A Milestone (Millstone?) for Christianity in England and Wales

Results from the decennial census show that for the first time ever, fewer than half of English and Welsh citizens identify as Christian. The decline has been precipitous, as shown by the graph.

It appears that most of the Christians jumping ship end up in the ‘no religion’ category rather than converting to another religion. No data on how many of them still believe in a god or gods, or in a ‘higher power’. Also interesting that if established trends continue, the ‘no religion’ folks will become a majority in the not very distant future.

The graph comes from this BBC article.

136 thoughts on “A Milestone (Millstone?) for Christianity in England and Wales

  1. The US lags behind England, Wales, and the rest of Europe, but Christianity is in a steady and unmistakable decline here, too. I would guess that the decline is slower here partly because such a large percentage of immigrants are Christian.

  2. It would be interesting to know how much of the exodus from practicing Christianity has to do with its incompatibility with the acceptance of LGBQ.

  3. My guess above appears to be incorrect. The following graph shows what the “steady switching” scenario would look like if all immigration and emigration ceased. There is virtually no change, so the percentage of immigrants who are Christian is not a significant factor in limiting the rate of Christianity’s decline in the US.

  4. Acartia:

    It would be interesting to know how much of the exodus from practicing Christianity has to do with its incompatibility with the acceptance of LGBQ.

    That’s a good question, and it’s part of a larger question about the compatibility of liberal values with various Christian denominations. I came across a Christianity Today article suggesting that there was a kind of double whammy going on: Conservative churches losing their more liberal members because of the value mismatch, AND, ironically, liberal churches losing ground because their members don’t need the churches as a focus for their liberal values.

    ETA:
    I found a quote from that article:

    Some, building on the work of the late sociologist Rodney Stark, have argued it’s caused by denominations growing more liberal. According to this argument, if a church emphasizes all the same issues and concerns as left-leaning political activists, then there’s no reason to do the extra work of belonging to a church. They point to shrinking mainline churches. The United Church of Christ, the first mainline denomination to embrace same-sex marriage, lost more than 40 percent of its members in the 17 years after that decision, for example.

    Others have connected the trend to conservative politics, arguing evangelical association with Republicans is driving young people away from church. The rise of the exvangelical moment and the uptick in the number of nones in some election years is cited as evidence.

  5. The drop in declared religious affiliation would be greater without immigration over the years. For example the influx of Hindu Asians following their expulsion from Idi Amin’s Uganda in 1972 changed the face of the city of Leicester dramatically. I witnessed it, living there for a few years in the seventies, and there seemed no downside at all. Things change, though.

    Muslim immigrants haven’t done so well.

    Lesson for US, the established church and its association with the monarchy and parliament, (the only) compulsory teaching in state-run schools (especially, I found) are counter-productive in maintaining religious belief. Put church and state back together, enforce religious teaching, and you’ll see.

    There could be a setback to the secularisation of the UK. Cultural religion persists as a social phenomenon where alternative social space is lacking. In UK, we have the pub. But pubs are closing, and maybe social Christianity will revive.

  6. I saw an editorial a couple days ago by far-right columnist Cal Thomas, where he was blaming the excessive gun deaths in the US on a decline in moral fiber, as illustrated by the above trends and statistics. Interestingly, he didn’t see the difference between gun deaths and church attendance in Europe. He did insist that US moral decline could also be blamed on knifing deaths, so the problem couldn’t be guns, it must be people turning away from Cal Thomas’s god.

  7. keiths: came across a Christianity Today article suggesting that there was a kind of double whammy going on: Conservative churches losing their more liberal members because of the value mismatch, AND, ironically, liberal churches losing ground because their members don’t need the churches as a focus for their liberal values.

    At the same time there is also a third trend in USA, unseen elsewhere: Radicalisation of churchgoers. There are militant pastors, openly advocating their own political preferences. Not sure if they are many, but there are certainly some rather loud voices speaking out in favour of abolishing the separation of church and state.

    I made a post about it. We’ll see if it gets published or buried.

  8. Erik: I made a post about it. We’ll see if it gets published or buried.

    Published. Thanks for the heads-up

  9. Flint:

    Interestingly, he [Cal Thomas] didn’t see the difference between gun deaths and church attendance in Europe.

    An example of convenient Americentrism. Ignore the rest of the world if it undercuts your claims.

    It reminds me of the headline The Onion reuses every time there is a mass shooting:

    ‘No Way To Prevent This,’ Says Only Nation Where This Regularly Happens

    When I last checked (June of this year), they had used that headline 21 times.

  10. Some data from Canada. The numbers and trends are similar to those of the US, which isn’t a surprise.

  11. Time for some data from outside the Anglosphere, so here’s France. The decline of Christianity in France seems about as precipitous as its decline in England and Wales. The numbers would look a bit odd if you plotted them; notice that Christianity plateaus at about 66% from 2004 to 2010. However, the Wikipedia article from which I plucked the table notes that “these are from different sources with likely different methodologies”, so I wouldn’t make too much of the plateau.

    The longer-term trend is obvious, and the rate of decline in recent decades is 1.33% per year, while in England and Wales it is 1.25% per year.

  12. keiths: Also interesting that if established trends continue, the ‘no religion’ folks will become a majority in the not very distant future.

    There are a bunch of countries where they already are the majority, such as the entire former Warsaw block. They were this way already when they were a live and kicking Warsaw block. Is this supposed to be good, bad or mean something else?

  13. Erik:

    There are a bunch of countries where they [the no-religion folks] already are the majority, such as the entire former Warsaw block. They were this way already when they were a live and kicking Warsaw block.

    Right. Communists have been hostile to religion going all the way back to Marx and Lenin (“religion is the opium of the people”), and religion was actively supressed in Eastern Bloc countries during Soviet times. Those countries got a head start; that’s why they are further along on the path toward secularization.

    Is this supposed to be good, bad or mean something else?

    I think it’s a mix. Religion has its benefits, such as providing a sense of community to believers. The decline of religion leaves gaps that secular institutions don’t always fill. On the other hand, I think it’s better for a society when citizens are based in reality and reject absurd beliefs (JFK Jr is still alive, the 2020 election was stolen, there are “implant stations” on Venus and Mars, Jesus could exorcise demons and cast them into pigs). It’s also better when citizens don’t put their faith in so-called “holy books” and, for example, run around cutting off the hands of thieves because they think God has ordered them to (via their “holy book”).

    I should add that the no-religion category includes people who have abandoned their religious beliefs only to replace them with beliefs that are equally absurd. Think Heaven’s Gate. It’s not clear that society benefits when that happens.

  14. keiths:…here’s France…

    Atheist (athée), as a word, was first recorded in France in 1572 apparently. I think the Enlightenment and the French Revolution have influenced how the French have declared their religious belief both in the past and recently. Prior to the Revolution, declaring atheism publicly was a capital crime. Following the Revolution, the Catholic Church was effectively criminalized and assets seized. Napoleon III achieved a rapprochement where the Church got use (but not title) of its property back, then there was a formal separation of church and state in 1905.

    As I found in England and the Church of England, in France there is a widespread cultural identity with Catholicism. Certainly in England in my youth, C of E was the default entry for form-filling with no opportunity for a write-in. But the practice of religion has almost disappeared. On my first visit to France in 1968, I was struck by seeing so many priests and nuns going about their daily routine. I’ve not seen anyone out and about in Catholic religious garb for years. Our village church has no priest and no services now apart from the occasional funeral.

    I don’t know whether cultural Catholicism has much of an element of belief but there is definitely a political element, declared atheists tending to be left-wing. There is also a hint of racism, immigrants from North Africa regarded as not adapting to French ways and importing alien Islam.

    In England, the Church of England used to be referred to as the Tory Party at prayer and perhaps part of the reason for its decline was the tension between its largely conservative flock and the teachings of the more egalitarian clergy.

    I suspect most people in Europe are quite pragmatic in conserving the cultural aspects of their native religion but its waning influence on daily life allows them to be open about their scepticism on religious dogma and authority.

    I do question whether trends can be inferred from snapshot polls and whether lines from point A to point B – straight or otherwise – tell us anything.

  15. keiths: I should add that the no-religion category includes people who have abandoned their religious beliefs only to replace them with beliefs that are equally absurd.

    I recall once reading that the majority of people declaring no religious affiliation still have unspecified spiritual beliefs. They were referred to as iets-ists then (= something-ists, as in: I believe there is “something” more between heaven and earth). That was a while ago, so this may be changing as well.

  16. Corneel: I recall once reading that the majority of people declaring no religious affiliation still have unspecified spiritual beliefs.

    Anecdotally, I come across that quite often. There is a marked failure of organised religion yet many people continue with a feeling that “this isn’t all there is” and “there is more to life”, resulting in some vague spirituality. Seems harmless.

  17. You should have defined, or at least try, what Christianity is, or means… If one of 30k so-called Christian denominations allows same sex marriage, are they Christians? Or, if the head of the so-called Christian church says it is okay to take gene therapies tested on fetal cell lines (cells originally isolated from fetal tissue) Should they be viewed as Christians?
    I’m not questioning your post, keiths. I’m questioning fake christianity and so-called christians like you know who…

  18. J-Mac,

    For the purposes of this OP, a Christian is anyone who identifies as Christian when asked by a census taker or pollster. No ideological purity tests are applied. That makes sense; how many respondents do you think would put up with being asked a bunch of doctrinal questions?

  19. keiths:
    J-Mac,

    For the purposes of this OP, a Christian is anyone who identifies as Christian when asked by a census taker or pollster. No ideological purity tests are applied. That makes sense; how many respondents do you think would put up with being asked a bunch of doctrinal questions?

    I get it, but would you ask the same question a pregnant women, or a man, or both?

  20. J-Mac:

    I get it, but would you ask the same question a pregnant women, or a man, or both?

    Huh? If I were a pollster and it was part of my job to ask people which religion they practiced, if any, then I would ask them that question. I wouldn’t ask them doctrinal questions, I wouldn’t ask if they were pregnant, and I wouldn’t ask them for their gender (unless such questions were part of the survey).

    You seem to be hinting at something here, but your question as written is nonsensical. I’ll answer it nonetheless. Yes, I would ask that question of men. Yes, I would ask that question of pregnant women. Yes, I would ask that question of both men and pregnant women.

    Were you trying to ask something else?

  21. keiths:
    J-Mac:

    Huh? If I were a pollster and it was part of my job to ask people which religion they practiced, if any, then I would ask them that question. I wouldn’t ask them doctrinal questions, I wouldn’t ask if they were pregnant, and I wouldn’t ask them for their gender (unless such questions were part of the survey).

    You seem to be hinting at something here, but your question as written is nonsensical. I’ll answer it nonetheless. Yes, I would ask that question of men. Yes, I would ask that question of pregnant women. Yes, I would ask that question of both men and pregnant women.

    Were you trying to ask something else?

    Well, what’s the difference between those who claim to be Christian and those who claim to be of another sex? Is it faith?

  22. J-Mac:

    Well, what’s the difference between those who claim to be Christian and those who claim to be of another sex? Is it faith?

    I’ll assume you’re referring to trans people when you speak of “those who claim to be of another sex”.

    As I’ve already indicated, a Christian, for the purposes of this OP, is someone who identifies as Christian in response to a census or poll question. Period.

    Next, your question as written implies that the set of people who claim to be Christian doesn’t overlap with the set of trans people. That’s obviously false. There are many trans people who claim to be Christian. (There are many transphobes who make that claim as well.)

    Maybe you don’t feel that trans people can be true Christians. If so, you are saying that a trans person who accepts Jesus as their Lord and Savior is not a Christian. Good luck defending that position.

  23. Alan:

    I do question whether trends can be inferred from snapshot polls…

    They definitely can. The numbers show that the percentage of Christians is declining in Australia, New Zealand, all three countries in North America, and every western European country I checked. The data was gathered independently for each of these places, yet they all exhibit a decline. No way is that a coincidence.

    Take a look at the graph for New Zealand and tell me that’s not a trend:

  24. Alan:

    …and whether lines from point A to point B – straight or otherwise – tell us anything.

    They definitely do. Designate point A as Christianity in NZ in 1991, and point B as Christianity in NZ in 2018. Draw a line from point A to point B. Notice how close that line comes to the intermediate data points. Point A and point B together specify a line, and the other data points confirm that this line is representative of the overall trend.

  25. J-Mac: If one of 30k so-called Christian denominations allows same sex marriage, are they Christians? Or, if the head of the so-called Christian church says it is okay to take gene therapies tested on fetal cell lines (cells originally isolated from fetal tissue) Should they be viewed as Christians?

    If they follow the teachings of Christ and believe that He was the Son of God then yes, they are Christians. You appear to be claiming that tolerating same-sex marriage or fetal cell research is somehow inconsistent with being a Christian. Convince me. You seem mite sectarian.

  26. keiths: For the purposes of this OP, a Christian is anyone who identifies as Christian when asked by a census taker or pollster.

    In the Brexit referendum the question was:

    Should the United Kingdom remain a member of the European Union or leave the European Union?

    An unasked question was “should UK also withdraw from free trade with the EU”.

    Another question could have been “Should UK remain but vigorously argue within the EU for change, limiting federalism and monetary union”.

    The result of asking a misleadingly binary question in the non-binding referendum is a situation very few were actually voting for.

    Similarly, asking “are you a Christian” (tick box: for yes, leave unticked for no) allows the ambiguity of cultural Christianity vs belief in a living (?) God.

    This was the point I was making about the change in attitude between inner belief and outward conformity to cultural norms. In my youth, outward conformity was common, the extent of genuine belief unknown. Now, overt public displays of fervour are rare (I’m talking about Europe), but declarations of a vague spirituality common (in my anecdotal experience).

  27. keiths: Designate point A as Christianity in NZ in 1991, and point B as Christianity in NZ in 2018. Draw a line from point A to point B. Notice how close that line comes to the intermediate data points. Point A and point B together specify a line, and the other data points confirm that this line is representative of the overall trend.

    Well, yes. The simplest model for data points marked on a two-dimensional graph is a best-fit straight line. And using that model on snapshot polling data predicts what the result would be at another moment.

  28. Inferring future trends by extrapolating from past polling data ignores a lot of context.

    Events have influence. Replacing religious social institutions with secular social services and having secular space for social interaction, media censorship or freedom, level of church-state separation, exposure of corruption such as paedophilia within the Catholic church, an unexpected and convincing second coming of Christ, all could buck the trend.

  29. Alan:

    The result of asking a misleadingly binary question in the non-binding referendum is a situation very few were actually voting for.

    Similarly, asking “are you a Christian” (tick box: for yes, leave unticked for no) allows the ambiguity of cultural Christianity vs belief in a living (?) God.

    The pollsters don’t ask the question in a binary way. Imagine how awkward that would be:

    P = pollster
    I = the interviewee, a Jain

    P: Are you a Christian?
    I: No.

    P: Are you an agnostic?
    I: No.

    P: Are you an atheist?
    I: No.

    P: Are you a Jew?
    I: No.

    P: Are you a Muslim?
    I: No.

    P: Are you a Buddhist?
    I: No.

    P: Are you a Hindu?
    I: No.

    P: Do you belong to some other faith?
    I: Yes.

    P: Are you spiritual but unaffiiated with any particular faith?
    I: No.

    P: Do you fall outside of the above categories?
    I: No.

    You might suggest that the pollster could stop asking the questions once they received a ‘yes’ answer. After all, if a respondent answers ‘yes’ to ‘Are you a Muslim?’, then why bother asking ‘Are you a Hindu?’ Under a stop-on-yes policy, most people wouldn’t have to suffer through the entire list of questions. And if you ordered the categories according to their prevalence, as I did here (using US data), you would minimize the average number of questions that a respondent would have to answer.

    It’s not a good idea. Some people, like the poor Jain in my example, would still have to suffer through most of the list. Worse still, a person would have to answer each question without knowing what the upcoming questions were, and that could skew the results. For example, our Jain might hesitate upon being asked the Hindu question. Jainism is a separate religion, but there is a very large overlap between it and Hinduism. (In fact, there has been debate over whether it really is a separate religion vs being a branch of Hinduism. It’s reminiscent of the language vs dialect debates.) Oftentimes Jainism is not one of the explicit choices on surveys, and in such cases our Jain might choose to answer ‘yes’ to the Hindu question, believing it to be more accurate and informative than selecting ‘some other faith’. Under the stop-on-yes policy, they wouldn’t know how to answer, being unaware of whether ‘Are you a Jain’ was among the upcoming questions.

    If you ditched the stop-on-yes policy in order to avoid the problem I just described, you would force everyone to answer all of the questions. And this would create a new problem of deciding what to do if someone answered ‘yes’ to more than one of them.

    For all of these reasons, multiple choice is the way to go. Here’s how Pew phrases the question:

    What is your present religion, if any? Are you Protestant, Roman Catholic, Mormon, Orthodox such as Greek or Russian Orthodox, Jewish, Muslim, Buddhist, Hindu, atheist, agnostic, something else, or nothing in particular?

    You pointed out that some people might identify as Christian for cultural reasons or because of pressure to conform, not because of their beliefs. That’s true, but a reduction in their numbers is also indicative of Christianity’s decline, just as a reduction in the number of genuine believers is. A reduction in the number of cultural or conformist pseudo-Christians is an indication that Christianity’s influence is waning, and that’s part of the overall decline.

  30. Alan:

    I’m not disputing individual religious belief and participation in public religious activity have changed, for the most part declining.

    But you question our ability to infer trends from poll results. That makes me curious about what evidence led you to conclude the above.

    keiths:

    Designate point A as Christianity in NZ in 1991, and point B as Christianity in NZ in 2018. Draw a line from point A to point B. Notice how close that line comes to the intermediate data points. Point A and point B together specify a line, and the other data points confirm that this line is representative of the overall trend.

    Alan:

    Well, yes. The simplest model for data points marked on a two-dimensional graph is a best-fit straight line. And using that model on snapshot polling data predicts what the result would be at another moment.

    Yet earlier you expressed doubts about that:

    I do question whether trends can be inferred from snapshot polls and whether lines from point A to point B – straight or otherwise – tell us anything.

    They definitely tell us something.

    Well, yes. The simplest model for data points marked on a two-dimensional graph is a best-fit straight line. And using that model on snapshot polling data predicts what the result would be at another moment.

    That’s dangerous. It’s not true in general that a straight line between two points allows us to predict the values at other points. To make that leap, we need to know that there are likely no significant excursions in the data between the endpoints of our line. That requirement is satisfied in the case of the religious polling data, but it isn’t satisfied in general. I can elaborate if needed.

  31. Alan:

    Inferring future trends by extrapolating from past polling data ignores a lot of context.

    Your skepticism was broader than that:

    I do question whether trends can be inferred from snapshot polls…

    Present and past trends are still trends, and they can definitely be inferred from poll results.

    Regarding extrapolation, there is of course no guarantee that present trends will continue. To give an extreme example, the near-constant slope of the line in the Canadian graph would abruptly change if an asteroid hit the earth and wiped out all of us. Zero Christians left in that case. People know that projections aren’t guaranteed. That is why, for example, I included a qualifier when I wrote

    Also interesting that if established trends continue, the ‘no religion’ folks will become a majority in the not very distant future.

    The future isn’t certain. Nevertheless, extrapolation can be accurate and useful. An extrapolation based on the Canadian graph from 1991-2001 would have been pretty damn accurate.

  32. keiths: That’s true, but a reduction in their numbers is also indicative of Christianity’s decline, just as a reduction in the number of genuine believers is.

    Yes, though my point was the rot had set in prior to the figures showing the decline. I’m restricting my comments to the UK where I have anecdotal experience and I think the decline in genuine religiosity that continues today began with events during and in the aftermath of World War I. The actuality of warfare was exposed as far removed from the jingoism of the ruling class supported by the Church of England.

  33. keiths: …extrapolation can be accurate and useful.

    “All models are wrong but some are useful”.

    Hari Seldon’s psycho-history was entertaining fiction.

  34. Alan:

    “All models are wrong but some are useful”.

    Better phrased as “No model is perfect, but some are pretty damn accurate.”

    Hari Seldon’s psycho-history was entertaining fiction.

    A fictional character made predictions. Therefore accurate extrapolation is impossible in real life?

  35. Alan:

    Yes, though my point was the rot had set in prior to the figures showing the decline. I’m restricting my comments to the UK where I have anecdotal experience and I think the decline in genuine religiosity that continues today began with events during and in the aftermath of World War I.

    Ironic that you question our ability to infer trends from actual polling data, but you’re fine with inferring a “rot” from your own anecdotal experience.

  36. keiths: Better phrased as “No model is perfect, but some are pretty damn accurate.”

    That would be a value judgment, though nothing wrong with that.

  37. keiths: Ironic that you question our ability to infer trends from actual polling data…

    Who do you include in “our”?

    The last UK census I took part in was in 2001. There was an on-line campaign, it may have started among University students, to enter “Jedi Knight” in the religious affiliation question write-in option, mainly as a joke and partly as a protest. 0.8% of the population declared themselves Jedi knights. Though the suggestion that future census forms would subsequently have to include Jedi Knights as a specific category didn’t happen.

    The Humanist Society weren’t pleased at the distortion and its possible effect on government policy and provision for the non-religious.

    Chief executive Andrew Copson said: “Our message is simple: if you don’t believe in or practise any religion and don’t want to be counted as if you do, then you should tick the ‘No religion’ box in this year’s Census.

    “You may be ticking a religious box out of cultural sympathy or family history, but the effect is that you will count as religious in policymakers’ eyes.

    “The best way to make clear that this is wrong is by everyone who is not religious in any meaningful sense ticking the ‘No religion’ box this year.”

  38. keiths: Ironic that you question our ability to infer trends from actual polling data.

    What I said was I do question whether trends can be inferred from snapshot polls and whether lines from point A to point B – straight or otherwise – tell us anything.

    Perhaps I wasn’t clear enough that I was talking about the lines between data points, not the data points themselves*. I could record outside temperature against time at various dates and times, enter them on a graph and join the points with straight lines. The lines provide no extra information.

    Not to say trends cannot be inferred, diurnal cycles, seasonal cycles, climate change. And one can record parameters continuously.

    *Though context matters, especially with data that is open to interpretation.

  39. I was wondering how many of the 50% self-declared Christians in 2021 were active Christians. How many UK citizens are regular attenders at Church services. I see it’s hugely less than half the population, around 2% in 2019.

    The figures is inflated by inclusion of children attending compulsory acts of worship in state schools (almost a third of the 2%).

    National Secularism Society article

    ETA this doesn’t include all faiths attendance at services.

  40. I wondered how the US compares on regular attendance at church services.

    Gallup says membership* has dropped more sharply in the last twenty years and is now under 50%.

    * I guess membership and regular attendance aren’t strictly comparable but still…

  41. keiths:

    Ironic that you question our ability to infer trends from actual polling data…

    Alan:

    Who do you include in “our”?

    Humanity.

    The last UK census I took part in was in 2001. There was an on-line campaign, it may have started among University students, to enter “Jedi Knight” in the religious affiliation question write-in option, mainly as a joke and partly as a protest. 0.8% of the population declared themselves Jedi knights.

    Some census figures were inaccurate in 2001. Therefore we can’t infer trends from polling data?

  42. Alan:

    Perhaps I wasn’t clear enough that I was talking about the lines between data points, not the data points themselves*. I could record outside temperature against time at various dates and times, enter them on a graph and join the points with straight lines. The lines provide no extra information.

    Not true. Suppose you are in Tucson on a calm, clear day. It is after sunset, and the temperature is falling, as you’d expect. You take temperature readings every 30 minutes using a precise, accurate thermometer. The reading at 8:15 is 72.0° F; the reading at 8:45 is 68.0° F. Draw a line between the two points. Does that line tell us anything? Absolutely. We can now estimate that the temperature at 8:30 was 70° F, and our estimate will be quite accurate.

    Does that work with any two points on any graph? Of course not. I addressed that earlier in the thread:

    It’s not true in general that a straight line between two points allows us to predict the values at other [intermediate] points. To make that leap, we need to know that there are likely no significant excursions in the data between the endpoints of our line. That requirement is satisfied in the case of the religious polling data, but it isn’t satisfied in general.

  43. keiths: The reading at 8:15 is 72.0° F; the reading at 8:45 is 68.0° F. Draw a line between the two points. Does that line tell us anything?

    Nothing that you didn’t already know.

  44. keiths:

    The reading at 8:15 is 72.0° F; the reading at 8:45 is 68.0° F. Draw a line between the two points. Does that line tell us anything? Absolutely. We can now estimate that the temperature at 8:30 was 70° F, and our estimate will be quite accurate.

    Alan:

    Nothing that you didn’t already know.

    My example is extremely (and deliberately) simple, and it’s easy to do the calculation in your head, but you nevertheless have to do a calculation. That calculation is equivalent to drawing a line between the two points and determining where it intersects the t=8:30 line. You don’t know the answer until you do the math. The line tells you something.

    To drive the point home, here’s another example: The reading at 8:03 is 73.8° F; the reading at 8:56 is 67.9° F. What’s the estimated temperature at 8:19? Don’t reach for pen and paper or a calculator. According to you, the line between the two points can’t tell you anything you don’t already know. Since you already know the answer, what is it, off the top of your head?

    You don’t know the answer until you do the calculation. The line tells you something.

  45. Just to forestall a couple of possible objections:

    Some people can do the math in their heads, even for the second problem, but it makes no difference whether they do it in their heads or elsewhere. They don’t know the answer until they do the calculation.

    Also, you might object that the answer is already implicit in the two endpoints, so there’s a sense in which you already know the answer even if you can’t produce it without doing the calculation. That depends on a pretty loose definition of ‘know’, however. By that reasoning, you already know the answer to the following problem:

    x^7 – 9x^3 + 12x^2 + 18x – 4 = 0
    Tell us all the values of x that satisfy that equation.

    Can’t do it off the top of your head? Don’t know the answer even after attempting to do the math? Then you don’t know the answer by any reasonable definition of the word ‘know’.

    The answer is implicit in the equation, which is telling you exactly what criterion x must satisfy. It is ruling out all values of x that do not meet that criterion. Does that mean that you know the answer? Obviously not.

    That one’s hard; the temperature examples are easier. Nevertheless, it remains true that you can’t determine the answer to the temperature problems until you’ve done the calculation. The calculation you need to do is equivalent to determining the line between the two endpoints and observing the value of that line at the desired time.

    Does the line tell you anything? Yes, obviously.

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