in the back yard an American Beech or a European Beech?


The dynamic evidence page
It's here: the law of evidence on Spindle Law. See also this post and this post.


Tim van Gelder said...

I have this kind of problem often! Especially with eucalypts, of which there are officially around 700 different kinds...

Unknown said...

Not only are inference problems universal, but so are questions about vegetation!


Don Mathias said...

Are you really trying to draw inferences? You are just trying to match known facts to given criteria. The criteria (in the book) are a bit confusing, but you are still after the best fit, assuming the best fit is the right answer. Inferences go beyond observed facts - the ones you observe and the ones the writers observe. Here you are trying to stay within the observed facts.

Unknown said...

Don, hmmm. Well, -- I'm thinking out loud -- the possible match between the number of veins listed in the book (9-14) and the number of veins on the leaf (8 or 9), does not conclusively establish whether the tree is an American beech or not. (Scott, by the way, remains convinced there are 9 veins on the leaf.) Same inconclusiveness is true even if the other criteria are considered. So? By the way, Scott also reasoned that there is natural variation in the characteristics such as the number of veins on trees such as the American beech. And that was a bit of [nonconclusive] reasoning, yes? So to me it appears that we have both uncertain inference and uncertain reasoning about inference. (I would and do say this sort of conclusion [American beech or not? can count as an inference even if the steps used to reach it are all tacit and do not involve explicit argument or reasoning.) But, withal, good question!

Don Mathias said...

Aren't plants classified by their reproductive structures?

Accepting your classification of this stage of the identification process as induction, this example can be extended to inference by deduction and inference by conditional probabilities.

For deduction, as we know, you need a major premise in the form: "only AB trees have the characteristics C". The book might say what they are.

For conditional probabilities (ah, Bayes!) you need the likelihood ratio: the probability of finding C, given that the tree is AB (this would be 1), divided by the probability of finding C, given that the tree is not AB (strictly this would be zero but let's just say it is very small).

I suppose what you are doing with the book is like trying to find a word that has a given meaning, in a dictionary instead of in a thesaurus.

Anyway, it's quite a big tree - perhaps it enjoys protected status?


Unknown said...

Don asked, "Aren't plants classified by their reproductive structures?"

My reply: What I know about the identification of trees is largely limited to the material in the book. I got tired of going into the countryside (infrequently) and not knowing the names of the trees I was gawking at. I bought the book that I did because it has, not only pictures of leaves, but only glossy pictures of tree trunks.

On induction and inference pertaining to the tree in Scott's back yard: I assumed, I think, that trees other than American beech trees might have leaves with 9-14 lateral veins, that some American beech trees might have leaves with fewer than 9 lateral veins, that it might be hard to determine exactly how many veins a leaf has (see the picture of the leaf; not that Scott and I disagreed on the number), that some American beech trees might have gnarled rather than smooth trunks (and,to reason along a different vein [so to speak] it might be necessary to decide whether the types of contortions seen on the the count as making the trunk non-smooth), etc. So, it seems to me, deduction alone won't do the trick. I'm unwilling (and perhaps unable) to say how all these uncertainties should be combined to yield a final probability about the identity of the tree. -- Incidentally (or not): after I made Scott and his mother (Betty) suffer through a discussion based on the statements in the tree-book, Betty produced printed material from the real estate agent who handled the sale of the property and this material declared (you'll have to take my word for it) that that the tree in the yard is (i) about 100 years old and (ii) European Beech.