Now, I've looked at the numbers a little, and I think the Cardinals were wise not to meet Pujols' contract demands. The nobler side of me hopes that I am wrong and that Pujols' best seasons are coming up. But the slightly more realistic and vindictive side of me thinks Pujols is likely to blow out his elbow soon and in any event, he is already on the wrong side of his peak. At least, that is what I see in the graph below:
The red line is a simple linear regression of WAR (wins above replacement) on years in the majors. The blue line is a regression of WAR on years and years squared. The green line is a three-year moving average. The dots use those various trend lines to predict what Pujols will do next season (his twelfth year in the major leagues).
Still, it's disappointing to lose Pujols. As one writer has it, Pujols leaving St. Louis is the death of romanticism in baseball. (Yes, that's overblown, but I still agree with the sentiment, overall.) Also, from a pure business perspective, there was surely reason to keep Albert in Cardinal red. Pujols puts fans in the seats and keeps eyes on the television. Pujols has been the face of the franchise.
Long set-up, I know, but stay with me, I am almost coming to my point. During the holiday break, one of Kerrith's cousins said to me that Pujols was especially valuable for all of the intangibles: the effect of his presence in the clubhouse, his effect on attendance at ball games, his influence in the community, etc. My typical response to this sort of line is that nothing exists that cannot be measured. The "intangibles" are only intangible because we have not yet been clever enough to find good ways of measuring them, not because they cannot be measured in principle.
I am pretty well convinced of the thesis that nothing exists that cannot be measured, but I admit that it has a number of difficulties. Some people will point to abstract notions, like love or justice, in arguing that some things exist that cannot be measured. Kerrith jibed that love could be measured by dollars spent. She meant the suggestion as a reductio ad absurdum of the idea that everything that exists can be measured, but I think dollars spent is a way of measuring love, just not a very good one. That is, keeping track of dollars spent tells us something about the spender's loves, even if it isn't especially accurate or precise.
But I actually think that more serious objections to the thesis come from singular cases, like that of Pujols' effect on his teammates. Just take last year's season as an example. Yadier Molina produced 4.1 WAR last season, and Matt Holliday produced 5.0 WAR last season. How much of that WAR was due to the influence of Albert Pujols in the clubhouse? Did Pujols help them with their approaches at the plate? Did they have conversations that helped them through slumps? Did Pujols hurt their performance?
We cannot directly perform any experiments to answer these questions. We cannot re-run the season with and without Pujols in the clubhouse. The best we can do, I think, is find proxies and analogues to help us build models of the Cardinals with and without Pujols. That is a very serious limitation, but as with love, I want to say that the result is an imperfect measurement of something that exists.
You make an interesting point that there may be subtle ways of measuring even things like love, though they might be "imperfect measurement[s] of something that exists." That is an intriguing idea and something to think about for sure.
ReplyDeleteJust be glad I wasn't pointing my elder wand at you when I said my reductio ad absurbum.
ReplyDeleteWithout a clear idea of what counts as measurement, I think the claim "nothing exists that can't be measured" is pretty meaningless. If you're allowing proxies and all sorts of very indirect sorts of things to count as measurement then sure, I bet I can find a way of "measuring" all sorts of things. But I can also, in this way, measure all sorts of thing I'm pretty sure DON'T exist. Like the correlation between pirates and temperature.
ReplyDeleteIndeed, now that I think about it, "existence" is tricky too. Do correlations EXIST? That's a funny way of putting it. Especially when we're talking about a correlation that I think we can agree is spurious.
Seamus,
ReplyDeleteThanks for the comment, it is really very rich (in a good way)!
I am definitely relying on an uncritical sense of "measurement," and you are right that more precision is called for. I don't have a well-developed spiel about measurement, but I would love to chat more about it. The only thing I am confident about is that typical measurements are such that the thing measured is a causal antecedent of the measurement. Anyway, I don't think we want to discard proxies and so forth. For example, I think we do have decent measurements of global temperature and CO2 concentrations thousands of years in the past. But maybe this is because I am already convinced that there is such a thing as global temperature in the distant past? How did I come to have that conviction?
As to the correlation between pirates and temperature, I have a couple of things to say. First, I don't know why anyone would want to deny that there is a correlation in the data you linked (although look at that graph, it's very weird -- especially how the x-axis goes like 35k, 45k, 20k).
Second, whether you think the correlation exists surely depends on what you mean by "the correlation." Specifically, I have the following contrast in mind: (a) the correlation with respect to the actually observed data; versus (b) the correlation with respect to the variables, anticipating further data. As before, if we are thinking of (a), then the correlation exists, right? If we are thinking of (b), then the correlation might not exist. But also, if we are thinking of (b), then the data we have collected is just a poor measurement of the correlation! That is, the correlation is not something we could ever actually observe, because we cannot take data fast enough and do not have direct access to the distant past or the distant future.
Third, what one usually means by saying that a correlation is "spurious" is that the correlation is not due to one variable causing the other but either (c) due to an unmeasured common cause or (d) due to chance. So, yes, I agree that the correlation (in the sense of (a), which exists) is spurious. I tend to think the correlation is due to chance and that it would go away with a larger sample.
Finally, note that my claim is a conditional: if X exists, then X can be measured. This does not imply that for every proposed measurement -- say a purported measurement of X -- something exists that corresponds to the measurement. Maybe the converse claim is true. If it is, it will probably be true in the weak sense of (a) above. Maybe the converse claim is false. But either way, it is not implied by my claim in this post.
I see. That's a good point about your claim being conditional. I'd got that wrong, I think.
ReplyDeleteI guess I'm a little uncomfortable with your use of "exist". With my metaphysical hat on, I'm just not sure correlations are in the category of things that exist. They aren't the right type of thing. Even if a correlation obtains, even if propositions about the correlation are true, I'm not sure I'm happy saying "correlations EXIST". That's maybe just a terminological thing.
But here's a worry about types and tokens. I'm fairly confident that dinosaurs existed. Why? Well, because of fossils. Let's count these as some sort of "measurement" or perhaps "observation" would be better. However, I am also confident (on the same evidence) that there existed dinosaurs whose fossils we don't have. That is, not every velociraptor that ever existed left a fossil. Let's say we have Vincent the Velociraptor's fossil, but not Victor's.
Now, for me to be able to make the claim that the dinosaur that didn't leave a fossil (Victor) EXISTED, I need a very odd kind of observation: I have a (already indirect) observation of a different token of the same type (Vincent). From Vincent I infer the past existence not only of the token Vincent, but also of the type Velociraptor.
I can't, even in principle, observe Victor any more directly, since ex hypothesi Victor didn't leave a fossil.
So one of the following must be true:
- There are things that exist (existed) that can't be measured
- Observation of Vincent's fossil counts as observation of Victor
- Only dinosaurs who left fossils existed
I think it's most reasonable to believe the first one…
Good points. I'm not sure the extent to which the issue about existence is terminological. I do want to say that relations exist. I don't think they are any more or less special than monadic predicates, which I also think exist. However, I am not so naive as to think this is an easy problem. It is basically the problem of the reality of universals. I am on the realist side, but good philosophers have been on the nominalist side.
ReplyDeleteThe dinosaur problem is really very excellent. I do have some replies, but I'm not sure I really like any of them. Still, let me try out a few.
Reply #1: Tense matters. While it may be true that Victor once existed, Victor does not now exist. It is not a threat to my thesis that Victor cannot be measured now, because my thesis is tensed. It is surprising that even some things that do not exist can be measured, but as before, my thesis does not require that everything that can be measured exists.
Reply #2: All that matters is measurement in principle, which might be counterfactual. This reply is related to the first. It may be the case that we cannot now measure Victor, but surely you agree that had we been contemporaries of Victor, we could have measured him. This is, of course, counterfactual: we are not contemporaries with Victor.
The first two replies suggest a slight reframing of the thesis as follows: If something exists at time T, then it may be measured at time T + dT for some dT. (The reason for the dT is to allow for lags in measurement processes, which will be limited by the speed of light if nothing else.)
Reply #3: Yes, the fossils we have (including Vincent's) count as a measurement of Victor. The reason should be pretty clear: I like proxies. Suppose you want to measure my height. One way of doing that is to measure the heights of all of the men in my region. Take an average. Now you can say a few useful things about my height. For example, you can put non-trivial bounds on my height. And you can tell me something about the likely error in your estimate of my height. In the case of dinosaurs, the measurements might not be very precise, and they might require making some strong assumptions. But still, this is a variety of measurement.
What do you think?
Slight edit on Reply #3. Instead of measuring the heights of all of the men in my region (which would include me!), measure the heights of a random sample of men in my region.
ReplyDeleteAs mentioned, I think this hinges on how we want to define 'measurement'. Whether some phenomenon can be measured depends not only on the nature of the phenomenon but also on the nature of the beings doing the measuring (including, of course, their knowledge and technology). So, are there things that humans cannot presently measure? Probably. Are there things that humans may never be able to measure? Again, I want to say that it's likely, but I realize that my grasp of the relevant probabilities is much too impoverished to attach any confidence to this (which, of course, is the reason I want to say yes!).
ReplyDeleteI like to think about measurement as detection. If humans can detect something (make causal contact with it), then it can be measured. If it can be measured, we can subject it scientific study (though our science of it may be _very_ limited). On the other hand, we can't measure things we can't detect, so we can't have a science of them. However, the fact that we can't detect them means that we're not justified in asserting their existence. So, I'd say that we're not really justified in claiming that things exist that cannot be justified, regardless of whether they actually exist or not!
So, are there things that humans cannot presently measure? Probably. Are there things that humans may never be able to measure?
ReplyDeleteI should have been clearer with my language. I am interested in measurement in principle, not necessarily in practice. But maybe that just weakens the thesis too much for it to be interesting.
Why not say everything that exists exists in some quantity. Doesn't that correspond to the concept of being "measurable in principle"?
ReplyDeleteIt seems clear that to be measurable, something must exist in some quantity; otherwise, there would be nothing to measure.
If existing in some quantity captures your intended idea, I wonder about things that are infinite, which are unmeasurable because infinity isn't a quantity?
Thanks for the comment, Stephen. I like your suggestion, as long as we are allowed to think of binary values as quantities. Some people want to reserve "quantity" or "quantitative" for continuous (or maybe just densely ordered) things. But I think that is just a kind of quibbling about choice of language.
ReplyDeleteAlso, I want to argue against people who might say that there are entities that have quantities that are not measurable. You might imagine a person saying that Faeries have lots of interesting properties: they have wings that beat at a certain rate, they have specific colorings, etc. It's just that we can't ever measure these quantities. To me, such "quantities" are figments.
As to infinity, I wonder why you think that infinities are not quantities. If we are Cantorian about set theory, then infinite sets are definite, completed objects, and they have definite "sizes." For example, the set of natural numbers N = {0, 1, 2, ...} has one cardinality ("size") -- usually denoted Aleph_0. The set of real numbers R has a larger cardinality -- usually denoted Aleph_1. These cardinalities can be compared, and it is a fun result that Aleph_1 > Aleph_0.
A more serious challenge from set theory might point at so-called non-measurable sets. Just now, I'm not sure what to say about such bizarre mathematical objects.
On Faeries--I think it's incoherent to say, "Each Faery's wings beat at a certain rate, but no average rate of wing-beating exists." But I don't think the fact that we can never measure it would contradict that it exists. (Is a hidden-variables interpretation of qm incoherent because it denies the hidden variables can ever be measured?
ReplyDeleteOn infinity--Can it be measured? Consider this hypothetical: "There are infinitely many Faeries, each has wings beating at a certain rate, but there's no average rate of wing-beating." This seems coherent (and if so, more befuddling than Hilbert's Hotel.)
To be clearer: "each has wings beating at a certain rate" should be read as "each has wings beating at its own rate." (If "certain rate" meant the same rate for each Faery, the claim would be incoherent.)
ReplyDeleteHmm ... as long as the collection of wing-beat rates for all of the faeries is bounded, we should be able to calculate a mean over the whole set by taking a limit, right? (I am not so much of a positivist to exclude such limit-cases from reality.)
ReplyDeleteIf the wing-beat rates are not bounded, then you could have infinitely many faeries that all beat their wings at a definite rate but such that there is no limit that the mean converges to. For example, if the wing beat-rates went like 1 beat per minute, 2 beats per minute, 3 beats per minute, ..., n beats per minute, ...
In that case, the relevant sequence would look like 1, 3/2, 2, 5/2, ..., (n+1)/2, which goes to infinity.
I don't pretend to know enough about quantum mechanics to pontificate about hidden-variable interpretations.
What I had in mind was an infinite collection of Faeries whose wing-beat rates don't form a series. The "practical" question that leads me to this puzzle is hypothesis of some cosmologists that the cosmos is infinite. It seems that it should be possible to to say of any collection that the mean value of some variable over it is ... something or other. An infinite cosmos with different densities of matter in different regions is a picture which doesn't imply (as far as I can see) that the densities must be arrangeable in any series. So the cosmos would have NO average density. This seems bizarre, although I can't articulate why (but perhaps in some sense because it means there's an "unmeasurable" involved) and I wonder why I never see this puzzle mentioned.
ReplyDeleteBut the unbounded series you construct might implicate the same perplexity. Although the unbounded series has no central tendency, it seems that an actual collection of Faeries just _has_ to have a central tendency (yet, it seems to exist--if at all--without the possibility of being measured).